DIFFERENTIAL POLARIZATION DELAY

LINE controller

D0215

Supervisor Supervisor Mony OrbachMony Orbach

Performed byPerformed byMaria TerushkinMaria Terushkin

Guy OvadiaGuy Ovadia

Technion ndash Israel Institute of TechnologyDepartment of Electrical EngineeringHigh Speed Digital Systems Lab

Project definitionProject definition

Build a controller for the Differential Delay Line module in the facultyrsquos EO lab

Precisely determine and control the position of the mirror inside the module

Closed loop positional control using the built in optical shaft encoder for feedback

Create a PC interface through a USB connection

Project FeaturesProject Features

Closed-loop motor control (PID algorithm)Closed-loop motor control (PID algorithm) Interface Functions Interface Functions

Go to specified positionGo to specified position Set zero positionSet zero position Read-back of current positionRead-back of current position

Apply motor break while holding positionApply motor break while holding position Slow down gradually near travel limitsSlow down gradually near travel limits Built In Tests (discussed later in the Built In Tests (discussed later in the

presentation)presentation)

Project SpecificationsProject Specifications

Encoder inputEncoder input A B Channels 5V TTL (internal 10kA B Channels 5V TTL (internal 10kΩΩ resistive resistive

pullup) Up to 72 kHzpullup) Up to 72 kHz 5V Vcc and Ground (10 mA maximum 5V Vcc and Ground (10 mA maximum

consumption)consumption) Limit switchesLimit switches

Two End-of-travel signals Open collector active Two End-of-travel signals Open collector active highhigh

USB IOUSB IO Maximum speed 1 MBytes (practical throughput Maximum speed 1 MBytes (practical throughput

is low)is low) Signals D+ D- 5V Vcc GndSignals D+ D- 5V Vcc Gnd

Mechanical aspectsMechanical aspects

Method of construction Wireup cardMethod of construction Wireup card Connections to the MMC card direct Connections to the MMC card direct

solderingsoldering Enclosure pre-made boxEnclosure pre-made box External connectorsExternal connectors

Power connectorPower connector DDL connectorDDL connector

No heatsinks are requiredNo heatsinks are required

Project SpecificationsProject Specifications

PerformancePerformance (preliminary requirements)(preliminary requirements)

Steady State Positional Error lt 05 microm (single Steady State Positional Error lt 05 microm (single encoder step)encoder step)

Commulative positional error 0 micromCommulative positional error 0 microm Overshoot 25 [] (non critical but should be Overshoot 25 [] (non critical but should be

lowered near travel limits)lowered near travel limits) Small Step settling time (to 05 microm) will be Small Step settling time (to 05 microm) will be

setted on the real modelsetted on the real model Full travel settling time (to 05 microm) will be Full travel settling time (to 05 microm) will be

setted on the real modelsetted on the real model Limit velocity to +- 1 [mms]Limit velocity to +- 1 [mms]

Block diagramBlock diagram

DDL

controller

PC + simple UI

USBCommunicationUnit

Laboratory measurement equipment

Fiber optics

DDL ndash controller diagramDDL ndash controller diagram

Limit Switches

DC motor

Encoder

H-bridge

Power supply

12MHz clk

FPGA

DDL

The chosen H-bridge The chosen H-bridge HIP4020 HIP4020

Two Independently controlled power Half-Bridges 3-12V operation 05A Maximum load CMOSTTL Compatible Input Logic Over-Temperature Shutdown Protection Over current Limit Protection Over current Fault Flag Output Direction Braking and PWM Control Manufacturer Intersil Low cost available from Farnell

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Project definitionProject definition

Build a controller for the Differential Delay Line module in the facultyrsquos EO lab

Precisely determine and control the position of the mirror inside the module

Closed loop positional control using the built in optical shaft encoder for feedback

Create a PC interface through a USB connection

Project FeaturesProject Features

Closed-loop motor control (PID algorithm)Closed-loop motor control (PID algorithm) Interface Functions Interface Functions

Go to specified positionGo to specified position Set zero positionSet zero position Read-back of current positionRead-back of current position

Apply motor break while holding positionApply motor break while holding position Slow down gradually near travel limitsSlow down gradually near travel limits Built In Tests (discussed later in the Built In Tests (discussed later in the

presentation)presentation)

Project SpecificationsProject Specifications

Encoder inputEncoder input A B Channels 5V TTL (internal 10kA B Channels 5V TTL (internal 10kΩΩ resistive resistive

pullup) Up to 72 kHzpullup) Up to 72 kHz 5V Vcc and Ground (10 mA maximum 5V Vcc and Ground (10 mA maximum

consumption)consumption) Limit switchesLimit switches

Two End-of-travel signals Open collector active Two End-of-travel signals Open collector active highhigh

USB IOUSB IO Maximum speed 1 MBytes (practical throughput Maximum speed 1 MBytes (practical throughput

is low)is low) Signals D+ D- 5V Vcc GndSignals D+ D- 5V Vcc Gnd

Mechanical aspectsMechanical aspects

Method of construction Wireup cardMethod of construction Wireup card Connections to the MMC card direct Connections to the MMC card direct

solderingsoldering Enclosure pre-made boxEnclosure pre-made box External connectorsExternal connectors

Power connectorPower connector DDL connectorDDL connector

No heatsinks are requiredNo heatsinks are required

Project SpecificationsProject Specifications

PerformancePerformance (preliminary requirements)(preliminary requirements)

Steady State Positional Error lt 05 microm (single Steady State Positional Error lt 05 microm (single encoder step)encoder step)

Commulative positional error 0 micromCommulative positional error 0 microm Overshoot 25 [] (non critical but should be Overshoot 25 [] (non critical but should be

lowered near travel limits)lowered near travel limits) Small Step settling time (to 05 microm) will be Small Step settling time (to 05 microm) will be

setted on the real modelsetted on the real model Full travel settling time (to 05 microm) will be Full travel settling time (to 05 microm) will be

setted on the real modelsetted on the real model Limit velocity to +- 1 [mms]Limit velocity to +- 1 [mms]

Block diagramBlock diagram

DDL

controller

PC + simple UI

USBCommunicationUnit

Laboratory measurement equipment

Fiber optics

DDL ndash controller diagramDDL ndash controller diagram

Limit Switches

DC motor

Encoder

H-bridge

Power supply

12MHz clk

FPGA

DDL

The chosen H-bridge The chosen H-bridge HIP4020 HIP4020

Two Independently controlled power Half-Bridges 3-12V operation 05A Maximum load CMOSTTL Compatible Input Logic Over-Temperature Shutdown Protection Over current Limit Protection Over current Fault Flag Output Direction Braking and PWM Control Manufacturer Intersil Low cost available from Farnell

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Project FeaturesProject Features

Closed-loop motor control (PID algorithm)Closed-loop motor control (PID algorithm) Interface Functions Interface Functions

Go to specified positionGo to specified position Set zero positionSet zero position Read-back of current positionRead-back of current position

Apply motor break while holding positionApply motor break while holding position Slow down gradually near travel limitsSlow down gradually near travel limits Built In Tests (discussed later in the Built In Tests (discussed later in the

presentation)presentation)

Project SpecificationsProject Specifications

Encoder inputEncoder input A B Channels 5V TTL (internal 10kA B Channels 5V TTL (internal 10kΩΩ resistive resistive

pullup) Up to 72 kHzpullup) Up to 72 kHz 5V Vcc and Ground (10 mA maximum 5V Vcc and Ground (10 mA maximum

consumption)consumption) Limit switchesLimit switches

Two End-of-travel signals Open collector active Two End-of-travel signals Open collector active highhigh

USB IOUSB IO Maximum speed 1 MBytes (practical throughput Maximum speed 1 MBytes (practical throughput

is low)is low) Signals D+ D- 5V Vcc GndSignals D+ D- 5V Vcc Gnd

Mechanical aspectsMechanical aspects

Method of construction Wireup cardMethod of construction Wireup card Connections to the MMC card direct Connections to the MMC card direct

solderingsoldering Enclosure pre-made boxEnclosure pre-made box External connectorsExternal connectors

Power connectorPower connector DDL connectorDDL connector

No heatsinks are requiredNo heatsinks are required

Project SpecificationsProject Specifications

PerformancePerformance (preliminary requirements)(preliminary requirements)

Steady State Positional Error lt 05 microm (single Steady State Positional Error lt 05 microm (single encoder step)encoder step)

Commulative positional error 0 micromCommulative positional error 0 microm Overshoot 25 [] (non critical but should be Overshoot 25 [] (non critical but should be

lowered near travel limits)lowered near travel limits) Small Step settling time (to 05 microm) will be Small Step settling time (to 05 microm) will be

setted on the real modelsetted on the real model Full travel settling time (to 05 microm) will be Full travel settling time (to 05 microm) will be

setted on the real modelsetted on the real model Limit velocity to +- 1 [mms]Limit velocity to +- 1 [mms]

Block diagramBlock diagram

DDL

controller

PC + simple UI

USBCommunicationUnit

Laboratory measurement equipment

Fiber optics

DDL ndash controller diagramDDL ndash controller diagram

Limit Switches

DC motor

Encoder

H-bridge

Power supply

12MHz clk

FPGA

DDL

The chosen H-bridge The chosen H-bridge HIP4020 HIP4020

Two Independently controlled power Half-Bridges 3-12V operation 05A Maximum load CMOSTTL Compatible Input Logic Over-Temperature Shutdown Protection Over current Limit Protection Over current Fault Flag Output Direction Braking and PWM Control Manufacturer Intersil Low cost available from Farnell

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Project SpecificationsProject Specifications

Encoder inputEncoder input A B Channels 5V TTL (internal 10kA B Channels 5V TTL (internal 10kΩΩ resistive resistive

pullup) Up to 72 kHzpullup) Up to 72 kHz 5V Vcc and Ground (10 mA maximum 5V Vcc and Ground (10 mA maximum

consumption)consumption) Limit switchesLimit switches

Two End-of-travel signals Open collector active Two End-of-travel signals Open collector active highhigh

USB IOUSB IO Maximum speed 1 MBytes (practical throughput Maximum speed 1 MBytes (practical throughput

is low)is low) Signals D+ D- 5V Vcc GndSignals D+ D- 5V Vcc Gnd

Mechanical aspectsMechanical aspects

Method of construction Wireup cardMethod of construction Wireup card Connections to the MMC card direct Connections to the MMC card direct

solderingsoldering Enclosure pre-made boxEnclosure pre-made box External connectorsExternal connectors

Power connectorPower connector DDL connectorDDL connector

No heatsinks are requiredNo heatsinks are required

Project SpecificationsProject Specifications

PerformancePerformance (preliminary requirements)(preliminary requirements)

Steady State Positional Error lt 05 microm (single Steady State Positional Error lt 05 microm (single encoder step)encoder step)

Commulative positional error 0 micromCommulative positional error 0 microm Overshoot 25 [] (non critical but should be Overshoot 25 [] (non critical but should be

lowered near travel limits)lowered near travel limits) Small Step settling time (to 05 microm) will be Small Step settling time (to 05 microm) will be

setted on the real modelsetted on the real model Full travel settling time (to 05 microm) will be Full travel settling time (to 05 microm) will be

setted on the real modelsetted on the real model Limit velocity to +- 1 [mms]Limit velocity to +- 1 [mms]

Block diagramBlock diagram

DDL

controller

PC + simple UI

USBCommunicationUnit

Laboratory measurement equipment

Fiber optics

DDL ndash controller diagramDDL ndash controller diagram

Limit Switches

DC motor

Encoder

H-bridge

Power supply

12MHz clk

FPGA

DDL

The chosen H-bridge The chosen H-bridge HIP4020 HIP4020

Two Independently controlled power Half-Bridges 3-12V operation 05A Maximum load CMOSTTL Compatible Input Logic Over-Temperature Shutdown Protection Over current Limit Protection Over current Fault Flag Output Direction Braking and PWM Control Manufacturer Intersil Low cost available from Farnell

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Mechanical aspectsMechanical aspects

Method of construction Wireup cardMethod of construction Wireup card Connections to the MMC card direct Connections to the MMC card direct

solderingsoldering Enclosure pre-made boxEnclosure pre-made box External connectorsExternal connectors

Power connectorPower connector DDL connectorDDL connector

No heatsinks are requiredNo heatsinks are required

Project SpecificationsProject Specifications

PerformancePerformance (preliminary requirements)(preliminary requirements)

Steady State Positional Error lt 05 microm (single Steady State Positional Error lt 05 microm (single encoder step)encoder step)

Commulative positional error 0 micromCommulative positional error 0 microm Overshoot 25 [] (non critical but should be Overshoot 25 [] (non critical but should be

lowered near travel limits)lowered near travel limits) Small Step settling time (to 05 microm) will be Small Step settling time (to 05 microm) will be

setted on the real modelsetted on the real model Full travel settling time (to 05 microm) will be Full travel settling time (to 05 microm) will be

setted on the real modelsetted on the real model Limit velocity to +- 1 [mms]Limit velocity to +- 1 [mms]

Block diagramBlock diagram

DDL

controller

PC + simple UI

USBCommunicationUnit

Laboratory measurement equipment

Fiber optics

DDL ndash controller diagramDDL ndash controller diagram

Limit Switches

DC motor

Encoder

H-bridge

Power supply

12MHz clk

FPGA

DDL

The chosen H-bridge The chosen H-bridge HIP4020 HIP4020

Two Independently controlled power Half-Bridges 3-12V operation 05A Maximum load CMOSTTL Compatible Input Logic Over-Temperature Shutdown Protection Over current Limit Protection Over current Fault Flag Output Direction Braking and PWM Control Manufacturer Intersil Low cost available from Farnell

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Project SpecificationsProject Specifications

PerformancePerformance (preliminary requirements)(preliminary requirements)

Steady State Positional Error lt 05 microm (single Steady State Positional Error lt 05 microm (single encoder step)encoder step)

Commulative positional error 0 micromCommulative positional error 0 microm Overshoot 25 [] (non critical but should be Overshoot 25 [] (non critical but should be

lowered near travel limits)lowered near travel limits) Small Step settling time (to 05 microm) will be Small Step settling time (to 05 microm) will be

setted on the real modelsetted on the real model Full travel settling time (to 05 microm) will be Full travel settling time (to 05 microm) will be

setted on the real modelsetted on the real model Limit velocity to +- 1 [mms]Limit velocity to +- 1 [mms]

Block diagramBlock diagram

DDL

controller

PC + simple UI

USBCommunicationUnit

Laboratory measurement equipment

Fiber optics

DDL ndash controller diagramDDL ndash controller diagram

Limit Switches

DC motor

Encoder

H-bridge

Power supply

12MHz clk

FPGA

DDL

The chosen H-bridge The chosen H-bridge HIP4020 HIP4020

Two Independently controlled power Half-Bridges 3-12V operation 05A Maximum load CMOSTTL Compatible Input Logic Over-Temperature Shutdown Protection Over current Limit Protection Over current Fault Flag Output Direction Braking and PWM Control Manufacturer Intersil Low cost available from Farnell

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Block diagramBlock diagram

DDL

controller

PC + simple UI

USBCommunicationUnit

Laboratory measurement equipment

Fiber optics

DDL ndash controller diagramDDL ndash controller diagram

Limit Switches

DC motor

Encoder

H-bridge

Power supply

12MHz clk

FPGA

DDL

The chosen H-bridge The chosen H-bridge HIP4020 HIP4020

Two Independently controlled power Half-Bridges 3-12V operation 05A Maximum load CMOSTTL Compatible Input Logic Over-Temperature Shutdown Protection Over current Limit Protection Over current Fault Flag Output Direction Braking and PWM Control Manufacturer Intersil Low cost available from Farnell

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

DDL ndash controller diagramDDL ndash controller diagram

Limit Switches

DC motor

Encoder

H-bridge

Power supply

12MHz clk

FPGA

DDL

The chosen H-bridge The chosen H-bridge HIP4020 HIP4020

Two Independently controlled power Half-Bridges 3-12V operation 05A Maximum load CMOSTTL Compatible Input Logic Over-Temperature Shutdown Protection Over current Limit Protection Over current Fault Flag Output Direction Braking and PWM Control Manufacturer Intersil Low cost available from Farnell

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

The chosen H-bridge The chosen H-bridge HIP4020 HIP4020

Two Independently controlled power Half-Bridges 3-12V operation 05A Maximum load CMOSTTL Compatible Input Logic Over-Temperature Shutdown Protection Over current Limit Protection Over current Fault Flag Output Direction Braking and PWM Control Manufacturer Intersil Low cost available from Farnell

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

MMC PlatformMMC Platform

The project is based on a platform The project is based on a platform previously designed in the HS-DSLpreviously designed in the HS-DSL

The platform we will use is the The platform we will use is the Momentum Measurement Card created Momentum Measurement Card created by Hadas Preminger amp Uri Nivby Hadas Preminger amp Uri Niv

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Project SpecificationsProject Specifications IO SignalsIO Signals

Input powerInput power 9V 1A wall adapter9V 1A wall adapter Typical consumption (motor running) TBDTypical consumption (motor running) TBD

estimated at 250mA (15W)estimated at 250mA (15W) Typical consumption (motor idle) TBD Typical consumption (motor idle) TBD

estimated at 50mA ( 025 W)estimated at 50mA ( 025 W) Motor outputMotor output

Fixed frequency PWM signal at 20 kHzFixed frequency PWM signal at 20 kHz Reversible polarityReversible polarity 6 V nominal adjustable by trimpot between 3-8 V for 6 V nominal adjustable by trimpot between 3-8 V for

calibration during development (unaccessible to user)calibration during development (unaccessible to user) 250mA max current (limited by motor resistance)250mA max current (limited by motor resistance)

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Cyclone FPGACyclone FPGA

Alterarsquos low cost simple FPGA

2910 Logic Elements ~60000 kBit RAM clock PLL gt100 IO pins JTAG support

Suitable for implementing glue logic MCU function signal processing and more

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Built In TestsBuilt In Tests

Test distance between limit Test distance between limit switchesswitchesresult must be in specific rangeresult must be in specific range

Move forward then backward by the Move forward then backward by the same amount Verify that the same amount Verify that the position is the sameposition is the same

Move to a specific location Perform Move to a specific location Perform readback of location Verify that it is readback of location Verify that it is the same positionthe same position

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Acceptance TestsAcceptance Tests

All Built In Tests are also acceptance testsAll Built In Tests are also acceptance tests Arriving a specified position by a preset time Arriving a specified position by a preset time

Separate tests for both directionsSeparate tests for both directions Test for small step (10um) medium step (1000um) Test for small step (10um) medium step (1000um)

and full travel rangeand full travel range Holding position position change while idle is Holding position position change while idle is

up to 1 encoder countup to 1 encoder count Travel near limit switches measured velocity Travel near limit switches measured velocity

drops near the limits Movement stops if limit drops near the limits Movement stops if limit switch is hitswitch is hit

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

The modelThe model

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

The modelThe model Two axis motion control mechanism (we Two axis motion control mechanism (we

use only one stage)use only one stage) Includes motor encoder and limit Includes motor encoder and limit

switchesswitches Model can work with the same interface Model can work with the same interface

with minimal adaptationswith minimal adaptations Some parameters will needed to be Some parameters will needed to be

adjusted separately to the modeladjusted separately to the model PID parameters Ki Kd KpPID parameters Ki Kd Kp Velocity and Acceleration planning adjustmentVelocity and Acceleration planning adjustment Supply voltageSupply voltage

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Controller typeController type

PID algorithms adjust the gain to the plant based on several characteristics of the feedback not just the current value The error term is derived by subtracting the feedback

(motor position) from the set point (set position) This is the error in terms of a number of encoder counts

1048708Simple proportional coefficient Kp is multiplied by the error term

Provides linear response to the error term Integral coefficient Ki is multiplied by the error term and

added to the sum of all previous integral terms 1048708Provides response to accumulated error

Derivative coefficient Kd is multiplied by the difference between the previous error and the current error

1048708Responds to change in error from one PID cycle to the next

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

PID controller - overviewPID controller - overview

Effects of changes in parametersEffects of changes in parameters Parameter Rise Time Overshoot Settling Time Parameter Rise Time Overshoot Settling Time

SSError SSError P P Decrease Increase Small Change Decrease Increase Small Change

Decrease Decrease I I Decrease Increase Increase Decrease Increase Increase

Eliminate Eliminate D D Small Change Decrease Decrease Small Change Decrease Decrease

Small Change Small ChangeVset

Vsensor

P

I

D

sensor

plant amp

Vout +

-+

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Pitfalls of PIDPitfalls of PID

Integral windupIntegral windup The problem arises when the actuator The problem arises when the actuator

saturatessaturates There is no longer a linear relation between There is no longer a linear relation between

the controller output to the plantrsquos reactionthe controller output to the plantrsquos reaction When this happens the integrator sums the When this happens the integrator sums the

large error and reaches a very high valuelarge error and reaches a very high value When the error is finally reduced it would When the error is finally reduced it would

take a long time for the integrator to take a long time for the integrator to ldquounwindrdquo and fall back to a normal valueldquounwindrdquo and fall back to a normal value

This is called ldquoIntegral Winduprdquo

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Commonly used schemes to reduce the effects of integrator windup

Clamp the integrator output This scheme simply involves clamping the integrator output at a specified maximum level

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

ContCont Stop integration on saturation This

scheme involves switching off the input to the integrator when the actuator goes into saturation

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

ContCont Saturation feedback This scheme

involves an extra feedback loop reducing the input to integrator in proportion to the saturation error signal

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Tuning the PID controllerTuning the PID controllerThe Ziegler-Nichols method The Ziegler-Nichols method The The closed loop methodclosed loop method prescribes the prescribes the

following procedure following procedure Step 1Step 1 Disable any D and I action of the controller Disable any D and I action of the controller

(--gt pure P-controller) (--gt pure P-controller) Step 2Step 2 Make a setpoint step test and observe the Make a setpoint step test and observe the

response response Step 3Step 3 Repeat the SP test with increased decreased Repeat the SP test with increased decreased

controller gain until a stable oscillation is achieved controller gain until a stable oscillation is achieved This gain is called the ultimate gain Ku This gain is called the ultimate gain Ku

Step 4Step 4 Read the oscillation period Pu Read the oscillation period Pu Step 5Step 5 Calculate the parameters according to the Calculate the parameters according to the

following formulas following formulas PIPI Proportional gain = 045 Ku integral time =Pu 12 Proportional gain = 045 Ku integral time =Pu 12 PIDPID Proportional gain = 06 Ku integral time =Pu 2 Proportional gain = 06 Ku integral time =Pu 2

derivative time = Tu 8derivative time = Tu 8

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

An alternativehellipAn alternativehellip

As an alternative to the table above As an alternative to the table above another set of tuning values have been another set of tuning values have been determined by Tyreus and Luyblen for determined by Tyreus and Luyblen for PI and PID often called the TLC tuning PI and PID often called the TLC tuning rules These values tend to reduce rules These values tend to reduce oscillatory effects and improves oscillatory effects and improves robustness robustness

Since in our system it is important to Since in our system it is important to avoid oscillatory effects wersquoll use this avoid oscillatory effects wersquoll use this methodmethod

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

Logic designLogic design

PID

Trajectory

Planning

Xf

M

err

Current via point

To

Tf

Tf1 Xf1

Tf2 Xf2

hellip hellip

Tff Xff

Yes

Yes

End of trajectory

Arrived via point ndash err=0

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

MilestonesMilestones 15012006 - Electrical schematics done15012006 - Electrical schematics done 25012006 - 25012006 -

Test system built and tested to satisfy our needs Test system built and tested to satisfy our needs Mechanical design completeMechanical design complete

03022006 - Logical design of the system finished03022006 - Logical design of the system finished 05022006 ndash system assembled and programmed05022006 ndash system assembled and programmed 08022006 ndash preliminary testing on the model done08022006 ndash preliminary testing on the model done 20022006 ndash debugging finished20022006 ndash debugging finished 23022006 - PC software written23022006 - PC software written 01032006 - Controller integrated with the real 01032006 - Controller integrated with the real

systemsystem 05032006 ndash Design finalized (including enclosure 05032006 ndash Design finalized (including enclosure

wiring etc) wiring etc) 06032006 - Integration with the setup at the EO lab06032006 - Integration with the setup at the EO lab

The enDThe enD

The enDThe enD