Demonstrator of advanced controllers Hans Dirne Supervisors prof.dr.ir. J. van Amerongen dr.ir. J.F....
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Transcript of Demonstrator of advanced controllers Hans Dirne Supervisors prof.dr.ir. J. van Amerongen dr.ir. J.F....
Demonstrator ofadvanced controllers
Hans Dirne
Supervisorsprof.dr.ir. J. van Amerongen
dr.ir. J.F. Broeninkdr.ir. T.J.A. de Vriesir. P.B.T. Weustink
May 25th, 2005
Master of Science assignment
May 25th, 2005 Demonstrator of advanced controllers 2
Why this assignment?
The Major ‘Mechatronics’ provides several courses in control theory, in which the theory is often supported by simulations.
A physical setup might, in addition to simulations,be an enrichment for demonstrating control theory.
Such a demonstration setup will be able to makethe theory more insightful and will show real limitations in practical setups.
May 25th, 2005 Demonstrator of advanced controllers 3
Objectives
1. To design, build and test a mechatronic demonstration setup, with which several control algorithms can be shown in practice
2. To be able to demonstrate performance differences of control algorithms in practice
May 25th, 2005 Demonstrator of advanced controllers 4
Overview
1. Demonstration setup options2. Control systems3. Design of the new demonstrator4. Experiments5. Demonstration6. Conclusions & recommendations
May 25th, 2005 Demonstrator of advanced controllers 5
Demonstration setup optionsDemonstration setup options
May 25th, 2005 Demonstrator of advanced controllers 6
1. Mechatronic system2. Portable and easy to set up3. Robust, safe and failsafe design4. High level of observability5. Representable by linear 4th order model6. Clear link with well known device
Criteria
May 25th, 2005 Demonstrator of advanced controllers 7
Three options
1. ‘Linix’ laboratory setup
2. Setup of ‘Controllab Products B.V.’
3. New build
May 25th, 2005 Demonstrator of advanced controllers 8
Option 1: ‘Linix’ Laboratory Setup
May 25th, 2005 Demonstrator of advanced controllers 9
‘Linix’ Laboratory Setup
motor
encoders
inertia 2
inertia 1transmission
May 25th, 2005 Demonstrator of advanced controllers 10
‘Linix’ Laboratory Setup
May 25th, 2005 Demonstrator of advanced controllers 11
‘Linix’ Laboratory Setup
Major disadvantage:
slip between belt and inertias
May 25th, 2005 Demonstrator of advanced controllers 12
Option 2: CLP setup
May 25th, 2005 Demonstrator of advanced controllers 13
CLP setup
May 25th, 2005 Demonstrator of advanced controllers 14
CLP setup
May 25th, 2005 Demonstrator of advanced controllers 15
Sensor positions
May 25th, 2005 Demonstrator of advanced controllers 16
Option 3: New Build
Advantage• Pure design freedom
Disadvantage• Requires very much time and
effort to design
New build Linix CLP-setupMechatronic system √ √ √
Linear 4th order model √ limited linear to bedetermined
Portable, easy to set up √ √ not in currentform
Robust, safe, failsafe √ √ feasible
Observability √ yes, 2 positionSensors
yes, 4 positionsensors
Link with practical device √ transmission printer
Shows controller differences √ no, due tononlinearities
To bedetermined
Remarks Time constraint
Overview demonstrators
May 25th, 2005 Demonstrator of advanced controllers 18
Control SystemsControl Systems
May 25th, 2005 Demonstrator of advanced controllers 19
Mathematical model – 6th order
NMotorCurrent
m
Load
P
LoadSensorWorld
F
Motor
m
Frame
FrameFlex
m
MotorInertia
BeltFlex
P
MotorSensor
P
LoadSensorFrame
K
MotorGain
Damper
ViscousPLUScoulomb friction
May 25th, 2005 Demonstrator of advanced controllers 20
Focus
1. Linear Quadratic Gaussian (LQG)2. Proportional, Integral, Differential (PID)
May 25th, 2005 Demonstrator of advanced controllers 21
LQG explanation
u y
statesLQG
Reference PLANT Output
LQE
LQR
A LQG control algorithm is a combination of1. Lin. Quad. Regulator (state feedback)2. Lin. Quad. Estimator (state estimation)
4th order linear model required!
May 25th, 2005 Demonstrator of advanced controllers 22
4th order linear model
Nremoved at order downsizing
m
Load
P
LoadSensorWorld
F
Motor
m
Frame
FrameFlex
m
MotorInertia
BeltFlex
P
MotorSensor
P
LoadSensorFrame
K
MotorGain
Damper
Required steps:1. Downsize system order2. Linearize system: discard coulomb friction
Result: linear 4th order model (e.g. State Space)
May 25th, 2005 Demonstrator of advanced controllers 23
V A
Xref
LQR
PLANT
LQE
Estimated States
.
L
Cx(k|k)=x(k|k-1) +Le(k|k-1)
+_
m
Load
P
LoadSensorWorld
F
motor
m
FrameFrameFlex
P
LoadSensorFrame Damper
K
Motor
K
Amplifier
m
motortraagheid
motorflex
P
motorsensor
K counter
AD
DA1
ENC encoder
K
A2V
M
K
_
ENCencoder2
Kcounter2
Z-1
LQG controlled system
May 25th, 2005 Demonstrator of advanced controllers 24
PID
Plant
anti-windup reset
PID-controller
m
Load
P
LoadSensorWorld
F
motor
m
FrameFrameFlex
Damper
reference
K
Motor
K
Amplifier
m
motortraagheid
motorflex
K
counter
AD
DA1
ENC
encoder
K
A2V
K
Kp
-1zddt
-1z
K
Kd
K
Ki
May 25th, 2005 Demonstrator of advanced controllers 25
Tuning (1)
For proper comparison of the PID with the LQG controlled system, tuning with the same criteria is required.
1. Avoid actuator saturation2. Minimization of criterion:
dtuuJ TT RQ ee
position error controller output
May 25th, 2005 Demonstrator of advanced controllers 26
Tuning (2)
Tuning procedure:1. Set Q and R2. Minimize criterion J by optimizing
controller gains (KLQG and KP,KI,KD)
Xref
PID
ref
u
x
K
Kp
d/dt
K
Ki
K
Kd
Process
Criterion
May 25th, 2005 Demonstrator of advanced controllers 27
Tuning (3)
Xref
PID
LQR
K
Kp
-1zddt
K
Ki
-1z
K
Kd
Plant1
M
K
_ Plant2
Optimization results
KP = 15.7
KI = 42
KD = 1.6
KLQG= [3.7, 74, 8.2, 70]T
May 25th, 2005 Demonstrator of advanced controllers 28
model
0 0.5 1 1.5 2 2.5 3 3.5 4time {s}
0
0.1
0.2
0.3
0.4PowerPIDPowerLQG
model
0 0.5 1 1.5 2 2.5 3 3.5 4time {s}
-0.001
-0.0005
0
0.0005
0.001
FramePIDFrameLQG
PID vs LQG (1)
• The PID controlled system consumes twice the power of the LQG system
• The maximum frame movement in the PIDcontrolled system is twice compared to LQG
May 25th, 2005 Demonstrator of advanced controllers 29
PID vs LQG (2)
model
0 0.5 1 1.5 2 2.5 3 3.5 4time {s}
0
0.05
0.1
0.15 xPositionPID {m}PositionLQG {m}
The LQG control algorithm leads to an unacceptable position error with the nonlinear process
May 25th, 2005 Demonstrator of advanced controllers 30
LQG+
Xref
LQR
LQE
FRAMEWORLDPlant
Estimated States
.
L
Cx(k|k)=x(k|k-1) +Le(k|k-1)
+_
Z-1
AO526
analog_output
ENC526
Encoder1
KCounter1
ENC526
Encoder2
K Counter2
K
A2V
K Kcomp
-1z
M
K
_
May 25th, 2005 Demonstrator of advanced controllers 31
LQG+ vs LQG
System Results
-0.05
0
0.05
0.1Reference
-0.05
0
0.05
0.1Output {m}
0 0.5 1 1.5 2 2.5 3 3.5time {s}
-0.05
0
0.05
0.1Error
Effect of integrator:Static error is minimized!
Interesting to seethe performance ofLQG+ in practice…
May 25th, 2005 Demonstrator of advanced controllers 32
Design of the new demonstratorDesign of the new demonstrator
May 25th, 2005 Demonstrator of advanced controllers 33
Goal: to test a control algorithm on a physical setup
Procedure
How?
ModelingCode
GenerationLoad Codeat Target
Testing
PC PlantPC(realtime server)(client)
May 25th, 2005 Demonstrator of advanced controllers 34
System overview (1)
PC PlantPC(realtime server)(client)
Client:• Runs MS Windows• Generating models• Model control (start/stop/upload/delete)• Setting parameters of controlled system real-time• View parameters of controlled system real-timeServer:• Runs Linux, with real-time kernel• Runs control system• Performs I/O
May 25th, 2005 Demonstrator of advanced controllers 35
System overview (2)
CPU
I/O interface
RouterStorageDevice
Demonstrator Actuator & Sensors
MotorAmplifier
Encoders MotorCurrent
Cable to PC
May 25th, 2005 Demonstrator of advanced controllers 36
Realization
Mechatronics
Embedded PC+ I/O
Power (CPU)
Power (motor)
Motor amplifier
May 25th, 2005 Demonstrator of advanced controllers 37
ExperimentsExperiments
May 25th, 2005 Demonstrator of advanced controllers 38
Experiments
• Comparison of PID/LQG/LQG+ performanceon the new demonstration setup
• Same controller parameters used as insimulation (after tuning)
• Performance comparison on:1. Static error2. Frame vibration3. Power usage
May 25th, 2005 Demonstrator of advanced controllers 39
0 2 40
0.05
Time
Pos
. [m
]
LQG without I-term
0 2 40
0.05
Time
[m]
LQG with I-term
0 2 40
0.05
Time
[m]
PID
0 2 4-0.04
-0.02
0
0.020.04
Time
Err
. [m
]
0 2 4-0.04
-0.02
0
0.020.04
Time
[m]
0 2 4-0.04
-0.02
0
0.020.04
Time
[m]
0 2 4
-0.2
0
0.2
Time
Fra
me
[mm
]
0 2 4
-0.2
0
0.2
Time
[mm
]
0 2 4
-0.2
0
0.2
Time
[mm
]
0 2 4-1
0
1
Time
Cur
r. [
A]
0 2 4-1
0
1
Time
[A]
0 2 4-1
0
1
Time
[A]
0 2 40
500
1000
Time
Pow
er [
A2]
0 2 40
500
1000
Time
[A2]
0 2 40
500
1000
Time
[A2]
May 25th, 2005 Demonstrator of advanced controllers 40
Results
The LQG+ controlled system outperforms the PID controlled system:
• Maximum frame movement differs factor 3• Total power consumption differs a factor 2• Both control algorithms minimize the static error, but the
LQG controlled system is faster
More performance increase is expected with a better model
Differences in performance between 2nd order PID and 4th order LQG have now been
demonstrated in practice
May 25th, 2005 Demonstrator of advanced controllers 41
DemonstrationDemonstration
May 25th, 2005 Demonstrator of advanced controllers 42
Demonstration
What will be shown:1. ‘Homing’ of the demonstrator
1. Determining absolute position2. PID controller in practice with various controller gains
Furthermore:1. Online adjustment of parameters2. Real-time variable monitoring3. Real-time animation of demonstration setup
May 25th, 2005 Demonstrator of advanced controllers 43
Conclusions Conclusions &&
RecommendationsRecommendations
May 25th, 2005 Demonstrator of advanced controllers 44
Conclusions
1. The new mechatronic demonstration setup is a compact, integrated machine that forms a versatile developmentenvironment for testing various control algorithms in practice
2. The new demonstrator allows for easy comparison of differentcontrol algorithms
3. Non-linear friction elements in the process will lead to lowerperformance in position control of a 4th order LQG-controlled system compared to a 2nd order PID control algorithm
4. Addition of an integrating term leads to an ‘LQG+’ control algorithm that can compensate for differences betweenprocess and reference model.
May 25th, 2005 Demonstrator of advanced controllers 45
Recommendations
Hardware• Expand safety system• Reduce weight of the demonstrator (next version)• Add parallel processing (e.g. distributed control)
Software / control• Experiment with more control systems (MRAS, (L)FF, ILC etc)• Perform system identification
General1. Set up lab work assignments for student
May 25th, 2005 Demonstrator of advanced controllers 46
Questions…?Questions…?
May 25th, 2005 Demonstrator of advanced controllers 47
THANK YOU FOR THANK YOU FOR YOUR ATTENTIONYOUR ATTENTION
you are all invited for you are all invited for DRINKSDRINKS
at ‘De Tombe’, floor 0at ‘De Tombe’, floor 0