ENT364/4 – Control System

Sazali YaacobBEng(Malaya), MSc(Surrey), PhD(Sheffield)

Chartered Engineer, CEng (United Kingdom)

Member Institute of Engineers and Technologist, MIET (United Kingdom)

s.yaacob@unimap.edu.my

019-4772260

Course Assessment

• Lecture 3 hours per week• Lab/Tutorial/Design 2 hours per week• Final Examination 50 marks• Mid-SemesterTest 10 marks• Quiz/Design 25 marks• Lab works 15 marks

Weekly Schedule

Week 1: Introduction

Week 2: Modeling

Week 3: Modeling

Week 4: Time Response

Week 5: Time Response

Week 6: Time Response/Root Locus

Week 7: Root Locus/Mid-Semester Revision

Weekly Schedule

Week 8: Frequency Response

Week 9: Frequency Response

Week 10: Frequency Response

Week 11: Frequency Response

Week 12: Design

Week 13: Design

Week 14: Revision

OBJECTIVES•Basic terminologies.•Open-loop and closed-loop•Block diagrams•Control structure•Advantages and Disadvantages of closed-loop

Introduction to control system

Human control

System control

GPS Control

Force Control

Vision Control

Primary Source(Loudspeaker)

Secondary source (Actuator)

Block Diagram for Active Noise Cancellation

24 cm

Error Microphone

Sensor Microphone 36 cm

Primary path Error path12 cm

BEFORE ANC AFTER ANC

Sound Control

Satellite Control

Satellite Control

Satellite Control

Magnetometer

Magnetorquer

Driver

OBC ACS

Torque command for the MT

Processed attitude data

Attitude Ref

Process Control

Pilot Plant

Servo Control

Steering Control

Complete System Set-up for Mobile Robot using Mecannum wheel

Omni-directional Motion for the Mobile Robot

Basics terminologies

• Sub-system and System

subsystem subsystem subsystem

– System is a combination of physical and non-physical components that are configured to serve certain tasks to maintain the output

– Subsystem is part of the system that is grouped for a certain function

blower room thermostat

Plant

subsystem

input output

• Plant is the main subsystem where the control signal will act on and produce the output .

plant

• Disturbance is unwanted signal that may sway the output • Controller is a subsystem that is used to ensure the output signal

follows the input signal

controller plantinput

disturbance

output

+

Disturance and Controller

Error

controller plant

-

+ ++

input

• Error is a signal made up of the difference of input and output

error

disturbance

Control Structure

• For any control system the following flow structure is needed

model

analysis

design

Objective

Example of an open-loop system

motor

Turn table

rheostat

amplifier

amplifier motorTurn-table

Required speed Actual speed

Open-loop system

Closed-loop system example of closed-up system

motor

tachometer

+

-

Turn-table

rheostat

Differential amplifier

amplifier motor Turn-table

tachometer

required

speed

Actual speed+

-

Block Diagram

Transfer function,

H

input, R output, Y

Transfer function is the ratio of the ouput over the input variables

The output signal can then be sderived as

rHy

R

YH

Example of multi-variables

++

+ -

R

C

E

B BCRE

Block diagram reduction

H G H.G=a b c a c

a

cHG

Feed Forward and Feedback Transfer function

+

-

R(s) E(s) Y(s)

B(s)

)(sG

)(sHE(s error signal

B(s) feedback

signalR(s) reference

signalY(s) output

signal Feed forward transfer

function)(

)()(

sE

sYsG

Feedback transfer function

)(

)()(

sY

sBsH

Open Loop Transfer Function

H(s) G(s) H(s)G(s)E(s) Y(s) B(s) E(s) B(s)

Open loop transfer function )()()(

)(sHsG

sE

sB

+

-

R(s) E(s) Y(s)

B(s)

)(sG

)(sH

Closed Loop Transfer Function

)()()( sHsYsB The feedback is

.

)()()()( sHsBsRsE )()()()( sYsHsRsE

)()()()(

)(sYsHsR

sG

sY

)()(1

)(

)(

)(

sHsG

sG

sR

sY

Variable difference

)()(1)( sHsGsT

Characteristic equation0)()(1 sHsG

Closed-loop transfer function

The error signal is

The closed loop transfer function is

The characteristic equation is very important in determining the behaviour of a system

Model

Many type of models:

• Physical model

• Graphical model

• Mathematical model

Example: Current-voltage relationship

iRv v – voltage in Vi – current in AR – resistance in Ohm

kxf Example: Force-deflection realtionship

f – force in Nk – spring constantx – displacement in mMass-spring model sistem jisim-pegas

From Newton’s law

kxf

maff

s

so

where m is the mass and a is the acceleration.

dt

dva

dt

dxv

Substituting2

2

dt

xdmkxfo

Example: Mass-spring model

of

sf

- applied forcex - displacement

- reaction force

Velocity

Acceleration

Black-box Modelling

g tyty

tu

Input-output reltionship

Speed

Tor

qu

e

Starting Torque(Standstill)

Stalling or Pull-OutTorque

Full-Load Torque

No-Load Torque

Normal OperationRange

Synchronous SpeedNo-Load Speed

Full-Load Speed

Torque-Speed Characteristics of a Squirrel-Cage Induction Motor

Identification Procedure

Data collection(experimental work)

Selecting modelstructure

Fitting the modelto the data

Validating the model

Accepting the model ?

Yes

No

Mod

el s

tru

ctu

re is

not

goo

d

Dat

a is

not

goo

dIn

sert

fil

tara

tion

fac

tor

if n

eces

sary

Neural Network Training

+

-

PlantPlantP

M

ty

ty

t

tu

Forward Plant Modeling

Neural Network Structure

Hiddenlayerj

Inputlayeri

Outputlayerk

vji wkj

Hidden unit’s neuron Output unit’s neuron

Biase Biase

A two layer Artificial Neural Network

Neural Network Control

F r e q u e n c y In v e r te r

C o m p u te r

C

L 1

L 2

L 3

U

V

W

N

In p u t P h a se D ig ita l P h a se O u tp u t P h a se

F r eq u en cy In v er ter C o n tro l U n it

In d u c tio n M o to rT a c h o m e te r

In te r fa c in g D a taA c q u is itio n C a r d

M a in T h r e e P h a seP o w e r S u p p ly

M a in T h r e e P h a seP o w e r S u p p ly

The Experimental Work

Input-output Data

0 1000 2000 3000 4000 5000 60000

500

1000

1500

2000

S a mple s

Out

put

Sig

nal

0 1000 2000 3000 4000 5000 60000

500

1000

1500

Inp

ut S

igna

l

The Input-Output Da ta S e t.

Analysis

Transient stateA state whereby the system response after a pertubation before the response approach to a steady condition

Steady stateA state whereby the system response becomes steady after a transient state

StabilityThe condition of the steady state. If the response converges to a finite value then it is said to be in a stable condition and if the response diverges, it is known to be unstable.

Time Response

MP

tr

tp

1.0

t

ts

Transient s state Steady state

Example of Time Response

Design

Analogue controller A controller that used analogue subsystem

Digital Controller A controller that used computer as its subsystem

computer drive plant

sensor

_

+ referene

input

Actual output

Adaptive Control

Controller PlantControl Action

Error

Output

Reference +

-

AdjustmentMechanism

Computer Control

Frequency Inverter

Interfacing DataAcquisition Card

Computer

C

L1

L2

L3

U

V

W

N

Input Phase Digital Phase Output Phase

Frequency Inverter Control Unit

Induction Motor

MagneticPowderBrake

Tachometer

Interfacing DataAcquisition Card

5

x 1

x 2

x 5 x 10

x 100

x 1000

5

x 1

x 2

x 5 x 10

x 100

x 1000

ON/OFF

x 1

x 2 x 5

x 10

Brake PowerBrake Reset

External Setpoint

Magnetic PowderBrake

SpeedLoad

Brake Control Unit

Main Three PhasePower Supply

Main Three PhasePower Supply

The Control Experiment.

Step Input

0 1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

1200

1400

1600

1800

Time [s e conds ]

Sp

ee

d [r

pm

]Unit S te p Re s pons e with Dire ct Inve rs e C ontrol.

The Induction Motor Unit Step Speed Response with the Direct Inverse Control Scheme

Sinusoidal Input

0 2 4 6 8 10 12 14 160

500

1000

1500

Time [s e conds ]

Sp

ee

d [r

pm

]S ine Wa ve Re fe re nce a nd S pe e d Re s pons e of Dire ct Inve rs e C ontrol S che me .

Speed Response to a Sine Wave Reference Signal under DIC Scheme.

Ramp Input

0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

Time [s e conds ]

Sp

ee

d [r

pm

]Ra mp Wa ve Re fe re nce a nd S pe e d Re s pons e of Dire ct Inve rs e C ontro l S che me .

Speed Response to a Ramp Wave Reference Signal under DIC Scheme.

Square-wave Input

0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

1400

1600

1800

Time [s e conds ]

Sp

ee

d [r

pm

]S qua re Wa ve Re fe re nce a nd S pe e d Re s pons e of Dire ct Inve rs e C ontrol S che me .

Speed Response to a Square Wave Reference Signal under DIC Scheme.

Advantage of Feedback Loop (1) Not susceptible to disturbance

H

1G2G

+

++

-

d

r y

0r

HGG

dG

GHyGdy

21

2

21

1

Assume

121 HGG

HG

dy

1

11 HG , then changes in y is negligible

Not sensitive to parameters changed

(2) Insensitive to changes in parameters

Consider

H

Gy +

-

r

Define sensitvity as

d

dT

Td

TdT

ofchange

TofchangeS T

%

%

where T is the transfer function of the system is the parameter of the system.

Closed-loop transfer function

GH

G

R

YT

1

Let us investigate the effect on the system when the plant is subjected to perturbance i.e .,

TGS

.

TGS

21

1

GHdG

dT

GHGHG

GHGSTG

1

1

1

112

1GH 0TGSIf , thus

.

TGS

(3) Increased in bandwidthConsider a first order

1)(

)(

sT

K

sR

sY

where K is the dc gain and T is the time constant

)(sR )(sY1sT

K

If a feedback is applied

a

1sT

K)(sY)(sR +

-

The closed-loop transfer function is

1)1

)1

1)(

)(

aKsT

aKK

aKsT

K

sR

sY

Hence the new time constant )1 aKT is reduced and increased the system bandwidth

)(sG )(sY)(sR

)()()( sRsGsY

)()()(1

)()( sR

sHsG

sGsY

1)()( sHsG

)()( sRsY

Output for open loop

Output for feedback system

. If

thus

.

(4) Accurate control.

+

-

R(s) Y(s) )(sG

)(sH

This means that the output will follow the input which signify a god control objective