ent364/4 – control system sazali yaacob beng(malaya), msc(surrey), phd(sheffield) chartered...
TRANSCRIPT
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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)
019-4772260
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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
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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
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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
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OBJECTIVES•Basic terminologies.•Open-loop and closed-loop•Block diagrams•Control structure•Advantages and Disadvantages of closed-loop
Introduction to control system
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Human control
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System control
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GPS Control
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Force Control
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Vision Control
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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
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Satellite Control
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Satellite Control
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Satellite Control
Magnetometer
Magnetorquer
Driver
OBC ACS
Torque command for the MT
Processed attitude data
Attitude Ref
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Process Control
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Pilot Plant
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Servo Control
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Steering Control
Complete System Set-up for Mobile Robot using Mecannum wheel
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Omni-directional Motion for the Mobile Robot
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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
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Plant
subsystem
input output
• Plant is the main subsystem where the control signal will act on and produce the output .
plant
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• 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
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Error
controller plant
-
+ ++
input
• Error is a signal made up of the difference of input and output
error
disturbance
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Control Structure
• For any control system the following flow structure is needed
model
analysis
design
Objective
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Example of an open-loop system
motor
Turn table
rheostat
amplifier
amplifier motorTurn-table
Required speed Actual speed
Open-loop system
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Closed-loop system example of closed-up system
motor
tachometer
+
-
Turn-table
rheostat
Differential amplifier
amplifier motor Turn-table
tachometer
required
speed
Actual speed+
-
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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
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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
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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
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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
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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
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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
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Black-box Modelling
g tyty
tu
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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
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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
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Neural Network Training
+
-
PlantPlantP
M
ty
ty
t
tu
Forward Plant Modeling
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Neural Network Structure
Hiddenlayerj
Inputlayeri
Outputlayerk
vji wkj
Hidden unit’s neuron Output unit’s neuron
Biase Biase
A two layer Artificial Neural Network
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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
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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.
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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.
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Time Response
MP
tr
tp
1.0
t
ts
Transient s state Steady state
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Example of Time Response
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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
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Adaptive Control
Controller PlantControl Action
Error
Output
Reference +
-
AdjustmentMechanism
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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.
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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
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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.
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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.
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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.
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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
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(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
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(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
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)(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