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
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