Lecture NotesLecture Notes
Introduction to Introduction to Control SystemsControl Systems
Instructor: Dr. Huynh Thai HoangDepartment of Automatic Control
Faculty of Electrical & Electronics EngineeringHo Chi Minh City University of TechnologyHo Chi Minh City University of Technology
Email: [email protected]@yahoo.com
Homepage: www4 hcmut edu vn/ hthoang/
16 November 2012 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 1
Homepage: www4.hcmut.edu.vn/~hthoang/
Chapter 7Chapter 7
Digital Control SystemsDigital Control SystemsDigital Control SystemsDigital Control Systems
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Introduction to digital control system
ContentContent
Introduction to digital control system Digital PID controller Examples of digital control system
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Introduction Introduction to digital control systemsto digital control systems
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Digital Digital control systemscontrol systems
Computer D/A Plantr(kT) y(t)u(kT) uR(t)
A/Dyfb(kT)
Sensor
“Computer” = computational equipments based on microprocessor technology (microprocessormicroprocessor technology (microprocessor, microcontroller, PC, DSP,…).
Advantages of digital control system:d a tages o d g ta co t o systeFlexibilityEasy to implement complex control algorithms
C t t l l t t th ti
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Computer can control many plants at the same time.
Digital controllerDigital controller
(kT) (t)Computer D/A Plantr(kT) y(t)u(kT) uR(t)
A/Dyfb(kT)
Sensor
A/D converter: to convert continuous signals to digital signals D/A converter: to convert digital signals to continuous signals Computer: to execute pre-programmed control algorithms
PID t ll PID controllerOptimal controllers Adaptive controllers
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Adaptive controllers,…
A/D conversionA/D conversion
x(t) x*(t)Tx(t) x (t)T
A/D( ) A/Dx(t) Sampling time (T): time interval between 2 samples.
[010 0 010]
t0
*( )
2 samples. Resolution: indicates
the number of digital /[010 0..010]x*(t) values an A/D can
produce over the range of analog
0t
T 2T kT
g gvalues.
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A/D conversion = time discretization + level quantization
D/A conversionD/A conversion
(t)x*(t) xR (t)D/A
[010 0..010]x*(t)
0t
T 2T kT0xR(t)T 2T kT
t
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0
Digital PID controllersDigital PID controllers
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Continuous Continuous PID controllerPID controller
r(t)+
y(t)e(t) u(t)G(s)PID
dttdeKdeKteKtu
t
DIP)()()()(
0
dt0
Discretize the continous PID control signal in order to implement the PID controller in microcontrollers or computers
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Discrete difference Discrete difference factorfactor
u(t)e(t) u(k)e(k)d/dt
u(t)e(t)
d )(
GD(z)u(k)e(k)
dttdetu )()( Continuous differential factor:
Discrete difference factor:T
kekeku )]1[()()(
Transfer function of discrete difference factor:
1)(U )1(1)()()( 1 z
TzEzUzGD
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Discrete integral Discrete integral factorfactor
u(t)e(t) u(k)e(k)
t
e()du(t)e(t)
GI(z)u(k)e(k)
detu 0
)()( Continuous integral:
Discrete integral:
dekTukT
0
)()( dedekT
Tk
Tk
)1(
)1(
0
)()(0 Tk )1(0
)]()1([2
)1()( kekeTkuku 2
Transfer function of discrete integral factor:
1)( zTG
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12)(
zzGI
Transfer function of discrete PID controllerTransfer function of discrete PID controller
C ti PID t ll Continuous PID controller:
sKKKsG DPPID )(
Discrete PID controller:
s DPPID )(
zKzTKKzG DIPPID
11)(
Discrete PID controller:
zTzKzG PPID 12
)(
P I DP I D
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Difference equation of discrete Difference equation of discrete PID controllerPID controller
zKzTK 11z
zT
KzzTKKzG DI
PPID1
11
2)(
1)( 1 KTKU )1(11
2)()( 1
1
1
zT
KzzTKK
zEzU DI
P
)()1()1(2
)1()()1( 21111 zEzT
KzTKzKzUz DIP
)]1()([
...)]1()([)1()(
kkTKkekeKkuku
I
P
)]2()1(2)([
...)]1()([2
kkkK
keke
D
I
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)]2()1(2)([ kekekeT
D
Digital PID control programming Digital PID control programming
float PID control(float setpoint float measure)float PID_control(float setpoint, float measure){
ek_2 = ek_1; ek_1 = ek; //update old erroruk_1 = uk; //update old control signalek = setpoint – measure; //calculate current erroruk = uk 1 + Kp*(ek-ek 1) + Ki*T/2*(ek+ek 1) +…uk uk_1 Kp (ek ek_1) Ki T/2 (ek ek_1) …
Kd/T*(ek – 2*ek_1+ek_2); //calculate PID control signalIf uk > Umax, uk = Umax;If uk < Umin uk = Umin;If uk < Umin, uk = Umin;return(uk)
}
Note: Kp, Ki, Kd, uk, uk_1, ek, ek_1, ek_2 must be declared as global variables; uk 1 ek 1 and ek 2 must be initialized to
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global variables; uk_1, ek_1 and ek_2 must be initialized to be zero. Umax and Umin are constants.
Approaches to design discrete controllersApproaches to design discrete controllers
Indirect design: First design a continuous controller Indirect design: First design a continuous controller,then discretize the controller to have a discrete controlsystem. The performances of the obtained discretey pcontrol system are approximate those of the continuouscontrol system provided that the sample time is small
henough.
Direct design: Directly design discrete controllers in Zdomain.Methods: root locus, pole placement, analyticalmethod, …
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Implementation of control systemsImplementation of control systems
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Knowlegde requiredKnowlegde required
C t l th Control theory
Electronic circuits
Sensors and measurement
Power electronic Power electronic
Microcontroller
Programming
Knowledge relalated to the plant to be controlled Knowledge relalated to the plant to be controlled
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Basic conponents of microcontrollersBasic conponents of microcontrollers
A i t ll b i ll t i f ll iA microcontroller basically contains one or more following components: Central processing unit(CPU) Central processing unit(CPU) Random Access Memory)(RAM) Read Only Memory(ROM)y y( ) Input/output ports Timers and Counters Interrupt Controls Analog to digital converters
Di it l l t Digital analog converters Serial interfacing ports Oscillatory circuits
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Oscillatory circuits
Digital control of DC motorDigital control of DC motor
UserMicro-
ControllerPower
amplifier MotorUser
Interface
MeasurementMeasurement
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Example of microcontroller based motor controlExample of microcontroller based motor control
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Digital control of thermal processDigital control of thermal process
UserMicro-
ControllerPower
amplifierHeaterUser
Interface
MeasurementMeasurement
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4.7k 4.7kVCC
4.7k 4.7k
Temperature controller and user interfaceTemperature controller and user interface
1k
D6LED 7DOAN1 4 5 7
1kPORTD<6>
Q2
A1015
Q3
A1015PORTD<4> 1k 1k
Q1
A1015PORTD<5>
Q4
A1015PORTD<7>
. . . .
LED_7DOAN4 5 7
VC
C1
AF
VC
C2
VC
C3
VC
C4
G CDO
T
DE B
DOT
238 910 1112 6
AFG CD DE B
G
C
ED
VCCVCC F
AB
D
SW4A
V_sensor
GF
B
VREF+SW4
10k
E
PIC16F877A
234567
3334353637383940
1
RA0/AN0RA1/AN1RA2/AN2/VREF-/CVREFRA3/AN3/VREF+RA4/T0CKI/C1OUT
RB0/INTRB1RB2
RB3/PGMRB4RB5
RB6/PGC
MCLR*/VPPDOT
10k
C
SW5
SW2
SW3
PORTD<5>
10MHz
C16
33p
SW3
SW4
PORTD<6>
PORTD<4>
G
SW1
SW2
7 40
1516171823242526
1920212227282930
1389
RA5/AN4/SS*/C2OUT RB7/PGD
RC0/T1OSO/T1CKIRC1/T1OSI/CCP2RC2/CCP1RC3/SCK/SCLRC4/SDI/SDARC5/SDORC6/TX/CKRC7/RX/DT
RD0/PSP0RD1/PSP1RD2/PSP2RD3/PSP3RD4/PSP4RD5/PSP5RD6/PSP6RD7/PSP7
OSC1/CLKINRE0/RD*/AN5
SW2
SW3
PORTC<2>
PORTD<7>
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10MHzCRYSTAL
VCC SW1
C17
33p
SW114
3211
3112
910
OSC2/CLKOUT
VDDVDD
VSSVSS
RE1/WR*/AN6RE2/CS*/AN7
Temperature measurement using thermocoupleTemperature measurement using thermocouple
5V
U27 1
5V
5VU1
LM35
1VC
C
2C1
10uF
-
+
OP07
3
26
4 8
5 5V 5
352
GN
D
VOUT
V V2 R1
25k
0
0
-5V
-
+
U4
OP07
3
26
7 1
5V 5V
-
+
U5
OP07
3
26
7 1
R5 PA0/ADC0
3G
V3 Vout
OP07
4 85V
R6R2J1Thermo couple
1 +
U3
36
7 1
OP07
4 8-5V -5VR41.8k
100
V1 R3
C210uF
3.9k1001
-5V
-OP07
26
4 8
V1 R3
100
0
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