Controller Process Output Comparison Measurementfaraday.ee.emu.edu.tr/eeng320/notes/EEE320-Dorf-Chp4.pdf · Controller Process Output Comparison Measurement FIGURE 4.1 ... A block

Controller Process

Output

Comparison Measurement

FIGURE 4.1

A closed-loop system.

Dorf/BishopModern Control Systems 9/E

© 2001 by Prentice Hall, Upper Saddle River, NJ.

R(s) G(s) Y(s)1

�H(s)

Ea(s) Ea(s)

�

�R(s) G(s)

H(s)

Y(s)

FIGURE 4.3

A closed-loop control system (a feedback system).



�

�

�

�

(a)

v in v0Gain�Ka

(b)

v in v0

Gain�Ka

Rp

R1

R2

FIGURE 4.4

(a) Open loop amplifier. (b) Amplifier with feedback.



�

��Ka

b

v in v0

FIGURE 4.5

Block diagram model of feedback amplifier assuming Rp W R0 of the amplifier.



�

�k2

Ra

EVa

Ia

Speedv(t)

J, bLoad

if � constant field current

FIGURE 4.7

Open-loop speed control system (without feedback).



�

�

(a)

Speedv (s)

AmplifierKa

Va(s)

Vt(s)

MotorG(s)

TachometerKt

R(s) � � k2Es �

��

�

�

(b)

Tachometer Motor

FIGURE 4.8

(a) Closed-loop speed control system. (b) Transistorized closed-loop speed control system.



Closed-loop

Open-loop(without feedback)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

v (t)

K1k2E

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Time (seconds)

FIGURE 4.9

The response of the open-loop and closed-loop speed control system whent 5 10 andK1KaKt � 100. The time to reach 98% of the final value for the open-loop and closed-

loop system is 40 seconds and 0.4 second, respectively.



Steel bar

Conveyor

Rolls

FIGURE 4.10

Steel rolling mill.



�

� �

�

1Js � b

Kb

Tm(s) TL(s)v (s)

SpeedVa(s)

Ia(s)

Motor back emf

1Ra

Km

DisturbanceTd(s)

FIGURE 4.11

Open-loop speed control system (without external feedback).



�

�

�

� �

�R(s) 1

Js � bKm

Ra

Vt(s)

Amplifier

Ea(s)Ka

Kb

Kt

Tm(s)

Td(s)

TL(s)v (s)

Tachometer

FIGURE 4.13

Closed-loop speed tachometer control system.



Td(s)

�1

�H(s)

R(s)

R(s)

G2(s)G1(s)1 Ea(s)

Ea(s)

�

� �

�G2(s)

(a)

(b)

Td(s)

G1(s)

H(s)

v (s)

v(s)

FIGURE 4.14

Closed-loop system. (a) Block diagram model. (b) Signal-flow graph model.



R(s)G2(s)G1(s)1

1

�H2(s) H1(s)Sensor

Y(s)

N(s)Noise

FIGURE 4.16

Closed-loop control system with measurement noise.



�

� �

�

1s(s � 1)

E(s)

D(s)

R(s)Desiredangle

K � 11sY(s)

Angle

G(s)Boring machine

FIGURE 4.21

A block diagram model of a boring machine control system.



0 0.5 1 1.5 2 2.5 3

Time (sec)

(a)

0

0.2

0.4

0.6

0.8

1.2

1.4

1

y(t)

(de

g)

0 0.5 1 1.5 2 2.5 30

0.002

0.004

0.006

0.01

0.012

0.008

y(t)

(de

g)

FIGURE 4.22

The response y(t) to (a) a unit input step r(t) and (b) a unitdisturbance step input D(s) 5 1/s for K � 100.



0 0.5 1 1.5 2 2.5 3

Time (sec)

0

0.2

0.4

0.6

0.8

1.2

1

y(t)

(de

g)

FIGURE 4.23

The response y(t) for a unit step input (solid line) and for a unit step disturbance (dashed line) for K � 20.



FIGURE 4.24

The solar-powered Mars rover, named Sojourner, landed on Mars on July 4, 1997 andwas deployed on its journey on July 5, 1997. The 23-pound rover is controlled by anoperator on Earth using controls on the rover [21, 22]. (Photo courtesy of NASA.)



�

�R(s)

r(t) � t,t � 0 �

�

R(s)

Controller

�

�K(s � 1)(s � 3)

s2 � 4s � 5

1(s � 1)(s � 3)

1(s � 1)(s � 3)

D(s)

D(s) Rover

RoverY(s)

Vehicleposition

Y(s)Vehicleposition

K

(a)

(b)

FIGURE 4.25

Control system for rover; (a) open-loop (without feedback) and (b) closed-loop with feedback. The input is R(s) � 1/s.



Magnitude of sensitivity vs. frequency

Frequency (rad/s)

Mag

nitu

de o

f se

nsiti

vity

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

10�1 100 101 102

FIGURE 4.26

The magnitude of the sensitivity of the closed-loop system for the Mars rover vehicle.



�

� �

�R(s)

1s(Js + b)

Km

R + L s

V(s)Amplifier Coil Load

Desiredhead

position

Actualposition

ErrorKa

H(s) = 1

DisturbanceD(s)

Y (s)

Sensor

FIGURE 4.32

Control system for disk drive head reader.



�

� �

�R(s)

E(s) 5000G1(s) =

(s + 1000)1

G2(s) =s(s + 20)

Coil Load

Ka

DisturbanceD(s)

Y (s)

FIGURE 4.33

Disk drive head control system with the typical parameters of Table 2.11.



Ka=10;nf=[5000]; df=[1 1000]; sysf=tf(nf,df);ng=[1]; dg=[1 20 0]; sysg=tf(ng,dg);sysa=series(Ka*sysf,sysg);sys=feedback(sysa,[1]);t=[0:0.01:2];step(sys,t);ylabel('y(t)'), xlabel('Time (sec)'), grid

Time (sec)

0 0.2 0.4 0.6 1.0 1.4 1.80.8 1.2 1.6 2.00

0.3

0.2

0.1

0.6

0.5

0.4

1.0

0.7

0.9

0.8

(b)

(a)

Time (sec)

0 0.2 0.4 0.6 1.0 1.4 1.80.8 1.2 1.6 2.00

0.6

0.4

0.2

1.0

1.2

0.8

y(t)

y(t)

Select Ka.

Ka = 10.

Ka = 80.

FIGURE 4.34

Closed-loop response. (a) MATLAB script. (b) Step response for Ka � 10 and Ka � 80.



Ka=80;nf=[5000]; df=[1 1000]; sysf=tf(nf,df);ng=[1]; dg=[1 20 0]; sysg=tf(ng,dg);sys=feedback(sysg,Ka*sysf);sys=–sys;t=[0:0.01:2];step(sys,t);plot(t,y), gridylabel('y(t)'), xlabel('Time (sec)'), grid

(b)

(a)

Time (sec)

0 0.2 0.4 0.6 1.0 1.4 1.80.8 1.2 1.6 2.0-3

-1.5

-2

-2.5

-0.5

0x 10-3

-1

y(t)Select Ka.

Disturbance enterssummer with anegative sign.

Ka = 80.

FIGURE 4.35

Disturbance step response. (a) MATLAB script. (b) Disturbance response for Ka � 80.



�

��

�KR(s) Y(s)

D(s)

1

(s � 1)2

(a)

(b)

1.40

1.00

0.70

00.08

0.50

�0.700 1 2 3 4 5

Time

e(t)

K � 1.0

K � 10

FIGURE 4.36

(a) A single-loop feedback control system. (b) The error response for a unit step disturbance when R(s) � 0.



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Controller Process Output Comparison Measurementfaraday.ee.emu.edu.tr/eeng320/notes/EEE320-Dorf-Chp4.pdf · Controller Process Output Comparison Measurement FIGURE 4.1 ... A block