controller process output comparison .controller process output comparison measurement figure 4.1

Download Controller Process Output Comparison .Controller Process Output Comparison Measurement FIGURE 4.1

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  • 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).

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • (a)

    v in v0GainKa

    (b)

    v in v0

    GainKa

    Rp

    R1

    R2

    FIGURE 4.4

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

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • Ka

    b

    v in v0

    FIGURE 4.5

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

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • k2

    Ra

    EVa

    Ia

    Speedv(t)

    J, bLoad

    if constant field current

    FIGURE 4.7

    Open-loop speed control system (without feedback).

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • (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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • Steel bar

    Conveyor

    Rolls

    FIGURE 4.10

    Steel rolling mill.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 1Js b

    Kb

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

    Va(s)Ia(s)

    Motor back emf

    1Ra

    Km

    DisturbanceTd(s)

    FIGURE 4.11

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

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • R(s) 1

    Js bKmRa

    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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.)

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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

    101 100 101 102

    FIGURE 4.26

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

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • R(s)

    1s(Js + b)

    KmR + 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • R(s)

    E(s) 5000G1(s) = (s + 1000)

    1G2(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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

  • 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.

    Dorf/BishopModern Control Systems 9/E

    2001 by Prentice Hall, Upper Saddle River, NJ.

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