Closed and Open Loop
Comments
Content
Dorf/Bishop Modern Control Systems 9/E
Controller
Process
Output
Comparison
Measurement
FIGURE 4.1 A closed-loop system.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
R (s)
ϩ Ϫ
E a(s)
G (s)
Y(s)
R (s)
1
E a(s)
G (s)
Y(s)
H (s)
ϪH (s)
FIGURE 4.3 A closed-loop control system (a feedback system).
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
ϩ v in Ϫ Gain ϪK a
ϩ v0 Ϫ
v in Gain ϪK a Rp
v0 R1 R2
(a)
(b)
FIGURE 4.4 (a) Open loop amplifier. (b) Amplifier with feedback.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
v in
ϩ ϩ
ϪK a
v0
b
FIGURE 4.5 Block diagram model of feedback amplifier assuming Rp W R0 of the amplifier.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
Ra i f ϭ constant field current Ia
k2 E
ϩ Va Ϫ Speed v (t)
J, b Load
FIGURE 4.7 Open-loop speed control system (without feedback).
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
R(s) ϭ
k 2E s
ϩ Ϫ
Amplifier Ka
V a (s)
Motor G (s)
Speed v (s)
V t (s)
Tachometer Kt (a)
Ϫ ϩ
Tachometer Ϫ ϩ
Motor
(b)
FIGURE 4.8 (a) Closed-loop speed control system. (b) Transistorized closed-loop speed control system.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
1.0 0.9 Closed-loop 0.8 0.7 0.6 v (t) 0.5 K1k 2 E 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Open-loop (without feedback)
Time (seconds)
FIGURE 4.9 The response of the open-loop and closed-loop speed control system whent 5 10 and K1 Ka Kt ϭ 100. The time to reach 98% of the final value for the open-loop and closedloop system is 40 seconds and 0.4 second, respectively.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
Rolls
Steel bar
Conveyor
FIGURE 4.10 Steel rolling mill.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
Disturbance Td (s) ϩ Ϫ 1 Ra I a(s) Tm(s) Ϫ ϩ TL(s) 1 Js ϩ b
Va (s)
Km
v (s) Speed
Motor back emf
Kb
FIGURE 4.11 Open-loop speed control system (without external feedback).
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
Td (s) Amplifier R (s) ϩ Ϫ Ea(s) Ka ϩ Ϫ Km Ra Tm(s) Ϫ ϩ Kb Tachometer Vt (s) Kt TL(s) 1 Js ϩ b
v (s)
FIGURE 4.13 Closed-loop speed tachometer control system.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
Td (s) Ϫ G1(s) ϩ G2(s) v (s)
R(s)
ϩ Ϫ
Ea(s)
H(s) (a)
Td (s) 1 R(s) Ea(s) Ϫ1 G1(s) ϪH(s) (b) G2(s) v(s)
FIGURE 4.14 Closed-loop system. (a) Block diagram model. (b) Signal-flow graph model.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
1 R(s)
G1(s) ϪH 2(s) 1
G2(s)
Y(s)
H 1(s) Sensor
N (s) Noise
FIGURE 4.16 Closed-loop control system with measurement noise.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
D (s) G (s) Boring machine 1 s(s ϩ 1) Y(s) Angle
R (s) Desired angle
ϩ Ϫ
E (s)
ϩ K ϩ 11s ϩ
FIGURE 4.21 A block diagram model of a boring machine control system.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
1.4 1.2 1 y(t) (deg) 0.8 0.6 0.4 0.2 0
0
0.5
1
1.5 Time (sec) (a)
2
2.5
3
0.012 0.01 0.008 y(t) (deg) 0.006 0.004 0.002 0
0
0.5
1
1.5
2
2.5
3
FIGURE 4.22 The response y(t) to (a) a unit input step r(t) and (b) a unit disturbance step input D(s) 5 1/s for K ϭ 100.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
1.2 1 0.8 y(t) (deg) 0.6 0.4 0.2 0
0
0.5
1
1.5 Time (sec)
2
2.5
3
FIGURE 4.23 The response y(t) for a unit step input (solid line) and for a unit step disturbance (dashed line) for K ϭ 20.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
FIGURE 4.24 The solar-powered Mars rover, named Sojourner, landed on Mars on July 4, 1997 and was deployed on its journey on July 5, 1997. The 23-pound rover is controlled by an operator on Earth using controls on the rover [21, 22]. (Photo courtesy of NASA.)
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
Controller R(s) K(s ϩ 1)(s ϩ 3) s2 ϩ 4s ϩ 5
D (s) ϩ ϩ (a) D (s) ϩ
Rover 1 (s ϩ 1)(s ϩ 3) Y(s) Vehicle position
Rover 1 (s ϩ 1)(s ϩ 3) Y(s) Vehicle position
R(s) r (t) ϭ t, tу0
ϩ Ϫ
K
ϩ
(b)
FIGURE 4.25 Control system for rover; (a) open-loop (without feedback) and (b) closed-loop with feedback. The input is R(s) ϭ 1/s.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
Magnitude of sensitivity vs. frequency 1.10 1.05 1.00 Magnitude of sensitivity 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 10Ϫ1 100 Frequency (rad/s) 101 10 2
FIGURE 4.26 The magnitude of the sensitivity of the closed-loop system for the Mars rover vehicle.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
Disturbance D(s) Amplifier R (s) Desired head position ϩ Ϫ Error V(s) Ka Coil Km R+Ls Ϫ ϩ Load 1 s(Js + b)
Y (s) Actual position
Sensor H(s) = 1
FIGURE 4.32 Control system for disk drive head reader.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
Disturbance D(s) Coil R (s) ϩ Ϫ E(s) Ka G1(s) = 5000 (s + 1000) Ϫ ϩ Load G2(s) = 1 s(s + 20) Y (s)
FIGURE 4.33 Disk drive head control system with the typical parameters of Table 2.11.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
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 Select Ka.
(a)
1.0 0.9 0.8 0.7 0.6 y(t) 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1.0 1.2 Time (sec) 1.4 1.6 1.8 2.0 Ka = 10.
(b) 1.2 1.0 0.8 y(t) 0.6 0.4 Ka = 80. 0.2 0 0 0.2 0.4 0.6 0.8 1.0 1.2 Time (sec) 1.4 1.6 1.8 2.0
FIGURE 4.34 Closed-loop response. (a) MATLAB script. (b) Step response for Ka ϭ 10 and Ka ϭ 80.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
(a)
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), grid ylabel('y(t)'), xlabel('Time (sec)'), grid
Select Ka.
Disturbance enters summer with a negative sign.
x 10-3 0 -0.5 -1 (b) y(t) Ka = 80. -1.5 -2 -2.5 -3 0 0.2 0.4 0.6 0.8 1.0 1.2 Time (sec) 1.4 1.6 1.8 2.0
FIGURE 4.35 Disturbance step response. (a) MATLAB script. (b) Disturbance response for Ka ϭ 80.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
Dorf/Bishop Modern Control Systems 9/E
D(s) R (s) ϩ Ϫ (a) 1.40 K ϩ ϩ 1 (s ϩ 1)2 Y(s)
1.00 0.70 0.50 e(t) 0.08 0 K ϭ 10 K ϭ 1.0
Ϫ0.70
0
1
2 Time (b)
3
4
5
FIGURE 4.36 (a) A single-loop feedback control system. (b) The error response for a unit step disturbance when R(s) ϭ 0.
© 2001 by Prentice Hall, Upper Saddle River, NJ.
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