Closed and Open Loop

Published on June 2016 | Categories: Documents | Downloads: 96 | Comments: 0 | Views: 682
of 23
Download PDF   Embed   Report

open and closed loop system

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.

Sponsor Documents

Or use your account on DocShare.tips

Hide

Forgot your password?

Or register your new account on DocShare.tips

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close