Controller Process Output Comparison Measurement FIGURE 4. A closed-loop system.
R(s) E a (s) G(s) Y(s) R(s) E a (s) G(s) Y(s) H(s) H(s) FIGURE 4.3 A closed-loop control system (a feedback system).
v in v 0 Gain v in v K 0 a R Gain R K p a R 2 (a) (b) FIGURE 4.4 (a) Open loop amplifier. (b) Amplifier with feedback.
v in K a v 0 b FIGURE 4.5 Block diagram model of feedback amplifier assuming R p W R 0 of the amplifier.
R a I a i f constant field current E k 2 V a Speed v(t) J, b Load FIGURE 4.7 Open-loop speed control system (without feedback).
R(s) k 2 E s Amplifier K a V a (s) Motor G(s) Speed v(s) V t (s) Tachometer K t (a) Tachometer Motor (b) FIGURE 4.8 (a) Closed-loop speed control system. (b) Transistorized closed-loop speed control system.
.0 0.9 0.8 Closed-loop 0.7 v(t) K k 2 E 0.6 0.5 0.4 0.3 Open-loop (without feedback) 0.2 0. 0 0 2 3 4 5 6 7 8 9 0 2 3 4 5 Time (seconds) FIGURE 4.9 The response of the open-loop and closed-loop speed control system whent 5 0 and K K a K t 00. The time to reach 98% of the final value for the open-loop and closedloop system is 40 seconds and 0.4 second, respectively.
Rolls Steel bar Conveyor FIGURE 4.0 Steel rolling mill.
Disturbance T d (s) V a (s) R a I a (s) K m T m (s) T L (s) Js b v(s) Speed Motor back emf K b FIGURE 4. Open-loop speed control system (without external feedback).
T d (s) R(s) E a (s) Amplifier K a K m R a T m (s) T L (s) Js b v(s) K b V t (s) Tachometer K t FIGURE 4.3 Closed-loop speed tachometer control system.
T d (s) R(s) E a (s) G (s) G 2 (s) v(s) H(s) (a) T d (s) R(s) E a (s) G (s) G 2 (s) v(s) H(s) (b) FIGURE 4.4 Closed-loop system. (a) Block diagram model. (b) Signal-flow graph model.
R(s) G (s) G 2 (s) Y(s) H 2 (s) H (s) Sensor N(s) Noise FIGURE 4.6 Closed-loop control system with measurement noise.
R(s) Desired angle E(s) K s D(s) G(s) Boring machine s(s ) Y(s) Angle FIGURE 4.2 A block diagram model of a boring machine control system.
.4.2 y(t) (deg) 0.8 0.6 0.4 0.2 0 0 0.5.5 2 2.5 3 Time (sec) (a) 0.02 0.0 0.008 y(t) (deg) 0.006 0.004 0.002 0 0 0.5.5 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 /s for K 00.
.2 0.8 y(t) (deg) 0.6 0.4 0.2 0 0 0.5.5 2 2.5 3 Time (sec) 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, 997 and was deployed on its journey on July 5, 997. The 23-pound rover is controlled by an operator on Earth using controls on the rover [2, 22]. (Photo courtesy of NASA.)
R(s) Controller K(s )(s 3) s 2 4s 5 D(s) Rover (s )(s 3) Y(s) Vehicle position (a) R(s) r(t) t, t 0 K D(s) Rover (s )(s 3) Y(s) Vehicle position (b) FIGURE 4.25 Control system for rover; (a) open-loop (without feedback) and (b) closed-loop with feedback. The input is R(s) /s.
.0 Magnitude of sensitivity vs. frequency.05.00 Magnitude of sensitivity 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0 0 0 0 0 2 Frequency (rad/s) FIGURE 4.26 The magnitude of the sensitivity of the closed-loop system for the Mars rover vehicle.
R(s) Desired head position Error Disturbance D(s) Amplifier Coil Load V(s) K m K a R + L s s(js + b) Sensor Y (s) Actual position H(s) = FIGURE 4.32 Control system for disk drive head reader.
R(s) Disturbance D(s) Coil Load E(s) 5000 K a G (s) = G (s + 000) 2 (s) = s(s + 20) Y (s) FIGURE 4.33 Disk drive head control system with the typical parameters of Table 2..
(a) Ka=0; nf=[5000]; df=[ 000]; sysf=tf(nf,df); ng=[]; dg=[ 20 0]; sysg=tf(ng,dg); sysa=series(ka*sysf,sysg); sys=feedback(sysa,[]); t=[0:0.0:2]; step(sys,t); ylabel('y(t)'), xlabel('time (sec)'), grid Select K a. (b) y(t) y(t).0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. 0 0 0.2 0.4 0.6 0.8.0.2.4.6.8 2.0 Time (sec).2.0 0.8 0.6 K a = 0. 0.4 0.2 K a = 80. 0 0 0.2 0.4 0.6 0.8.0.2.4.6.8 2.0 Time (sec) FIGURE 4.34 Closed-loop response. (a) MATLAB script. (b) Step response for Ka 0 and Ka 80.
(a) Ka=80; nf=[5000]; df=[ 000]; sysf=tf(nf,df); ng=[]; dg=[ 20 0]; sysg=tf(ng,dg); sys=feedback(sysg,ka*sysf); sys= sys; t=[0:0.0:2]; step(sys,t); plot(t,y), grid ylabel('y(t)'), xlabel('time (sec)'), grid Select K a. Disturbance enters summer with a negative sign. 0 x 0-3 -0.5 (b) y(t) - -.5 K a = 80. -2-2.5-3 0 0.2 0.4 0.6 0.8.0.2.4.6.8 2.0 Time (sec) FIGURE 4.35 Disturbance step response. (a) MATLAB script. (b) Disturbance response for K a 80.
D(s) R(s) K (s ) 2 Y(s) (a).40.00 0.70 e(t) 0.50 0.08 0 K.0 K 0 0.70 0 2 3 4 5 Time (b) FIGURE 4.36 (a) A single-loop feedback control system. (b) The error response for a unit step disturbance when R(s) 0.