Modern Control Engineering

Problems 643

Obtain the response of the I-PD-controlled system to
the unit-step reference input with MATLAB. Compare the
unit-step response curves of the two systems.

B–8–5.Referring to Problem B–8–4, obtain the response
of the PID-controlled system shown in Figure 8–73(a) to the
unit-step disturbance input.
Show that for the disturbance input, the responses of
the PID-controlled system shown in Figure 8–73(a) and of
the I-PD-controlled system shown in Figure 8–73(b) are

exactly the same. [When consideringD(s)to be the input, as-

sume that the reference input R(s)is zero, and vice versa.]

Also, compare the closed-loop transfer functionC(s)/R(s)

of both systems.

B–8–6.Consider the system shown in Figure 8–74. This sys-

tem is subjected to three input signals: the reference input,

disturbance input, and noise input. Show that the charac-

teristic equation of this system is the same regardless of

which input signal is chosen as input.

(a)

(b)

R(s) C(s)

D(s)

PID contoller

39.42 (1 +^1

3.077s

+ 0.7692s)^1

s(s+ 1) (s+ 5)

D(s)

R(s) C(s)

1 + 0.7692s

3.077^1 s 39.42 s(s+ 1) (^1 s+ 5)

+

+

+

+– +– +

+

Figure 8–73

(a) PID-controlled system; (b) I-PD-controlled system.

G 2 (s)

H(s)

C(s)

Noise

N(s)

R(s)

Disturbance

D(s)

G 1 (s) +

+

+

+

+–

Figure 8–74

Control system.