Modern Control Engineering

636 Chapter 8 / PID Controllers and Modified PID Controllers

From the sorttable, it seems that

K=29, a=0.25(max overshoot=9.52%, settling time=1.78sec)

and

K=27, a=0.2(max overshoot=5.5%, settling time=2.89sec)

are two of the best choices. The unit-step response curves for these two cases are shown in Figure 8–65.

From these curves, we might conclude that the best choice depends on the system objective. If a small

maximum overshoot is desired,K=27, a=0.2will be the best choice. If the shorter settling time is

more important than a small maximum overshoot, then K=29, a=0.25will be the best choice.

A–8–13. Consider the two-degrees-of-freedom control system shown in Figure 8–66. The plant is

given by

Assuming that the noise input N(s)is zero, design controllers and such that the

designed system satisfies the following:

1.The response to the step disturbance input has a small amplitude and settles to zero quickly

(on the order of 1 sec to 2 sec).

Gc1(s) Gc2(s)

Gp(s)=

100

s(s+1)

Gp(s)

num = [K 2Ka K*a^2];

den = [1 6 5+K 2Ka K*a^2];

y = step(num,den,t);

plot(t,y)

title('Unit-Step Response Curves')

xlabel('t (sec)')

ylabel('Output')

text(1.22,1.22,'K = 29, a = 0.25')

text(1.22,0.72,'K = 27, a = 0.2')

Output

t (sec)

Unit-Step Response Curves

1.4

1.2

1

0.8

0.6

0.4

0.2

0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

K= 29, a = 0.25

K= 27, a = 0.2

Figure 8–65

Unit-step response

curves.

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