Modern Control Engineering

MATLAB Program 8–13 produces the unit-ramp response curve of the designed system. The

resulting response curve is shown in Figure 8–56.

626 Chapter 8 / PID Controllers and Modified PID Controllers

MATLAB Program 8–13

% Unit-Ramp Response

num = [0 0 6.104 40.6104 4];

den = [1 6.104 41.6104 4 0];

t = 0:0.01:20;

c = step(num,den,t);

plot(t,c,'-.',t,t,'-')

title('Unit-Ramp Response')

xlabel('t(sec)')

ylabel('Input Ramp Function and Output')

text(3,11.5,'Input Ramp Function')

text(13.8,11.2,'Output')

Figure 8–56

Unit-ramp response

ofC(s)/R(s)=

(6.104s^2 +40.6104s+

4)/(s^3 +6.104s^2 +

41.6104s+4).

Input Ramp Function Output

t (sec)

0 2 4 6 8 10 12 14 16 18 20

Input Ramp Function and Output

20

8

0

12

18

4

2

16

10

14

6

Unit-Ramp Response

Nyquist Plot. Earlier we found that the three closed-loop poles of the designed system are

all in the left-half splane. Hence the designed system is stable. The purpose of plotting Nyquist

diagram here is not to test the stability of the system, but to enhance our understanding of Nyquist

stability analysis. For a complicated system, Nyquist plot will look complicated enough that it is

not easy to count the number of encirclements of the − 1 +j0point.

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