Modern Control Engineering

Section 8–4 / Design of PID Controllers with Computational Optimization Approach 589

3.0000 1.0000 1.1469 2.7700

5.0000 0.8000 1.1485 2.2100

4.0000 0.9000 1.1497 2.3800

% Plot the response curve with the smallest overshoot shown in

sortsolution table.

K = sortsolution(1,1), a = sortsolution(1,2)

K =

3.2000

a =

0.9000

num = [4K 8Ka 4K*a^2];

den = [1 6 8+4K 4+8Ka 4K*a^2];

num

num =

12.8000 23.0400 10.3680

den

den =

1.0000 6.0000 20.8000 27.0400 10.3680

y = step(num,den,t);

plot(t,y) % See Figure 8–24.

grid

title('Unit-Step Response')

xlabel('t sec')

ylabel('Output y(t)')

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

2468

t sec

Output

y(

t)

Unit-Step Response

Figure 8–24
Unit-step response
curve of the system
withK=3.2 and
a=0.9.