Modern Control Engineering

586 Chapter 8 / PID Controllers and Modified PID Controllers

Amplitude

Time (sec)

Step Response

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

Figure 8–20

Unit-step response of

the system with

K=2.4anda=0.9.

(The maximum

overshoot is 9.23%.)

To plot the unit-step response curve of the last set of the Kandavalues in the sorted table,

we enter the commands

K = sortsolution (k,1)

a = sortsolution (k,2)

and use the stepcommand. (The resulting unit-step response curve is shown in Figure 8–20.) To

plot the unit-step response curve with the smallest overshoot that is greater than 0%found in the

sorted table, enter the commands

K = sortsolution (11,1)

a = sortsolution (11,2)

and use the stepcommand. (The resulting unit-step response curve is shown in Figure 8–21.)

Amplitude

Time (sec)

Step Response

1.2

1.4

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

Figure 8–21

Unit-step response of

the system with

K=2.8anda=0.7.

(The maximum

overshoot is 0.24%.)

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