Modern Control Engineering

overshoot in the unit-step response is approximately 25%and the settling time is approximately

1.2 sec. The steady-state errors in the ramp response and acceleration response are zero. There-

fore, the designed controller given by Equation (8–18) is satisfactory.

Finally, we determine Noting that

Gc2(s)=Gc(s)-Gc1(s)

Gc2(s).

Gc(s)

640 Chapter 8 / PID Controllers and Modified PID Controllers

(b)

t (sec)

Response to Unit-Ramp Reference Input

1.5

2

2.5

3

1

0.5

0

0 0.5 1 1.5 2 2.5 3

Input

Output

y(r

t)

(c)

y(r

t)

t (sec)

Response to Unit-Acceleration Reference Input

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.4

0.2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Input

Output

Figure 8–68

(continued)

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