Modern Control Engineering

608 Chapter 8 / PID Controllers and Modified PID Controllers

The response to the unit-ramp reference input and that to the unit-acceleration reference input

are shown in Figures 8–38(a) and (b), respectively. The steady-state errors in following the ramp

input and acceleration input are zero. Thus, all the requirements of the problem are satisfied.

Hence, the designed controllers and are acceptable.

EXAMPLE 8–5 Consider the control system shown in Figure 8–39. This is a two-degrees-of-freedom system. In the

design problem considered here, we assume that the noise input N(s)is zero. Assume that the

plant transfer function is given by

Gp(s)=

5

(s+1)(s+5)

Gp(s)

Gc1(s) Gc2(s)

Unit-Ramp Response

t (sec)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Unit-Ramp Input and Output

2

0

0.4

0.2

0.6

0.8

1

1.2

1.4

1.6

1.8

(a)

Output

Unit-Ramp Input

Figure 8–38

(a) Response to unit-

ramp reference

input; (b) response to

unit-acceleration

reference input.

Unit-Acceleration Response

t (sec)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Unit-Acceleration Input and Output

2.5

0

0.5

1

1.5

2

(b)

Unit-Acceleration Input

Output

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