Modern Control Engineering

638 Chapter 8 / PID Controllers and Modified PID Controllers

Since

we obtain

The controller thus becomes

(8–17)

Then, the closed-loop transfer function Y(s)/D(s)is obtained as follows:

The response curve whenD(s)is a unit-step disturbance is shown in Figure 8–67.

=

100 s

s^3 +12.403s^2 +74.028s+120.148

=

100

s(s+ 1 )

1 +

0.11403(s+3.2460)^2

s

100

s(s+ 1 )

Y(s)

D(s)

=

Gp(s)

1 +Gc 1 (s)Gp(s)

=0.74028+

1.20148

s

+0.11403s

=

0.11403s^2 +0.74028s+1.20148

s

Gc 1 (s)=

0.11403(s+3.2460)^2

s

Gc1(s)

=0.11403

K =^2

s^2 (s+1)

100(s+3.2460)^2

2

s=- 5 +j5

Gc1(s)Gp(s)=

K(s+3.2460)^2

s

100

s(s+1)

yd

(t)

t (sec)

Response to Unit-Step Disturbance Input

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.4

0.2

0

0 0.5 1 1.5 2 2.5 3 3.5 4

Figure 8–67

Response to unit-

step disturbance

input.

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