Modern Control Engineering

592 Chapter 8 / PID Controllers and Modified PID Controllers

1

Tis Gp(s)

Y(s)

N(s)

R(s)

B(s)

B(s)

U(s)

D(s)

Kp

1 Tds

+

• 
  

+– +

+

++

Figure 8–27

I-PD-controlled

system.

The closed-loop transfer function Y(s)/R(s)in the absence of the disturbance input

and noise input is given by

It is noted that in the absence of the reference input and noise signals, the closed-loop

transfer function between the disturbance input and the output is given by

This expression is the same as that for PID control or PI-D control.

Two-Degrees-of-Freedom PID Control. We have shown that PI-D control is ob-

tained by moving the derivative control action to the feedback path, and I-PD control

is obtained by moving the proportional control and derivative control actions to the

feedback path. Instead of moving the entire derivative control action or proportional

control action to the feedback path, it is possible to move only portions of these control

actions to the feedback path, retaining the remaining portions in the feedforward path.

In the literature, PI-PD control has been proposed. The characteristics of this control

scheme lie between PID control and I-PD control. Similarly, PID-PD control can be

considered. In these control schemes, we have a controller in the feedforward path and

another controller in the feedback path. Such control schemes lead us to a more gener-

al two-degrees-of-freedom control scheme. We shall discuss details of such a two-degrees-

of-freedom control scheme in subsequent sections of this chapter.

8–6 Two-Degrees-of-Freedom Control

Consider the system shown in Figure 8–28, where the system is subjected to the

disturbance inputD(s)and noise inputN(s),in addition to the reference inputR(s).

is the transfer function of the controller and is the transfer function of the

plant. We assume that Gp(s)is fixed and unalterable.

Gc(s) Gp(s)

Y(s)

D(s)

=

Gp(s)

1 +Kp Gp(s)a 1 +

1

Ti s

+Td sb

Y(s)

R(s)

= a

1

Ti s

b

Kp Gp(s)

1 +Kp Gp(s)a 1 +

1

Ti s

+Td sb

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