Modern Control Engineering

Section 8–5 / Modifications of PID Control Schemes 591

Notice that in the absence of the disturbances and noises, the closed-loop transfer

function of the basic PID control system [shown in Figure 8–25(b)] and the PI-D control

system (shown in Figure 8–26) are given, respectively, by

and

It is important to point out that in the absence of the reference input and noises, the

closed-loop transfer function between the disturbance D(s)and the output Y(s)in

either case is the same and is given by

I-PD Control. Consider the case where the reference input is a step function. Both

PID control and PI-D control involve a step function in the manipulated signal. Such a

step change in the manipulated signal may not be desirable in many occasions. There-

fore, it may be advantageous to move the proportional action and derivative action to

the feedback path so that these actions affect the feedback signal only. Figure 8–27 shows

such a control scheme. It is called the I-PD control. The manipulated signal is given by

Notice that the reference input R(s)appears only in the integral control part. Thus, in

I-PD control, it is imperative to have the integral control action for proper operation of

the control system.

U(s)=Kp

1

Ti s

R(s)-Kpa 1 +

1

Ti s

+Td sbB(s)

Y(s)

D(s)

=

Gp(s)

1 +Kp Gp(s)a 1 +

1

Ti s

+Td sb

Y(s)

R(s)

= a 1 +

1

Ti s

b

Kp Gp(s)

1 + a 1 +

1

Ti s

+Td sbKp Gp(s)

Y(s)

R(s)

= a 1 +

1

Ti s

+Td sb

Kp Gp(s)

1 + a 1 +

1

Ti s

+Td sbKp Gp(s)

1

Tis

1

Gp(s)

Y(s)

N(s)

R(s) E(s)

B(s)

U(s)

D(s)

Kp

Tds

B(s)

+

• 
  

+

• 
  

+

+

+

++

Figure 8–26
PI-D-controlled
system.