Modern Control Engineering

590 Chapter 8 / PID Controllers and Modified PID Controllers

8–5 Modifications of PID Control Schemes

Consider the basic PID control system shown in Figure 8–25(a), where the system is sub-

jected to disturbances and noises. Figure 8–25(b) is a modified block diagram of the same

system. In the basic PID control system such as the one shown in Figure 8–25(b), if the ref-

erence input is a step function, then, because of the presence of the derivative term in the

control action, the manipulated variable u(t)will involve an impulse function (delta func-

tion). In an actual PID controller, instead of the pure derivative term , we employ

where the value ofgis somewhere around 0.1. Therefore, when the reference input is a

step function, the manipulated variable u(t)will not involve an impulse function, but will

involve a sharp pulse function. Such a phenomenon is called set-point kick.

PI-D Control. To avoid the set-point kick phenomenon, we may wish to operate

the derivative action only in the feedback path so that differentiation occurs only on

the feedback signal and not on the reference signal. The control scheme arranged in this

way is called the PI-D control. Figure 8–26 shows a PI-D-controlled system.

From Figure 8–26, it can be seen that the manipulated signal U(s)is given by

U(s)=Kpa 1 +

1

Ti s

bR(s)-Kpa 1 +

1

Ti s

+Td sbB(s)

Td s

1 +gTd s

Td s

PID

controller

Plant

Gp(s)

1

Tis

1

Tds

Output

Y(s)

Noise

N(s)

Reference

inputR(s)

(a)

(b)

Disturbance

D(s)

Gp(s)

Y(s)

N(s)

R(s) E(s)

B(s)

Observed signal B(s)

U(s)

D(s)

Kp

+

• 
  

+

+

++

+

+

+

+

+

+ ++

• 
  

Figure 8–25

(a) PID-controlled

system;

(b) equivalent block

diagram.

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