**2. Tuning methods for pid controller**

The primary function of a close-loop system is to make the controlled variable a desired value established by the set-point. Whenever the controlled variable becomes different then the set-point, the objective of the closed-loop system is to make then the same as quickly as possible. The controlled variable becomes different than the set-point under tree conditions:


One of the traditional ways to design a PID controller was to use empirical tuning rules based on measurements made on the real plant. Today is preferable for the PID designer to employ model based techniques. There is a large number of tuning methods, but in this chapter we describes for calculating proper values of the PID parameters (kc, ti, td) two methods: Relay Methods and Process Reaction Curve.

Relay Methods and Process Reaction Curves: Practical Applications 251

The one can obtain the PID settings via Ziegler-Nichols tuning for different values of ߬ and

1 1

The use of polymers has been growing gradually in many industrial products, such as: automobile, electronic devices, food packaging, and building and medicine materials. Among these products stands the polystyrene, usually produced in batch or semi-batch reactors.

<sup>1</sup> ( )1 <sup>2</sup> *<sup>u</sup> u p*

*T*

 *K K* 

> 2 *u*

Ku and Tu parameters are obtained from the experiment using the relay method.

*T*

 2

2 arctan

*T* 

*u*

  P

; ߬ଵ ൌ ߬ (3.4)

; (3.5)

t, time

Fig. 3.1. Plant with the PID regulator temporarily disabled

Fig. 3.2. Plant oscillating under relay feedback

output

input, u

ߛ. These parameters can be calculated using:

**3.1 Case study** 
