PID Control System Design and Automatic Tuning using MATLAB/Simulink. Liuping Wang

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Table 1.5 Padula and Visioli tuning rules (PID controller).

      They were derived using optimization methods for minimizing an error function together with the sensitivity peak in the frequency domain (see Chapter 2).

Here, we only include two sets of the tuning rules introduced for disturbance rejection in their paper. Tables 1.4 and 1.5 present the tuning rules for PI and PID controllers, respectively. Each table contains two sets of rules. For the specification of ( corresponds to the sensitivity peak (see Chapter 2)), the set of tuning rules is expected to produce a slower closed-loop response in comparison to that with . It is worthwhile mentioning from Tables (1.4) and (1.5) that both PI and PID controller parameters are invalid for the time delay because as , the proportional control gain .

A frequency response analysis for the Padula and Visioli tuning rules based control system will be presented in Chapter 2 where an example (see Example 2.4) will be given to show the sensitivity functions and their Nyquist diagrams.

      1.4.3 Wang and Cluett Tuning Rules

In Wang and Cluett (2000), a first order plus delay model was used to derive several tuning rules for PID controllers. The rules were calculated using a frequency response analysis based on the ratio of the time constant to the time delay , which is defined as . A desired closed-loop time constant is chosen as a scale of the time delay . Among them, which works quite well in applications, is a particular choice with the desired closed-loop time constant being equal to the time delay . For this choice, the PID controller parameters are presented in Table 1.6.

Table 1.6 Wang–Cluett tuning rules with reaction curve (

).

P
PI
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