Читать книгу PID Control System Design and Automatic Tuning using MATLAB/Simulink - Liuping Wang - Страница 33

Several sets of tuning rules were introduced in Padula and Visioli (2011) and Padula and Visioli (2012). These tuning rules are based on the first order plus delay model:

Table 1.4 Padula and Visioli tuning rules (PI controller).

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.