Rule-of-Thumb Methods

Rule-of-thumb or heuristic methods were developed for cases in which modelling gives poor results or simply no model is available. They are used when the way the system works is not precisely known. We treat the system as a black box and control it without knowing its internal structure and behaviour. The heuristic methods are summarised in a very good Wikipedia article.

The inflection tangent method, which you got to know in the chapter Non-oscillating systems, falls into the category of rule-of-thumb methods. In this tutorial I only go into the Ziegler–Nichols method in more detail. There are others that are also quite good.

Ziegler–Nichols method

You can only use the Ziegler–Nichols method if your system is capable of oscillation (i.e. has at least two storage elements). It is important that the system cannot be damaged by overshoot. If these conditions are not met, use another method. With Ziegler–Nichols you proceed in the following steps:

1. Control the system with a P controller

2. Increase K_PR until a stable sustained oscillation sets in. The minimum value of K_PR required for this is called K_PR,Krit (critical gain).

3. Measure the period of the sustained oscillation. It is called T_Krit (critical period).

4. Use these two parameters to design the controller parameters according to the following table:

The table gives numerical values of the controller parameters for pure P controllers, PI controllers and PID controllers. A PI controller is a PID controller with K_DR = 0.

If you need the parameters for the alternative representation of the controllers, use the following table: