Chapter 9. PID Tuning
Although the functional form of a PID controller is fixed, the gain parameters kp, ki, and kd are initially undetermined. To obtain a concrete implementation, we must select values for these parameters. At the same time, we are free to choose values that will lead to the most desirable behavior, given the situation and our objectives.
Finding appropriate values for the controller gains (“tuning” the controller) can be a frustrating exercise: with two (for a PI controller) or even three (for a PID controller) parameters, the number of possible combinations to try out is very large. Moreover, it is often difficult to predict intuitively what effect an increase or decrease of any one of the parameters will have on the performance of the entire feedback loop. Some sort of guidance is therefore highly desirable.
If a good analytical model of the process is available, then root locus techniques (Chapter 24) can be extremely helpful. But if no analytical expression for the transfer function is known, then we must resort to measuring the dynamic response of the system and base our tuning strategy on the experimental results. The Ziegler–Nichols rules are a classic set of heuristics that require only a little information about the process. We can go a step further and first “fit” a phenomenological transfer function model to the experimental data (Chapter 8). That model is then used to derive suitable values for the controller gains analytically. Methods taking this ...