Proportional-integral-derivative (PID) controllers have been still widely used more than 90% in industrial process controllers despite a wealthy of modern control approaches. First-order controller is also very frequently accepted for compensating its gain and phase margins. These two types of controllers are sometimes referred to the three-parameter controller. Design approaches of the three-parameter controllers can be classified into the model based and model free designs. In particular, the latter is one of the most advantages of the three-parameter controllers because the mathematical model of the process is not required when such a controller is designed.
Many improved tuning rules for PID controller have been developed since the Ziegler and Nichols rule was presented in 1942. A relay feedback tuning method by Astrom is the most popular one among them. However, there are few tuning methods that can be used for the time-response design specifications such as overshoot and settling time. Moreover, the tuning rules for the first-order controller have been hardly reported in the literature.
Main concern in this thesis is to propose a new closed-loop tuning rule of three-parameters controllers so that the resulting closed-loop system satisfies the desired time-response. The key idea is to find the parameters of a three-parameter controller such that the k-th moment of the resulting closed-loop system matches that of the reference model from the zero moment to the third moment by each. The reference model of proper order that meets the desired transient response can be previously composed by using different methods. In this thesis, we use the method synthesizing a transfer function model based on the K-polynomial. Two kinds of controller structures and two types of controllers are considered. Theses are (1) PI/PID and first-order controllers in cascade structure, and (2) PI/PID and first-order controllers in two parameter configuration. We have derived two theoretical results. One is that moments of unknown process can be determined by using a rectangular pulse response of the closed-loop system associated with an arbitrary proportional controller. The other is that each controller of four cases above can be algebraically calculated in terms of both moments of process and reference model. In other words, all these controller result in the same moments as those of the given reference model. This means that the step response of the closed-loop system shall coincide with the reference model according to the Zadeh and Desoer’s theorem. Based on these results, we propose a closed-loop tuning algorithm which consists of 4 steps. It is remarkable that this algorithm requires only a rectangular pulse test for the preliminary closed-loop system with a stable proportional controller. Remaining problem is that the controller obtained by the proposed moment matching method does not guarantee the closed-loop stability. This is caused by the fact that a finite set of moments is not sufficient to represent a whole model of process. To check the stability, after an approximate model of the process is first obtained by using the previous pulse response data, the Nyquist stability criterion is applied. Finally, the effects of zeros of a cascade controller on the time response have been investigated. Then we suggest some measures to overcome the bad effects. It is shown through various examples that the proposed tuning rule is very useful and easy to implement.