Auto-ajustement de régulateurs PID robustes dans le domaine fréquentiel

Abstract

This work considers the adjustment of proportional-integral-derivative (PID) controllers. Because of their very simple structures, this kind of controllers are very appreciated, and used abundantly by the industrial community. The restricted number of the controller parameters often implies moderate performances, compared to those that can be obtained by high order control structures. In compensation, it is highly desired to use simple and fast procedures for the tuning of PID controllers. In practice, the methods using minimal a priori information about the plant are largely preferred. This thesis falls in this context. The adjustment is considered in the frequency domain, because as well as stability and robustness, the time domain performances of the closed-loop system can be represented. The traditional robustness indicators, which consist of the phase and gain margins, the crossover frequency, as well as more advanced parameters, which are the infinity-norm of the sensitivity and complementary sensitivity functions, can be taken into account by the presented approaches. In the first chapters, the synthesis is realized in a model-free framework. First of all, the simplicity of the modified Ziegler-Nichols method is exploited. By measuring only one point of the system frequency response, the approach mentioned above proposes to adjust the PID controller parameters in order to obtain a desired value for the phase margin. In this work, it is also desired to calibrate the slope of the loop frequency response at the crossover frequency in order to satisfy constraints on the infinity-norm of the sensitivity functions. This calibration can be done by using approximations arising from Bode's integrals, without requiring any other information about the plant. This approach often improves the results compared to the original modified Ziegler-Nichols method, without loosing its extreme ease of implementation. Next, an iterative model-free tuning approach, is studied. Robustness margins are measured directly on the plant using limit cycles generated by non-linear closed loop experiments. A frequency criterion is then defined as the weighted sum of the squared errors between the desired and the measured values of the considered margins. The criterion minimization is carried out iteratively using a gradient algorithm, without requiring any other information about the plant than that measured previously. Finally, a model-based approach is presented. The existing methods are usually based on simple first or second order plant model. Many uncertainties rise often from such approaches, due in particular to unmodeled dynamics. In this work, the model uncertainties are directly taken into account in order to guarantee robust performance and stability for the closed-loop system. Finally, a direct application of this methodology is formulated for the decentralized control of multivariable systems. In each chapter a real-time application is presented to illustrate the methods and to show their effectiveness and simplicity.