Design of robust LAG/LEAD controllers

ABSTRACT M. S. Thesis DESIGN OF ROBUST LAG/LEAD CONTROLLERS Münevver Mine ÖZYETKİN İnönü University Graduate School of Natural and Applied Sciences Department of Electrical and Electronics Engineering 135+x pages 2006 Supervisor: Assoc. Prof. Dr. Nusret TAN Classical controllers such as lag/lead and PID are still used extensively in control system design. There are many reasons for this which include: 1) They are often successful to meet the design specifications. 2) They are well understood by practising engineers since the structure of these controllers are simple. 3) Having only two or three adjustable parameters they can often be tuned quite easly. Although PID controllers are used extensively, a phase lead or lag controller can be used to control plants which contains integral action and thus often have better low pass filtering than plants controlled by PID controller such as servomechanism, where integration exists in the plant transfer function. One of the central problems in control theory relates to the design of controllers for stabilization of systems. The aim of this thesis is to investigate the methods related to the design of lag/lead controllers and obtain robust design tecniques for this controller structure. Design of robust lag/lead controller is especially important for real applications which have parameter uncertainity. Because, parameter uncertainity in the systems is unavoidable fact. Therefore, obtaining a desired control besides uncertainity in systems is important. In the thesis, a method is developed for computation of the stabilizing parameters of a lag/lead controller. Similiar to a PID controller, a lag/lead controller has three parameters which need to be tuned. Computation of the parameters of lag/lead controller in classical control theory can be done using root locus method and frequency response method. However, both of these methods are in the categories of the trial and error approach to control system design. Therefore, it is not possible to find all the stabilizing values of the parameters using these methods. The method presented is based on the stability boundary locus which can be easily obtained. Thus, a very fast way of calculating the stabilizing lag/lead controller for a given control system is presented. The method has also been applied to the control system with uncertain parameters. Thus, robust lag/lead controllers are designed using Kharitonov theorem. Related simulation studies have been done and required programs have been prepared in the MATLAB enviroment. The results developed in this research work, have potential features to be used for practical applications and for future work within this direction. KEYWORDS: Stability, controller, compansator, lag/lead kontroller, PID controller, stability region, parameter uncertainity, Kharitonov theorem, performance 11