Design of robust output static controller to achieve fuzzy tracking for nonlinear systems described by Takagi-Sugno T-S model.

Abstract

Design of robust output static controller to achieve fuzzy tracking for nonlinear systems described by Takagi-Sugno T-S model

The topic of this thesis is related to the problem of designing a robust output static controller in order to achieve fuzzy tracking for systems with time delay and uncertainty that can be modeled by Takagi-Sugno (T-S) fuzzy modeling. The controller is in the form of parallel distributed compensation (PDC). The final controller should result in the stability of the closed loop system and achieve tracking according to the reference signal and in the presence of limited signals. A set of linear matrix inequalities (LMI) along with a linear matrix equation (LME) have been used to design the final static gains for each local controller. A basic and important step in this research field is modeling the nonlinear system using the Takagi-Sugno T-S fuzzy modeling technique. With the help of this modeling, the initial nonlinear system is approximated by combining a set of linear subsystems. Each linear subsystem is described by an IF-Then Rule statement. In the second step, which is the design of the desired controller, a specific controller is designed for each linear subsystem, considering all the linear subsystems. The final step will be the appropriate fuzzy combination of all the designed linear controllers to make the final controller. This controller design method is called Parallel Distributed Compensation.

Not only the stabilization of a non-linear system, but also the proper control of that system is considered. In this treatise, our focus will be on the issue of persecution. This problem has a 12-year background in fuzzy control theory and it started with the publication of the article published in source [1]. During the years after the publication of this article, other methods and applications have been added to this research field. Among other things, you can refer to other sources [9[-] 2[]. The noteworthy point in all these fuzzy controller designs is the use of modern control mode observer structure to base the controller structure. This structure has several features, it is simply stated, but the designs of the observer interest and the controller interest are very complex; Because these gains must be calculated from the information of all linear subsystems in the Takagi-Sugno model. Another point to consider in this structure is the same degree of the controller and the system under control.

In this thesis, our goal is to design the fuzzy static output controller to solve the tracking problem for non-linear systems. The static output controller consists of only one or more gains that produce a control signal proportional to the instantaneous value of the output and the instantaneous value of the base signal. Compared to the dynamic output controller, this controller is designed very simply and is very simply used in practice, and the controller is of the first order and is not the same level as the system under control. Our main reason for choosing this research is the advantages of static output controller. It should be noted that until the preparation of this treatise, no basic work has been done and no article has been published in this field.

As stated, the purpose of this treatise is to investigate the problem of designing the output static fuzzy controller to achieve a low error in tracking a base signal in the tracking problem. In this thesis, after going through the initial stages, our goal is to develop an innovative method for systems that have delayed components in the structure of their equations. Latency exists in many physical systems. The addition of delayed components to any dynamic system leads to the instability of the closed-loop system or its poor control performance. Our final goal in this research is to solve the fuzzy control problem in pursuit of delayed systems.Our final goal in this research is to solve the fuzzy control problem in pursuit of systems with delays. The next step in this thesis is to generalize this control problem to systems that have uncertainty. In fact, the main goal is to design a robust output static fuzzy controller. The main reason for choosing this goal is the need to design a resistant controller. In any control problem in which a nonlinear system is expressed by Takagi-Sugno modeling to a set of linear subsystems, many approximations are introduced. If these approximations are not taken into account in the design of the controller, the possibility of instability of the closed loop system arises. To avoid this defect, a robust controller should be designed. This work requires considering the uncertain components in the Takagi-Sugno fuzzy model of the nonlinear system. Now, considering these components, the final compensator should be designed.

The tools that we will use in the statement of the tracking problem and the tracking fuzzy control problem in the design of the controller are matrix linear inequalities. In the last 18 years, many articles have been published in various control fields, in which the problem statement and controller design were based on the theory of linear matrix inequalities. We will also use this theory in this research to reach the final design, [10]. rtl;">By

ABOLHASAN AKHONDI_SURKI

    This paper is concerned with the problem of robust static output feedback fuzzy tracking control design for nonlinear uncertain time-delay systems which can be modeled by Takagi and Sugeno (T-S) fuzzy modeling scheme. The controller is in a Parallel Distributed Compensation (PDC) form. The final controller should result in quadratic stability of the closed-loop system and guaranteeing the tracking control norm to some reference and bounded signals. A Linear Matrix Inequality (LMI) together with a Linear Matrix Equality (LME) is developed to design the final static gains for each local controller. The design is also a robust one. In an example, the approach is clearly investigated on a nonlinear uncertain time-delay system.