Building on the takagisugeno fuzzy model, authors tanaka and wang address a number of important issues in fuzzy control systems, including stability analysis, systematic. The design of the flcs is based on heuristic fuzzy rules. This paper studies the stability analysis of multivariable fuzzy control systems. Pdf stability and robustness analysis and gain design. Stability analysis and design of a class of mimo fuzzy. This study employs a novel fuzzy copositive lyapunov function to investigate the stability of discretetime polynomialfuzzymodelbased control systems under positivity constraint.
We derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks. One approach is to design a robust control system which can accommodate component failures, random changes in the system structure 1. First, we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams. The absolute stability analysis in fuzzy control systems with parametric uncertainties and reference inputs bingfei wua, member, lishan ma. Stability analysis of fuzzymodelbased control systems. Stability analysis method for fuzzy control systems dedicated. An introduction to nonlinear analysis of fuzzy control. As pdlf approach includes information of the membership function time derivatives of membership functions, it has been reported that relaxed stability conditions can be achieved compared to the parameterindependent lyapunov. We provide examples to illustrate how to design stable fuzzy control systems and.
Today, there exist preoccupations reported in the literature 6, 7 on the stability analysis and design of ts fuzzy control systems. Stability analysis and control design for 2d fuzzy. In the proposed, model impulse is viewed as control input of ts model, and impulsive distance is the major controller to be designed. The problem of stability in closedloop control systems has received a considerable degree of academic interest and there are a number of wellestablished theories to determine the stability limits of conventional controllers. The application of fuzzy control systems is supported by numerous hardware and. The design procedure is conceptually simple and natural.
The fuzzy copositive lyapunov function consists of a number of local sublyapunov function candidates which includes the positivity property of a nonlinear system and the contribution of. Comparison of adaptive fuzzy systems with artificial neural networks 8. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model. This balanced treatment features an overview of fuzzy control, modeling, and stability analysis, as well as a section on the use of linear matrix inequalities. Abstract this paper focuses on the problem of constraint control for a. The absolute stability analysis in fuzzy control systems. Building on the takagisugeno fuzzy model, authors tanaka and wangaddress a number of important issues in fuzzy control systems,including stability analysis. The results presented in the paper make possible the application of both inputoutput and frequency response methods to ts systems identified from inputoutput data. Presented are a method of stability analysis and design of fuzzy control systems, which consist of a family of local tstakagisugeno fuzzy models with aggregation. A structural system with a tuned mass damper is modeled using a ts type fuzzy model. The interconnected fuzzy systems consist of interconnected fuzzy subsystems, and the stability analysis is based on lyapunov functions. Section 3 gives a stability theorem for nonlinear systems with ts flcs and an algorithm for the design of a stable fuzzy control system.
However, analysis of fuzzy systems using the conventional analysis methods is. This paper presents the stability analysis and performance design for nonlinear systems. A survey on analysis and design of modelbased fuzzy. The fuzzy lyapunov method is investigated for use with a class of interconnected fuzzy systems. Stability analysis and design of fuzzy control systems.
Stability analysis and design of fuzzy control systems sciencedirect. This volume develops a variety of adaptive fuzzy systems and applies them to a variety of engineering problems. The stability analysis of a class of mimo fuzzy control systems was carried out using mostly used linear matrix inequality lmi approach 76, and in 77 another method using lasalles global. First, we show the concept of fuzzy blocks and consider the connection problems. In addition, the paper includes an illustrative example that describes one application of this algorithm in the design of a stable fuzzy logic control system.
The takagisugeno ts fuzzy system is a breakthrough in the stability analysis and controller design of fuzzy control systems. Stability analysis and design of timevarying nonlinear. Stability analysis and systematic control design are certainly among the most important issues for fuzzy control systems. Fuzzy control systems design and analysis wiley online books. Stability analysis and control design are performed to both systems using. In chapter 1 we provide an overview of the general methodology for conventional control system design. This paper develops a general analysis and design theory for nonlinear timevarying systems represented by impulsive ts fuzzy control model, which extends conventional ts fuzzy model. Particularly, the stability of takagisugeno ts systems is addressed. This paper presents a design method for a class of fuzzy control systems. Stability analysis and design of a class of fuzzy control. Fuzzy logic control was originally introduced and developed as a model free control design approach. That is the reason why recently, there have been significant research efforts in this direction.
Therefore the complexity of the stability analysis is reduced and the adding of new fuzzy rules can be conducted easily. Stable indirect adaptive fuzzy control of nonlinear systems 9. An introduction to nonlinear analysis of fuzzy control systems. Robust stability conditions for this class of systems are derived by applying the relaxed stability conditions described in chapter 3. Stable direct adaptive fuzzy control of nonlinear systems 10. Pdf stability analysis and control design of fuzzy. Hence, the fuzzy controller under such design criterion is not suitable for handling nonlinear system subject to parameter uncertain ties. Moreover, it is shown in this chapter that the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems. A constructive algorithm is developed to obtain the stabilizing feedback control law for the system. The stability analysis of the fcss is carried out using lasalles g lobal invariant set theorem by the separate stability analysis of each fuzzy rule in mimo fuzzy control systems. Griffin, mf ieee transactions on fuzzy systems 898 fuzzy regulators and fuzzy observers. Bishop published 1993 computer science matlab basics mathematical modelling of systems control system characteristics control system performance.
Stability analysis and control design of fuzzy systems. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. These include stability analysis, systematic design procedures, incorporation of performance specifications. Stability analysis of multivariable fuzzy control systems. If the system has a considerable time delay, the analysis and the design of the controller are.
The 2d fuzzy system model is established based on the fornasinimarchesini local statespace model, and a control design procedure is proposed based on a relaxed approach in which basisdependent lyapunov. Sugeno, m fuzzy sets and systems 902 an approach to fuzzy control of nonlinear systems. New approaches to fuzzy modeling and control series in. Therefore, maintaining the system stability in the face of uncertainties is a primary concern for the design engineer. Stability analysis of fuzzy control systems springerlink. The main contribution of this paper is the development of an. In this study two different fuzzy systems are studied. Robust fuzzy control fuzzy control systems design and. This chapter also gives a design method that selects the robust fuzzy controller so as to maximize the norm of the uncertain blocks out of the class of stabilizing pdc controllers. Pdf stability analysis and design of fuzzy control. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. Design and stability analysis 9780996312 by wang, lixin and a great selection of similar new, used and collectible books available now at great prices.
Based on traditional lyapunov stability theory, we further propose a fuzzy lyapunov method for the stability analysis of interconnected fuzzy. However, with fuzzy controllers the situation is different. In particular, the methods described allow rigorous analysis of the stability and robustness of the systems, which are crucial issues in control theory. The paper studies the stability analysis and the systematic control design of fuzzy systems which have been successfully applied to many practical industrial applications in the recent years. The paper presents a design method of fuzzy controllers fcs derived from a stability analysis method aracil, et al. Stability qconstraint on the control input qconstraint on the output r 81 references r 81 4 fuzzy observer design 83 4. The majority of these papers is based on linear matrix inequality. Stability and sensitivity analysis of fuzzy control systems. Several criteria on general stability, asymptotic stability. A comprehensive treatment of modelbased fuzzy controlsystems this volume offers full coverage of the systematic framework forthe stability and design of nonlinear fuzzy control systems.
The work of mamdani and his colleagues on fuzzy control 12was motivated by zadehs work on the theory of fuzzy sets, 34 and its application to linguistics and systems analysis. Fuzzy control has emerged as one of the most active and promising control areas, especially because it can control highly nonlinear, timevariant, and illdefined systems. Fuzzy systems may perform different tasks within an automatic control system leading to different structural schemes. The stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed. The controller is designed by state feedback for each local model. An important design approach is the development of fault tolerant control systems. Finally, it is shown that this controller guarantees global stability of the closedloop fuzzy system.
The proposed stability analysis is applied to the fmb control systems of which the ts fuzzy model and fuzzy controller do not share the same premise membership functions and, thus, is able to. Stability and sensitivity analysis of fuzzy control. Stability analysis and design for a class of continuous. We begin by overviewing several approaches to stability analysis includ ing lyapunovs direct and indirect methods, and the circle criterion. Pdf stability analysis method for fuzzy control systems dedicated. Pdf fuzzy logic control system stability analysis based on. The result of a nonlinear system control by simulation. Stability analysis and design of ts fuzzy control system. The first theme of the book is a new approach to the systematic design and analysis of fuzzy controllers, given linguistic information concerning the plant and the control objective. Design of adaptive fuzzy controllers using inputoutput linearization concept 11. Fuzzy control systems design and analysis addresses these issues in the framework of parallel distributed compensation, a controller structure devised in accordance with the fuzzy model. Then we summarize the fuzzy control system design process and contrast the two. Nowadays, fuzzy control systems are successfully applied in many technical and nontechnical fields. The book also provides rigorous analysis of nonlinear fuzzy control systems, and outlines a simple method to guarantee the stability of nonlinear control systems.
Stability analysis of interconnected fuzzy systems using. Stability analysis method for fuzzy control systems. The ts fuzzy model is employed to represent the nonlinear plant to facilitate the stability analysis. Lixin wang this volume develops a variety of adaptive fuzzy systems and applies them to a variety of engineering problems. Mechatronics applications 62 involving the use of popovs hyperstability theory. We provide examples to illustrate how to design stable fuzzy control systems and test for stability, includ ing an application of lyapunovs direct method to. It summarizes the stateoftheart methods for automatic tuning of the parameters and. The stability analysis of these fuzzy control systems is performed using lasalles invariant set principle. A fuzzy controller, under imperfect premise matching such that the ts fuzzy model and the fuzzy controller do not share the same membership functions, is. It summarizes the stateoftheart methods for automatic tuning of the parameters and structures of fuzzy logic systems, and shows both the details of how to apply them to a variety of control and signal processing problems, and how to analyze the. Pdf an improved stability analysis method is presented for fuzzy logic control systems which is not restricted to plants requiring a linear control.
Stability analysis and performance design for fuzzymodel. We first study the design method of digital fuzzy controllerdfc considering time delay. Secondly, the paper performs the sensitivity analysis of fcss with respect to the parametric variations of the. The stability of a fuzzy feedback control system consisting of a fuzzy controller connected in series with a plant described by a fuzzy model is discussed. Fuzzy control, aerospace control, stability analysis. A comprehensive treatment of modelbased fuzzy control systems this volume offers full coverage of the systematic framework for the stability and design of nonlinear fuzzy control systems. Stability analysis of ts fuzzy control systems using. Pdf stability analysis of fuzzy logic control systems researchgate. Using the parallel distributed compensation pdc scheme, we design a nonlinear fuzzy controller for the tuned mass. Stability analysis of fuzzy control systems subject to. Design and stability analysis of fuzzy identifiers of nonlinear. It shows, step by step, how to combine linguistics and numerical information using various kinds of adaptive fuzzy systems.
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