Representing the nonlinear plant using a takagisugeno ts fuzzy model, a fuzzy controller is employed to close the feedback loop. Fuzzy control of industrial systems download book pdf fuzzy control of industrial systems pp 1118 cite as. The membershipfunctiondependent analysis offers a new research. Stability analysis and design for a class of continuoustime. 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.
Conclusions glossary bibliography biographical sketches summary this chapter presents a perspective of fuzzy control systems. Xvii analysis and stability of fuzzy systems ralf mikut and georg bretthauer encyclopedia of life support systems eolss an online analysis can be done by means of a further fuzzy system for supervision. Stability analysis of fuzzy control systems sciencedirect. Loparo department of systems, control and industrial engineering case western reserve university january, 1994 i. An example is given to illustrate the application of the method.
Stability analysis and design of a class of mimo fuzzy. The stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed. 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. However, with fuzzy controllers the situation is different. Membershipfunctiondependent stability analysis and control. Stability analysis and systematic control design are certainly among the most important issues for fuzzy control systems. Stability analysis of ts fuzzy control systems using. That is the reason why recently, there have been significant research efforts in this direction. Stability analysis and design of fuzzy control systems, fuzzy sets and systems 45 2. Pdf a stability analysis method for nonlinear processes controlled by takagi sugeno ts fuzzy logic controllers flcs is proposed.
An introduction to nonlinear analysis of fuzzy control. Two cases, namely perfect and imperfect premise matching, are considered. This paper investigates the problem of stability analysis and fuzzysmith compensation control for semiactive suspension systems with time delay. Stability analysis of nonlinear multivariable takagisugeno. Indeed, the majority of these studies concern tsk fuzzysystems since. In the paper, the application of mimo frequencydomain methods to predict the existence of multiple equilibria and of limit. Stability analysis of fuzzy modelbased control systems. Tutorial 7 stability analysis this tutorial is specifically written for students studying the ec module d227 control system engineering but is also useful for any student studying control.
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. The stability conditions issued fromvector norms correspond to a vector lyapunov function. The main contribution of this paper is the development of an equivalent principle. It summarizes the stateoftheart methods for automatic tuning of the parameters and. The stability analysis of fuzzy control systems is one of the important concepts in the analysis of control systems. 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 function pilf. A linear matrix inequality approach, wiley, new york, ny. 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. Various nonpdc fuzzy controllers are proposed to close the feedback loop.
The class of fuzzy systems considered can be represented by the takagisugeno fuzzy model which is a type of dynamic fuzzy model. In the mean time, theorists will attempt to develop a mathematical the ory for the verification and certification of fuzzy control systems. Abstract this paper proposes a practical stability analysis of aparticular class of continuous pilike fuzzy control systems based onthe convergence of regular vector norms. Pdf stability analysis of continuous pilike fuzzy control. A fuzzy logic controller is designed to control a nuclear reactor. Today, there exist preoccupations reported in the literature 6, 7 on the stability analysis and design of ts fuzzy control systems. This paper presents a new stability analysis method for nonlinear processes with. 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. Pdf a stability analysis method for nonlinear processes controlled by takagisugeno ts fuzzy logic controllers flcs is proposed. In this chapter, let us discuss the stability analysis in the s domain using the routhhurwitz stability criterion. Lixin wang this volume develops a variety of adaptive fuzzy systems and applies them to a variety of engineering problems.
Stability analysis of interconnected fuzzy systems using. The takagisugeno ts fuzzy system is a breakthrough in the stability analysis and controller design of fuzzy control systems. Nowadays, fuzzy control systems are successfully applied in many technical and nontechnical fields. This study presents an improved sumofsquares sosbased stability analysis result for the polynomial fuzzymodelbased control system, formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop.
Points out how the nonlinearities involved in multivariable takagisugeno ts fuzzy control systems could originate complex behavior phenomena, such as multiple equilibrium points or limit cycles, that cannot be detected using conventional stability analysis techniques. Pdf stability analysis and design of fuzzy control. Stability analysis method for fuzzy control systems. The stability analysis of discretetime fuzzy logic control systems has received considerable attention recently and many significant results have been reported recently. Stability analysis and control design for 2d fuzzy.
In chapter 1 we provide an overview of the general methodology for conventional control system design. The stability analysis and the design technique of fuzzy control systems using fuzzy block. Fuzzy systems may perform different tasks within an automatic control system leading to different structural schemes. In this criterion, we require the characteristic equation to find the stability of the closed loop control systems. The book also provides rigorous analysis of nonlinear fuzzy control systems, and outlines a simple method to the stability of nonlinear control systems. Fuzzy sets and systems 45 1992 5156 5 northholland stability analysis and design of fuzzy control systems kazuo tanaka and michio sugeno department of systems science, tokyo institute of technology, 4259 nagatsuta, midoriku, yokohama 227, japan received november 1989 revised may 1990 abstract. Stability analysis of linear control systems with uncertain parameters by yuguang fang submitted in partial ful.
In this way, many researches have been done on the stabilitystudy of fuzzy control systems since their appearance in themiddle of the 70s 17. The absolute stability analysis in fuzzy control systems. Based on traditional lyapunov stability theory, we further propose a fuzzy lyapunov method for the stability analysis of interconnected fuzzy systems. This paper investigates the system stability of ts fuzzymodelbased control systems based on an improved fuzzy lyapunov function. Routhhurwitz stability criterion is having one necessary condition and one sufficient condition for stability. Stability analysis of fuzzy control systems subject to. The stability analysis of the fcss is carried out using lasalles global invariant set theorem by the separate. This theory will have a synergistic effect by driving the develop ment of fuzzy control systems for applications where there is a need. It shows, step by step, how to combine linguistics and numerical information using various kinds of adaptive fuzzy systems. Stability analysis method for fuzzy control systems dedicated. In particular, the methods described allow rigorous analysis of the stability and robustness of the systems, which are crucial issues in control theory. Stability analysis of polynomial fuzzymodelbased control.
In this book, the stateoftheart fuzzymodelbased fmb based control approaches are covered. This approach is based onthe comparison, the overvaluing principle and the application ofborne and gentina criterion. The absolute stability analysis in fuzzy control systems with. We can design theoretically a modelbased fuzzy controller if we have a useful stability criterion for fuzzy control systems. Stability analysis of a type of takagisugeno pi fuzzy. Secondly, the paper performs the sensitivity analysis of fcss with respect to the parametric variations of the. The system stability of ts fuzzymodelbased control systems with a parameterdependent lyapunov function pdlf is investigated. Stability analysis of fuzzy control systems springerlink.
This theory will have a synergistic effect by driving the develop ment of. This paper summarises several results on the stability of multivariable fuzzy control system obtained in the famimo project. Mechatronics applications 62 involving the use of popovs hyperstability theory. Membershipfunctiondependent stability analysis and. Pdf stability analysis and design of fuzzy control systems. Stability analysis and fuzzy smith compensation control. Stability and sensitivity analysis of fuzzy control. We derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks. The contributions are based on a large subset of the stability analysis techniques commonly used in nonlinear control such as the small gain theorem and its related techniques, qualitative methods and the lyapunov stability theory, among. First, we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams. Stability analysis of fuzzy logic control systems for a.
Then we summarize the fuzzy control system design process and contrast the two. This paper presents a design method for a class of fuzzy control systems. The application of fuzzy control systems is supported by numerous hardware and. 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. Stability analysis of interconnected fuzzy systems using the. This paper presents a new stability analysis method dedicated to a class of fuzzy control systems fcss controlling multi inputmulti output mimo nonlinear processes by means of takagisugenokang fuzzy logic controllers flcs. These global problems rise, for instance, when an unstable plant is controlled with a controller that saturates. Stability analysis of fuzzy logic control systems for a class.
A fuzzy control system is a control system based on fuzzy logica mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values. Under the perfect premise matching, the polynomial fuzzy model and polynomial fuzzy. The concept of stability and the general criterion used for fuzzy control systems are discussed. Fuzzy control systems design and analysis wiley online books. Building on the takagisugeno fuzzy model, authors tanaka and wang address a number of important issues in fuzzy control systems, including stability analysis, systematic design procedures, incorporation of. However, analysis of fuzzy systems using the conventional analysis methods is. Stability analysis of fuzzy logic control systems article pdf available in electronics letters 3612.
The characteristic of ts fuzzy model is considered to facilitate the stability analysis. Stability analysis of a class of mimo fuzzy control systems. Unesco eolss sample chapters control systems, robotics and automation vol. Further concepts based on fuzzy sets applied to control systems 5. These include stability analysis, systematic design procedures, incorporation of performance specifications, robustness, optimality, numerical implementations. Stability analysis of fuzzy control systems subject to uncertain grades of membership h. Stability analysis of multivariable fuzzy control systems. Sep 12, 2001 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. A fuzzy control system is a control system based on fuzzy logica mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 true or false, respectively. Pdf stability analysis of fuzzy logic control systems researchgate.
The majority of these papers is based on linear matrix inequality. The stability analysis of this control system is addressed. This book presents recent research on the stability analysis of polynomialfuzzymodelbased control systems where the concept of partiallyimperfectly matched premises and membershipfunction dependent analysis are considered. Abstract this paper investigates the problem of stability analysis and stabilization for twodimensional 2d discrete fuzzy systems.
An introduction to nonlinear analysis of fuzzy control systems an introduction to nonlinear analysis of fuzzy control systems david f. New approaches to fuzzy modeling and control series in. In this study two different fuzzy systems are studied. Stability analysis and design of fuzzy control systems. Pdf stability analysis of fuzzy logic control systems. Mamdani fuzzy controllers, stability analysis, sensitivity analysis, mechatronics. Stability analysis of nonlinear multivariable takagi. The stable indirect adaptive fuzzy logic control of nonlinear discretetime systems is investigated in qi and brdys, 2008. Pdf stability analysis method for fuzzy control systems dedicated. The stability analysis of the fcss is carried out using lasalles global invariant set theorem by the separate stability analysis of each fuzzy rule in mimo fuzzy control systems. Stability analysis of ts fuzzymodelbased control systems. 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. A linear matrix inequality approach kazuo tanaka, hua o.
The development of an autonomous road following embedded system for intelligent vehicles is the focus of this paper. A collection of contributions to the stability analysis of fuzzy control systems is presented in this book. The absolute stability analysis in fuzzy control systems with parametric uncertainties and reference inputs bingfei wua, member, lishan ma. A fuzzy logic controller flc is designed for visionbased autonomous road following. Stability analysis and design for a class of continuous. 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. On completion of this tutorial, you should be able to do the following. Stability analysis of a type of takagisugeno pi fuzzy control systems using circle criterion. International journal of computational intelligence systems. In this book, the stateoftheart fuzzy modelbased fmb based control approaches are covered. Autonomous road following is one of the major goals in intelligent vehicle applications. An introduction to nonlinear analysis of fuzzy control systems. Inparticular, stability analysis of control systems is an essentialstep before synthesizing and elaborating the control law. Zhang department of computer science and engineering, university of south florida.
This paper focuses on the guaranteed cost stability analysis of fuzzymodelbased fmb control systems. A constructive algorithm is developed to obtain the stabilizing feedback control law for the system. The interconnected fuzzy systems consist of interconnected fuzzy subsystems, and the stability analysis is based on lyapunov functions. Pdf fuzzy logic control system stability analysis based on. 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 takagi. Then, the stability and the robustness of the overall system is studied by using the recent.
The fuzzy lyapunov method is investigated for use with a class of interconnected fuzzy systems. Xvii analysis and stability of fuzzy systems ralf mikut and georg bretthauer encyclopedia of life support systems eolss in many practical applications, however, the input and output variables of fuzzy systems take on numerical values. Stability analysis and design for a class of continuoustime fuzzy control systems. Thus any design method in linear control system theory can be used to design a fuzzy control system. Design and lyapunov stability analysis of a fuzzy logic. Stability analysis and control design of fuzzy systems. Elsevier fuzzy sets and systems 105 1999 3348 zzy sets and systems stability analysis of fuzzy control systems a. The dynamic system of the suspension system with time delay is first formulated in terms of control objectives, such as ride comfort, road handling, and suspension deflection. Polynomial fuzzy modelbased control systems stability. In this book, the state of theart fuzzy modelbased fmb based control approaches are covered.
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