Applications of fuzzy sets to systems analysis negoita. Specially, the stabilization of a feedback system containing a fuzzy regulator and a fuzzy observer for discrete fuzzy systems was discussed in 12. Stability and design issues of simple ts fuzzy control system with simplified linear rule consequent tss are investigated. To improve the solvability of the stability conditions, we establish a multigain controller with comprehensive information of the lower and upper membership grades. Stability analysis method for 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 is concerned with the stability analysis for ts fuzzy control systems. As a result, the closedloop fuzzy control system is also represented as weighted sums of some linear subcontrol systems. Simplicity and flexibility of fuzzy controllers have. Senior member, ieee abstract advances in nonlinear control theory have provided. Stability analysis of interconnected fuzzy systems using.
A fuzzy neural network for rule acquiring on fuzzy control. An introduction to nonlinear analysis of fuzzy control. The book also provides rigorous analysis of nonlinear fuzzy control systems, and outlines a simple method to guarantee the stability of nonlinear control. Stability and sensitivity analysis of fuzzy control systems. They can be found either as standalone control elements or as integral parts of a wide range of industrial process control systems and. This paper presents relaxed stability conditions for fuzzy control systems subject to parameter uncertainties. The stability analysis is reduced to a problem of finding a common lyapunov function. Fuzzy sets and systems publishes highquality research articles, surveys as well as case studies. The overall focus for these nonlinear analysis methods is on understanding fundamental problems. The fuzzy lyapunov method is investigated for use with a class of interconnected fuzzy systems. Theories and methods 119 optimization problems, models and some wellknown methods. Stability analysis of fuzzy control systems subject to uncertain grades of membership. A fuzzy control system is a control system based on fuzzy logica mathematical system that.
Three kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities lmis. An introduction to nonlinear analysis of fuzzy control systems. The fuzzy mathematics has broad applications in many fields including statistics and numerical analysis, systems and control. Building on the socalled takagisugeno fuzzy model, a number of most important issues in fuzzy control systems are addressed. A fuzzy descriptor system is defined in this paper. It shows, step by step, how to combine linguistics and numerical information using various kinds of adaptive fuzzy systems. Stability analysis of fuzzy control systems subject to. 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. Stability analysis of fuzzy control systems sciencedirect. Though, various kinds of fuzzy systems are widely used nowadays, this variety is issued from the types of fuzzy controllers in the closed loop of the system to be studied.
Zhang department of computer science and engineering, university of south florida. A modelbased approach automation and control engineering book 37 kindle edition by gang feng. In this study two different fuzzy systems are studied. Perspectives of fuzzy systems and control antonio salaa thierry marie guerrab robert babuska. Fuzzy systems may perform different tasks within an automatic control system leading to different structural schemes. Block diagram of the fuzzy adaptive control system the defuzzi. 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.
The architecture of these networks is referred to as anfis hi h t d fanfis, which stands for adti t kdaptive networkbased fuzzy inference system or semantically equivalently, adaptive neurofuzzy inferencefuzzy inference system. Stabililty analysis of parallel fuzzy p plus fuzzy i plus fuzzy d control systems was done with the help of mathematical models of the controllers kumar et al. Neural networks are capable of approximating any multidimensional nonlinear functions andas suchthey canbe very useful in nonlinear. However, when a nonlinear system has complex nonlinearities, the constructed ts fuzzy model will have to consist of a number of fuzzy local models.
Stability analysis and systematic control design are certainly among the most important issues for fuzzy control systems. Pdf stability analysis of ts fuzzy control systems by. Abstractone of the most important problems today is robotics and its control, due to the vast application of inverted pendulum in robots. The springer international series in engineering and computer science, vol 457. Online interactive demonstration of a system with 3 fuzzy rules. Download it once and read it on your kindle device, pc, phones or tablets. 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.
In identification of ts fuzzy models, the structure determination and parameter identification. Fuzzy modeling and adaptive control of uncertain system uncertain system controller x u x d fuzzy adaptive law fuzzy modelling fig. 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. In consequence, for stability analysis methods from nonlinear systems are used. Analytical structure and stability analysis of a fuzzy two. Fuzzy blocks used in control systems have a nonlinear character, for any variant of implementation. Today there recognition that for understanding vagueness, a fuzzy approach is required. A fuzzy neural network for rule acquiring on fuzzy control systems j. Then, stability analysis and control synthesis for.
Hence, the ts fuzzy models are becoming powerful engineering tools for modeling and control systems 2. Robust control of inverted pendulum using fuzzy sliding. The stability analysis of these fuzzy control systems is performed using lasalles. A simple fuzzy control is built up by a group of rules based on the human knowledge of system behavior. A study of an modeling method of ts fuzzy system based on. Stability analysis of fuzzymodelbased control systems. This theory will have a synergistic effect by driving the develop ment of. By exploiting the property of the structure of fuzzy inference engine, an equivalence relation on index set of. Analytical structure and stability analysis of a fuzzy twoterm controller with multifuzzy sets. The application of fuzzy control systems is supported by numerous hardware and. Fuzzy logic controller, lyapunov stability, nonlinear system. Researcharticle improved approach to robust control for type2 ts fuzzy systems bumyongpark 1 andjaewookshin 2 divisionofelectricalengineer. Control synthesis of continuoustime ts fuzzy systems. Stability analysis and design of fuzzy descriptor systems.
That is the reason why recently, there have been significant research efforts in this direction. It provides an overview of their theory of operation, followed by elementary examples of their use. This study provides a new method of fault diagnosis and tolerance control of. Stability analysis method for fuzzy control systems dedicated controlling nonlinear processes it should be noted that with x x0, an inactive fuzzy rule will not affect the controller output ux0. Fuzzy control has been a successful application of this theory and implemented in many industrial systems. Nowadays, fuzzy control systems are successfully applied in many technical and nontechnical fields. Pdf stability analysis method for fuzzy control systems dedicated. Use features like bookmarks, note taking and highlighting while reading analysis and synthesis of fuzzy control systems. In this book, the stateoftheart fuzzymodelbased fmb based control approaches are covered. Pdf stability analysis and design of fuzzy control.
The importance of interpretation of the problem and formulation of optimal solution in a fuzzy sense are emphasized. This paper is concerned with the robust stability conditions to stabilize the type 2 takagisugeno ts fuzzy systems. A linear matrix inequality approach kazuo tanaka, hua o. In power engineering area, fuzzy set theory is applied in power system control, planning and some other aspects. Recently, the issue of stability of fuzzy control systems has been considered extensively in nonlinear stability frameworks 15, 12, 16.
Stability and sensitivity analysis of fuzzy control. Takagisugeno fuzzy systems, linear matrix inequalities, stability analysis 1 introduction stability analysis and control design for takagisugeno fuzzy systems takagi and sugeno, 1985 have been routinely formulated as feasibility and optimization problems in lmi linear matrix inequalities form tanaka and wang, 2001. As it appears from the literature, mizumoto 2 has investigated fuzzy control problem by considering multifuzzy sets and different fuzzy. Fu department of computer science and information engineering, national chiaotung university, hsinchu, taiwan 300, roc abstract this paper presents a layerstructured fuzzy neural network fnn for learning rules of fuzzylogic control systems. Stability analysis and control design of fuzzy systems.
In this paper, by using a acombination of fuzzy sliding mode methods and genetic algorithms, we have. An introduction to fuzzy control fuzzy controllers are a class of knowledge based controllers using artificial intelligence techniques with origins in fuzzy logic. A course in fuzzy systems and control lixin wang prenticehall international, inc. From discussions of general philosophy to practical methods for system analysis.
The conditions effectively handle parameter uncertainties using lower and upper membership functions. Stability analysis of fuzzy control systems springerlink. These adaptive systems are best handled with methods of computational intelligence such as neural networks and fuzzy systems. The stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed. Application of the lyapunov stability criteria to synthesize the fuzzy controller requires the addition of a control input to the original system equation and subsequent transformation into a. We derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks. 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 and design of ts fuzzy control system. Pdf stability analysis of fuzzy logic control systems. Stability analysis and state feedback control of continuoustime ts fuzzy systems via anew. Scientists no is an increasing less than poets strike off words that fit a situation. Stability analysis and design of fuzzy control systems. A systematic approach to find a common matrix p for tss fuzzy system. Review and cite fuzzy control protocol, troubleshooting and other.
Stability study of fuzzy control processes application to. The interconnected fuzzy systems consist of interconnected fuzzy subsystems, and the stability analysis is based on lyapunov functions. The stability analysis and the design technique of fuzzy control systems using fuzzy block. Mechatronics applications 64 the inference engine in bfc employs mamdanis maxmin compositional rule of inference assisted by the rule base presented in table 1, and the center of gravity. In the mean time, theorists will attempt to develop a mathematical the ory for the verification and certification of fuzzy control systems. Improved approach to robust control for type2 ts fuzzy. Cut approach for fuzzy product and its use in computing solutions of fully fuzzy linear systems.
First, we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams. However, developments of neural or fuzzy systemsarenottrivial. Stability analysis of such systems is still an open problem, in this way, many contributions were. Coordination of excitation and governing control based on. Base fuzzy system modeling modeling of the static fuzzy systems stability analysis of discretetime dynamic fuzzy systems modeling of. A modelbased approach offers a unique reference devoted to the systematic analysis and synthesis of modelbased fuzzy control systems. Elsevier fuzzy sets and systems 105 1999 3348 zzy sets and systems stability analysis of fuzzy control systems a. Hence 4 can be rewritten so as to consider all active. Cut approach for fuzzy product and its use in computing. As a bench test a nonlinear system is selected to demonstrate the feasibility and efficiency though numerical analysis.
685 1028 807 1597 1573 1086 332 1388 1442 537 1542 779 1472 838 1265 767 127 1108 423 258 535 537 225 561 593 265 1413 402 1274 510 1542 1158 179 1439 970 655 179 630 448 347 1261 108 492 277 828