Application of limit fuzzy controllers to stability analysis

In this paper, the robust stability of fuzzy control systems with uncertainties or nonlinearities is studied through the Popov-Lyapunov approach. Since solving an algebraic Riccati equation is the kernel of the proposed algorithm the method is feasible and easy to implement. In additional the proposed method has no fuzzy rule, inference engine, fuzzifier, or defuzzifier limitations. The resultant allowable uncertainty or nonlinearity bounds can help us to estimate the robust stability of a fuzzy control system; then such elements as the appropriate gauges can be chosen so that the stability can be guaranteed.

Design of a mixed fuzzy controller for multiple-input multiple-output systems

Stable controller design for T–S fuzzy systems based on Lie algebras

There are some different methods to evaluate the stability behaviour of fuzzy control systems depending on the availability of a mathematical process model. Two possibilities are discussed, stability by linearization and stability supervision by an additional fuzzy unit. The stability supervision is very adequate to the application of fuzzy control because a mathematical process model seems to be not necessary. In many cases of stability proof, relations to linear systems can be exploited.

This correspondence deals with the problems of analysis and design for a class of continuous-time Takagi-Sugeno fuzzy control systems. Sufficient conditions for the stability of fuzzy control systems are derived based on a fuzzy Lyapunov function. Both parallel and nonparallel distributed compensation controllers are considered. Sufficient conditions for the solvability of the controller design problem are given in the form of linear matrix inequalities. Unlike the fuzzy Lyapunov function approaches reported in the literature, the bound of the time derivatives of the fuzzy basis functions is not required in the proposed approaches. The effectiveness of the proposed approaches is shown through a numerical example.

This paper concentrates on the development of robust maximum power control for variable speed wind turbines with a double feed induction generator in the presence of wind disturbance and parameter uncertainties. To increment the actual manner for the wind turbine system, the effects of the mechanical and electrical part are taken in consideration. The algorithm is based on Takagi-Sugeno fuzzy model to increases the efficiency of the wind power generation systems and guarantees almost convergence. Conditions for the stability of fuzzy control systems are proved using a fuzzy Lyapunov function and formulated by Linear Matrix Inequalities. A Parallel Distributed Compensation scheme of fuzzy controllers is stated for closing the feedback loop. The advantages of the proposed strategy are: i) Enough stability conditions in the LMI is given for uncertain nonlinear system; ii) stabilizes the system over a wide range of wind speed variations and parameter uncertainties; iii) maximize output power from the system; iv) improving the system efficiency than other techniques. The influence of the proposed controller is finally proved through numerical simulations and compared with different strategies.

EXTENDED CIRCLE CRITERION: STABLE FUZZY CONTROL OF A MILLING PROCESS.

In this paper, a new fuzzy controller is proposed by introducing nonlinear functions into the analytical fuzzy controller, and the methods of to on-line adjust the rules of this fuzzy controller is present. The application of this new fuzzy controller in generator excitation systems is studied. The structures of the fuzzy logic controller for generator excitation control are established, through which both the voltage regulation accuracy and enhance damping requirements are satisfied. Mathematical analysis indicates that the proposed controller is an intrinsic non-linear PID controller with adaptive rules. In the application, the engineers needn't to design the control rules, instead, they only need to choose initially control parameters according to engineering control experience. So the design and implementation of the controllers are simplified. The simulation results show that the proposed fuzzy controller can improve the accuracy of voltage control and strengthen the stability of electric power systems.

138 Stability of Fuzzy control systems by using nonlinear system theory

The paper is concerned with two types of fuzzy PID controllers, the rule-based fuzzy PID controller and the learning fuzzy PID controller. Initially, the development of the rule-based fuzzy PID controller is studied, and subsequently, the development of the learning fuzzy PID controller is outlined. For the rule-based fuzzy PID controller, the PID gains are firstly tuned using a conventional tuning method. The rule buffer of the rule-based fuzzy then readjusts the PID gains during the system operation. The learning fuzzy PID controller not only readjusts the PID gains, it also creates and updates the rules in the rule-buffer automatically during the application of the learning fuzzy PID controller to the process. The rule-based fuzzy PID controller and the learning fuzzy PID controller are both applied to a non-linear revolute-joint robot-arm for path tracking experiments. The results of the experiments for the rule-based fuzzy PID controller and the learning fuzzy controller are compared with a conventional PID controller in order to evaluate the results.

In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed time-delays. For fuzzy systems with discrete time-delays, both delay-independent stability conditions and delay-dependent stability conditions have already been obtained. However, no stability condition for fuzzy systems with distributed time-delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed time-delays. With the aid of the stability theorems of linear systems with distributed time-delays, we employ a similar Lyapunov functional for the stability of fuzzy time-delay systems. Then we introduce many free matrices to such a Lyapunov functional, in order to obtain delay-dependent stability conditions. These techniques lead to generalized and less conservative stability conditions. In fact, delay-dependent stability conditions thus obtained are given in linear matrix inequalities(LMIs) and guarantee a wide stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed time-delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we take some examples to illustrate our results.

The semi-active control of MR damper is established, using a simplified model of landing gear system and DSP2812 as the code control board. The fuzzy control system is created based on software fuzzyTECH and simulation mode was established in matlab\simulink. Compared with passive control, the fuzzy control damping effect of the aircraft body vertical acceleration, body relative displacement and wheel dynamic load at different moments in the process of plane's taking off and landing. Software fuzzyTECH platform can generate the corresponding code for the DSP controller, applied directly to the fuzzy control system design and debugging, and shorten the development cycle of fuzzy algorithm control. Passive control and fuzzy control test are carried out on the landing gear vibration test platform. The results show that the application of fuzzy algorithm controller has higher adaptability and more real-time control effect, fuzzy control is better than passive control.

Stability is one of the most important concepts of analysis and design of control systems. Stability analysis of fuzzy control systems has been difficult since fuzzy systems are essentially nonlinear systems. Recently, stability analysis techniques [l]-[6] [13]-[16] based on nonlinear stability theory have been reported. Langari and Tomizuka [2, 6] analyzed stability of fuzzy linguistic control systems. Kitamura [3] realized stability analysis of fuzzy control systems by using extended circle criterion. Farinwata [5] and Kato [14] utilized phase plane analysis type of techniques, tanaka and co-authors [1,3,4] applied Lyapunov approach to fuzzy control systems and recently developed LMI-based designs [10, 17, 28-37], where LMI stands for nonlinear matrix inequality.

This paper overviews the research investigations pertaining to stability and stabilization of control systems with time‐delays. The prime focus is the fundamental results and recent progress in theory and applications. The overview sheds light on the contemporary development on the linear matrix inequality (LMI) techniques in deriving both delay‐independent and delay‐dependent stability results for time‐delay systems. Particular emphases will be placed on issues concerned with the conservatism and the computational complexity of the results. Key technical bounding lemmas and slack variable introduction approaches will be presented. The results will be compared and connections of certain delay‐dependent stability results are also discussed.

We apply the fuzzy control method to the temperature control system with moisture analyzer because of its uncertainty and variation in the parameters and nonlinear lag. Fuzzy control has fast response speed, short regulation time and strong robustness. But it has a steady-state error mainly because the fuzzy control rules are based on the designers' experience in the operation process and fuzzy information. The non-linearity and time-variation of the controlled process result in imperfectness of the fuzzy control rules and these will affect the result of the control from varying degrees. To make up the imperfectness, we designed the self-adjusting parameter fuzzy controller composed of basic fuzzy controller and self-adjusting parameter models. The task of self-adjusting parameter model is to regulate the quantification factor and scale factor on-line and optimize the basic fuzzy controller in order to largely perfect the response performance of the system. We have successfully controlled the temperature control system with infrared moisture analyzer with controller using this algorithm.