Manabu Sano

A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer

A robust stabilization problem for fuzzy systems is discussed in accordance with the definition of stability in the sense of Lyapunov. We consider two design problems: nonrobust controller design and robust controller design. The former is a design problem for fuzzy systems with no premise parameter uncertainty. The latter is a design problem for fuzzy systems with premise parameter uncertainty. To realize two design problems, we derive four stability conditions from a basic stability condition proposed by Tanaka and Sugeno: nonrobust condition, weak nonrobust condition, robust condition, and weak robust condition. We introduce concept of robust stability for fuzzy control systems with premise parameter uncertainty from the weak robust condition. To introduce robust stability, admissible region and variation region, which correspond to stability margin in the ordinary control theory, are defined. Furthermore, we develop a control system for backing up a computer simulated truck-trailer which is nonlinear and unstable. By approximating the truck-trailer by a fuzzy system with premise parameter uncertainty and by using concept of robust stability, we design a fuzzy controller which guarantees stability of the control system under a condition. The simulation results show that the designed fuzzy controller smoothly achieves backing up control of the truck-trailer from all initial positions. >

Modeling and control of carbon monoxide concentration using a neuro-fuzzy technique

Modeling and control of carbon monoxide (CO) concentration using a neuro-fuzzy technique are discussed. A self-organizing fuzzy identification algorithm (SOFIA) for identifying complex systems such as CO concentration is proposed. The main purpose of SOFIA is to reduce the computational requirement for identifying a fuzzy model. In particular, the authors simplify a procedure for finding the optimal structure of fuzzy partition. The /spl delta/ rule, which is a basic learning method in neural networks, is used for parameter identification of a fuzzy model. SOFIA consists of four stages which effectively realize structure identification and parameter identification. The procedure of SOFIA is concretely demonstrated by a simple example which has been used in some modeling exercises. The identification result shows effectiveness of SOFIA. Next, the authors apply SOFIA to a prediction problem for CO concentration in the air at the busiest traffic intersection in a large city of Japan. Prediction results show that the fuzzy model is much better than a linear model. Furthermore, the authors simulate a control system for keeping CO concentration at a constant level by using the identified fuzzy model. A self-learning method for adaptively modifying controller parameters by /spl delta/ rule is introduced because the dynamics of real CO concentration system changes gradually over a long period of time. Two self-learning controllers are designed in this simulation. One is a self-learning linear PI controller. The other is a self-learning fuzzy PI controller. The authors investigate robustness and adaptability of this control system for disturbance and parameter perturbation of the CO concentration model. Simulation results show that the self-learning fuzzy controller is more robust and adaptive. >

Fuzzy stability criterion of a class of nonlinear systems

Abstract A fuzzy stability criterion of a class of nonlinear systems is discussed in accordance with the definition of stability in the sense of Lyapunov. First, a sufficient condition that guarantees stability of a fuzzy system is given in terms of Lyapunovs direct method. Two concepts for stability of fuzzy systems are defined: locally stable and globally table. Second, a construction procedure for Lyapunov functions is presented. Finally, the construction procedure is applied to the fuzzy stability criterion of a class of nonlinear systems that can be approximated by fuzzy systems.

Trajectory stabilization of a model car via fuzzy control

Abstract This paper deals with trajectory stabilization of a computer simulated model car via fuzzy control. Stability conditions of fuzzy systems are given in accordance with the definition of stability in the sense of Lyapunov. First, we approximate a computer simulated model car, whose dynamics is nonlinear, by T-S (Takagi and Sugeno) fuzzy model. Fuzzy control rules, which guarantee stability of the control system under a condition, are derived from the approximated fuzzy model. The simulation results show that the fuzzy control rules effectively realize trajectory stabilization of the model car along a given reference trajectory from all initial positions under a condition and the dynamics of the approximated fuzzy model agrees well with that of the model car.

Concept of stability margin for fuzzy systems and design of robust fuzzy controllers

The authors discuss robust stability for fuzzy systems with premise parameter uncertainty and the design problem for robust fuzzy controllers. They derive four conditions for ensuring stability of fuzzy control systems by weakening a stability condition proposed by K. Tanaka and M. Sugeno (1990). The concept of stability margin is introduced and a design problem of robust controllers for fuzzy systems with premise parameter uncertainty is considered. Simulation results show the robustness of the fuzzy controller.<<ETX>>

Analysis and design of fuzzy controllers in frequency domain

This paper describes analysis and design of fuzzy phase-lead compensators in frequency domain. The main feature of fuzzy phase-lead compensators is to have parameters for effectively compensating phase characteristics in control systems. We show an important theorem, which realizes a phase-lead compensation, by introducing concept of frequency characteristics. Two design procedures of fuzzy phase-lead compensators are presented: cases of linear plant and unknown nonlinear plant. We apply one of the design procedures to tank level control which is a non linear system with dead time. Simulation results show validity of the design method.<<ETX>>

Model-based fuzzy control system design for magnetic bearings

This paper describes the application of a model-based fuzzy control technique to active magnetic bearing systems. The stabilization problem of the magnetic bearing systems is reduced to a two degrees-of-freedom control problem about rotational motion including interaction. We derive a multivariable fuzzy controller for this problem from the fuzzy model of rotor dynamics using the concept of parallel distributed compensation. Moreover, the stability of the designed control system is proved by means of the Lyapunov stability condition. A common Lyapunov function is found by solving an optimization problem based on linear matrix inequality conditions. The performance of the developed fuzzy controller is verified through simulation.

Design of fuzzy controllers based on frequency and transient characteristics

The authors propose design methods for fuzzy phase-lead compensators based on frequency and transient characteristics in fuzzy control systems. The main feature of these fuzzy phase-lead compensators is that they have parameters for effectively compensating phase characteristics in control systems. Two theorems based on the concept of frequency and transient characteristics are derived. One is a theorem for judging whether a fuzzy phase-lead compensator should be used or not. The other is a theorem for realizing phase-lead compensation. A method for designing a fuzzy phase-lead compensator for linear controlled objects is constructed using these theorems. The method is extended to unknown or nonlinear controlled objects. Simulation results show the validity of these design methods. >

Frequency shaping for fuzzy control systems with unknown non-linear plants by a learning method of neural network

Abstract This paper deals with a frequency shaping, which means an improvement of frequency response, for fuzzy control systems with unknown non-linear plants by a learning method of neural network. We derive an important theorem, which is related to phase-lead compensation, by introducing concept of frequency characteristics such as gain crossover frequency and phase margin. Using the theorem, a fuzzy phase-lead compensator, which have parameters for effectively compensating phase characteristics of control systems, is constructed. After proposing a design procedure of the fuzzy phase-lead compensator for linear plants, we extend it to a design procedure for unknown non-linear plants. A frequency shaping for unknown non-linear plants is realized by Widrow-Hoff learning rule which is a basic learning algorithm of neural networks. Simulation results show the effect of frequency shaping by Widrow-Hoff learning rule.

Identification and analysis of fuzzy model for air pollution-an approach to self-learning control of CO concentration

The authors present identification and control for a fuzzy prediction model of CO (carbon monoxide) concentration. There are many uncertainty (imprecise) factors for predicting CO concentration. The basic approach proposed is to handle this imprecision by fuzzy-logic-based techniques. The fuzzy modeling technique proposed by G.T. Kang and M. Sugeno (see Fuzzy Sets and Systems, vol.18, no.3, p.329-46, 1986) is used for identifying a fuzzy prediction model. The model identified concerns the prediction of CO concentration in the air at a traffic intersection point of a large city of Japan. It is shown that the identified fuzzy model is very useful for predicting CO concentration. Furthermore an attempt is made to simulate a self-learning control of CO concentration by the Widrow-Hoff learning rule. Simulation results show that this self-learning controller is useful for CO concentration control.<<ETX>>