Sensitivity Study of a Class of Fuzzy Control Systems

The paper performs the sensitivity study with respect to the parametric variations of the controlled plant in case of a class of fuzzy control systems dedicated to servo systems. The presentation is particularized to fuzzy control systems to solve the tracking control problem in case of wheeled mobile robots of tricycle type with two degrees of freedom. There is proposed a new development method for Takagi-Sugeno PI-fuzzy controllers based on the application of the Extended Symmetrical Optimum method to the basic linear PI controllers in a cascaded control system structure. There are derived sensitivity models, validated by considering a case study concerning the speed control of a servo system with DC motor as actuator in mobile robot control. Experimental results validate the development method for Takagi-Sugeno PI-fuzzy controllers

Lorenz System Stabilization Using Fuzzy Controllers

The paper suggests a Takagi Sugeno (TS) fuzzy logic controller (FLC) designed to stabilize the Lorentz chaotic systems. The stability analysis of the fuzzy control system is performed using Barbashin-Krasovskii theorem. This paper proves that if the derivative of Lyapunov function is negative semi-definite for each fuzzy rule then the controlled Lorentz system is asymptotically stable in the sense of Lyapunov. The stability theorem suggested here offers sufficient conditions for the stability of the Lorenz system controlled by TS FLCs. An illustrative example describes the application of the new stability analysis method

A LOW-COST APPROACH TO DATA-DRIVEN FUZZY CONTROL OF SERVO SYSTEMS

Servo systems become more and more important in control systems applications in various fields as both separate control systems and actuators. Ensuring very good control system performance using few information on the servo system model (viewed as a controlled process) is a challenging task. Starting with authors’ results on data-driven model-free control, fuzzy control and the indirect model-free tuning of fuzzy controllers, this paper suggests a low-cost approach to the data-driven fuzzy control of servo systems. The data-driven fuzzy control approach consists of six steps: (i) open-loop data-driven system identification to produce the process model from input-output data expressed as the system step response, (ii) Proportional-Integral (PI) controller tuning using the Extended Symmetrical Optimum (ESO) method, (iii) PI controller parameters mapping onto parameters of Takagi-Sugeno PI-fuzzy controller in terms of the modal equivalence principle, (iv) closed-loop data-driven system identification, (v) PI controller tuning using the ESO method, (vi) PI controller parameters mapping onto parameters of Takagi-Sugeno PI-fuzzy controller. The steps (iv), (v) and (vi) are optional. The approach is applied to the position control of a nonlinear servo system. The experimental results obtained on laboratory equipment validate the approach

A CENTER MANIFOLD THEORY-BASED APPROACH TO THE STABILITY ANALYSIS OF STATE FEEDBACK TAKAGI-SUGENO-KANG FUZZY CONTROL SYSTEMS

The aim of this paper is to propose a stability analysis approach based on the application of the center manifold theory and applied to state feedback Takagi-Sugeno-Kang fuzzy control systems. The approach is built upon a similar approach developed for Mamdani fuzzy controllers. It starts with a linearized mathematical model of the process that is accepted to belong to the family of single input second-order nonlinear systems which are linear with respect to the control signal. In addition, smooth right-hand terms of the state-space equations that model the processes are assumed. The paper includes the validation of the approach by application to stable state feedback Takagi-Sugeno-Kang fuzzy control system for the position control of an electro-hydraulic servo-system

An Approach to Fuzzy Modeling of Electromagnetic Actuated Clutch Systems

This paper proposes an approach to fuzzy modeling of a nonlinear servo system application represented by an electromagnetic actuated clutch system. The nonlinear model of the process is simplified and linearized around several operating points of the input-output static map of the process. Discrete-time Takagi-Sugeno (T-S) fuzzy models of the processes are derived on the basis of the modal equivalence principle; the rule consequents of these T-S fuzzy models contain the state-space models of the process. Three discrete-time T-S fuzzy models are suggested and compared. The simulation results validate the new fuzzy models of the electromagnetic actuated clutch system

Proportional-Integral-Derivative Gain-Scheduling Control of a Magnetic Levitation System

The paper presents a gain-scheduling control design procedure for classical Proportional-Integral-Derivative controllers (PID-GS-C) for positioning system. The method is applied to a Magnetic Levitation System with Two Electromagnets (MLS2EM) laboratory equipment, which allows several experimental verifications of the proposed solution. The nonlinear model of MLS2EM is linearized at seven operating points. A state feedback control structure is first designed to stabilize the process. PID control and PID-GS-C structures are next designed to ensure zero steady-state control error and bumpless switching between PID controllers for the linearized models. Real-time experimental results are presented for validation.

AUTOMOTIVE APPLICATIONS OF EVOLVING TAKAGI-SUGENO-KANG FUZZY MODELS

This paper presents theoretical and application results concerning the development of evolving Takagi-Sugeno-Kang fuzzy models for two dynamic systems, which will be viewed as controlled processes, in the field of automotive applications. The two dynamic systems models are nonlinear dynamics of the longitudinal slip in the Anti-lock Braking Systems (ABS) and the vehicle speed in vehicles with the Continuously Variable Transmission (CVT) systems. The evolving Takagi-Sugeno-Kang fuzzy models are obtained as discrete-time fuzzy models by incremental online identification algorithms. The fuzzy models are validated against experimental results in the case of the ABS and the first principles simulation results in the case of the vehicle with the CVT

DESCRIBING FUNCTION METHOD FOR PI-FUZZY CONTROLLED SYSTEMS STABILITY ANALYSIS

The paper proposes a global stability analysis method dedicated to fuzzy control systems containing Mamdani PI-fuzzy controllers with output integration to control SISO linear / linearized plants. The method is expressed in terms of relatively simple steps, and it is based on: the generalization of the describing function method for the considered fuzzy control systems to the MIMO case, the approximation of the describing functions by applying the least squares method. The method is applied to the stability analysis of a class of PI-fuzzy controlled servo-systems, and validated by considering a case study