Olivier Pagès

Improved fuzzy sliding mode control for a class of MIMO nonlinear uncertain and perturbed systems

In this paper, a stable adaptive fuzzy sliding mode based tracking control is developed for a class of nonlinear MIMO systems that are represented by input output models involving system uncertainties and external disturbances. The main contribution of the proposed method is that the structure of the controller system is partially unknown and does not require the bounds of uncertainties and disturbance to be known. First, a fuzzy logic system is designed to estimate the unknown function. Secondly, in order to eliminate the chattering phenomenon brought by the conventional variable structure control, the signum function is replaced by an adaptive Proportional Derivative (PD) term in the proposed approach. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis, so that convergence to zero of tracking errors and boudedness of all signals in the closed-loop system can be guaranteed. Finally, a mass-spring-damper system is simulated to demonstrate the validity and the effectiveness of the proposed controller.

Observer-based robust fuzzy control for vehicle lateral dynamics

In this paper, the robust fuzzy control for four wheels steering (4WS) vehicle dynamics is studied via a Takagi-Sugeno (T-S) uncertain fuzzy model when the road adhesion conditions change and the sideslip angle is unavailable for measurement. After giving the nonlinear model of the vehicle, its representation by a T-S uncertain fuzzy model is discussed. Next, based on the uncertain fuzzy model of the 4WS Vehicle a fuzzy controller and a fuzzy observer are developed. The closed loop stability conditions of a vehicle with the fuzzy controller and the observer are parameterized in terms of linear matrix inequality (LMI) problem which can be solved very efficiently using the convex optimization techniques. The numerical simulation of the vehicle handling with and without the use of the developed observer and controller has been carried out. The simulation results obtained indicate that considerable improvements in the vehicle handling can be achieved whenever the vehicle is governed by the proposed fuzzy observer and fuzzy controller

Observer-based robust control of uncertain fuzzy dynamic systems with pole placement constraints: an LMI approach

This paper investigates both analysis and synthesis techniques for robust pole placement in linear matrix inequality (LMI) regions involving observer-based fuzzy control. The class of systems considered here is the continuous Takagi-Sugeno (T-S) fuzzy model with parametric structured uncertainties and unavailable state variables. Sufficient global stability conditions are established which make it possible to robustly assign the closed-loop poles of the augmented system containing both the fuzzy controller and observer in the left half complex plane and also to guarantee control performances by imposing a pole placement. Because of uncertainties, the separation property is not applicable to design the fuzzy controller and observer separately. The idea of the proposed approach is to assign both state and estimation error poles to a desired LMI region and to use the Hinfin technique in order to guarantee that the estimation error converges faster to the equilibrium point zero. An example is given to illustrate the effectiveness of the proposed approach

Four-Wheel Steering Vehicle Control using Takagi-Sugeno Fuzzy Models

This paper deals with the problem of vehicle active control. The focus is to improve the vehicle stability and handling. Vehicle dynamics is described by a 10-DOF (degree of freedom) model which include lateral, longitudinal, yaw and roll dynamics. Parametric variations (due to the variation of road conditions) and also, a variation of vehicle velocity are taken into account in the controller synthesis. The nonlinear vehicle model is approximated by a Takagi-Sugeno (T-S) fuzzy model with structured parametric uncertainties. State variables are not always available. Thus, fuzzy observer-based algorithm will be proposed to ensure control with performance specifications. Robust pole placement LMI (linear matrix inequalities) conditions are obtained using Lyapunov and Hinfin approach, which ensure desired performances of the closed loop system.

Observer-Based Robust Control of Vehicle Dynamics for Rollover Mitigation in Critical Situations

This paper describes a vehicle dynamics fuzzy control design to improve stability and minimize the rollover risk of the vehicle in critical situations. To obtain a robust controller, several aspects that directly affect the behavior of the vehicle have been considered. Nonlinearities of the lateral forces have been considered by using a Takagi-Sugeno (TS) representation, changes in road friction have been taken into account by introducing parameter uncertainties, and, finally, the road bank angle is considered as an unknown input in the used vehicle dynamics model. A TS observer has been proposed and designed with unmeasurable premise variables in order to consider the unavailability of the sideslip angle measurement. The observer and controller gains are simultaneously obtained by solving the proposed linear matrix inequalities constraints. A fishhook test is conducted in a CarSim simulator in order to illustrate the performance of the designed controller.

Robust Adaptive Fuzzy Sliding Mode Control Design for a class of MIMO underactuated system

Abstract In this paper, a robust adaptive fuzzy controller which combines the sliding mode control with an adaptive Proportional Integral (PI) term is developed for a class of nonlinear Multi Inputs Multi Outputs (MIMO) underactuated systems with unknown parameters and in presence of external disturbances. The main contribution of the proposed method is that underactuated systems can be controlled in their original non square form. The problem of matrix singularity for this class of systems is solved by using the property of the regularized inverse and by introducing a compensator term in the proposed control law. The free parameters of the adaptive fuzzy controller are tuned on-line based on the Lyapunov approach. The overall adaptive fuzzy scheme guarantees the boundedness of all the closed-loop signals as well as the tracking errors. The validity of the proposed approach is shown by computer simulations.

Improved observer-based adaptive fuzzy tracking control for MIMO nonlinear systems

In this paper, a stable observer-based adaptive fuzzy controller which combines a sliding mode and an adaptive Proportional Integral (PI) controllers is developed for a class of nonlinear Multiple Input Multiple Output (MIMO) systems with unknown parameters and in presence of external disturbances. The free parameters of the adaptive fuzzy controller are tuned on-line based on the Lyapunov approach. The overall adaptive fuzzy scheme guarantees the uniform ultimate boundedness of all the closed-loop signals as well as the tracking errors. The validity of the proposed approach is shown by computer simulations of a two-link robotic manipulator.

Adaptive Sliding Mode Control for a class of nonlinear MIMO systems: Application to a Turbocharged Diesel Engine

An Adaptive Sliding Mode Control (ASMC) for a class of nonlinear Multi Input Multi Output (MIMO) systems is presented in this paper. In order to reduce the chattering phenomenon without deteriorating the tracking performance, the discontinuous term of the classical sliding mode law is substituted with an adaptive Proportional Derivative (PD) term. The effect of the approximation error which arises from the PD term is reduced by adding a robust term in the proposed control law. All parameters, adaptive laws and robust control term, are derived based on the Lyapunov stability analysis. The overall adaptive sliding mode scheme guarantees the asymptotic convergence to zero of tracking errors and the boundedness of all signals in the closed-loop system. The proposed approach is applied to a Turbocharged Diesel Engine. Simulation results are presented to show the efficiency of the proposed method.

Observer-Based State Feedback Control for Vehicle Chassis Stability in Critical Situations

This brief describes an observer-based state feedback tracking controller for vehicle dynamics with a four-wheel active steering system as well as an active suspension system. The objective of the proposed controller is to improve the vehicle behavior by forcing the lateral dynamics and the load transfer ratio to achieve the desired vehicle behavior in critical situations. A Takagi-Sugeno (TS) representation of the lateral forces has been used in order to take the nonlinearities into account. Based on the obtained fuzzy model, a TS observer has been designed with estimated membership functions in order to consider the unavailability of the sideslip and the roll angles for measurement. Based on the Lyapunov function and the H∞ approach, the observer and controller design has been formulated in terms of Linear Matrix Inequality constraints. The proposed techniques have been evaluated through a fishhook test conducted in the CarSim professional software package.

Generalized fuzzy sliding mode control for MIMO nonlinear uncertain and perturbed systems

In this paper, a stable adaptive fuzzy sliding mode based tracking control is developed for a class of non-square nonlinear systems that are represented by input output models involving system uncertainties and external disturbances. The main contribution of the proposed method is that non-square systems are be controlled in their original non-square form instead of squaring them by adding or eliminating variables. First, a fuzzy logic system is designed to estimate the unknown function. Secondly, in order to eliminate the chattering phenomenon brought by the conventional variable structure control, the signum function is replaced by an adaptive Proportional Derivative (PD) term in the proposed approach. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis, so that the convergence to zero of tracking errors and the boudedness of all signals in the closed-loop system can be guaranteed. The efficiency of the proposed approach is shown by computer simulations.