Slim Dhahri

An H∞ Sliding Mode Observer for Takagi-Sugeno Nonlinear Systems with Simultaneous Actuator and Sensor Faults

Abstract This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observer

Design of new fuzzy sliding mode controller based on parallel distributed compensation controller and using the scalar sign function

This paper presents a new design of fuzzy sliding mode controller based on parallel distributed compensation and using a scalar sign function. The proposed fuzzy sliding mode controller (FSMC) uses the parallel distributed compensation (PDC) scheme to design the state feedback control law. The controller gains are determined in offline mode via linear quadratic regulator technique. Moreover, the fuzzy sliding surface of the system is designed using stable eigenvectors and the scalar sign function in order to overcome the discontinuous switching. This later is obtained by a sign function of the standard FSMC. The advantages of the proposed design are a minimum energy control effort, faster response and zero steady-state error. Finally, the validity of the proposed design strategy is demonstrated through the simulation of a flexible joint robot.

Robust sensor fault detection and isolation for a Steer-by-Wire system based on sliding mode observer

A new approach for the design of robust H∞ sliding mode observer for Steer-by-Wire (SBW) systems with parametric uncertainties and sensor faults is proposed based on linear matrix inequalities (LMIs). The resulting H∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against parametric uncertainties. A sensor fault estimation scheme is presented where the estimated signal can approximate the fault signal to any accuracy. The effectiveness of the proposed approach is verified by simulations.

Design of Robust Supertwisting Algorithm Based Second-Order Sliding Mode Controller for Nonlinear Systems with Both Matched and Unmatched Uncertainty

This paper proposes a robust supertwisting algorithm (STA) design for nonlinear systems where both matched and unmatched uncertainties are considered. The main contributions reside primarily to conceive a novel structure of STA, in order to ensure the desired performance of the uncertain nonlinear system. The modified algorithm is formed of double closed-loop feedback, in which two linear terms are added to the classical STA. In addition, an integral sliding mode switching surface is proposed to construct the attractiveness and reachability of sliding mode. Sufficient conditions are derived to guarantee the exact differentiation stability in finite time based on Lyapunov function theory. Finally, a comparative study for a variable-length pendulum system illustrates the robustness and the effectiveness of the proposed approach compared to other STA schemes.

Second order and classical sliding mode control of a MAXPID system: A comparison performance

This paper deals with the problem of Sliding Mode Control (SMC) design for a class of non linear system. Two different control designs are developed for a dynamic system Maxpid. The first type is the define of traditional Sliding Mode (SM) control. The second is the Higher Order Sliding Mode (HOSM) control. These two kinds have the same properties of robustness and precision. Note that the implementation drawback of the first type has a chattering phenomenon. The HOSM control is proposed to reduce the phenomenon. The simulation results obtained from the two types are finally compared in terms of good performances.

Robust and simultaneous reconstruction of actuator and sensor faults via sliding mode observer

This paper proposes a method for robust and simultaneous actuator and sensor faults reconstruction of linear uncertain system based on sliding mode observer (SMO). In comparison with existing work, the observer contains two discontinuous terms to solve the problem of simultaneous faults. The idea is to introduce an appropriate filter on the systems output to transform the sensor faults in the fictitious actuator faults and hence the proposed SMO can be applied.

Multiplicative Fault Estimation-Based Adaptive Sliding Mode Fault-Tolerant Control Design for Nonlinear Systems

This article deals with the sliding mode fault-tolerant control (FTC) problem for a nonlinear system described under Takagi-Sugeno (T-S) fuzzy representation. In particular, the nonlinear system is corrupted with multiplicative actuator faults, process faults, and uncertainties. We start by constructing the separated FTC design to ensure robust stability of the closed-loop nonlinear system. First, we propose to conceive an adaptive observer in order to estimate nonlinear system states, as well as robust multiplicative fault estimation. The novelty of the proposed approach is that the observer gains are obtained by solving the multiobjective linear matrix inequality (LMI) optimization problem. Second, an adaptive sliding mode controller is suggested to offer a solution to stabilize the closed-loop system despite the occurrence of real fault effects. Compared with the separated FTC, this paper provides an integrated sliding mode FTC in order to achieve an optimal robustness interaction between observer and controller models. Thus, in a single-step LMI formulation, sufficient conditions are developed with multiobjective optimization performances to guarantee the stability of the closed-loop system. At last, nonlinear simulation results are given to illustrate the effectiveness of the proposed FTC to treat multiplicative faults.

Sliding Mode Observers Based-Simultaneous Actuator and Sensor Faults Estimation for Linear Parameter Varying Systems

This paper proposes a scheme to estimate actuator and sensor faults simultaneously for a class of linear parameter varying system expressed in polytopic structure where its parameters evolve in the hypercube domain. Transformed coordinate system design is adopted to decouple faults in actuators and sensors during the course of the system’s operation coincidentally, and then two polytopic subsystems are constructed. The first subsystem includes the effect of actuator faults but is free from sensor faults and the second one is affected only by sensor faults. The main contribution is to conceive two polytopic sliding mode observers in order to estimate the system states and actuator and sensor faults at the same time. Meanwhile, in linear matrix inequality optimization formalism, sufficient conditions are derived with performances to guarantee the stability of estimation error and to minimize the effect of disturbances. Therefore, all parameters of observers can be designed by solving these conditions. Finally, simulation results are given to illustrate the effectiveness of the proposed simultaneous actuator and sensor faults estimation.

Finite time stability of uncertain second order systems using sliding mode control

A finite time stability for uncertain second order systems is proposed in this paper using a Sliding Mode Control (SMC), the uncertainties being matched and norm bounded. A sliding surface is designed so that it gives good behavior during the SM and a controller signal strategy is developed to get the stability of the systems. Moreover the finite time convergence of the exact differentiator is established by means of Lyapunov functions. Finally, a simulation for a Pendulum system is illustrate the efficiency of the proposed method in terms of high robustness with respect to uncertainties and eliminate the chattering phenomenon.

Observer design for simultaneous robust actuator and sensor faults reconstruction

This paper describes a robust fault reconstruction and estimation design for a class of nonlinear system described by Takagi-Sugeno structure subject to faults affecting actuators, sensor faults and disturbances. The premise variables are assumed to be unmeasurable. The main innovation is focused primarily to conceive Sliding Mode Observer (SMO) designed to compensate faults behaviors from the system states estimation. In formalism of multi-objective optimisation, we derive sufficient conditions to guarantee the states estimation error stability and to obtain the observer gains. Simulation result is given to evaluate the proposed approach performances.