Fault-Tolerant Tracking Control for Linear Parameter-Varying Systems under Actuator and Sensor Faults

In this study, we delve into the intricacies of addressing the challenge posed by simultaneous external disturbances and ever-changing actuator and sensor faults in the context of linear parameter-varying (LPV) systems. Our focus is on fault estimation (FE) and the pursuit of fault-tolerant tracking control (FTTC). LPV systems are described through a polytopic LPV representation with measurable gain scheduling functions. An adaptive LPV sliding mode observer (ASMO) is developed for the purpose of simultaneously estimating the system states and faults despite external disturbances. Compared with other conventional ASMO designs, the proposed observer has the capability to reconstruct the actuator faults by exploiting the equivalent output error injection signal required to maintain sliding motion and to directly estimate sensor faults using an adaptive algorithm. Based on online FE information, an FTTC is synthesized to compensate for the fault effect and to force closed-loop system states to track their desired reference signals. Sufficient conditions to ensure the stability of the state estimation errors and closed-loop system are established using Lyapunov stability theory together with H∞ techniques. These requirements are articulated using linear matrix inequalities (LMIs), which can be effortlessly addressed through optimization problem-solving methods. To illustrate the potency of the proposed approaches, an illustrative example is provided. To illustrate the potency of the proposed approaches and to validate their practical effectiveness, we offer an illustrative example featuring a vertical takeoff and landing aircraft. This real-world case study serves as a practical application of our theoretical contributions, demonstrating the adaptability and robustness of our approach in the face of complex, real-world challenges

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

An H∞ sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults An

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 observe

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 H∞ 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