Robust fault-tolerant control of nonlinear inverted pendulum and cart system with simultaneous actuator and sensor faults sliding-mode observer

Robust fault-tolerant control of nonlinear inverted pendulum and cart system with simultaneous actuator and sensor faults sliding-mode observer

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In this chapter, we propose a robust active fault-tolerant control (AFTC) scheme for a class of uncertain nonlinear systems with simultaneous actuator and sensor faults described via Takagi-Sugeno (T-S) multiple models. First, by transforming the sensor fault into pseudoactuator fault, a novel T-S sliding-mode observer (TS-SMO) with two discontinuous terms is developed to provide separate estimates of the actuator and sensor faults for the purpose of fault compensation. The robustness of the proposed observer against uncertainties has been taken into account via H norm minimization. Second, we use obtained on-line fault estimation information to design dynamic output feedback controller (DOFC) for robustly compensating the effects of actuator and sensor faults from the system inputs and outputs and guarantee the stability of the overall closed-loop system. The stability proof with H performances and D-stability constraints is formulated as a linear matrix inequalities (LMI) optimization problem. The effectiveness of the proposed robust AFTC approach to treat simultaneous actuator and sensor faults is illustrated using a nonlinear inverted pendulum with cart system.

Chapter Contents:

  • 13.1 Introduction
  • 13.2 Problem formulation
  • 13.2.1 Motivation
  • 13.2.2 Inverted-pendulum modeling
  • Mathematical model
  • T-S model
  • 13.3 Fault reconstruction by sliding-mode observation
  • 13.3.1 System description
  • 13.3.2 Existence conditions
  • 13.3.3 T-S model in canonical form
  • 13.3.4 Sliding motion stability
  • 13.3.5 Sliding motion reachability
  • 13.3.6 Simultaneous actuator and sensor faults estimation
  • 13.4 Fault-tolerant controller design for T-S fuzzy systems
  • 13.5 Simulation results
  • 13.5.1 TS-SMO design
  • 13.5.2 Simultaneous faults estimation design
  • 13.5.3 TS-DOFC design
  • 13.6 Conclusion
  • References

Inspec keywords: control system synthesis; uncertain systems; H∞ control; pendulums; variable structure systems; robust control; minimisation; closed loop systems; fuzzy systems; fault tolerant control; linear matrix inequalities; observers; feedback; nonlinear control systems; compensation

Other keywords: simultaneous actuator and sensor faults; fault compensation; discontinuous terms; Takagi-Sugeno multiple models; online fault estimation information; pseudoactuator fault; T-S sliding-mode observer; D-stability constraints; dynamic output feedback controller design; H∞ norm minimization; nonlinear inverted pendulum and cart system; linear matrix inequalities optimization problem; uncertain nonlinear systems; robust active fault-tolerant control scheme; uncertainty robustness; LMI optimization problem; robust AFTC approach; TS-SMO; H∞ performance; closed-loop system; DOFC design

Subjects: Linear algebra (numerical analysis); Fuzzy control; Nonlinear control systems; Optimal control; Multivariable control systems; Stability in control theory; Simulation, modelling and identification; Optimisation techniques; Control system analysis and synthesis methods

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