Estimation of Actuator and System Faults Via an Unknown Input Interval Observer for Takagi–Sugeno Systems

Citlaly Martínez-García,Carlos-M. Astorga-Zaragoza,Juan Reyes-Reyes,Vicenç Puig,Guadalupe Madrigal-Espinosa

doi:10.3390/pr8010061

Abstract

This paper presents a simultaneous state variables and system and actuator fault estimation, based on an unknown input interval observer design for a discrete-time parametric uncertain Takagi–Sugeno system under actuator fault, with disturbances in the process and measurement noise. The observer design is synthesized by considering unknown but bounded process disturbances, output noise, as well as bounded parametric uncertainties. By taking into account these considerations, the upper and lower bounds of the considered faults are estimated. The gain of the unknown input interval observer is computed through a linear matrix inequalities (LMIs) approach using the robust H ∞ criteria in order to ensure attenuation of process disturbances and output noise. The interval observer scheme is experimentally evaluated by estimating the upper and lower bounds of a torque load perturbation, a friction parameter and a fault in the input voltage of a permanent magnet DC motor.

Highlights

An observer is an scheme for state estimation through the system input and output measurements
Many advantageous opportunities arise when interval observers are designed for processes modeled in T–S form: (i) Pole placement via linear matrix inequalities (LMI) regions is considered to compute the observer gains, in contrast with many nonlinear approaches where the observer gains are heuristically tuned; (ii) a standard methodological procedure can be used to compute the observer gains; (iii) many approaches originally conceived for linear systems can be extended to T–S systems
For the unknown input T–S interval observer design, the criterion H∞ for the robust estimation problem of T–S system is considered to minimize the effects of noise and disturbance signals: lim ε(k ) = 0 for δ(k) = 0 ∀k, (35)

Summary

Introduction

An observer is an scheme for state estimation through the system input and output measurements. Many advantageous opportunities arise when interval observers are designed for processes modeled in T–S form: (i) Pole placement via linear matrix inequalities (LMI) regions is considered to compute the observer gains, in contrast with many nonlinear approaches where the observer gains are heuristically tuned; (ii) a standard methodological procedure can be used to compute the observer gains; (iii) many approaches originally conceived for linear systems can be extended to T–S systems. The main contribution of this paper consists in the design of an interval observer that performs a simultaneous estimation of unmeasured states, actuator and system faults for processes modeled in T–S form with uncertainties. These cases are typical faults that, if not detected in time, can become catastrophic failures such as short-circuits or machinery damages due to damaged bearings

Problem Formulation and Preliminaries

Observer Design

Case Study

Experimental Tests

Conclusions