Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems

Abstract

In this paper a new integrated observer-based fault estimation and accommodation strategy for discretetime piecewise linear (PWL) systems subject to actuator faults is proposed. A robust estimator is designed to simultaneously estimate the state of the system and the actuator fault. Then, the estimate of fault is used to compensate for the effect of the fault. By using the estimate of fault and the states, a fault tolerant controller using a PWL state feedback is designed. The observer-based fault-tolerant controller is obtained by the interconnection of the estimator and the state feedback controller. We show that separate design of the state feedback and the estimator results in the stability of the overall closed-loop system. In addition, the input-tostate stability (ISS) gain for the closed-loop system is obtained and a procedure for minimizing it is given. All of the design conditions are formulated in terms of linear matrix inequalities (LMI) which can be solved efficiently. Also, performance of the estimator and the state feedback controller are minimized by solving convex optimization problems. The efficiency of the method is demonstrated by means of a numerical example.

Characterization of the minimum detectable fault of interval observers by using set-invariance theory

“…According to (12), the sensitivity of the residual to a given fault is needed. Thus, the residual affected by the output sensor fault can be obtained as…”

“…Due to unexpected existence of perturbations, disturbances and noises, estimating the fault value is quite difficult in a faulty system by using current FDI approaches [1], [8]. Therefore, the estimation of the magnitude of the fault, known as fault estimation, and its related approaches has been started to be researched, see e.g., [12], [17], [8] and the references therein. Moreover, having the accurate fault information can increase designing accuracy of the controller with FTC techniques [18].…”

Iterative Learning Fault Estimation Design for Nonlinear System with Random Trial Length

“…Over the past decades, observer-based fault estimation [12,13] has received considerable attention both in academic research and in industrial application domains. It has made significant progress and covered a wide scope of research issues such as linear systems [14], nonlinear systems [15], time-delay systems [16], uncertain systems [17], multiagent systems [18] and fuzzy systems [19].…”

Robust Fault Reconstruction in Discrete-Time Lipschitz Nonlinear Systems via Euler-Approximate Proportional Integral Observers

“…On the other hand, it is well known that fault reconstruction for nonlinear discrete-time systems is considerably practical and challenging because the nonlinearities inherently exist in nature, and most continuous-time systems are implemented digitally in practical applications. Under the assumption that nonlinear discrete-time models are accurate, numerous fault-reconstructing strategies have 2 Mathematical Problems in Engineering been reported [12][13][14][15]. However, the availability of the exact models, originated from discretization of a continuous-time plant, is usually unrealistic.…”