Actuator and sensor fault estimation based on a proportional multiple‐integral sliding mode observer for linear parameter varying systems with inexact scheduling parameters

Abstract

This article proposes an approach for the estimation of states, actuator, and sensor faults in nonlinear systems represented by a polytopic linear parameter varying (LPV) system with inexact scheduling parameters. In the traditional LPV approaches, the scheduling variables are considered to be perfectly known.However, in practical applications, their measurement may contain precision and calibration errors or noise that can affect the performance of the diagnostic systems. Therefore, this work proposes the design of a proportional multiple-integral sliding mode observer for fault diagnosis (FD) that copes with LPV systems with inexact scheduling parameters. Due to the introduction of some nonlinear functions, the proposed observer is a nonlinear parameter varying system for which stability and robustness performance are formulated using the Lyapunov technique and a H ∞ performance criterion. It is shown that the design conditions boil down to a set of linear matrix inequalities whose solution allows computing the observer gain matrix along with the tunable parameters of the nonlinear functions. Results obtained using the simulator of an octocopter-type unmanned aerial vehicle are used to demonstrate the applicability and performance of the proposed FD scheme. K E Y W O R D Sfault diagnosis, linear matrix inequalities, nonlinear parameter varying systems, proportional multiple-integral sliding mode observer INTRODUCTIONModern control systems are prone to faults, which can damage the systems themselves or the environments in which they operate. For this reason, fault diagnosis (FD) algorithms become essential, since they enable fault-tolerant actions that minimize the effect of faults and improve the overall system's reliability and safety. An FD algorithm can be seen as a two-step process in which at first the fault is detected, that is, a Boolean logic value about the presence of a fault is provided, 8420

Fault Diagnosis Algorithm Based on Adjustable Nonlinear PI State Observer and Its Application in UAV Fault Diagnosis

“…Similarly, if h e y is chosen appropriately for any t > 0, it is easy to get a result for Equation (16). The convergence rate of the state observer with Equation ( 16) is better than that of the PI state observer with Equation (4).…”

“…In the simulation, the overshoot of fault estimation process was obviously reduced, and the robustness of PI control system was effectively improved. In References [15][16][17], a fault estimation method based on PI observer and considering imprecise scheduling parameters is proposed for a class of nonlinear systems described by linear variable parameter mathematical model.…”

Simultaneous actuator and sensor fault reconstruction of singular delayed linear parameter varying systems in the presence of unknown time varying delays and inexact parameters

“…29 The idea of adding multiple integrals is also applied in SMO design for LPV systems. 30 The designed PDIUIO in this article has the advantage of not needing to assume that the actuator faults to be piecewise constant which is normally needed in the design of traditional proportional integral unknown input observers (PIUIOs); thus, it can be applied for diagnosis of a broader class of faults. The assumption which is needed for designing the PDIUIO is that the second derivative of actuator faults should be almost zero that is satisfied for piecewise constant faults (including abrupt faults), incipient faults and slow time-varying faults.…”

Robust Polytopic-LPV Body-Weight-Dependent Control of Blood Glucose in Type-1 Diabetes

“…That approach assumes that the absolute value of the error between the actual and inexactly measured scheduling parameters is less than a proportion of the actual value. In [34] and [35], it is considered that inexactly measured parameters are proportional to their actual value by a time-varying unknown coefficient. Then, the inexactly measured parameter LPV system is represented by an exactly measured system with uncertainties.…”

“…Then, the inexactly measured parameter LPV system is represented by an exactly measured system with uncertainties. In [34] and [35], a constant upper bound for uncertainties is suggested, meanwhile in [36], the uncertainties satisfy a Lipchitz condition. In [37], the problem of inexactly measured scheduling parameters is considered by taking into account additive and multiplicative relation between the actual and inexactly measured parameters.…”