Adaptive Fault Estimation and Fault Tolerant Control for Polynomial Systems: Application to Electronic and Mechanical Systems

A Messaoudi,A El Hajjaji,H Gassara

doi:10.1155/2021/6342604

A Messaoudi, A El Hajjaji + Show 1 more

Open Access

https://doi.org/10.1155/2021/6342604

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Abstract

This paper presents a sum of squares (SOS) approach for active fault tolerant control (AFTC) of nonlinear polynomial systems. A polynomial adaptive fault estimation algorithm for polynomial systems is firstly proposed. Then, sufficient conditions for the existence of the fault estimator are given in terms of SOS which can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. Based on the obtained online fault estimation information, a fault-tolerant control strategy is designed for both compensating the effect of actuator faults in real time and stabilizing the closed-loop system. Finally, tunnel diode circuit and mass-spring-damper systems are used to demonstrate the applicability of the proposed approach.

Highlights

E latest developments in sum of squares (SOS) programming techniques make it possible to deal directly with polynomial systems
In the direction of investigating several classes of time delay polynomial systems, some results have been proposed in the literature, e.g., stabilization by Gassara et al [14]; control under actuator saturation by Gassara et al [15], and observer-based control for positive polynomial systems with time delay by Iben Ammar et al [16]. ese various results are presented in terms of sum of squares (SOS), in which conditions are numerically solved via the recently developed SOSTOOLS by Prajna et al [17]
We have developed an adaptive actuator FTC strategy for a class of polynomial models, and sufficient analysis and design conditions in terms of SOS are proposed

Summary

Problem Formulation

Consider the following polynomial model with additive actuator faults: x_(t) A(ζ(t))x + B(ζ(t))(u(t) + f(t)),. Y(t) Cx(t), where x(t) ∈ Rnx is the state vector, u(t) ∈ Rnu is the input vector, f(t) ∈ Rnf is the additive actuator fault vector, ζ(t) is available, such as the partial system state variables and the system outputs as in Pang and Zhang’s study [22], y(t) ∈ Rny is the measurement output vector, C is constant real matrix, and A(ζ(t)) and B(ζ(t)) are polynomial matrices in ζ(t). E derivative of f(t) with respect to time is normbounded:. The following polynomial adaptive fault diagnosis observer is considered:. To lighten the notation, we will drop the notation with respect to time t. We will employ x, x􏽢, and ζ instead of x(t), x􏽢(t), and ζ(t), respectively

Main Results

Example 1

Example 2

Conclusion