Mickael Rodrigues

Observer-based fault tolerant control design for a class of LPV descriptor systems

This paper presents a new Fault Tolerant Control (FTC) methodology for a class of LPV descriptor systems that are represented under a polytopic LPV form. The aim of this FTC strategy is to compensate the effects of time-varying or constant actuator faults by designing an Adaptive Polytopic Observer (APO) which is able to estimate both the states of the system and the magnitude of the actuator faults. Based on the information provided by this APO, a new state feedback control law is derived in order to stabilize the system. Stability conditions of the designed observer and the state-feedback control are provided and solved through a set of Linear Matrix Inequalities (LMI) under equality constraints. The performance of the proposed Fault Tolerant Control scheme is illustrated using a two-phase flash system.

State Estimation for Polytopic LPV Descriptor Systems: Application to Fault Diagnosis

Abstract In this paper, the design of a polytopic Unknown Input Observer (UIO) for polytopic Linear Varying Parameter (LPV) descriptor systems is investigated. The method presented is based on the representation of affine LPV descriptor systems where parameters evolve in a hypercube domain. The considered polytopic UIO is able to estimate the states of the system in spite of the presence of unknown inputs. This approach is also applied to actuator fault detection, isolation and estimation. Stability conditions of such observer are expressed in terms of Linear Matrix Inequalities (LMI). An example illustrates the effectiveness and performances of such polytopic LPV observer.

A multi-model approach to Saint-Venant equations

Abstract This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.

Robust H ∞ fault diagnosis for multi-model descriptor systems: A multi-objective approach

A large class of engineering systems are modeled by coupled Differential and algebraic Equations (DAEs), called also singular or descriptor systems. Due to the singular nature of the algebraic equations, descriptor systems do not satisfy the standard state-space description and require special techniques. So far, the literature has concentrated mostly on the numerical analysis and control aspects of descriptor or DAEs systems. This paper investigates the problem of faults detection in nonlinear DAE systems described by a multi-model with the design of an Unknown Input Observer. The stability and robustness properties of the fault diagnosis scheme are investigated in term of LMIs. A simulation example illustrating the ability of the proposed fault diagnosis architecture to detect multiple faults is presented.

A Proportional Integral Feedback for Open Channels Control trough LMI Design

This paper deals with the controller design for systems described by Partial Differential nonlinear Equation (PDE) of Saint-Venant. The proposed approach is based on Multi-Models concept which takes into account Linear Time Invariant models defined around a set of operating points. This method allows to describe the dynamic of this nonlinear system over a wide operating range. By the means of an Internal Model Boundary Control (IMBC), the design of a Proportional Integral (PI) feedback is performed through Linear Matrix Inequality (LMI). The method is applied to simulation and also compared to previous experimentations on a micro-channel, illustrating the new theoretical results developed in the paper.

Sensor Fault and Unknown Input Estimation Based on Proportional Integral Observer Applied to LPV Descriptor Systems

In this paper a detection, isolation and fault estimation scheme using a Proportional- Integral (PI) Observer that provides a robust estimation against measurements noise and unknown inputs is presented. The main contribution consists in the synthesis of a PI-Observer for descriptor LPV systems, can be useful not only for state estimation, but also to estimate sensor faults and unknown inputs. The proposed PI-Observer can provide an alternative fault diagnosis scheme. Once a fault is detected, a bank of observers is activated for the purpose of fault isolation. This scheme reconstructs the sensor faults based on augmented state equations where an auxiliary state is assigned to represent the dynamic behavior of the fault. An illustrative example is presented in simulation.

Design of an active fault tolerant control for nonlinear systems described by a multi-model representation

In this paper, a new active fault tolerant control (FTC) strategy is developed to nonlinear systems described by multiple linear models to prevent the system deterioration by the synthesis of adapted controllers. When a fault is detected by the fault detection and diagnosis scheme, the reconfigurable controller is designed automatically using a robust gain scheduling strategy. The main contribution concerns the design of state feedback gains through LMI both in fault-free and faulty cases in order to preserve the system performances over a wide operating range. For each separate actuator with which the system is robustly stabilizable, a robust pole placement is designed by pole clustering. The effectiveness and performances of the method have been illustrated in simulation considering a classical nonlinear benchmark

Fault Diagnosis Based on Adaptive Polytopic Observer for LPV Descriptor Systems

This paper presents an Adaptive Polytopic Observer (APO) design in order to develop a fault detection and estimation method dedicated to polytopic Linear Parameter Varying (LPV) descriptor systems under time-varying actuator faults. This paper extends a Fault Diagnosis (FD) method developed for regular LTI systems to polytopic LPV descriptor systems. The design and stability conditions of this APO are provided. The design is formulated through LMI (Linear Matrix Inequalities) techniques under equality constraints. The performances of the proposed fault detection and estimation scheme are illustrated using an electrical circuit.

Sensor Fault Estimation Filter Design for Discrete-time Linear Time-varying Systems

Abstract This paper proposes a sensor fault diagnosis method for a class of discrete-time linear time-varying (LTV) systems. In this paper, the considered system is firstly formulated as a descriptor system representation by considering the sensor faults as auxiliary state variables. Based on the descriptor system model, a fault estimation filter which can simultaneously estimate the state and the sensor fault magnitudes is designed via a minimum-variance principle. Then, a fault diagnosis scheme is presented by using a bank of the proposed fault estimation filters. The novelty of this paper lies in developing a sensor fault diagnosis method for discrete LTV systems without any assumption on the dynamic of fault. Another advantage of the proposed method is its ability to detect, isolate and estimate sensor faults in the presence of process noise and measurement noise. Simulation results are given to illustrate the effectiveness of the proposed method.

Design of a Proportional Integral Control Using Operator Theory for Infinite Dimensional Hyperbolic Systems

This brief considers the control design of a nonlinear distributed parameter system in infinite dimension, described by the hyperbolic partial differential equations of de Saint-Venant. The nonlinear system dynamic is formulated by a multimodels approach over a wide operating range, where each local model is defined around a set of operating regimes. A new proportional integral feedback is designed and performed through bilinear operator inequality and linear operator inequality techniques for infinite dimensional systems. The new results have been simulated and also compared with previous results in finite and infinite dimension, to illustrate the new theoretical contribution.