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Development of a guaranteed minimum detectable sensor fault diagnosis scheme

Witczak Marcin, Pazera Marcin, Majdzik Paweł, Matysiak Ryszard

International Journal of Applied Mathematics and Computer Science

2024

Vol. 34, no. 3

409--423

The paper deals with the estimation of sensor faults for dynamic systems as well as the assessment of the uncertainty of the resulting estimates. For that purpose, it is assumed that the external disturbances are bounded within an ellipsoidal domain. This allows considering both stochastic and deterministic process and measurement uncertainties. Under such an assumption, a fault diagnosis scheme is developed with a prescribed convergence rate and accuracy. To achieve fault estimation, a conversion into an equivalent descriptor system is utilized. The paper provides a full stability and convergence analysis of the estimator including observability analysis. As a result, a set of complementary fault uncertainty intervals is obtained, which are minimized in such a way as to obtain a minimum detectable sensor fault. The final part of the paper exhibits a numerical example concerning fault estimation of a multi-tank system. The obtained results clearly confirm the performance of the proposed estimator expressed in the minimum detectable fault intervals.

Fault tolerant multicontrollers for nonlinear systems: A real validation on a chemical process

Mejdi Sondess, Messaoud Anis, Ben Abdennour Ridha

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 1

61--74

An active sensor fault tolerant controller for nonlinear systems represented by a decoupled multimodel is proposed. Active fault tolerant control requires accurate fault estimation. Thus, to estimate both state variables and sensor faults, a discrete unknown input multiobserver, based on an augmented state multimodel, is designed. The multiobserver gains are computed by solving linear matrix inequalities with equality constraints. A multicontrol strategy is proposed for the compensation of the sensor fault and recovering the desired performances. This strategy integrates a bank of controllers, corresponding to a set of partial models, to generate a set of control laws compensating the fault effect. Then, a switching strategy between the generated local control laws is established in order to apply the most suitable control law that tolerates the fault and maintains good closed loop performances. The effectiveness of the proposed strategy is proven through a numerical example and also through a real time application on a chemical reactor. The obtained results confirm satisfactory closed loop performance in terms of trajectory tracking and fault tolerance.

Robust multiple sensor fault-tolerant control for dynamic non-linear systems: Application to the aerodynamical twin-rotor system

Pazera M., Buciakowski M., Witczak M.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 2

297--308

The paper deals with the problem of designing sensor-fault tolerant control for a class of non-linear systems. The scheme is composed of a robust state and fault estimator as well as a controller. The estimator aims at recovering the real system state irrespective of sensor faults. Subsequently, the fault-free state is used for control purposes. Also, the robust sensor fault estimator is developed in a such a way that a level of disturbances attenuation can be reached pertaining to the fault estimation error. Fault-tolerant control is designed using similar criteria. Moreover, a separation principle is proposed, which makes it possible to design the fault estimator and control separately. The final part of the paper is devoted to the comprehensive experimental study related to the application of the proposed approach to a non-linear twin-rotor system, which clearly exhibits the performance of the new strategy.