Set theoretic fault tolerant control for classes of nonlinear systems

Automatic control systems are vulnerable to faults due to malfunction of the sensors, actuators or other components in the plant. This faulty operation affects the performance and may cause system failures if no detection and action are taken at an early stage. For this reason, most automatic control systems particularly safety-critical systems integrate fault tolerance characteristics in their automatic control design. The main purpose of fault tolerant control (FTC) systems is to provide information of the fault situation and perform modifications in the controller to minimise or eliminate the effects of the faults. The focus of this thesis is to develop methodologies for analysis and design of FTC schemes for nonlinear systems, since realistically, systems exhibit nonlinear behaviours. Inspired by the active FTC strategy which guarantees optimal performance, the proposed methodologies combine set-based fault detection and isolation (FDI) algorithms and controller reconfiguration mechanisms. The FTC schemes are designed for two classes of nonlinear systems, Lure systems and feedback-linearisable nonlinear systems, which are assumed subject to process disturbances, noisy measurements and under sensor or actuator faults. The developed set-based FDI utilises the concept of invariant set and ultimate bound to characterise the healthy and faulty behaviours of the systems. The analytical tools redefine the nonlinearities in the dynamics as a time-varying parameter to represent the system as linear parameter varying (LPV) model. This LPV-embedding approach allows the use of linear design tools in the design of state feedback controllers. The computation of invariant sets and ultimate bounds is based on the convex polytopic description and componentwise analysis for the closed-loop dynamics. The FDI unit is then combined with controller reconfiguration mechanisms for which we consider three different approaches; (i) fault estimation and controller adaptation, (ii) switching between pre-designed multiple controllers, and (iii) virtual actuators. Analysis of the overall FTC schemes is performed to establish conditions to guarantee the closed-loop stability and fault tolerance properties. Indeed, the presented results establish conditions in terms of system matrices and parameters that guarantee the existence of invariant sets and ultimate bounds for the classes of nonlinear systems considered. Several numerical examples of physically motivated systems are provided which show that the proposed FTC schemes can be designed to guarantee correct fault detection, fault isolation and reliable reconfiguration while preserving the system's performance and closed-loop stability.