Fault tolerant control of systems with convex polytopic uncertainty and LPV description

This thesis aims at developing new methodologies in analysis and design of FTC for systems with model uncertainties. The proposed robust FTC schemes guarantee robust stability of the integrated system in the entire uncertainty domain in the presence of unknown bounded noises and disturbances under a wide range of sensor or actuator fault scenarios. The FTC designs proposed in this thesis integrate set-based fault detection and isolation [FDI] mechanisms with controller reconfiguration [CR] modules based on virtual sensors and virtual actuators. The proposed FDI principle in this work is based on the computation of sets to which appropriately defined residual variables move or converge both under faulty and healthy operation. We first present a strategy for the problem of sensor FTC of linear time invariant (LTI) systems with disturbances but no other model uncertainties. As mentioned above, the strategy combines a set-based FDI technique and the virtual sensor approach to CR. This complements an existing similar technique using virtual actuators for the dual problem of actuator faults in perturbed LTI systems. In the next step, we study the FTC design for systems with structured model uncertainties, where the uncertainty model can be described by an element – e.g. components of a system matrix in the state-space realisation – lying in some pre-specified uncertainty set. Among structured uncertainty models, we focus on convex polytopic model uncertainties both for the cases where its polytopic property is the only information available on the uncertainty and for the case of Linear Parameter Varying [LPV] model description, where the uncertainty is assumed to be described as a function of a measurable time-varying parameter. The LPV description can be used in modelling a wide range of non-linear systems and hence has received major attention from the identification and control research community. In this research we extend the invariant-set based FDI and the virtual sensor based methodology to the systems with polytopic LPV model description. We show that by employing self-scheduling parameters in fault tolerant control design, where the parameters of the control system and the virtual sensor are scheduled in real time according to the current value of the varying parameter, the robust stability of the integrated closed-loop system under some assumptions is guaranteed. The robust FDI technique proposed for LPV systems is based on the separation of relevant sets defined for measurable residual signals, which are computed using the virtual sensors and taking into account system disturbances and model uncertainty. To develop a robust FTC scheme for systems with convex polytopic uncertainties where the uncertainty is not a function of a measurable parameter, the use of scheduled control is no longer possible. Hence, the controller and the virtual sensor are designed for the centre of the uncertainty polytope, which inevitably introduces an error in the controller reconfiguration. Another study carried out as part of this work focuses on the design of a robust FTC strategy for systems with polytopic model uncertainty description under a finite set of considered actuator faults. In parallel with the sensor fault case, the proposed actuator FTC strategy combines a robust FDI based on an invariant-set approach with controller reconfiguration based on the use of a bank of virtual actuators. In addition, we extend the actuator FTC analysis to the case of convex polytopic LPV systems under errors in the measurement of the varying parameter. In this analysis conditions are derived that guarantee closed-loop stability of the overall virtual-actuator based FTC system when the varying parameter is not exactly known but measured with bounded errors. In summary, this work develops new methods for the analysis and design of FTC for systems with model uncertainties; the FTC schemes proposed for either sensor or actuator faults guarantee robust stability of the integrated system in the entire uncertainty domain in the presence of unknown bounded sensor noises, process disturbances, and varying parameter measurement errors, under a wide range of fault scenarios.