Fault-tolerant control system design

Abstract

This thesis presents several fault/failure-tolerant switching control system structures and proposes design methodologies for systems vulnerable to actuator and sensor faults/failures. The working effectiveness of each actuator/sensor (which is assumed to be known by a fault detection scheme) is represented as a time varying parameter \delta(t). Distinct values/factors are set to \delta(t) in order to model components with different functional status and the number is s. If the total number of components is m, then at any time t, there are s^m fault scenarios. The resulting controller is reconfigurable but with a special structure that the system matrices are fixed while the switching is on the parameter \delta(t). Recognizing that it is unlikely that all components will have serious faults at the same time, the design objective is to maintain an acceptable performance level only for a group of faulty systems imposed by a tolerance measure. At the same time, the no-fault nominal performance is optimized.

Several relaxation procedures for the fault/failure-tolerant control are proposed to overcome the combinatorial nature of the problem. Sufficient conditions are derived to guarantee that a matrix inequality, which is a quadratic function of a linear fractional function of a structured matrix \Delta, is satisfied for all \Delta satisfying a set of quadratic matrix equalities and inequalities. This new robustness result extends the S-procedure to a wider setting by tackling structured uncertainties that satisfy constraints other than a norm bound and problems that require quadratic rather than linear inequalities. The extension is given in terms of general matrix products and defines dual variables that are required to satisfy definiteness properties for these products. Weaker commutation and definiteness assumptions for standard and block Hadamard matrix products are derived. We also introduce a new generalized block matrix product and extend the Schur product theorem for this product. The weaker constraints on the dual variables, together with the above fault/failure tolerance measure give significantly less conservative designs than current approaches.