Robust Residual Generator Synthesis for Uncertain LPV Systems Applied to Lateral Vehicle Dynamics

Abstract

In the residual generator design problem, a method to ensure the residual's fault sensitivity is to minimise the difference between the fault-to-residual response and a reference model. However, an inappropriate reference model with unattainable ratios between sensitivities from multiple faults can have a detrimental impact on disturbance decoupling performance. This impact is reduced in the proposed design method for uncertain linear parameter-varying (LPV) systems by optimising these sensitivity ratios. The synthesis method involves solving an induced-L2$ robust estimator synthesis problem, in which parameter uncertainty is handled via integral quadratic constraints. Optimisation of the sensitivity ratios is integrated into the ensuing semi-definite program. The resulting residual generator synthesis method achieves perfect decoupling when this is possible, and more generally improves performance compared to when arbitrary references are used, without the pre-computation of an attainable reference as seen in other approaches. The effectiveness of this method is demonstrated in a vehicle lateral dynamics application and validated using experimental data.