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 minimize 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 systems by optimizing these sensitivity ratios. The synthesis method involves solving an induced- $\mathcal {L}_{2}$ robust estimator synthesis problem, in which parameter uncertainty is handled via integral quadratic constraints. Optimization of the sensitivity ratios is integrated into the ensuing a semidefinite program. The resulting residual generator synthesis method achieves perfect decoupling when this is possible, and more generally improves performance compared with when arbitrary references are used, without the precomputation 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.