Optimal robust fault detection of discrete‐time LPV systems with measurement error‐affected scheduling variables combining ZKF and pQP

Abstract

SummaryOptimal robust state estimation (SE) and fault detection (FD) methods of discrete‐time linear parameter varying systems with measurement error‐affected scheduling variables are proposed under the boundedness assumption of system uncertainties. By using the weighted Frobenius norm of the generator matrix of SE zonotope to characterize the set size, the optimal observer gain can be computed by a zonotopic Kalman filter (ZKF) procedure for the purpose of observation. Meanwhile, by minimizing the influence of system uncertainties while maximizing that of faults on SE to enhance the sensitivity of FD, the optimal FD criterion is characterized based on an on‐line fractional programming problem, which can be equivalently transformed into a parametric quadratic programming (pQP) problem. The pQP problem can be efficiently solved by searching the root of its nonlinear characteristic equation using secant method. In general, as long as sensors with sufficiently high precision are equipped to measure the scheduling variables, the bounds of measurement errors of scheduling variables can be less conservative than those direct bounds of scheduling variables, which can reduce the conservatism of FD or SE in this way. At the end of this article, a case study based on a practical circuit model is used to illustrate the effectiveness of the proposed method.