Search

This paper characterises and analyses the minimum detectable fault (MDF) (named generalised MDF here) for multiple multiplicative actuator faults based on set-separation constraints of healthy and faulty residual sets for discrete-time linear parameter varying (LPV) systems with bounded inputs and uncertainties. First, multiple multiplicative actuator faults are equivalently transformed into the form of multiple additive actuator faults for the sake of obtaining the simplified faulty residual set explicitly. Then, two different generalised MDF for different multiple actuator faults are, respectively, defined, which can be computed via solving simple linear programming (LP) problems. Moreover, we propose three detectability conditions to guarantee the detection of multiple multiplicative actuator faults by using the invariant set-based method. Finally, we provide effective selection guidance for the detection of different multiple multiplicative actuator faults by systematically analysing the conservatism and characteristics of these three guaranteed detectability conditions. At the end of this paper, an electrical circuit example is used to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: Optimal 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. [ABSTRACT FROM AUTHOR]

This paper proposes an invariant set-based robust fault detection (FD) and optimal fault estimation (FE) method for discrete-time linear parameter varying (LPV) systems with bounded uncertainties. Firstly, a novel invariant-set construction method for discrete-time LPV systems is proposed if and only if the system is poly-quadratically stable, which need not satisfy the condition that there must exist a common quadratic Lyapunov function for all vertex matrices of the system compared to the traditional invariant-set construction methods. Furthermore, by using a shrinking procedure, we provide minimal robust positively invariant (mRPI) set approximations that are always positively invariant at each step of iteration and allow a priori desired precision to obtain a high sensitivity of FD. Owing to the existence of invariant set-based FD phase, the assumption that the initial faults should be bounded by a given set can be avoided for FE. We compute an optimal parametric matrix gain by minimising the Frobenius norm-based size of the corresponding FE set to obtain the optimal FE performance. Theoretically, any trajectory in the FE tube can be chosen as a specific-value estimation for the real fault signals. Finally, a vehicle dynamics system is used to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]