Simultaneous fault detection and antisaturated control based on dynamic observer for inverted pendulum control system

This article studies the H∞ fault estimation (FE) problem for linear discrete time‐variant systems with actuator and sensor saturations. To handle the saturation nonlinearities for FE problem, a pair of an auxiliary linear model and an associated performance function augmenting from the conventional H∞ performance index are constructed. Based on this pair, the original FE problem is readdressed as a two‐step optimization issue with an indefinite quadratic cost function. For a feasible optimization solution, the partial equivalence between a stationary point for a quadratic optimization problem and a projection for vectors in indefinite inner‐product space is utilized. A Krein‐space based inner product interpretation for the indefinite cost function is established and optimal linear estimation technique is employed to derive the stationary point of the aforementioned indefinite quadratic cost function. The existence condition of the fault estimator is explicitly obtained, and the fault is reconstructed analytically via a forward recursion algorithm. Two examples are given to show the effectiveness of the proposed FE scheme.

“…Here,

π_{i, \max}

denotes the i th element of the saturation level

π_{\max}

. Accordingly,

σ (\cdot)

with subscripts u and y , namely,

σ_{u} (\cdot)

and

σ_{y} (\cdot)

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fault estimation for discrete time‐variant systems subject to actuator and sensor saturations

Liu

et al. 2020

“…However, most FDI‐based active FTC (such as References 13–15) designs the FD, fault isolation (FI) and FTC modules/units separately, and have not considered the effect of FDI on FTC (such as the critical reaction time). There have been some works that consider the time delay from FDI, for example, Pang et al 16 focused on the problem of simultaneous FD and antisaturated control for an inverted pendulum control system, where the detector and controller were integrated by solving a bank of matrix inequalities; Shen et al 17 quantitatively analyzed the effect of the time delay due to fault diagnosis on the faulty system's performance; Zhang et al 18,19 presented a unified methodology for detecting, isolating and accommodating faults in a class of nonlinear dynamic systems, where the nominal controller (NC) was reconfigured after FD and before FI in order to ensure the boundedness of system states, and Mu et al 20 developed an FD‐based FDI scheme for distributed parameter system. It is noted that full states were assumed to be available in References 17–20.…”

Section: Introductionmentioning

confidence: 99%

Active fault tolerant control based on adaptive interval observer for uncertain systems with sensor faults

Wang

Tan

Wang

et al. 2021

In this article, we present an active fault tolerant control scheme based on fault detection and isolation (FDI) for a class of uncertain systems subject to sensor faults. The FDI unit consists of a fault detection (FD) module and a fault isolation (FI) module, to determine when and where the sensor fault happens. It is noted that the FD module is based on a proposed adaptive interval observer where adaptive parameters instead of conservative uncertainty bounds are used, as a result, the sensitivity to faults is improved. When the FD module detects a fault, a compensation controller (CC) and an FI module are activated. The CC is designed to maintain some level of performance assuming all sensors are faulty. After the FI module determines the location of the fault, a reconfigured controller is activated to give improved performance with reduced conservatism. Importantly, the unmeasurable states and faulty output are approximated as a linear combination of their upper and lower bounds, and linear parameter are determined by adaptive laws. Finally, a simulation example is utilized to verify the effectiveness of the proposed scheme.

“…A large amount of intelligent FTC algorithms have been developed including sliding mode technique, 3 fuzzy control strategy, 4 neural networks theory, 5 and adaptive backstepping technique 6 . In addition, many researchers are committed to applying FTC methods to practical systems, for example aerospace aircrafts, 7 underactuated mechanical systems, 8 power equipments, 9 unmanned autonomous helicopters, 10 etc. In practice, since finite‐time stability 11 exhibits some appealing features such as higher accuracies, better robustness as well as faster convergence, 12‐14 the attention of recent research on the FTC scheme has moved to the finite‐time control issue.…”

Section: Introductionmentioning

confidence: 99%

Event‐triggered adaptive fixed‐time output feedback fault tolerant control for perturbed planar nonlinear systems

Zhu

Zhang

Xin

et al. 2021

This paper considers an event‐triggered adaptive fixed‐time output feedback fault tolerant control problem for a class of uncertain planar nonlinear systems, in which the actuator has an unknown drift fault and the loss of effectiveness fault. Firstly, by using the adaptive backstepping technique and event‐triggered theory, a constructive event‐triggered adaptive fixed‐time state feedback controller is presented under a generalized Lipschitz continuous condition. Secondly, for the unmeasured state, a continuous fixed‐time observer is constructed. It is shown that the global practically fixed‐time stability of the closed‐loop systems is ensured by the bilimit homogeneity technique and Lyapunov theory analysis. Moreover, the system is demonstrated by contradiction to be nonzeno. Finally, the fan speed control system is constructed to demonstrate the validity of the proposed strategy and the application of the general systems.