Dynamic event-triggered fault estimation and sliding mode fault-tolerant control for networked control systems with sensor faults
Introduction
Networked control systems(NCSs) are feedback control systems connected by network, which are composed of actuators, sensors and controllers [1]. The system components are usually spatially isolated from each other, operating in an asynchronous manner, and communicating over a wide area by wired and wireless links [2]. Because of their advantages of low cost, strong flexibility, and simple installation and maintenance, NCSs have been widely concerned and studied [3]. However, some challenging problems inevitably arise due to the addition of communication network, such as transmission delay, packet dropouts and network bandwidth limitation, which may reduce the performance of the system or even lead to system instability. In recent years, the stability and performance analyses of NCSs have been extensively studied and made some progress [4]. In [5], a novel high-order adaptive sliding-mode control algorithm is proposed to study the problem of tracking control of networked control systems with external disturbance and network-induced disturbance. The fault-tolerant control for NCSs with additive fault and external disturbance are researched in [6], and the results are verified by networked aircraft engine model.
It is worth noting that although NCSs have many advantages, the communication resource is limited due to the limitation of network bandwidth. Traditional time-triggered control requires communication resource to be updated at every moment, which wastes a lot of communication resource that do not need to be transmitted [7]. Compared with time-triggered, event-triggered mechanism can save communication resource [8]. Therefore, the event-triggered mechanism has received extensive attention. For example, a new neural-network event-triggering strategy is designed to investigate the problem of uncertain descriptor systems with exogenous disturbance [9]. In [10], aiming at the consensus problem of multi-agent systems with general linear dynamics under a general directed graph, two observer-based output feedback event-triggered control schemes are presented to solve the problem. However, the above event-triggered schemes are all static event-triggered schemes (SETSs), because it only relates to the relationship between the current system output and the error about the current system measurement value and the latest transmission value. And also the event-triggered parameter is a fixed value [11]. To further reduce the burden on the network, a new class of event triggering mechanisms for event-triggered control systems is proposed in [12]. The dynamic event-triggered scheme(DETS) is characterized by the introduction of an internal dynamic variable, which has been extend to stochastic systems [13], uncertain fuzzy systems [14] and switched systems [15]. Such as, in [16], to reduce networks burden, a dynamic event-triggered mechanism is firstly introduced to the design of cluster synchronization controllers for a class of switched complex networks. The problem of non-fragile H∞ state estimation for a class of discrete-time complex networks is investigated under a dynamic event-triggered mechanism [17]. In [18], a novel event-triggered control strategy for a class of nonlinear feedback systems is presented to guarantee a finite -gain and a strictly positive lower bound on the inter-event times.
In addition, the system will inevitably fail due to long-term uninterrupted work or human error. For example, when a sensor or actuator failure that produces undesirable effects occurs in a system, the traditional control scheme cannot work properly and may lead to degraded performance or even system instability [19], [20]. Therefore, fault-tolerant control(FTC) opens up a new way to ensure the effective operation of the system and improve the safety and reliability of the system in the event of a fault, which has attracted extensive attention from scholars [21], [22]. So far, there have been some effective fault-tolerant controller design methods, such as sliding mode fault-tolerant control [23], adaptive fault-tolerant control [24], etc. Among them, sliding mode control(SMC) is applied more and more widely in switched systems [25], complex network [26], nonlinear systems [27] and fuzzy systems [28]. For example, an adaptive fuzzy hierarchical sliding mode control method is proposed to deal with the control problem of under-actuated switched nonlinear systems [29]. In [30], a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. The design problem of asynchronous output feedback controller is researched by sliding mode for fuzzy Markovian jump systems [31].
In the above work, at present, there are few research results on dynamic event-triggered sliding mode fault-tolerant controller designed for networked control systems with sensor faults. In [32], according to using an integrated design of static event-triggered fault/state estimator with a fault-tolerant controller, the problem of event-triggered active fault-tolerant control of linear systems is investigated. Static event-triggered fault observer and FTC for networked control systems with system fault and external disturbance is studied [33]. However, the problem of fault estimation and sliding mode fault-tolerant control for networked control systems with sensor faults and external disturbances under dynamic event-triggered scheme has not been studied in the existing works.
Based on the above discussion, this paper studies fault estimation and sliding mode fault-tolerant controller design for networked control systems with sensor faults and external disturbances under dynamic event-triggered scheme. The main contributions of this paper can be summarized as follows: (1) The system state is reconstruct, and a DETS is designed to conserve the limited communication resources considering network delay, system fault and external interference. (2) Considering the influence of network delay, dynamic event-triggered scheme and system fault, fault/state observer is designed and sliding mode surface is constructed. (3) By the Lyapunov-Krasovskii function, a novel design condition in the form of linear matrix inequality is obtained via H∞ optimization problem to analyse system stability and gain parameters. And considering dynamic event-triggered method, a sliding mode controller is designed to ensure that the trajectories of the system can reach the sliding surface.
The rest of this paper is summarized as follows. The problem formulation is presented in Section 2. The main results are provided in Section 3. The simulation results to illustrate the effectiveness of the method is given in Section 4. Finally, Section 5 concludes this paper. In order to facilitate reading, some notations and descriptions are listed in Table. 1.
Section snippets
Plant
Consider the following discrete-time systems with sensor fault:where and are the system state vector and measured output vector, respectively. devotes control input, indicates the unknown sensor fault and represents the disturbance in the system. Here A0, B0, C0, E0 and M0 are matrices of appropriate dimensions. Assumption 2.1 The pairs (C0, A0) and (A0, B0) are observable and controllable respectively, rank
Main results
In this section, the dynamic event-triggered fault/state observer is designed to estimate system the system state and fault at the same time. Then, a sliding mode surface under event-triggering is constructed. Moreover, the novel conditions are obtained to ensure that the overall NCSs tend to be stable with H∞ performance. Finally, a sliding mode FTC law is constructed to guarantee that the trajectories of system states can be arrived to the sliding surface in a finite time.
Simulation results
In the section, two examples are supplied to verify the effectiveness of the method. First, the fault-tolerant controller designed in the paper shows better performance compared with the controller in [33]. Besides, The model of an aircraft provides more evidence for the effectiveness of the method.
Conclusion
The problem of fault estimation and sliding mode fault-tolerant control(FTC) for networked control systems with sensor faults under dynamic event-triggered scheme is investigated in this paper. First, sensor faults are processed into system states via filtering. Then, the fault/state observer is designed and a sliding mode surface is constructed considering system faults and network delay. Based on the Lyapunov-Krasovskii function, the stability conditions of the system in the form of linear
Acknowledgment
The work was supported in part by the National Science and Technology Major Project of China under Grant 2017-V-0010-0061, and in part by the National Natural Science Foundation of China under Grant (61803153, 51676068, 71801196).
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