Elsevier

Applied Mathematics and Computation

Volume 359, 15 October 2019, Pages 433-455
Applied Mathematics and Computation

Fault tolerant control of UMV based on sliding mode output feedback

https://doi.org/10.1016/j.amc.2019.04.069Get rights and content

Abstract

This paper designs the robust fault tolerant controller for unmanned marine vehicle (UMV) systems with thruster faults and external disturbances via sliding mode output feedback. A comprehensive and unified fault model including thruster partial, complete and stuck faults is built for the first time. Based on input matrix full-rank decomposition technique and H technique, a sufficient condition of sliding mode in the form of linear matrix inequality (LMI) is given. Then taking advantage of adaptive mechanism, a nonlinear discontinuous control term and an output feedback controller are aimed to reduce the oscillation amplitudes of the yaw velocity error and the yaw angle. Compared with the existing methods, the general faults including time-varying stuck fault can be dealt with. Eventually, the comparative simulation results have demonstrated the effectiveness and feasibility of the presented strategy in this paper.

Introduction

With the development of global marine resources and the increasingly fierce competition of military equipment, the control of unmanned marine vehicle (UMV) systems is attracting more and more attention from research domestic and overseas. Critical technology topics of UMV include propulsion, power, positioning and software, and each issue is still under research [1]. UMV is divided into unmanned surface vehicle (USV) and unmanned underwater vehicle (UUV) [2], [3], which includes autonomous underwater vehicle (AUV) [4], [5] and remotely operated vehicle (ROV) [6], [7].

The marine vehicles are subject to breakdown, meanwhile the thruster is one of the most malfunctioning sources [8], so some different forms of fault recovery/fault tolerance exist in the control system [9]. When the UMV carry out tasks, the oscillation of yaw velocity error and yaw angle arised by external disturbances is undesired in applications [10]. For the fault tolerant control problems in different fields, the establishment of FDI mechanism [11] or fault model [12], [13] is usually considered in the basic work, and developing the fault mode for control systems is a more intuitive way by contrast. In terms of the UMV, how to establish the fault model is essential to FTC systems, and how to design a satisfactory control strategy to attenuate above oscillation amplitudes is significative and attractive.

It is well-known that the sliding mode control is an effective method of handling nonlinear systems such as the chaotic system [14], [15] and the Lur’s systems [16], [17] with unexpected faults due to its features including ease of implementation, prompt response and excellent robust ability to system uncertainties and external disturbances in practical situations [7], [18], [19]. For example, Soylu, et al. [20], [21] work on a sliding mode controller with fault-tolerant thruster allocation for ROVs, and the propeller is assumed to fail completely and partially; an actuator FTC strategy applied different techniques such as PID, backstepping and sliding mode approaches has been studied in fault-free and fault conditions for a ROV [22]. Among the most existing FTC methods of UMV [23], [24], [25], thrusters with non-fault, complete fault, and partial fault are frequently considered. However, the time-varying stuck fault is easy to occur as well and has a severe influence on the efficiency of thrusters. Therefore, when thrusters encounter different faults, the fault model is the key of FTC systems. The first motivation is to build a comprehensive and unified fault model including the time-varying stuck fault for UMV thrusters.

Since the marine environment is full of wind, waves, and current, external disturbances against the marine vehicle system may cause the vibration of yaw velocity error and yaw angle. A passive fault tolerant control allocation for small UUVs is discussed without external disturbances in [2]. On the contrary, the FTC system includes the external disturbance term all the time to handle the robust problem of the control system in this paper. Some researches depending on conditions where state feedback information can be obtained directly or indirectly address the FTC and other problems of UMV systems [26], [27], [28]. It is noted that the surge velocity, sway velocity, and yaw velocity of a UMV are not always obtainable in applications, particularly the yaw velocity. Thus, dynamic output feedback is a reasonable solution for UMV systems. For instance, an output feedback controller for a UMV in network environments is proposed in [10]. Besides, there is a common assumption in current sliding mode control methods that the dimension of measured output is not less than that of control input [29], [30], [31]. In this paper, the assumption is eliminated by utilizing input matrix full-rank decomposition technique. This technique has been studied in robust adaptive FTC of uncertain linear systems based on sliding mode output feedback [32], but it has not been applied to ship nonlinear systems. The LMI framework is a common means to ensure that the designed controller satisfies the existence conditions in linear systems [33], [34] and nonlinear systems [35], [36], [37]. Based on input matrix full-rank decomposition technique and H technique, a sufficient condition of sliding mode in the form of LMIs is given [38]. From the above, relatively little attention has been focused on research into FTC for UMV systems comprising the two classes of methods, namely sliding mode control and output feedback. As a result, the second motivation is to develop a UMV fault tolerant control method based on sliding mode output feedback to reduce the amplitudes of yaw velocity error and yaw angle, where the situation is more complicated than the existing strategies.

This paper is concerned with the fault tolerant controller of UMV with thruster faults based on sliding mode output feedback. The main contributions are twofold: (1) a comprehensive fault model is established for UMV thrusters with non-fault, partial fault, complete fault and stuck fault for the first time; (2) a fault tolerant controller of UMV with thruster faults and external disturbances based on sliding mode output feedback is put forward.

The rest of this paper is arranged as follows: Section 2 presents some useful definitions and lemmas; Section 3 states UMV and fault model, and describes the system with thruster fault model; Section 4 presents the stability analysis at first, then gives the design of the output feedback controller and sliding surface; Section 5 shows the comparative simulation results, and Section 6 concludes the paper.

Section snippets

Definition of adaptive H performance

Definition 1

[39] Consider the following closed-loop systemξ˙(t)=Ac(a^(t),a)ξ(t)+Bc(a^(t),a)ω(t),z(t)=Cc(a^(t),a)ξ(t),ξ(0)=0,where ξ(t) ∈ Rn is the state vector, ω(t) is an external disturbance in L2[0,), z(t) ∈ Rr is the controlled output, a is parameter vector and a^(t) is the time-varying vector to be estimated. Ac(a^(t),a), Bc(a^(t),a) and Cc(a^(t),a) are time-varying matrices that depend on a and a^. For a positive constant γ, if the system (1) has the following properties:

(1) The system is

UMV and fault model

The kinematics and dynamics model of a nonlinear anchored marine vehicle in [44] is in 6 degrees of freedom and the environmental disturbances involve waves, wind, and current. For a UMV, the positions xp, yp and the yaw angle ψ are presented in the earth-fixed reference frame, while the surge velocity, sway velocity and yaw velocity (q, v, r) are presented in the body-fixed reference frame. First:ν(t)=[q(t)v(t)r(t)]T,η(t)=[xp(t)yp(t)ψ(t)]T,η˙(t)=J(η(t))ν(t),J(η(t))=[cos(ψ(t))sin(ψ(t))0sin(ψ(t)

Stability analysis

First, suppose the input matrix E can be decomposed intoE=E2dN,where NRl0×p and E2dRn×l0 have the same rank l0 ≤ p. There is an important lemma given as follows.

Lemma 5

[45] For matrix decomposition (18) and all ρΔρj, j ∈ I(1, L), there is a positive constant μ which makes the following inequality trueNρNTμNNT.

Remark 4

The matrix full-rank decomposition technique is utilized to decompose input matrix E into E2dN, which guarantees m > l0 and the matrix E2dTPE2d is nonsingular. This technique has been studied

Simulation results

Simulation results are represented to demonstrate the effectiveness and feasibility of the proposed FTC method of unmanned marine vehicles with thruster faults based on the sliding mode output feedback. The continuous-time system (13) parameters areA=[1.08520002.05750.408700.40870.2153],C=[0.03890000.02660000],B=[0.08650000.07620.015100.01510.031],B0=[1100000011110.04720.04720.41080.38580.45540.3373].In the simulation,C1=[001000],C2=[100010010001001010000101],E1=[111000010000001000]T,D=[

Conclusions

A fault tolerant controller based on sliding mode output feedback for UMV has been studied to deal with thruster faults during missions. It is utilized to reduce the oscillation of yaw velocity error and yaw angle. Compared with the state feedback control and incomprehensive fault types, the proposed approach concludes a unified fault model including non-fault, complete fault, partial fault and stuck fault, which is more in line with the actual situations of UMV thrusters. Via adaptive sliding

Acknowledgement

This work is supported by the National Natural Science Foundation of China (Grant nos. 61503055, 61602077, 71831002), Dalian Innovative Support Scheme for High-level Talents (2017RQ072), Program for Innovative Research Team in University of Ministry of Education of China (IRT_17R13) and the Fundamental Research Funds for the Central University (3132019104, 3132019501, 31322019502).

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