Finite-time fault-tolerant trajectory tracking control of an autonomous surface vehicle

https://doi.org/10.1016/j.jfranklin.2019.05.016Get rights and content

Highlights

  • A finite-time passive FTC (F-PFTC) scheme using integral sliding mode (ISM) manifold is developed by exploiting partial knowledge on faults and disturbances, and achieves fast and accurate tracking with passive fault tolerance.

  • An online finite-time fault estimator (FFE) is devised to detect, isolate, and accommodate unknown faults and disturbances, and thereby eventually contributing to the finite-time active FTC (F-AFTC) scheme without using a priori knowledge.

  • Suffering from both unknown faults and disturbances, the proposed F-PFTC and F-AFTC schemes can track exactly an ASV to the desired trajectory.

Abstract

In this paper, finite-time fault-tolerant control (FTC) for trajectory tracking of an autonomous surface vehicle (ASV) is solved. Main contributions are summarized as follows: (1) a finite-time passive FTC (F-PFTC) scheme using integral sliding mode (ISM) manifold is developed by exploiting partial knowledge on faults and disturbances, and achieves fast and accurate tracking with passive fault tolerance; (2) an online finite-time fault estimator (FFE) is devised to detect, isolate, and accommodate unknown faults and disturbances, and thereby eventually contributing to the finite-time active FTC (F-AFTC) scheme without using a priori knowledge; (3) suffering from both unknown faults and disturbances, the proposed F-PFTC and F-AFTC schemes can track exactly an ASV to the desired trajectory. Comprehensive simulations and comparisons conducted on CyberShip II demonstrate the effectiveness and superiority of the proposed schemes.

Introduction

Due to the remarkable ability to tackle uncertainties and/or external disturbances, the sliding mode control (SMC) approach [1], [2], [3], [4], [5], [6], [7], [8], [9] has been increasingly studied and has been widely applied to various industrial areas including electric vehicles [10], stochastic systems [11], [12], [13], robotic manipulators [14], [15], [16], [17], rigid spacecrafts [18], [19], [20], and marine vehicles and equipments [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], etc. Note that traditional sliding surfaces can only achieve asymptotic (exponential) convergence. The terminal sliding mode (TSM) surface [36] has been defined to realize finite-time convergence within the sliding surface. However, the TSM dynamics would inevitably suffer from the singularity around the origin. Accordingly, the nonsingular TSM (NTSM) surface [37] has been proposed to overcome the foregoing singularity issue, and has attracted increasing attention in the literature. In [37], the singularity issue associated with TSM-based approaches has been removed, and can facilitate a finite-time control strategy. By virtue of the NTSM approach, a trajectory tracking control scheme for an autonomous surface vessel has been presented in [38], whereby, however, unknowns and disturbances have not been sufficiently addressed.

In order to further deal with external disturbances and/or uncertainties, disturbance observers have been widely incorporated in various manners. In [39], a nonlinear disturbance observer has been proposed to compensate frictions and disturbances, and thereby improving the robustness and reliability using economic control efforts. By virtue of a reduced-order disturbance observer, the trajectory tracking of a rotating shaft has been achieved in [40], whereby precise motion control can be achieved. Unlike aforementioned conventional nonlinear disturbance observers whereby asymptotically/exponentially convergent observation errors are derived, a finite-time disturbance observer (FTDO) has been innovatively proposed in [41] whereby global finite-time stability of the entire FTDO-based control system can be guaranteed.

In addition, under the complex marine environment, a surface vehicle inevitably suffers from unknown external disturbances caused by ocean winds, waves and currents, etc. [42], and thereby leading to great challenges in accurate trajectory tracking control synthesis. In the literature, trajectory tracking control approaches using various intelligent methods including fuzzy logic systems (FLS) [43], [44], [45], neural networks (NN) [46], [47], [48], fuzzy neural networks (FNN) [49], and latest merging self-constructive intelligent approximators [50], [51], [52] have been developed to handle unknown disturbances and/or system uncertainties. It is apparent that foregoing adaptive approximation-based approaches are computationally expensive, and can only achieve asymptotic/exponential convergence. It is well known that, compared to asymptotic and/or exponential approaches, finite-time convergence can contribute to rapid response and stronger robustness to complex unknowns.

A highly autonomous and reliable vehicle system is expected to achieve high-precision tracking control in the presence of external disturbances and even actuator faults. In practice, actuator fault is a most typical case of input constraints appearing in an autonomous surface vehicle (ASV) system, and probably gives rise to terrible performance. Therefore, it is meaningful to solve the fault-tolerant control (FTC) problem of ASV systems with actuator faults in addition to complex unknowns. In the literature, the existing FTC approaches can be classified into two categories, i.e., passive and active manners. Within the passive FTC (PFTC) framework, partial knowledge of the fault is usually required to be exactly known in advance while remaining unknowns pertaining to the fault are capsulated as uncertainties and/or disturbances. In this context, a robust-like controller is synthesized to compensate various faults using preservative tolerance [53], [54], [55]. Alternatively, an active FTC (AFTC) approach reconfigures the controller by virtue of a fault estimator (FE) which can online identify fault information [56], [57], [58], and thereby, to some extent, achieving superior performance in terms of fault detection and compensation.

Note that both traditional PFTC and AFTC approaches with asymptotic convergence are actually fault-sensitive since exact tracking performance cannot be obtained within a finite time. Motivated by above observations, in this paper, finite-time versions of PFTC and AFTC schemes for an ASV with actuator faults and disturbances are developed by incorporating finite-time fault estimator (FFE) into integral sliding mode (ISM) technique so as to accommodate both actuator faults and external disturbances. Firstly, by virtue of the ISM technique, a finite-time PFTC (F-PFTC) scheme is developed by incorporating a robust compensator which is derived to exploit partially known knowledge on faults and disturbances. Aiming to relax the preservation pertaining to the F-PFTC scheme that partial fault information is required to be known a priori, the finite-time AFTC (F-AFTC) scheme combining with the ISM manifold and the FFE is further created to enhance abilities of fault detection and compensation. Eventually, within the proposed F-PFTC and F-AFTC schemes, both kinematics and dynamics tracking errors can be rendered globally finite-time stable, under actuator faults and unknown disturbances. More interestingly, rigorous analysis shows that, by virtue of the FFE, the F-AFTC scheme can exactly detect, isolate, and accommodate faults together with disturbances without using any a priori knowledge.

The rest of this paper is organized as follows. In Section 2, trajectory tracking problem of an ASV with actuator faults and disturbances is formulated. The F-PFTC and F-AFTC schemes together with stability analysis are presented in Section 3. Simulation studies and discussions are carried out in Section 4. Section 5 concludes this paper.

Section snippets

Problem formulation

An ASV kinematics and dynamics can be modeled by [42]η˙=R(ψ)υMυ˙=J(η,υ)+τ+τδwhereJ(η,υ)=C(υ)υD(υ)υg(η,υ)here, η=[x,y,ψ]T is the 3-DOF position (x, y) and heading angle (ψ) of the ASV, υ=[u,v,r]T is the corresponding linear velocities (u, v), i.e., surge and sway velocities, and angular rate (r) in the body-fixed frame, see Fig. 1, τ=[τ1,τ2,τ3]T and τδ ≔ MRT(ψ)δ(t) with δ(t)=[δ1(t),δ2(t),δ3(t)]T are control inputs and mixed disturbances, respectively, and R(ψ)=[cosψsinψ0sinψcosψ0001] with

Integral sliding mode manifold design

Consider coordinate transformations as follows:μ=Rν,μ{ω,ωd},ν{υ,υd},R{R,Rd}where ω=[ω1,ω2,ω3]T, ωd=[ωd1,ωd2,ωd3]T, R=R(ψ) and Rd=R(ψd).

Together with Eqs. (6) and (9), we can obtainη˙=ωω˙=RM1τn+H(η,ω)+N(δ,τn)whereH(η,ω)=(S(ω3)RM1(C(RTω)+D(RTω))RTω)RM1g(η,RTω)N(δ,τn)=RM1B(tt0)((EI)τn+τ¯)+δ

Similarly, from Eqs. (7) to (9), we obtainη˙d=ωdω˙d=RdM1τd+Hd(ηd,ωd)whereHd(ηd,ωd)=RdM1(C(RdTωd)+D(RdTωd))RdTωd+S(ωd3)ωd

Let ηe=ηηd=[ηe1,ηe2,ηe3]T and ωe=ωωd=[ωe1,ωe2,ωe3]T. Together with (10),

Simulation studies and discussions

In order to evaluate the proposed F-PFTC and F-AFTC schemes, comprehensive simulation studies are conducted on a well-known surface vehicle named CyberShip II [64], whereby main hydrodynamic coefficients are collected in Table 1.

To comprehensively evaluate the ability of the proposed F-PFTC and F-AFTC schemes in terms of fault detection, isolation, and estimation, as shown in Table 2, various kinds of typical faults are addressed as follows: (1) bias faults only (BFO); (2) partial loss of

Conclusion

In this paper, fault tolerant control (FTC) schemes of tracking an ASV with actuator faults and external disturbances have been addressed by combining integral sliding mode (ISM) technique with a finite-time fault estimator (FFE). By exploiting a priori knowledge on actuator faults, a finite-time passive FTC (F-PFTC) scheme using the ISM approach has been proposed to guarantee finite-time stability of the closed-loop tracking system. Pursuing superior performance, an FFE has been innovatively

Declarations of interest

None.

Acknowledgment

The authors would like to thank the Editor-in-Chief, Associate Editor and anonymous referees for their invaluable comments and suggestions. This work is supported by the National Natural Science Foundation of P. R. China (under Grants 51009017 and 51379002), the Liaoning Revitalization Talents Program (under Grant XLYC1807013), the Fund for Dalian Distinguished Young Scholars (under Grant 2016RJ10), the Fund for Liaoning Innovative Talents in Colleges and Universities (under Grant LR2017024),

References (66)

  • TangY.

    Terminal sliding mode control for rigid robots

    Automatica

    (1998)
  • FengY. et al.

    Non-singular terminal sliding mode control of rigid manipulators

    Automatica

    (2002)
  • SunJ. et al.

    Extreme learning control of surface vehicles with unknown dynamics and disturbances

    Neurocomputing

    (2015)
  • ZuoZ. et al.

    Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation

    Automatica

    (2010)
  • JinX.

    Fault tolerant finite-time leader–follower formation control for autonomous surface vessels with LOS range and angle constraints

    Automatica

    (2016)
  • Y.B. Shtessel et al.

    Smooth second-order sliding modes: missile guidance application

    Automatica

    (2007)
  • R. Skjetne et al.

    Adaptive maneuvering, with experiments, for a model ship in a marine control laboratory

    Automatica

    (2005)
  • HongY. et al.

    Finite-time control for robot manipulators

    Syst. Control Lett.

    (2002)
  • R. Sakthivel et al.

    Resilient sampled-data control for Markovian jump systems with an adaptive fault-tolerant mechanism

    IEEE Trans. Circuit. Syst. II Brief Pap.

    (2017)
  • S.K. Kommuri et al.

    A robust observer-based sensor fault-tolerant control for PMSM in electric vehicles

    IEEE Trans. Ind. Electron.

    (2016)
  • LiS. et al.

    Mixed l_/l1 fault detection observer design for positive switched systems with time-varying delay via delta operator approach

    Int. J. Control Autom. Syst.

    (2014)
  • WangN. et al.

    Accurate trajectory tracking of disturbed surface vehicles: a finite-time control approach

    IEEE/ASME Trans. Mechatron.

    (2019)
  • WangY. et al.

    Reliable fuzzy tracking control of near-space hypersonic vehicle using aperiodic measurement information

    IEEE Trans. Ind. Electron.

    (2019)
  • WangY. et al.

    Reliable control of fuzzy singularly perturbed systems and its application to electronic circuits

    IEEE Trans. Circuit. Syst. I Regul. Pap.

    (2018)
  • WangN. et al.

    Backpropagating constraints based trajectory tracking control of a quadrotor with constrained actuator dynamics and complex unknowns

    IEEE Trans. Syst. Man Cybern. Syst.

    (2018)
  • WangN. et al.

    Hybrid finite-time trajectory tracking control of a quadrotor

    ISA Trans.

    (2019)
  • XiaoB. et al.

    Reconfigurable tolerant control of uncertain mechanical systems with actuator faults: a sliding mode observer-based approach

    IEEE Trans. Control Syst. Technol.

    (2018)
  • ZhouQ. et al.

    Prescribed performance observer-based adaptive fuzzy control for nonstrict-feedback stochastic nonlinear systems

    IEEE Trans. Syst. Man Cybern. Syst.

    (2018)
  • LiH. et al.

    Adaptive neural control of uncertain nonstrict-feedback stochastic nonlinear systems with output constraint and unknown dead zone

    IEEE Trans. Syst. Man Cybern. Syst.

    (2017)
  • LiH. et al.

    Adaptive fuzzy control of nonstrict-feedback stochastic nonlinear systems with input saturation

    IEEE Trans. Syst. Man Cybern. Syst.

    (2017)
  • HeW. et al.

    Adaptive neural impedance control of a robotic manipulator with input saturation

    IEEE Trans. Syst. Man Cynbern. Syst.

    (2016)
  • HeW. et al.

    Adaptive neural network control of an uncertain robot with full-state constraints

    IEEE Trans. Cynbern.

    (2016)
  • Z. Man et al.

    A robust mimo terminal sliding mode control scheme for rigid robotic manipulators

    IEEE Trans. Autom. Control

    (1994)
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