Adaptive fuzzy finite-time fault-tolerant attitude control of rigid spacecraft

https://doi.org/10.1016/j.jfranklin.2015.05.042Get rights and content

Abstract

This paper presents the finite-time adaptive fuzzy control to regulate thruster faults in rigid spacecraft system. The considered faults are that the thrusters losing power partially or even totally. Fuzzy logic systems are used to approximate the unknown nonlinear function which is produced by the external disturbances, unknown inertia matrix and thrusters faults. Uniting fast nonsingular terminal sliding mode surface (FNTSMS) and the fault-tolerant control (FTC), two novel adaptive fuzzy finite-time FTC schemes are developed. It has been testified that this control method can make sure that the rigid spacecraft has excellent property of fault-tolerant and all the signals are finite-time convergence. Simulation examples on a rigid body spacecraft with three thrusters and six thrusters are done to indicate that the finite-time FTC schemes are available in achieving high attitude tracking with faults and uncertainty of the system.

Introduction

The attitude control of the rigid spacecraft has fascinated a lot of notice recently. Most of these systems have characters of inertia uncertainties, nonlinearities and unexpected external disturbances, so sliding-mode control (SMC) has been presented as one of the most important methods to deal with these problems. SMC has been widely used in the attitude control of rigid body, [1] proposed a robust SMC law to deal with the rigid attitude tracking problem. A class of linear sliding manifolds was selected in [2] to apply to quaternion-based rigid spacecraft attitude tracking maneuvers. The SMC with perturbation estimation steps were followed for an output tracking control in [3]. Ref. [4] proposed a novel type of adaptive fuzzy sliding mode control (AFSMC) to work out the dynamic model with network-induced delay, nonlinear and uncertain parameters. However, these control laws make the time that tracking errors converge to the equilibrium points infinite. In order to achieve finite-time convergence, [5], [6], [7] presented terminal SMC (TSMC), which has the superiority that the attitude tracking error of the system converges to the equilibrium points in finite time. Ref. [5] introduced the TSM to make sure the control performance with full model information. Ref. [7] presented a continuous non-singular TSM control scheme so that the system stability and finite-time convergence can be guaranteed. However, the initial TSMC cannot dispose the singularity problem [8], and the convergence of TSM is tardier than the previous linear sliding-mode when the system states are aloof from the equilibrium. Thus, [7], [9] suggested a nonsingular TSM (NTSM) control (NTSMC) to handle the singularity with the initial TSMC. In [10], the fast TSM surface (FTSMS) is proposed to offer a faster response, but it brings the problem of singularity. To conquer these shortcomings, a modified nonsingular FTSMS (FNTSMS) is recommended in [11], which not only prevents the problem of singularity, but also contains the advantages of the NTSM and the traditional sliding-mode together. We work along the improved way and present a reformative scheme in this paper.

The fuzzy logic systems (FLSs) [7], [12], [13] and neural networks (NNs) [16], [17], [18] have been used proverbially to approximate the unknown nonlinear functions because of the better approximation ability, and it is validated that FLSs and NNs are very effectually methods. An adaptive fuzzy tracking control scheme was proposed in [14] for a class of uncertain multiple-input–multiple-output (MIMO) pure-feedback nonlinear systems. In [15], a way of estimating errors for direct adaptive fuzzy control systems was presented. Thus, because fuzzy systems are the universal function approximator, they are usually used to solve the uncertainty that emerged in the attitude control of spacecraft [19], [20], [21]. Ref. [19] presented an adaptive fuzzy mixed H2/H attitude control of rigid spacecraft. A neural network way called fuzzy cerebellar model arithmetic computer (CMAC) was proposed in [20] to handle the attitude control problem. Ref. [21] demonstrated the optimal and robust controller for continuous-time TS fuzzy systems. Despite many achievements about attitude control of spacecraft using FLS, none of these ways can achieve finite-time convergence. Recently, [22] offers a finite-time attitude control technique for rigid using Chebyshev Neural Network (CNN) and terminal sliding mode. In [23], a NN based TSMC plan is put forward for robotics manipulators. However, these control methods assume that all the components of the considered rigid systems are in good operating conditions. As we know, in practical manipulation for controlling projects, a bunch of components for instance, actuators, sensors, and processors may undergo abrupt failures individually or simultaneously [24], [25]. The faults occurred in the actuators in [24], [25] are presented as two kinds: loss of effectiveness and lock-in-place. In [26], the attitude control of rigid with actuator failures and control input constraints has been developed. Ref. [27] presented a joint sensor based backstepping way, and the way was extended to handle sudden structural changes problem. Ref. [28] presented an indirect (nonregressor-based) way to attitude control of rigid system. It was shown that the control algorithms were able to accommodate actuator failures under limited thrusts. Unfortunately, these results cannot give a finite-time convergence process which is just the require in practice. Ref. [29] presented the velocity-free feedback control method with finite time attitude stabilization of a rigid spacecraft, and its kinematics model was based on Rodrigues parameters. Ref. [30] proposed a velocity-free nonlinear proportional-integral (PI) control allocation scheme for fault-tolerant attitude control.

This paper presents the rigid spacecraft system with the external disturbances, unknown inertia matrix and thrusters faults, and the system model in this paper has been established. In real life, since the modern systems become more and more complicated, physical model is usually hard to obtain. Data-driven method, which is not based on model, is becoming more and more important. Ref. [31] introduced a robust approach for key performance indicator related prediction and diagnosis against outliers and missing data. A robust data-driven fault detection way was proposed in [32] to a wind turbine. Ref. [33] presented two online schemes for an integrated design of FTC systems. Ref. [34] presented an improved partial least squares (IPLS) method, and the corresponding test statistics were used to offer fault diagnosis information. The way offered in [35] only needed measurements of accelerometers which were fixed on the four corners. Ref. [36] focused on fault detection and isolation for vehicle suspension system. Fault detection and diagnosis (FDD) was carried out using an interacting multiple model (IMM) estimator in [37].

In this paper, we will design FNTSM fault-tolerant control laws (FNTSMFTCLs) for the rigid spacecraft system which has some uncertainties. The main dedications of this paper are as follows: (1) A novel FNTSMS is proposed to avert the singularity problem and offers faster responses for rigid body system. (2) The recommendatory adaptive fuzzy method in this paper does not need that the nonlinear functions are known or the desired angular velocity ωd, ω̇d, desired attitude qd, q̇d, and the external disturbances are assumed to be bounded like [11], [28]. It utilizes the FLSs to approximate the unknown functions and transforms the considered uncertain spacecraft system into an uncertain parameterized model. Furthermore, the proposed control scheme is fault-tolerant to thruster faults. (3) By the Lyapunov stable theory and the finite-time fault-tolerant technique, the strict finite-time fault-tolerant stable process of proof has been achieved.

The remainder of the paper is organized as follows. Section 2 states the nonlinear model and problem formulation. In Section 3, we present the description of FLS. The main researches are developed in Section 4, in which the adaptive fuzzy finite-time fault-tolerant control schemes are presented to achieve high accurate tracking in finite time. Simulation results are provided in Section 5. Finally, conclusions are shown in Section 6.

Section snippets

Attitude kinematics and dynamics

The spacecraft in this paper is modeled as a rigid body with three or more than three thrusters to provide torques along three mutually perpendicular axes that define a body fixed frame. The unit quaternion q¯=(q,q0)R3×R represents the attitude orientation of the rigid spacecraft in a body frame with respect to an inertial frame, satisfying qTq+q02=1, in which q=[q1,q2,q3]TR3 is a vector, and q0R is a scalar, the kinematics and dynamics of the rigid body can be given by [28]{q̇=0.5(q×+q0I3)ωq

Description of FLS

A fuzzy logic system (FLS) consists of four parts: the knowledge base, the fuzzifier, the fuzzy inference engine working on fuzzy rules, and the defuzzifier. The knowledge base for FLS comprises a collection of fuzzy if–then rules of the following form: Rl:Ifx1isF1landx2isF2landandxnisFnl,thenyisGl,l=1,2,,Nwhere x=(x1,,xn)T and y are the FLS input and output, respectively. Fuzzy sets Fil and Gl are associated with the fuzzy membership functions μFil(xi) and μGl(y), respectively. N is the

Finite-time FTC laws design

In this section, two cases are considered, one is that the vehicle endowed with only three thrusters, each of which, works as fading actuation, but they are still active; the other is that with more than three thrusters, some of which might experience losing power partially or totally.

Simulation studies

In this section, simulations on a vehicle are departed into two parts to verify the effectiveness of the proposed control scheme (25), (31), (51), (54). One is with three thrusters and the other is with six thrusters. Each part contains two different cases: (1) healthy thrusters, (2) thrusters with fading or failed actuation. Note that the controllers (31), (54) can deal with both case 1 and case 2. One only needs to select the same control parameters as shown in Table 1. We choose the fuzzy

Conclusions

This paper has shown two finite-time fault-tolerant attitude control schemes. Although there are some results on fault-tolerant attitude control for spacecraft, but few results can provide finite-time control. It has been corroborated that the proposed fault-tolerant attitude control approach can guarantee that all the signals of the closed-loop system converge to small neighborhoods in finite time, even in the presence of the actuator failures, external disturbances and inertia uncertainties.

Acknowledgements

The work of Yuanqing Xia was supported by the National Basic Research Program of China (973 Program) (2012CB720000), the National Natural Science Foundation of China (61225015), Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant no. 61321002), respectively.

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