Authors: Ran Zhang Jianzhong Qiao Tao Li Lei Guo
Publish Date: 2014/01/30
Volume: 76, Issue: 3, Pages: 1753-1760
Abstract
In this paper we present a robust faulttolerant control scheme to achieve attitude control of flexible spacecraft with disturbances and actuator failures It is shown that the control algorithms are not only attenuate exogenous bounded disturbances with attenuation level but also able to tolerate partial loss of actuator effectiveness The proposed controller design is simple and can guarantee the faulty closedloop system to be quadratically stable with a prescribed upper bound of the cost function The design algorithms are obtained by combining free weighting matrices method with linear matrix inequality technique The effectiveness of the proposed design method is demonstrated in a spacecraft attitude control system subject to loss of actuator effectivenessHigh precision attitude control has been a difficult and important problem for flexible spacecraft in communication navigation remote sensing and other spacerelated missions It is because modern spacecraft often employ large deployed and light damping structures such as solar paddles and antenna reflectors to provide sufficient power supply and reduce launch costs 1 2 3 4 5 6 During the control of the rigid body attitude actuators play an important role of linking control commands to physical actions 7 8 Normally the actuators should execute commands demanded by the controller faithfully and completely In this condition the actuators need to be 100~ effective However when a fault occurs in the actuator the handicapped actuator may not complete the control command fully Naturally the control channel effectiveness or lack of it becomes an appropriate measure of the severity of the actuator fault 9 In an spacecraft actuator faults may cause discrepancies between the desired and the actual movements of these control surfaces due to incorrect supply pressure in the hydraulic lines change in hydraulic compliance and line leakage 10 Any of these problems can prevent the primary control surfaces such as elevators ailerons or rudder from moving to the positions demanded by the controller 9 On the other hand the complex space structure may lead to the decreased rigidity and lowfrequency elastic modes However elastic vibration of the flexible appendages may cause degradation of the performance of attitude control 7 11 Thus the desired control scheme should tolerate partial loss of actuator effectiveness and be robust enough to overcome various disturbances from structural vibrations of the flexible appendagesDue to the increasing demands for high reliability and survivability of the complex control systems the faulttolerant control FTC has attracted extensive interests and attention 12 13 14 15 16 17 18 19 20 21 FTC can be divided into passive FTC 12 13 and active ones 14 15 An active FTC uses the diagnosis results provided by the fault detection and diagnosis to actively adjust the control efforts thus is potentially capable of dealing with a larger number of faults 14 15 Compared with the active FTC the passive one has the advantage of not requiring the exact actuator fault information thus it is simple to implement The passive FTC can also ensure system stability and desired performance after the actuator fault occurs and before the fault detection and diagnosis phase finishes 12 13Motivated by the preceding discussion in this paper a passive FTC scheme for flexible spacecraft with disturbances and partial loss of actuator effectiveness is studied First the partial loss of actuator effectiveness problem is transformed into uncertain parameters problem Second the fault tolerant control is designed by combining H infty control technique and robust control method The proposed control algorithms are not only attenuate disturbances from structural vibrations of the flexible appendages with H infty attenuation level but also able to robust to partial loss of actuator effectiveness Meanwhile the resultant FT controller may be simply designed and can guarantee the faulty closedloop system to be quadratically stable with a prescribed upper bound of the cost function Finally a numerical example is shown to demonstrate the good performance of our methodThe rest of this paper is organized as follows The singleaxis model of flexible spacecraft model and partial loss of actuator effectiveness are described in Sect 2 The passive FT controller is designed and analyzed in Sect 3 Numerical simulations on different control effectiveness factor situations are presented in Sect 4 to demonstrate the performance of the proposed control method Finally we conclude the paper in Sect 5Notation Throughout this paper Rn denotes the ndimensional Euclidean space the space of squareintegrable vector functions over 0 infty is denoted by l 20 infty the superscripts “top ” and “1” stand for matrix transposition and matrix inverse respectively Pge 0 means that P is real symmetric and positive definite semidefinite The identity and zero matrices are denoted by I and 0 respectively with appropriate dimensions In symmetric block matrices or complex matrix expressions mathrm diag ldots stands for a blockdiagonal matrix and represents a term that is induced by symmetry For a vector nu t its norm is given by Vert nu tVert 2=int infty 0nu top tnu tmathrmdt Matrices if their dimensions are not explicitly stated are assumed to be compatible for related algebraic operationsWhen underlineomega i=overlineomega i=1 then the ith actuator is considered to be faultfree Nevertheless when 0le omega i1 the considered fault is a partial loss of control effectiveness Specially when omega i =0 the ith actuator is considered to be failure and the actuator is out of order On the other hand it is noted that loss of actuator effectiveness problem may be transformed into uncertain parameters problem by using fault description method in 7 which will also make the partial actuator failures problem to easily solve in subsequent section
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