Finite-Time Control for 6DOF Spacecraft Formation Flying Systems
Publication: Journal of Aerospace Engineering
Volume 28, Issue 5
Abstract
This paper considers the finite-time control problem of 6DOF spacecraft formation flying (SFF) systems in the presence of external disturbances. First of all, based on nonsingular terminal sliding mode (NTSM) method, a local finite-time control law is proposed. Then a finite-time disturbance observer (FTDOB) is introduced to estimate the disturbances, and a composite control law which consists of a feedback control law based on NTSM method and a feed-forward compensation term based on FTDOB technique is constructed such that the follower spacecraft can track the desired trajectory in finite time. The major merit of the proposed method is that chattering is substantially reduced because the switching gain of the discontinuous control law is only required to be greater than the bound of disturbance estimation error rather than that of the disturbances. Furthermore, based on switching control method, continuous NTSM and FTDOB technique, a global finite-time control law is developed for 6DOF SFF systems. Finally, the effectiveness of the proposed methods are validated by numerical simulations.
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Acknowledgments
This work is supported in part by the National Natural Science Foundation of China (61473080) and Program for New Century Excellent Talents in University (NCET-10-0328), Science Foundation for Distinguished Young Scholars of Jiangsu Province (BK20130018), High-level Talents Program in Six Industries of Jiangsu Province (DZXX-30), and Scientific Research Foundation of Graduate School of Southeast University (YBJJ1332).
References
Battin, R. H. (1999). An introduction to the mathematics and methods of astrodynamics, AIAA Education Series, American Institute of Astronauts and Astronautics, Reston, VA.
Bhat, S. P., and Bernstein, D. S. (1998). “Continuous finite-time stabilization of the translational and rotational double integrators.” IEEE Trans. Autom. Control, 43(5), 678–682.
Bhat, S. P., and Bernstein, D. S. (2000). “Finite time stability of continuous autonomous systems.” SIAM J. Control Optim., 38(3), 751–766.
Chen, W. H. (2004). “Disturbance observer based control for nonlinear systems.” IEEE/ASME Trans. Mechatron., 9(4), 706–710.
Chen, W. H., Ballance, D. J., Gawthrop, P. J., and O’Reilly, J. (2000). “A nonlinear disturbance observer for robotic manipulators.” IEEE Trans. Ind. Electron., 47(4), 932–938.
Chen, Y. P., and Lo, S. C. (2004). “Sling-mode controller design for spacecraft attitude tracking maneuvers.” IEEE Trans. Aerosp. Electron. Syst., 29(4), 1328–1333.
Clohessy, W. H., and Wiltshire, R. S. (1960). “Terminal guidance system for satellite rendezvous.” J. Aerosp. Sci., 27(9), 653–658.
De Queiroz, M., Kapila, V., and Yan, Q. (2000). “Adaptive nonlinear control of multiple spacecraft formation flying.” J. Guidance Control Dyn., 23(3), 385–390.
Ding, S. H., and Li, S. H. (2009). “Stabilization of the attitude of a rigid spacecraft with external disturbances using ftc techniques.” Aerosp. Sci. Technol., 13(4), 256–265.
Dixon, W. E., Dawson, D. M., Zergerpglu, E., and Behal, A. (2000). Nonlinear control of wheeled mobile robots, Springer, London, 156–157.
Du, H. B., and Li, S. H. (2012). “Finite-time attitude stabilization for a spacecraft using homogeneous method.” J. Guidance Control, 35(3), 740–748.
Egeland, O., and Gravdhl, J. T. (2002). Modeling and simulation for automatica control, Marine Cybernetics, Trondheim, Norway.
Feng, Y., Yu, X. H., and Man, Z. H. (2002). “Non-singular terminal sliding mode control of rigid manipulators.” Automatica, 38(12), 2159–2167.
Hong, Y. G., Wang, J. K., and Cheng, D. Z. (2006). “Adaptive finite time control of nonlinear system with parameter uncertainty.” IEEE Trans. Autom. Control, 51(5), 858–862.
Huang, X. Q., Lin, W., and Yang, B. (2005). “Global finite time stabilization of a class of uncertain nonlinear systems.” Automatica, 41(5), 881–888.
Jin, E. D., and Sun, Z. W. (2008). “Robust controllers design with finite time convergence for rigid spacecraft attitude tracking control.” Aerosp. Sci. Technol., 12(4), 324–330.
Kristiansen, R., Grotli, E. I., Nicklasson, P. J., and Jan, T. (2007). “A model of relative translation and rotation in leader-follower spacecraft formations.” Modell. Ident. Control, 28(1), 3–14.
Kristiansen, R., Nicklasson, P. J., and Gravdahl, J. T. (2008). “Spacecraft coordination control in 6DOF: Integrator backstepping vs passivity-based control.” Automatica, 44(11), 2896–2901.
Levant, A. (2003). “Higher-order sliding modes, differentiation and output-feedback control.” Int. J. Control, 76(9), 924–941.
Levant, A. (2005). “Quasi-continuous high-order sliding-mode controllers.” IEEE Trans. Autom. Control, 50(11), 1812–1816.
Li, J. Q., Pan, Y. D., and Kumar, K. D. (2012). “Design of asymptotic second-order sliding mode control for satellite formation flying.” J. Guidance Control Dyn., 35(1), 309–316.
Li, S. H., Ding, S. H., and Li, Q. (2009). “Global set stabilization of the spacecraft attitude using ftc technique.” Int. J. Control, 82(5), 822–836.
Li, S. H., and Tian, Y. P. (2007). “Finite-time stability of cascaded time-varying systems.” Int. J. Control, 80(4), 646–657.
Li, S. H., Wang, Z., and Fei, S. M. (2011). “Comments on the paper: Robust controllers design with finite time convergence for rigid spacecraft attitude tracking control.” Aerosp. Sci. Technol., 15(3), 193–195.
Liu, H., and Li, J. F. (2009). “Terminal sliding mode control for spacecraft formation flying.” IEEE Trans. Aerosp. Electron. Syst., 45(3), 835–846.
Lizarralde, F., and Wen, J. T. (1996). “Attitude control without angular velocity measurement: A passivity approach.” IEEE Trans. Autom. Control, 41(3), 468–472.
Lv, Y. Y., Hu, Q. L., Ma, G. F., and Zhou, J. K. (2011). “6DOF synchronized control for spacecraft formation flying with input constraint and parameter uncertainties.” ISA Trans., 50(4), 573–580.
Pan, H., and Kaplia, V. (2001). “Adaptive nonlinear control for spacecraft formation flying with coupled translational and attitude dynamics.” Proc., Conf. on Decision and Controls, Orlando, FL, 2057–2062.
Qian, C. J., and Li, J. (2005). “Global finite-time stabilization by output feedback for planar systems without observable linearization.” IEEE Trans. Autom. Control, 50(6), 885–890.
Shtessel, Y. B., Shkolnikov, I. A., and Levant, A. (2007). “Smooth second-order sliding modes: Missile guidance application.” Automatica, 43(8), 1470–1476.
Shtessel, Y. B., Shkolnikov, I. A., and Levant, A. (2009). “Guidance and control of missile interceptor using second-order sliding modes.” IEEE Trans. Aerosp. Electron. Syst., 45(1), 110–124.
Sun, H. B., Li, S. H., and Fei, S. M. (2011). “A composite control scheme for 6dof spacecraft formation control.” Acta Astronaut., 69(7), 595–611.
Wang, J. Y., and Sun, Z. W. (2012). “6-DOF robust adaptive terminal sliding mode control for spacecraft formation flying.” Acta Astronaut., 73(1), 76–87.
Wang, P. K. C., and Hadaegh, F. Y. (1996). “Coordination and control of multiple microspacecraft moving in formation.” J. Astronaut. Sci., 44(3), 315–355.
Wang, P. K. C., Hadaegh, F. Y., and Lau, K. (1999). “Synchronized formation rotation and attitude control of multiple free-flying spacecraft.” J. Guidance Control Dyn., 22(1), 28–35.
Wei, X. J., and Guo, L. (2009). “Composite disturbance-observer-based control and terminal sliding mode control for nonlinear systems with disturbance.” Int. J. Control, 82(6), 1082–1098.
Wei, X. J., and Guo, L. (2010). “Composite disturbance-observer-based control and h∞ control for complex continuous models.” Int. J. Robust Nonlinear Control, 20(1), 106–118.
Wertz, J. R. (1978). Spacecraft attitude determination and control, Kluwer Academic Publishers, London.
Wong, H., Pan, H., and Kapila, V. (2005). “Output feedback control for spacecraft formation flying with coupled translation and attitude dynamics.” American Control Conf., Portland, OR, 2419–2426.
Xue, D. Y., and Chen, Y. Q. (2009). Solving applied mathematical problems with Matlab, Chapman & Hall, CRC, London.
Yu, S. H., Yu, X. H., Shirinzadeh, B., and Man, Z. H. (2005). “Continuous finite-time control for robotic manipulators with terminal sliding mode.” Automatica, 41(11), 1957–1964.
Zhao, D., Li, S., Zhu, Q., and Gao, F. (2010). “Robust ftc approach for robotic manipulators.” IET Control Theory Appl., 4(1), 1–15.
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Published In
Journal of Aerospace Engineering
Volume 28 • Issue 5 • September 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 14, 2012
Accepted: Sep 24, 2014
Published online: Nov 5, 2014
Discussion open until: Apr 5, 2015
Published in print: Sep 1, 2015
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