This paper addresses a composite two-time-scale control system for simultaneous three-axis attitude maneuvering and elastic mode stabilization of flexible spacecraft. By choosing an appropriate time coordinates transformation system, the spacecraft dynamics can be divided into double time-scale subsystems using singular perturbation theory (SPT). Attitude and vibration control laws are successively designed by considering a time bandwidths separation between the oscillatory flexible parts motion describing a fast subsystem and rigid body attitude dynamics as a slow subsystem. A nonlinear quaternion feedback control, based on modified sliding mode (MSM), is chosen for attitude control design and a strain rate feedback (SRF) scheme is developed for suppression of vibrational modes. In the attitude control law, the modification to sliding manifold for slow subsystem ensures that the spacecraft follows the shortest possible path to the sliding manifold and highly reduces the switching action. Stability proof of the overall closed-loop system is given via Lyapunov analysis. The proposed design approach is demonstrated to combine excellent performance in the compensation of residual flexible vibrations for the fully nonlinear system under consideration, as well as computational simplicity. 1. Introduction In many missions of today’s spacecraft with high resolution earth observation payloads and/or large flexible systems, the operation plan requires high precision control capability in order to point at certain area of interest. These missions impose increasingly severe requirements over the modeling and control of spacecraft dynamics. However the flexible structural elements such as solar arrays, antennas, and other light weight parts have received significant focus on providing the control effort for targeting flexible parts such as payloads and tracking maneuver with simultaneous vibration suppression to accomplish mission objectives. Design of such control system poses a challenging problem, including spill-over effects due to the unmodeled dynamics, nonlinear characteristics of rigid-flexible fully coupled dynamics, and unexpected perturbations [1]. From the mathematical point of view, the dynamics of flexible spacecraft involves the coupling of ODEs for attitude dynamics and PDEs for vibration of flexible appendages. This represented by a set of hybrid differential equations (HDE) of motion. Therefore, control strategies have emerged for smoothly shaped maneuvers with vibration excited [2]. Also, the actual performance of controllers is highly sensitive
References
[1]
D. C. Hyland, J. L. Junkins, and R. W. Longman, “Active control technology for large space structures,” Journal of Guidance, Control, and Dynamics, vol. 16, no. 5, pp. 801–821, 1993.
[2]
T. Singh and S. R. Vadali, “Input-shaped control of three-dimensional maneuvers of flexible spacecraft,” Journal of Guidance, Control, and Dynamics, vol. 16, no. 6, pp. 1061–1068, 1993.
[3]
Q. Liu and B. Wie, “Robust time-optimal control of uncertain flexible spacecraft,” Journal of Guidance, Control, and Dynamics, vol. 15, no. 3, pp. 597–604, 1992.
[4]
S. Vadali, “Feedback control of flexible spacecraft large angle maneuvers using the Liapunov theory,” in Proceedings of the IEEE American Control Conference, Piscataway, NJ, USA, 1984.
[5]
S. Vadali, J. Junkins, and R. Byers, “Near-minimum time, closed-loop slewing of flexible spacecraft,” Journal of Guidance, Control, and Dynamics, vol. 13, no. 1, pp. 57–65, 1990.
[6]
S. V. Drakunov and V. Utkin, “Sliding mode control in dynamic systems,” International Journal of Control, vol. 55, no. 4, pp. 1029–1037, 1992.
[7]
J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control. A survey,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 2–22, 1993.
[8]
J. D. Bo？kovi？, S.-M. Li, and R. K. Mehra, “Robust tracking control design for spacecraft under control input saturation,” Journal of Guidance, Control, and Dynamics, vol. 27, no. 4, pp. 627–633, 2004.
[9]
J. L. Crassidis and F. L. Markley, “Sliding mode control using modified Rodrigues parameters,” Journal of Guidance, Control, and Dynamics, vol. 19, no. 6, pp. 1381–1383, 1996.
[10]
Q. Hu, “Variable structure maneuvering control with time-varying sliding surface and active vibration damping of flexible spacecraft with input saturation,” Acta Astronautica, vol. 64, no. 11-12, pp. 1085–1108, 2009.
[11]
Q. Hu, “Sliding mode attitude control with L2-gain performance and vibration reduction of flexible spacecraft with actuator dynamics,” Acta Astronautica, vol. 67, no. 5-6, pp. 572–583, 2010.
[12]
Q.-L. Hu, Z. Wang, and H. Gao, “Sliding mode and shaped input vibration control of flexible systems,” IEEE Transactions on Aerospace and Electronic Systems, vol. 44, no. 2, pp. 503–519, 2008.
[13]
J. Kim, J. Kim, and J. L. Crassidis, “Disturbance accommodating sliding mode controller for spacecraft attitude maneuvers,” Advances in the Astronautical Sciences, vol. 100, pp. 141–154, 1998.
[14]
S.-C. Lo and Y.-P. Chen, “Smooth sliding-mode control for spacecraft attitude tracking maneuvers,” Journal of Guidance, Control, and Dynamics, vol. 18, no. 6, pp. 1345–1349, 1995.
[15]
Q. Hu and G. Ma, “Vibration suppression of flexible spacecraft during attitude maneuvers,” Journal of Guidance, Control, and Dynamics, vol. 28, no. 2, pp. 377–380, 2005.
[16]
M. Azadi, S. A. Fazelzadeh, M. Eghtesad, and E. Azadi, “Vibration suppression and adaptive-robust control of a smart flexible satellite with three axes maneuvering,” Acta Astronautica, vol. 69, no. 5-6, pp. 307–322, 2011.
[17]
M. D. Shuster, “Survey of attitude representations,” Journal of the Astronautical Sciences, vol. 41, no. 4, pp. 439–517, 1993.
[18]
B. Siciliano and W. J. Book, “A singular perturbation approach to control of lightweight flexible manipulators,” The International Journal of Robotics Research, vol. 7, no. 4, pp. 79–90, 1988.
[19]
E. Mirzaee, M. Eghtesad, and S. A. Fazelzadeh, “Maneuver control and active vibration suppression of a two-link flexible arm using a hybrid variable structure/Lyapunov control design,” Acta Astronautica, vol. 67, no. 9-10, pp. 1218–1232, 2010.
[20]
A. H. Meitzler, H. F. Tiersten, A. W. Warner, et al., IEEE Standard on Piezoelectricity, IEEE Ultrasonics, Ferroelectrics, and Frequency Control Society, 1988.
