×

Control strategy of optimal deployment for spacecraft solar array system with initial state uncertainty. (English) Zbl 1402.70026

Summary: A control strategy combining feedforward control and feedback control is presented for the optimal deployment of a spacecraft solar array system with the initial state uncertainty. A dynamic equation of the spacecraft solar array system is established under the assumption that the initial linear momentum and angular momentum of the system are zero. In the design of feedforward control, the dissipation energy of each revolute joint is selected as the performance index of the system. A Legendre pseudospectral method (LPM) is used to transform the optimal control problem into a nonlinear programming problem. Then, a sequential quadratic programming algorithm is used to solve the nonlinear programming problem and offline generate the optimal reference trajectory of the system. In the design of feedback control, the dynamic equation is linearized along the reference trajectory in the presence of initial state errors. A trajectory tracking problem is converted to a two-point boundary value problem based on Pontryagin’s minimum principle. The LPM is used to discretize the two-point boundary value problem and transform it into a set of linear algebraic equations which can be easily calculated. Then, the closed-loop state feedback control law is designed based on the resulting optimal feedback control and achieves good performance in real time. Numerical simulations demonstrate the feasibility and effectiveness of the proposed control strategy.

MSC:

70Q05 Control of mechanical systems
37N35 Dynamical systems in control

Software:

SNOPT
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Wallrapp, O.; Wiedemann, B., Dynamics of satellite with deployable rigid solar arrays, Multibody System Dynamics, 7, 101-125, (2002) · Zbl 1035.70004 · doi:10.1023/A:1015295720991
[2] Kuang, J.; Meehanb, P. A.; Leung, A. Y. T.; Tan, S., Nonlinear dynamics of a satellite with deployable solar panel arrays, International Journal of Non-Linear Mechanics, 39, 1161-1173, (2004) · Zbl 1348.70031 · doi:10.1016/j.ijnonlinmec.2003.07.001
[3] Kwak, M. K.; Heo, S.; Kim, H. B., Dynamics of satellite with deployable rigid solar arrays, Multibody System Dynamics, 20, 271-286, (2008) · Zbl 1347.70035 · doi:10.1007/s11044-008-9119-1
[4] Zhang, D. G.; Zhou, S. F., Dynamic analysis of flexible-link flexible-joint robots, Applied Mathematics and Mechanics (English Edition), 27, 695-704, (2006) · Zbl 1145.70003 · doi:10.1007/s10483-006-0516-1
[5] Zhang, D. G., Recursive Lagrangian dynamic modeling and simulation of mult-link spatial flexi-ble manipulator arms, Applied Mathematics and Mechanics (English Edition), 30, 1283-1294, (2009) · Zbl 1207.70007 · doi:10.1007/s10483-009-1008-2
[6] Ge, X. S.; Chen, L. Q.; Liu, Y. Z., Optimal control of the deployment process of solar wings on spacecraft, Acta Astronautica, 60, 684-690, (2007) · doi:10.1016/j.actaastro.2006.07.020
[7] Ge, X. S.; Sun, K., Optimal control of a spacecraft with deployable solar arrays using particle swarm optimization algorithm, Science China Technological Sciences, 54, 1107-1112, (2011) · Zbl 1237.93121 · doi:10.1007/s11431-011-4350-z
[8] Yao, Q. J.; Ge, X. S., Optimal control of stretching process of flexible solar arrays on spacecraft based on a hybrid optimization strategy, Theoretical and Applied Mechanics Letters, 7, 258-263, (2017) · doi:10.1016/j.taml.2017.05.002
[9] Guo, Y. S.; Chen, L., Adaptive neural network control for coordinated motion of a dual-arm space robot system with uncertain parameters, Applied Mathematics and Mechanics (English Edition), 29, 1131-1140, (2008) · Zbl 1163.93333 · doi:10.1007/s10483-008-0903-z
[10] Dong, Q. H.; Chen, L., Impact dynamics analysis of free-floating space manipulator capturing satellite on orbit and robust adaptive compound control algorithm design for sup-pressing motion, Applied Mathematics and Mechanics (English Edition), 35, 413-422, (2014) · Zbl 1294.70019 · doi:10.1007/s10483-014-1801-7
[11] Yu, X. Y.; Chen, L., Modeling and observer-based augmented adaptive control of flexible-joint free-floating space manipulators, Acta Astronautica, 108, 146-155, (2015) · doi:10.1016/j.actaastro.2014.12.002
[12] Yu, X. Y.; Chen, L., Observer-based two-time scale robust control of free-flying flexible-joint space manipulators with external disturbances, Robotica, 35, 2201-2217, (2017) · doi:10.1017/S0263574716000801
[13] Jiang, J. P.; Li, D. X., Robust H1 vibration control for smart solar array structures, Journal of Vibration and Control, 17, 505-515, (2011) · Zbl 1271.74338 · doi:10.1177/1077546310370688
[14] Jiang, J. P.; Li, D. X., Decentralized robust vibration control of smart structures with parameter uncertainties, Journal of Intelligent Material Systems and Structures, 22, 137-147, (2011) · doi:10.1177/1045389X10391496
[15] Zhang, L. X.; Bai, Z. F.; Zhao, Y.; Cao, X. B., Dynamic response of solar panel de-ployment on spacecraft system considering joint clearance, Acta Astronautica, 81, 174-185, (2012) · doi:10.1016/j.actaastro.2012.07.020
[16] Liu, L.; Cao, D. Q.; Tan, X. J., Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh-Ritz method, Archive of Applied Mechanics, 86, 1927-1946, (2016) · doi:10.1007/s00419-016-1155-3
[17] Liu, L.; Cao, D. Q., Dynamic modeling for a flexible spacecraft with solar arrays composed of honeycomb panels and its proportional-derivative control with input shaper, Journal of Dynamic Systems, Measurement, and Control, 138, 081008, (2016) · doi:10.1115/1.4033020
[18] Liu, L.; Cao, D. Q.; Wei, J.; Tan, X. J.; Yu, T. H., Rigid-flexible coupling dynamic modeling and vibration control for a three-axis stabilized spacecraft, Journal of Vibration and Acoustics, 139, 041006, (2017) · doi:10.1115/1.4036213
[19] Liu, L.; Cao, D. Q.; Huang, H.; Shao, C. H.; Xu, Y. Q., Thermal-structural analysis for an attitude maneuvering flexible spacecraft under solar radiation, International Journal of Mechanical Sciences, 126, 161-170, (2017) · doi:10.1016/j.ijmecsci.2017.03.028
[20] Li, H. Q.; Liu, X. F.; Duan, L. C.; Cai, G. P., Deployment and control of spacecraft solar array considering joint stick-slip friction, Aerospace Science and Technology, 42, 342-352, (2015) · doi:10.1016/j.ast.2015.02.001
[21] Li, H. Q.; Liu, X. F.; Guo, S. J.; Cai, G. P., Deployment dynamics of large-scale flexible solar arrays, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 230, 147-158, (2015)
[22] Li, H. Q.; Duan, L. C.; Liu, X. F.; Cai, G. P., Deployment and control of flexible solar array system considering joint friction, Multibody System Dynamics, 39, 249-265, (2017) · doi:10.1007/s11044-016-9534-7
[23] Li, H. Q.; Duan, L. C.; Liu, X. F.; Cai, G. P., Deployment and control of cable-driven flexible solar arrays, Aircraft Engineering and Aerospace Technology, 89, 835-844, (2017) · doi:10.1108/AEAT-05-2015-0133
[24] Garg, D.; Patterson, M.; Hager, W. W.; Rao, A. V.; Benson, D. A.; Hunting-Ton, G. T., A unified framework for the numerical solution of optimal control problems using pseudospectral methods, Automatica, 46, 1843-1851, (2010) · Zbl 1219.49028 · doi:10.1016/j.automatica.2010.06.048
[25] Ross, I. M.; Karpenko, M., A review of pseudospectral optimal control: from theory to flight, Annual Reviews in Control, 36, 182-197, (2012) · doi:10.1016/j.arcontrol.2012.09.002
[26] Huang, X.; Yan, Y.; Zhou, Y.; Zhang, H., Pseudospectral method for optimal propellant-less rendezvous using geomagnetic Lorentz force, Applied Mathematics and Mechanics (English Edition), 36, 609-618, (2015) · doi:10.1007/s10483-015-1936-7
[27] Ge, X. S.; Yi, Z. G.; Chen, L. Q., Optimal control of attitude for coupled-rigid-body space-craft via Chebyshev-Gauss pseudospectral method, Applied Mathematics and Mechanics (English Edition), 38, 1257-1272, (2017) · Zbl 1373.70023 · doi:10.1007/s10483-017-2236-8
[28] Fahroo, F.; Ross, I. M., Costate estimation by a Legendre pseudospectral method, Journal of Guidance, Control, and Dynamics, 24, 270-277, (2001) · doi:10.2514/2.4709
[29] Yan, H.; Ross, I. M.; Alfriend, K. T., Pseudospectral feedback control for three-axis magnetic attitude stabilization in elliptic orbits, Journal of Guidance, Control, and Dynamics, 30, 1107-1115, (2007) · doi:10.2514/1.26591
[30] Tian, B. L.; Zong, Q., Optimal guidance for reentry vehicles based on indirect Legendre pseudospectral method, Acta Astronautica, 68, 1176-1184, (2011) · doi:10.1016/j.actaastro.2010.10.010
[31] Yang, L.; Zhou, H.; Chen, W. C., Application of linear Gauss pseudospectral method in model predictive control, Acta Astronautica, 96, 175-187, (2014) · doi:10.1016/j.actaastro.2013.11.038
[32] Liao, Y. X.; Li, H. F.; Bao, W. M., Indirect Radau pseudospectral method for the receding horizon control problem, Chinese Journal of Aeronautics, 29, 215-227, (2016) · doi:10.1016/j.cja.2015.12.023
[33] Yao, Q. J.; Ge, X. S., Optimal reorientation of a free-floating space robot subject to initial state uncertainties, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, 146, (2018) · doi:10.1007/s40430-018-1064-1
[34] Gill, P. E.; Murray, W.; Saunders, M. A., SNOPT: an SQP algorithm for large-scale constrainted optimization, SIAM Review, 47, 99-131, (2005) · Zbl 1210.90176 · doi:10.1137/S0036144504446096
[35] BRYSON, A. E. and HO, Y. C. Applied Optimal Control: Optimization, Estimation, and Control, Hemisphere, New York (1975)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.