Stabilization of Rotational Motion of Spacecrafts Using Quantized Two Torque Inputs Based on Random Dither

Authors: Yusuke Kuramitsu, Tomoaki Hashimoto, Hirokazu Tahara

Abstract:

The control problem of underactuated spacecrafts has attracted a considerable amount of interest. The control method for a spacecraft equipped with less than three control torques is useful when one of the three control torques had failed. On the other hand, the quantized control of systems is one of the important research topics in recent years. The random dither quantization method that transforms a given continuous signal to a discrete signal by adding artificial random noise to the continuous signal before quantization has also attracted a considerable amount of interest. The objective of this study is to develop the control method based on random dither quantization method for stabilizing the rotational motion of a rigid spacecraft with two control inputs. In this paper, the effectiveness of random dither quantization control method for the stabilization of rotational motion of spacecrafts with two torque inputs is verified by numerical simulations.

Keywords: Spacecraft control, quantized control, nonlinear control, random dither method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1475034

References:

[1] P. E. Crouch, Spacecraft Attitude Control and Stabilization: Applications of Geometric Control Theory to Rigid Body Models, IEEE Transaction on Automatic Control, Vol. 29, No. 4, pp. 321-331, 1984.
[2] R. W. Brockett, Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, Birkh¨auser, pp. 181-191, 1983.
[3] D. Aeyels, Stabilization by smooth feedback of the angular velocity of a rigid body, Systems & Control Letters, Vol. 6, No. 1, pp. 59-63, 1985.
[4] R. Outbib and G. Sallet, Stabilizability of the angular velocity of a rigid body revisited, Systems & Control Letters, Vol. 18, No. 2, pp. 93-98, 1992.
[5] R. T. M’Closkey and R. M. Murray, Exponential Stabilization of Driftless Nonlinear Control Systems Using Homogeneous Feedback, IEEE Transaction on Automatic Control, Vol. 42, No. 5, pp. 614-628, 1997.
[6] C. I. Byrnes and A. Isidori, On the Attitude Stabilization of Rigid Spacecraft, Automatica, Vol. 27, No. 1, pp. 87-95, 1991.
[7] J.-M. Coron and E.-Y. Kera¨ı, Explicit Feedbacks Stabilizing the Attitude of a Rigid Spacecraft with Two Control Torques, Automatica, Vol. 32, No. 5, pp. 669-677, 1996.
[8] P. Morin and C. Samson, Time-Varying Exponential Stabilization of a Rigid Spacecraft with Two Control Torques, IEEE Transaction on Automatic Control, Vol. 42, No. 4, pp. 528-533, 1997.
[9] T. Hashimoto, I. Yoshimoto, T. Ohtsuka, Probabilistic Constrained Model Predictive Control for Schr¨odinger Equation with Finite Approximation, Proceedings of SICE Annual Conference, pp. 1613-1618, 2012.
[10] T. Hashimoto, Probabilistic Constrained Model Predictive Control for Linear Discrete-time Systems with Additive Stochastic Disturbances, Proceedings of IEEE Conference on Decision and Control, pp. 6434-6439, 2013.
[11] T. Hashimoto, Computational Simulations on Stability of Model Predictive Control for Linear Discrete-time Stochastic Systems, International Journal of Computer, Electrical, Automation, Control and Information Engineering, Vol. 9, No. 8, pp. 1385-1390, 2015.
[12] T. Hashimoto, Y. Yoshioka, T. Ohtsuka, Receding Horizon Control with Numerical Solution for Thermal Fluid Systems, Proceedings of SICE Annual Conference, pp. 1298-1303, 2012.
[13] T. Hashimoto, Y. Yoshioka, T. Ohtsuka, Receding Horizon Control with Numerical Solution for Spatiotemporal Dynamic Systems, Proceedings of IEEE Conference on Decision and Control, pp. 2920-2925, 2012.
[14] T. Hashimoto, Y. Takiguchi and T. Ohtsuka, Output Feedback Receding Horizon Control for Spatiotemporal Dynamic Systems, Proceedings of Asian Control Conference, 2013.
[15] T. Hashimoto, Y. Yoshioka and T. Ohtsuka, Receding Horizon Control for Hot Strip Mill Cooling Systems, IEEE/ASME Transactions on Mechatronics, Vol. 18, No. 3, pp. 998-1005, 2013.
[16] T. Hashimoto, Y. Yoshioka and T. Ohtsuka, Receding Horizon Control With Numerical Solution for Nonlinear Parabolic Partial Differential Equations, IEEE Transactions on Automatic Control, Vol. 58, No. 3, pp. 725-730, 2013.
[17] T. Hashimoto, Y. Takiguchi and T. Ohtsuka, Receding Horizon Control for High-Dimensional Burgersf Equations with Boundary Control Inputs, Transactions of the Japan Society for Aeronautical and Space Sciences, Vol. 56, No.3, pp. 137-144, 2013.
[18] T. Hashimoto, Conservativeness of Probabilistic Constrained Optimal Control Method for Unknown Probability Distribution, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol. 9, No. 9, pp. 11-15, 2015.
[19] T. Hashimoto, A Method for Solving Optimal Control Problems subject to Probabilistic Affine State Constraints for Linear Discrete-time Uncertain Systems, International Journal of Mechanical and Production Engineering, Vol. 3, Issue 12, pp. 6-10, 2015.
[20] T. Hashimoto, Solutions to Probabilistic Constrained Optimal Control Problems Using Concentration Inequalities, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol. 10, No. 10, pp. 441-446, 2016.
[21] T. Hashimoto, Stability of Stochastic Model Predictive Control for Schr¨odinger Equation with Finite Approximation, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol. 11, No. 1, pp. 12-17, 2017.
[22] T. Hashimoto, Stochastic Model Predictive Control for Linear Discrete-time Systems with Random Dither Quantization, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol. 11, No. 2, pp. 130-134, 2017.
[23] K. Okada, T. Hashimoto, H. Tahara, Attitude Stabilization of Satellites using Random Dither Quantization, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol. 11, No. 8, pp.883-887, 2017.
[24] T. Hashimoto, T. Amemiya and H. A. Fujii, Stabilization of Linear Uncertain Delay Systems with Antisymmetric Stepwise Configurations, Journal of Dynamical and Control Systems, Vol. 14, No. 1, pp. 1-31, 2008.
[25] T. Hashimoto, T. Amemiya and H. A. Fujii, Output Feedback Stabilization of Linear Time-varying Uncertain Delay Systems, Mathematical Problems in Engineering, Vol. 2009, Article ID. 457468, 2009.
[26] T. Hashimoto and T. Amemiya, Stabilization of Linear Time-varying Uncertain Delay Systems with Double Triangular Configuration, WSEAS Transactions on Systems and Control, Vol. 4, No.9, pp.465-475, 2009.
[27] T. Hashimoto, Stabilization of Abstract Delay Systems on Banach Lattices using Nonnegative Semigroups, Proceedings of the 50th IEEE Conference on Decision and Control, pp. 1872-1877, 2011.
[28] T. Hashimoto, A Variable Transformation Method for Stabilizing Abstract Delay Systems on Banach Lattices, Journal of Mathematics Research, Vol. 4, No. 2, pp.2-9, 2012.
[29] T. Hashimoto, An Optimization Algorithm for Designing a Stabilizing Controller for Linear Time-varying Uncertain Systems with State Delays, Computational Mathematics and Modeling, Vol.24, No.1, pp.90-102, 2013.