Nonlinear H∞ based underactuated attitude control for small satellites with two reaction wheels

Abstract Underactuated attitude control is supposed to be used on spacecraft when failure happens with onboard actuators. One main problem with existing underactuated attitude control designs is their limited capabilities against disturbances. In order to solve this problem, an approach based on the theory of H ∞ is proposed in this paper. Two propositions are derived from the H ∞ theory to improve the robustness of one popular underactuated attitude control design, which was presented by Tsiotras et al. It is proved mathematically that the controller satisfying these two propositions respectively can stabilize the underactuated attitude system locally or globally. The numerical simulations show that the improved controllers based on the H ∞ theory could provide higher pointing accuracy for small satellites against disturbances. This validates the effectiveness of the proposed H ∞ based approach to improve existing underactuated attitude control designs.

[1]  M. Corless,et al.  An ℒ2 disturbance attenuation solution to the nonlinear benchmark problem , 1998 .

[2]  R.S. Erwin,et al.  Shape change maneuvers for attitude control of underactuated satellites , 2005, Proceedings of the 2005, American Control Conference, 2005..

[3]  S. Shankar Sastry,et al.  Orientation control of the dynamic satellite , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[4]  Shinichi Nakasuka,et al.  TARGET TRACKING ATTITUDE MANEUVER OF A BIAS MOMENTUM MICRO SATELLITE USING TWO WHEELS , 2000 .

[5]  Haichao Gui,et al.  Controllability of an underactuated spacecraft with one thruster under disturbance , 2012 .

[6]  J. Marsden,et al.  Stabilization of rigid body dynamicsby the Energy-Casimir method , 1990 .

[7]  Quan Hu,et al.  Attitude Stabilization of a Spacecraft by Two Skew Single-Gimbal Control Moment Gyros , 2013 .

[8]  C. Samson,et al.  Time-varying exponential stabilization of a rigid spacecraft with two control torques , 1997, IEEE Trans. Autom. Control..

[9]  Thomas Parisini,et al.  Global asymptotic stabilization of the attitude and the angular rates of an underactuated non-symmetric rigid body , 2008, Autom..

[10]  Krishna Dev Kumar,et al.  Robust attitude stabilization of spacecraft subject to actuator failures , 2011 .

[11]  Alexandre N. Pechev,et al.  Feedback-Based Steering Law for Control Moment Gyros , 2007 .

[12]  N. Harris McClamroch,et al.  Attitude stabilization of a rigid spacecraft using two momentum wheel actuators , 1993 .

[13]  Shijie Xu,et al.  Underactuated spacecraft angular velocity stabilization and three-axis attitude stabilization using two single gimbal control moment gyros , 2010 .

[14]  Li-Qun Chen,et al.  Optimal reorientation of underactuated spacecraft using genetic algorithm with wavelet approximation , 2009 .

[15]  Zhong-Ping Jiang,et al.  Time-varying feedback stabilization of the attitude of a rigid spacecraft with two controls , 1994 .

[16]  M. Corless,et al.  Invariant manifold techniques for attitude control of symmetric spacecraft , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[17]  Panagiotis Tsiotras,et al.  Reduced Effort Control Laws for Underactuated Rigid Spacecraft , 1997 .

[18]  H. Krishnan,et al.  Attitude stabilization of a rigid spacecraft using gas jet actuators operating in a failure mode , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[19]  Dirk Aeyes,et al.  Comments on the stabilization of the angular velocity of a rigid body , 1988 .

[20]  Hirohisa Kojima,et al.  Spacecraft attitude maneuver using two single-gimbal control moment gyros , 2013 .

[21]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[22]  Jean-Michel Coron,et al.  Explicit feedbacks stabilizing the attitude of a rigid spacecraft with two control torques , 1996, Autom..

[23]  Congying Han,et al.  Underactuated Satellite Attitude Control with Two Parallel CMGs , 2007, 2007 IEEE International Conference on Control and Automation.

[24]  Panagiotis Tsiotras,et al.  Control of underactuated spacecraft with bounded inputs , 2000, Autom..

[25]  Abdulrahman H. Bajodah,et al.  Asymptotic perturbed feedback linearisation of underactuated Euler's dynamics , 2009, Int. J. Control.

[26]  Youdan Kim,et al.  Sliding mode stabilizing control law of underactuated spacecraft , 2000 .

[27]  Kazuo Tsuchiya,et al.  Attitude Control of a Spacecraft with Two Reaction Wheels , 2004 .

[28]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[29]  Mazen Alamir,et al.  Further Results on the Controllability of a Two-Wheeled Satellite , 2007 .

[30]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[31]  Alexandre N. Pechev,et al.  Nonlinear H∞ controllers for electromagnetic suspension systems , 2004, IEEE Trans. Autom. Control..

[32]  N. Horri,et al.  Practical Implementation of Attitude-Control Algorithms for an Underactuated Satellite , 2012 .

[33]  P. Tsiotras,et al.  CONTROL OF SPACECRAFT SUBJECT TO ACTUATOR FAILURES : STATE-OFTHE-ART AND OPEN PROBLEMS , 2000 .

[34]  Khashayar Khorasani,et al.  On the attitude recovery of an underactuated spacecraft using two control moment gyroscopes , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[35]  O. J. Sørdalen,et al.  Attitude stabilization with a nonholonomic constraint , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[36]  Haichao Gui,et al.  Attitude control of a rigid spacecraft with one variable-speed control moment gyro , 2013 .

[37]  Pavel Trivailo,et al.  Spin-axis stabilisation of underactuated rigid spacecraft under sinusoidal disturbance , 2008, Int. J. Control.

[38]  Panagiotis Tsiotras,et al.  A novel approach to the attitude control of axisymmetric spacecraft , 1995, Autom..

[39]  Olav Egeland,et al.  Attitude control of an underactuated satellite , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[40]  Erkan Zergeroglu,et al.  Nonlinear tracking control of an underactuated spacecraft , 2002 .

[41]  Hirohisa Kojima.  Stabilization of Angular Velocity of Asymmetrical Rigid Body Using Two Constant Torques , 2007 .

[42]  Congying Han,et al.  Time-varying nonlinear designs for underactuated attitude control with two reaction wheels , 2008 .

[43]  Hiroshi Okubo,et al.  Pointing control of spacecraft using two SGCMGs via LPV control theory , 2011 .

[44]  D. Aeyels.  Stabilization of a class of nonlinear systems by a smooth feedback control , 1985 .

[45]  Sergey V. Drakunov,et al.  Stabilization of a nonholonomic system via sliding modes , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[46]  A. Isidori,et al.  Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems , 1992 .

[47]  Youdan Kim,et al.  Spin-Axis Stabilization of a Rigid Spacecraft Using Two Reaction Wheels , 2001 .

[48]  Sergey V. Drakunov,et al.  Stabilization and tracking in the nonholonomic integrator via sliding modes , 1996 .

[49]  J. Wen,et al.  The attitude control problem , 1991 .

[50]  Haichao Gui,et al.  Attitude maneuver control of a two-wheeled spacecraft with bounded wheel speeds , 2013 .

[51]  Congying Han,et al.  Time-Varying Underactuated Attitude Control Design With Feedback Linearization Using Two Pairs of Gas Jet Actuators , 2008 .

[52]  Valeria Andriano.  Global feedback stabilization of the angular velocity of a symmetric rigid body , 1993 .

[53]  Christopher I. Byrnes,et al.  On the attitude stabilization of rigid spacecraft , 1991, Autom..

[54]  Yao Zhang,et al.  Attitude control for part actuator failure of agile small satellite , 2008 .

[55]  Hyungjoo Yoon,et al.  Spacecraft Line-of-Sight Control Using a Single Variable-Speed Control Moment Gyro , 2006 .

[56]  Hyochoong Bang,et al.  Momentum transfer control of a spacecraft with two wheels by feedback linearization , 2008, 2008 International Conference on Control, Automation and Systems.

[57]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[58]  Nadjim Horri,et al.  Attitude stabilization of an underactuated satellite using two wheels , 2003, 2003 IEEE Aerospace Conference Proceedings (Cat. No.03TH8652).

[59]  Dirk Aeyels,et al.  Stabilization by smooth feedback of the angular velocity of a rigid body , 1985 .

[60]  J. S. Hall,et al.  Quaternion feedback regulator for large angle maneuvers of underactuated spacecraft , 2010, Proceedings of the 2010 American Control Conference.

[61]  Shijie Xu,et al.  Global Feedback Control for Attitude Maneuvers of a Spacecraft by Two Reaction Wheels , 2012 .

[62]  Mahmut Reyhanoglu,et al.  Attitude stabilization of a rigid spacecraft using two control torques: A nonlinear control approach based on the spacecraft attitude dynamics , 1994, Autom..

[63]  P. Crouch,et al.  Spacecraft attitude control and stabilization: Applications of geometric control theory to rigid body models , 1984 .