ABSTRACT The attitude control problem of the kinetic kill vehicle is studied in this work. A new mathematical model of the kinetic kill vehicle is proposed, the linear quadratic regulator technique is used to design the optimal attitude controller, and the pulse-width pulse-frequency modulator is used to shape the continuous control command to pulse or on-off signals to meet the requirements of the reaction thrusters. The methods to select the appropriate parameters of pulse-width pulse-frequency are presented in detail. Numerical simulations show that the performance of the LQR/PWPF approach can achieve good control performance such as pseudo-linear operation, high accuracy, and fast enough tracking speed.
Cite this paper
nullX. Xu and Y. Cai, "Pulse-Width Pulse-Frequency Based Optimal Controller Design for Kinetic Kill Vehicle Attitude Tracking Control," Applied Mathematics, Vol. 2 No. 5, 2011, pp. 565-574. doi: 10.4236/am.2011.25075.
 R. C. Schindler, “SDI Thinks Small-Miniaturized Propulsion is Needed for Ground- and Space-Based Kill Vehicles,” Proceedings of the 27th AIAA/SAE/ASME Joint Propulsion Conference, AIAA Paper, No. 1991-1932, Sacramento, 1991.
 J. Pavlinsky, “Advanced Thrust Chambers for Miniaturized Engines,” Proceedings of the 28th AIAA/SAE/ASME/ ASEE Joint Propulsion Conference and Exhibit, AIAA Paper, No. 1992-3258, Nashville, 1992.
 E. D. Bushway and E. Nelson, “Design and Development of Lightweight Integrated Valve/Injector for the THAAD Program,” Proceedings of the 30th AIAA/SAE/ASME/ ASEE Joint Propulsion Conference, AIAA Paper, No. 1994-3383, Indianapolis, 1994.
 T. W. Hwang, C. S. Park, M. J. Tahk and H. Bang, “Upper-Stage Launch Vehicle Servo Controller Design Considering Optimal Thruster Configuration,” Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA Paper, No. 2003-5330, Austin, 2003.
 G. Avanzini and G. Matteis, “Bifurcation Analysis of Attitude Dynamics in Rigid Spacecraft with Switching Control Logics,” Journal of Guidance, Control and Dynamics, Vol. 24, No. 5, 2001, pp. 953-959. doi:10.2514/2.4802
 H. Fenghua, M. Kemao and Y. Yu, “Firing Logic Optimization Design of Lateral Jets in Missile Attitude Control Systems,” Proceedings of the 17th IEEE International Conference on Control Applications Part of 2008 IEEE Multi-Conference on Systems and Control San Antonio, San Antonio, 3-5 September 2008, pp. 936-941.
 W. Bao, B. Li, J. Chang, W. Yu and D. Ren, “Switching Control of Thrust Regulation and Inlet Buzz Protection for Ducted Rocket,” Acta Astronautica, Vol. 67, No. 7-8, 2010, pp. 764-773. doi:10.1016/j.actaastro.2010.04.022
 Y. Z. Luo, J. Zhang, H. Y. Li and G. J. Tang, “Interactive Optimization Approach for Optimal Impulsive Rendezvous Using Primer Vector and Evolutionary Algorithms,” Acta Astronautica, Vol. 67, No. 3-4, 2010, pp. 396-405. doi:10.1016/j.actaastro.2010.02.014
 A. M. Zou and K. D. Kumar, “Adaptive Attitude Control of Spacecraft Without Velocity Measurements Using Chebyshev Neural Network,” Acta Astronautica, Vol. 66, No. 5-6, 2010, pp. 769-779. doi:10.1016/j.actaastro.2009.08.020
 Y. Wu, X. Cao, Y. Xing, P. Zheng and S. Zhang, “Relative Motion Decoupled Control for Spacecraft Formation with Coupled Translational and Rotational Dynamics,” Proceedings of the International Conference on Computer Modeling and Simulation, 2009, pp. 63-68. doi:10.1109/ICCMS.2009.12
 Q. L. 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, 2009, pp. 1085-1108. doi:10.1016/j.actaastro.2009.01.009
 Q. L. 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, 2010, pp. 572-583. doi:10.1016/j.actaastro.2010.04.018
 T. D. Krovel, “Optimal Tunning of PWPF Modulator for Attitude Control,” M.S. Thesis, Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, 2005.
 G. Song, N. V. Buck and B. N. Agrawal, “Spacecraft Vibration Reduction Using Pulse-Width Pulse-Frequency Modulated Input Shaper,” Journal of Guidance, Control and Dynamics, Vol. 22, No. 3, 1999, pp. 433-440. doi:10.2514/2.4415
 G. Song and B. N. Agrawal, “Vibration Suppression of Flexible Spacecraft During Attitude Control,” Acta Astronautica, Vol. 49, No. 2, 2001, pp. 73-83.
 G. Arantes, L. S. Martins-Filho and A. C. Santana, “Optimal On-off Attitude Control for the Brazilian Multimission Platform Satellite,” Mathematical Problems in Engineering, Vol. 2009, No. 1, 2009, pp. 1-17. doi:10.1016/S0094-5765(00)00163-6
 B. D. Anderson and J. B. Moore, “Optimal Control: Linear Quadratic Methods,” Prentice Hall, Englewood Cliffs, 1990.
 R. Bevilacqua, T. Lehmann and M. Romano, “Development and Experimental of LQR/APF Guidance and Control for Autonomous Proximity Maneuvers of Multiple Spacecraft,” Acta Astronautica, Vol. 68, No. 7-8, 2011, pp. 1260-1275.
 G. Y. Tang, “Suboptimal Control for Nonlinear Systems: A Successive Approximation Approach,” Systems & Control Letters, Vol. 54, No. 5, 2005, pp. 429-434. doi:10.1016/j.sysconle.2004.09.012