عنوان مقاله [English]
In this study, the preferred regions of Pulse-Width Pulse-Frequency Modulator (PWPFM) are obtained analytically for the static analysis. For this purpose, a comprehensive parametric study is carried out based on the two performance indices of fuel consumption and the number of thruster firings. The preferred regions are presented by normalized relations and curves. Moreover, the exact analytical solutions of the two performance indices are obtained for a class of modulators with the assumption of constant inputs. The advantages of the present study are non dimensional analysis and obtaining the preferred regions in terms of each others, resulting in more accurate regions as opposed to inequality relations using constant values for a specified input signal. In addition, in the case of specified minimum pulse width (having the update frequency and thruster time constant), determining the preferred regions becomes more limited. In this regard, useful relations and curves based on the maximum possible value for the number of the thruster firings are derived and presented.
 Wertz, J. R., Spacecraft Attitude Determination and Control, D. Reidel Publishing Company, Massachusetts, 1978.
 Sidi, M. J., Spacecraft Dynamics and Control: A Practical Engineering Approach, Cambridge University Press, Cambridge, 1997.
 Wie, B., Space Vehicle Dynamics and Control, AIAA Education Series, Reston, Virginia, 1998.
 Anthony, T., Wei, B., and Carroll, S., “Pulse Modulated Control Synthesis for a Spacecraft,” Journal of Guidance, Control, Dynamics, Vol. 13, No. 6, pp. 1014–1015, 1990.
 McClelland, R. S., Spacecraft Attitude Control System Performance Using Pulse-Width Pulse-Frequency Modulated Thrusters, Master Thesis, Naval Postgraduate School, Monterey CA, 1994.
 Navabi, M. and Rangraz, H., “Comparing Optimum Operation of Pulse Width-Pulse Frequency and Pseudo-Rate Modulators in Spacecraft Attitude Control Subsystem Employing Thruster,” Recent Advances in Space Technologies (RAST), 2013, pp. 625-630.
 Navabi, M. and Rangraz, H., “Comparing Optimum Operation of Pulse Width-Pulse Frequency and Pseudo-Rate Modulators Regarding Subsystem Life Duration in Control Subsystem Employing Thruster,” The 12th Conference of Iranian Aerospace Society, 2013.
 Hyland, D. C., Junkins, J. L., and Longman, R. W., “Active Control Technology for Large Space Structures,” Journal of Guidance, Control, and Dynamics, Vol. 16, No. 5, 1993,pp. 801-821.
 Singhose, W., Biediger, E., Okada, H., and Matunaga, S., “Control of Flexible Satellites Using Analytic On–Off Thruster Commands,” In Proceedings of AIAA Guidance, Navigation, and Control Conference, 2003.
Santana, C.,Martins, L. S., and Arantes, G., “Attitude Stabilization of the PMM Satellite Using a LQG-Based Control Strategy,”Trends in Applied and Computational Mathematics, Vol. 9, No. 2, 2008, pp. 321-330.
Wie, B.and Plescia, C. T.,“Attitude Stabilization of Flexible Spacecraft During Stationkeeping Maneuvers,” Journal of Guidance, Control, and Dynamics, Vol. 7, No. 4, 1984, pp. 430-436.
Mousavi, F.,Roshanian, J., and Emami, M. R., “Hardware-in-the-Loop Simulation for Attitude Control of a Suborbital Module Using Cold Gas Thrusters,” Modares MechanicalEngineering, Vol. 14, No. 10, 2014, pp. 177-186(in Persian)
Lian, Y. and Tang, G., “Libration Point Orbit Rendezvous Using PWPF Modulated Terminal Sliding Mode Control,”Advances in Space Research, Vol. 52, No. 12, 2013, pp. 2156-2167.
Xu, X. and Cai, Y., “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.
Topland, M. P., Nonlinear Attitude Control of the Micro-Satellite ESEO, M. Sc. Thesis, Norwegian University of Science and Technology, Trondheim, 2004.
Arantes, G., Martins-Filho, L. S., and Santana, A. C.,“Optimal On-Off Attitude Control for the Brazilian Multi Mission Platform Satellite,”Mathematical Problems in Engineering, Vol. 2009, No. 1, 2009, pp. 1- 17.
Buck, N. V., “Minimum Vibration Maneuvers Using Input Shaping and Pulse-Width Pulse-Frequency Modulated Thruster Control,” Naval Postgraduate School, Monterey, CA, 1996.
Song, G., Buck, N. V., and Agrawal, B. N., “Spacecraft Vibration Reduction Using Pulse-Width Pulse-Frequency Modulated Input Shaper,” Journal of Guidance, Control and Dynamics, Vol. 22, 1999, pp. 433-440.
Krovel. T., Optimal Tuning of PWPF Modulator for Attitude Control, Master Thesis, Norwegian University of Science and Technology, Trondheim, Spring 2005.
Jalali-Naini, S. H. and Ahmadi Darani, Sh., “Parametric Optimization of Spacecraft Attitude Control with Pulse-Width Pulse-Frequency Modulator Using Quasi-Normalized Equations,” the 13th Conference of Iranian Aerospace Society, 2014.
Hu, Q. and Ma, G., “Variable Structure Control and Active Vibration Suppression of Flexible Spacecraft DuringAttitude Maneuver,” Aerospace Science and Technology, Vol. 9, No. 4, 2005, pp. 307-317.
Hu, Q., “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, 2009, pp. 1085-1108.
Fazlyab, A., Ajorkar, A.,and Kabganian, M., “Design of an Adaptive Controller of a Satellite Using Thruster Actuator,” Journal of Computer Applications, Vol. 102, No. 10, 2014, pp. 6-12.
Song, G. , and Agrawal, B. N. , “Vibration Suppression of Flexible Spacecraft During Attitude Control,” Acta Astronautica, Vol. 49, No. 2, 2001, pp. 73–83.
Jalali-Naini, S. H. , and Bohlouri, V. , “Quasi-Normalized Analysis of Satellite Stabilization with Pulse-Width Pulse-Frequency Modulator in Presence of Noise,” Modares Mechanical Engineering, Vol. 18, No. 1, 2018, pp. 165-176 (in Persian).
Jalali-Naini, S. H. and Bohlouri, V., “Quasi-Normalized Static and Dynamic Analysis of Pulse-Width Pulse-Frequency Modulator in Presence of Input Noise,” Modares Mechanical Engineering, Vol. 16, No. 2, 2016, pp. 455-466 (in Persian).