Hypersonic Glider Autopilot Using Adaptive Higher Order Sliding Mode Control with Impulsive Actions
Hypersonic glider designs often exhibit limited control authority and poor transversal stability. Furthermore, the methods used for aerodynamic performance estimation at high flight altitudes and hypersonic speeds are inevitably inaccurate and uncertain. Hypersonic Glider performance could be severely degraded by using traditional control and autopilot techniques that rely on an accurate knowledge of the aerodynamic coefficients. A new autopilot and control approach, presented in this paper, is based on recently developed special Higher Order Sliding Mode Control (HOSMC) algorithms that are mostly based on relative degrees but not on the glider’s mathematical model. Specifically, this autopilot and control approach includes robust continuous aerodynamic control augmented by impulsive reaction control thrusters. Control gain-adaptation allows addressing the vehicle bounded uncertainties and perturbations without overestimating the control gains. The impulsive augmentation of the continuous Higher Order Sliding Mode control provides almost instantaneous convergence thereby mitigating the risk of control loss caused by sideslip angle departures due to poor transversal stability and small lateral control authority. While Higher Order Sliding Mode control algorithms are inherently insensitive to the matched uncertainties and disturbances, the observers embedded in the Continuous Higher Order Sliding Mode Control algorithms reduce the time response of the control compensation. Simulation of a representative hypersonic glider executing normal and bank-to-turn maneuvers and controlled by the studied algorithms demonstrate excellent performance in the presence of significant model uncertainties and perturbations.
Hypersonic Glider Autopilot Using Adaptive Higher Order Sliding Mode Control with Impulsive Actions, American Journal of Aerospace Engineering.
Vol. 5, No. 2,
2018, pp. 71-86.
Parker J., Serrani A., Yurkovich S., Bolender M., Doman D. “Control-oriented modeling of an air-breathing hypersonic vehicle, “Journal of Guidance, Control, and Dynamics, Vol. 30, No. 3, 2007, pp. 856–869, DOI: 10.2514/1.27830.
Fiorentini L., Serrani. A., Bolender. M. A., and Doman D. B., “Robust Nonlinear Sequential Loop Closure Control Design for an Air-breathing Hypersonic Vehicle Model, “Proceedings of American Control Conference, 2008, pp. 3458-3463, DOI: 10.1109/ACC.2008.4587028.
Farwell, J., Sharma, M., Polycarpou, M., “Backstepping-Based Flight Control with Adaptive Function Approximation,” Journal of Guidance, Control, and Dynamics, Vol. 28, No.6, 2005, pp. 1089–1102, DOI: 10.2514/1.13030.
Chen, W. H., “Observer Enhanced Dynamic Inversion of Missiles,” Journal of Guidance, Control, and Dynamics, Vol. 25, No.1, 2002, pp. 161–166, DOI: 10.2514/2.5027
C. Tournes, Y. Shtessel, and I. Shkolnikov, “Autopilot for Missiles Steered by Aerodynamic Lift and Divert Thrusters Using Nonlinear Dynamic Sliding Manifolds,” AIAA Journal on Guidance, Control, and Dynamics, Vol. 29, No. 3, (May-June), 2006, pp. 617-625, DOI: 10.2514/1.15486
A. Levant, “Quasi-continuous high-order sliding-mode controllers,” IEEE Trans. Automat. Control, Vol. 50, No. 11, 2006, pp. 1812-1816, DOI: 10.1109/TAC.2005.858646
Y. Shtessel, C. Edwards, L. Fridman, and A. Levant, Sliding Mode Control and Observation, Birkhauser, Springer, New York, 2014, ISBN 978-0-8176-4893-0.
Levant, A. (Levantovsky, L. V.), “Sliding order and sliding accuracy in sliding mode control”, International Journal of Control, Vol. 86, 1993, pp. 1247-1263, DOI: https://doi.org/10.1080/00207179308923053
A. Thukral and M. Innocenti, “Sliding Mode Missile Pitch Autopilot Synthesis for High angle of Attack Maneuvering,” IEEE transactions on Control Systems Technology, Vol. 6, No. 3 1998, pp. 359-371, DOI: 10.1109/87.668037
Y. Shtessel, I. Shkolnikov and A. Levant, “Smooth Second Order Sliding Modes: Missile Guidance application,” Automatica, Vol. 43, No.8, 2007, pp. 1470-1476, DOI: https://doi.org/10.1016/j.automatica.2007.01.008
P. Yu, Y. Shtessel, and C. Edwards, “Continuous Higher Order Sliding Mode Control with Adaptation of Air Breathing Hypersonic Missile,” Int. J. Adapt. Control Signal Process, Vol. 30, Issues 8-10, August-October 2016, pp. 1099-1118, DOI: 10.1002/acs.2664.
W. Zhang, X. Huang, and X.-Z. Gao, “Dynamic output feedback H∞ attitude control for hypersonic gliding vehicles,” International Journal of Innovative Computing, Information & Control, Volume 13, Issue 4, pp. 1351-1368, 2017.
X. Yu, P. Li, and Y. Zhang, “The Design of Fixed-Time Observer and Finite-Time Fault-Tolerant Control for Hypersonic Gliding Vehicles,” IEEE Transactions on Industrial Electronics, Volume 65, Issue 5, pp. 4135-4144, 2018.
G. Kumar, A. Sakar, and S. Talole, “Dynamic pressure based mid-course guidance scheme for hypersonic boost-glide vehicle,” Proceedings of the Institute of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Published online: August 24, 2018, https://doi.org/10.1177/0954410018795265
K. Zhao, D.-Q. Cao, and W.-H. Huang, “Maneuver control of the hypersonic gliding vehicle with a scissored pair of control moment gyros,” Science China Technological Sciences, Volume 61, Issue 8, pp. 1150-1160, August 2018.
C. Edwards and Y. Shtessel "Adaptive Continuous Higher Order Sliding Mode Control," Automatica, Vol. 65, 2016, pp 183-190, DOI: https://doi.org/10.1016/j.automatica.2015.11.038
Bhat, S. P., and Bernstein, D. S., “Geometric homogeneity with applications to finite time stability”, Math. Control Signals Systems, Vol. 17, 2005, pp. 101–127, DOI: https://doi.org/10.1007/s00498-005-0151-x
M. T. Angulo, J. A. Moreno and L. Fridman, “An Exact and Uniformly Convergent Arbitrary Order Differentiator,” Proceedings of CDC-ECC, Orlando, 2011, pp.7629-7634, DOI:10.1109/CDC.2011.6160926
B. Miller and E. Rubinovich, Impulsive Control in Continuous and Discrete- Continuous Systems. Amsterdam: Kluwer Academic Publishers, 2002, DOI: 10.1007/978-1-4615-0095-7
Y. Orlov, Discontinuous Systems: Lyapunov Analysis and Robust Synthesis Under Uncertainty Conditions, Springer, London, 2008, ISBN 978-1-84800-984-4.
A. Levant, “Higher-order sliding modes, differentiation and output-feedback control”. International Journal of Control, 76, 9/10, 2003, 924-941, DOI: https://doi.org/10.1080/0020717031000099029.
F. M. Aldukali, and Y. B. Shtessel, “Continuous Higher Order Sliding Mode Control with Impulsive Action,” Proceedings of the Conference on Decision and Control, Osaka, Japan, December 2015, DOI: 10.1109/CDC.2015.7403068.
Y. Shtessel, A. Glumineau, F. Plestan, and F. Aldukali, “Hybrid-impulsive second-order sliding mode control: Lyapunov approach,” International Journal on Robust and Nonlinear Control,”- Volume 27, Issue 7, May 2017, pp. 1064–1093, DOI: 10.1002/rnc.3618.
M. Weiss and Y. Shtessel, “An Impulsive Input Approach to Short Time Convergence for Linear Systems,” Advances in Aerospace Guidance Navigation and Control, Q. Chu, B. Mulder, D. Choukroun, E. van Kampen, C. de Visser and G. Looye (Eds.) Springer, July 2013, pp. 99-119, DOI https://doi.org/10.1007/978-3-642-38253-6_8, ISBN 978-3-642-38252-9.
I. Gel’fand and G. Shilov, “Generalized functions,” Academic Press, 1964, ISBN-10: 1-4704-2658-7.
Recommended Practice for Atmospheric Flight Vehicles Coordinate Systems, ANSI/AIAA R-004-1992.
Tournes, C., “Compendium of Flight Mechanics Formulae Applied to Hypersonic Gliders, AIAA Paper 2013 4609, Aug. 2013, DOI: 10.2514/6.2013-4609
Vallado, D., “Fundamentals of Astrodynamics and Application,” Space Technology Library, El Segundo, CA, 2001, pp. 141-151, ISBN 1-881883-12-4
A. Tiwari, “Atmospheric and Space Flight Dynamics,” Birkhauser, Springler, New York, 2006, pp. 53-289 ISBN-10:0-8176-4373-7
P. Faurre, “Navigation Inertielle Optimale et Filtrage Statistique,” Dunod, Paris, 1971, p. 268 (in French)
Stevens, B. L., Lewis, F. L, “Equations of Motion, “Aircraft Control and Simulation, Willey, New York, 1992, pp. 1-48, ISBN 0-471-61397-5
Y. Shtessel, B. Chava, and C. Edwards, “Second Order Sliding Mode Control using Nonlinear Dynamic Sliding Manifold: Lyapunov Approach,” Proceedings of the Conference on Decision and Control, Osaka, Japan, December 2015, DOI 10.1109/CDC.2015.7