Fractional-Order Sliding Mode Control of Air-Breathing Hypersonic Vehicles Based on Linear-Quadratic Regulator
Publication: Journal of Aerospace Engineering
Volume 31, Issue 3
Abstract
A new fractional-order sliding mode control (FOSMC) scheme is investigated for air-breathing hypersonic vehicles (AHVs). The control scheme proposed is designed based on linear-quadratic optimal theory. First, by using the technique of input/output feedback linearization, the longitudinal model of AHVs is linearized to be decoupled tracking-error dynamics. Second, a linear-quadratic regulator (LQR) is designed to ensure that the tracking-error dynamics converge to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding manifold is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, Lyapunov stability theory is used to prove the finite-time convergence of the closed-loop system. The simulations indicate that the proposed control scheme shows excellent performance and robustness in the absence of uncertainties. Compared with conventional integer-order sliding mode control (IOSMC), the high-frequency chattering of control input is drastically depressed.
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Acknowledgments
This work was partly supported by the National Natural Science Fund of China (No. 11672235). The authors would like to acknowledge their help with information and financial support.
References
Aghababa, M. P. (2013). “A fractional-order controller for vibration suppression of uncertain structures.” ISA Trans., 52(6), 881–887.
Bolender, M., Oppenheimer, M., and Doman, D. (2007). “Effects of unsteady and viscous aerodynamics on the dynamics of a flexible air-breathing hypersonic vehicle.” AIAA Atmospheric Flight Mechanics Conf. and Exhibit, AIAA, Reston, VA, 6397.
Cao, L., Zhang, D., and Tang, S. (2016). “A practical parameter determination strategy based on improved hybrid PSO algorithm for higher-order sliding mode control of air-breathing hypersonic vehicles.” Aerosp. Sci. Technol., 59, 1–10.
Dadras, S., and Momeni, H. R. (2012). “Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty.” Commun. Nonlinear Sci. Numer. Simul., 17(1), 367–377.
Fernández, B. R., and Hedrick, J. K. (1987). “Control of multivariable nonlinear systems by the sliding mode method.” Int. J. Control, 46(3), 1019–1040.
Hu, X. X., Wu, L. G., Hu, C. H., and Gao, H. J. (2012). “Adaptive sliding mode tracking control for a flexible air-breathing hypersonic vehicle.” J. Franklin Inst., 349(2), 559–577.
Jiacai, H., Hongsheng, L., Fulin, T., and Di, L. (2012). “Fractional order sliding mode controller for the speed control of a permanent magnet synchronous motor.” 24th Chinese Control and Decision Conf., IEEE, New York, 1203–1208.
Li, K., Cao, J., and Yu, F. (2013). “Study on the nonsingular problem of fractional-order terminal sliding mode control.” Math. Prob. Eng., 2013, 1–7.
Li, S. H., Sun, H. B., and Sun, C. Y. (2012). “Robust adaptive integral sliding mode fault-tolerant control for air-breathing hypersonic vehicles.” Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng., 226(10), 1344–1355.
Monje, C. A., Chen, Y. Q., Vinagre, B. M., Xue, D. Y., and Feliu, V. (2010). Fractional-order systems and controls, Springer, Berlin.
Moses, P. L., and Nguyen, V. L. (2004). “NASA hypersonic flight demonstrators-overview, status, and future plans.” Acta Astronaut., 55(3–9), 619–630.
Mujumdar, A., Kurode, S., and Tamhane, B. (2013). “Fractional order sliding mode control for single link flexible manipulator.” IEEE Int. Conf. on Control Applications, IEEE, New York, 288–293.
Petráš, I. (2011). Fractional-order nonlinear systems: Modeling, analysis and simulation, Springer, Berlin.
Rodriguez, A. A., and Dickeson, J. J. (2007). “Modeling and control of scramjet-powered hypersonic vehicles: Challenges, trends, and tradeoffs.” AIAA Guidance, Navigation and Control Conf. and Exhibit, AIAA, Reston, VA.
Shtessel, Y., Edwards, C., Spurgeon, S., and Kochalummoottil, J. (2010). “Adaptive finite reaching time control and continuous second order sliding modes.” 49th IEEE Conf. on Decision and Control, IEEE, New York, 5126–5131.
Sun, H. B., Li, S. H., and Sun, C. Y. (2013). “Finite time integral sliding mode control of hypersonic vehicles.” Nonlinear Dyn., 73(1–2), 229–244.
Tang, Y., Wang, Y., Han, M., and Lian, Q. (2016). “Adaptive fuzzy fractional-order sliding mode controller design for antilock braking systems.” J. Dyn. Syst. Meas. Control, 138(4), 041008.
Tang, Y., Zhang, X., Zhang, D., Zhao, G., and Guan, X. (2013). “Fractional order sliding mode controller design for antilock braking systems.” Neurocomputing, 111, 122–130.
Utkin, V. I. (1977). “Variable structure systems with sliding modes.” IEEE Trans. Autom. Control, 22(2), 212–222.
Utkin, V. I., Guldner, J., and Shi, J. (1999). Sliding mode in control in electromechanical systems, Taylor & Francis, London.
Wang, Q., and Stengel, R. F. (2000). “Robust nonlinear control of a hypersonic aircraft.” J. Guidance Control Dyn., 23(4), 577–585.
Williams, T., Bolender, M., Doman, D., and Morataya, O. (2006). “An aerothermal flexible mode analysis of a hypersonic vehicle.” AIAA Atmospheric Flight Mechanics Conf. and Exhibit, AIAA, Reston, VA, 6647.
Xu, H. J., Mirmirani, M. D., and Ioannou, P. A. (2004). “Adaptive sliding mode control design for a hypersonic flight vehicle.” J. Guidance Control Dyn., 27(5), 829–838.
Yin, C., Chen, Y. H., Chen, Y. Q., Stark, B., and Zhong, S. M. (2015). “Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems.” Nonlinear Dyn., 82(1–2), 39–52.
Yin, C., Chen, Y. Q., and Zhong, S. M. (2014). “Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems.” Automatica, 50(12), 3173–3181.
Yin, C., Huang, X., Chen, Y., Dadras, S., Zhong, S. M., and Chen, Y. (2017). “Fractional-order exponential switching technique to enhance sliding mode control.” Appl. Math. Modell., 44, 705–726.
Zhang, B. T., Pi, Y. G., and Luo, Y. (2012). “Fractional-order sliding mode control based on parameter auto-tuning for velocity control of permanent magnet synchronous motor.” ISA Trans., 51(5), 649–656.
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©2018 American Society of Civil Engineers.
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Received: Mar 3, 2017
Accepted: Nov 20, 2017
Published online: Mar 14, 2018
Published in print: May 1, 2018
Discussion open until: Aug 14, 2018
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