On modeling and control of a flexible air-breathing hypersonic vehicle based on LPV method

Abstract

This article develops a polytopic linear parameter varying (LPV) model and presents a non-fragile H₂ gain-scheduled control for a flexible air-breathing hypersonic vehicle (FAHV). First, the polytopic LPV model of the FAHV can be obtained by using Jacobian linearization and tensor-product (TP) model transformation approach, simulation verification illustrates that the polytopic LPV model captures the local nonlinearities of the original nonlinear system. Second, based on the developed polytopic LPV model, a non-fragile gainscheduled control method is proposed in order to reduce the fragility encountered in controller implementation, a convex optimisation problem with linear matrix inequalities (LMIs) constraints is formulated for designing a velocity and altitude tracking controller, which guarantees H₂ control performance index. Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.

Keywords

linear parameter varying (LPV) / nonfragile / gain-scheduled control / flexible air-breathing hypersonic vehicle (FAHV)

References

[1] Colgren R, Keshmiri S, Mirmirani M. Nonlinear ten-degreeof-freedom dynamic model of a generic hypersonic vehicle. Journal of Aircraft, 2009, 46(3): 800-813

[2] Mirmirani M, Kuipers M, Levin J, Clark A D. Flight dynamic characteristics of a scramjet-powered generic hypersonic vehicle. In: Proceedings of the 2009 American Control Conference. 2009, 2525-2532

[3] Schmidt D K, Hermann J A. Use of energy-state analysis on a generic air-breathing hypersonic vehicle. Journal of Guidance, Control, and Dynamics, 1998, 21(1): 71-76

[4] Skujins T, Cesnik C E S. Reduced-order modeling of hypersonic vehicle unsteady aerodynamics. In: Proceedings of the 2010 AIAA Guidance, Navigation, and Control Conference. 2010, AIAA-2010-8127

[5] Gao H J, Si Y L, Li H Y, Hu X X, Wang C H. Modeling and control of an air-breathing hypersonic vehicle. In: Proceedings of the 7th Asian Control Conference. 2009, 304-307

[6] Bolender M A, Doman D B. A nonlinear longitudinal dynamical model of an air-breathing hypersonic vehicle. Journal of Spacecraft and Rockets, 2007, 44(2): 374-387

[7] Parker J T, Serrani A, Yurkovich S, Bolender M A, Doman D B. Control-oriented modeling of an air-breathing hypersonic vehicle. Journal of Guidance, Control, and Dynamics, 2007, 30(3): 856-869

[8] Sigthorsson D O, Serrani A. Development of linear parameter-varying models of hypersonic air-breathing vehicles. In: Proceedings of the 2009 AIAA Guidance, Navigation, and Control Conference. 2009, AIAA-2009-6282

[9] Bolender M A, Oppenheimer M W, Doman D B. Effects of unsteady and viscous aerodynamics on the dynamics of a flexible air-breathing hypersonic vehicle. In: Proceedings of the 2007 AIAA Atmospheric Flight Mechanics Conference. 2007, AIAA-2007-6397

[10] Williams T, Bolender M A, Doman D B, Morataya O. An aerothermal flexible mode analysis of a hypersonic vehicle. In: Proceedings of the 2006 AIAA Atmospheric Flight Mechanics Conference. 2006, AIAA-2006-6647

[11] Cai G B, Duan G R, Hu C H. A velocity-based LPV modeling and control framework for an air-breathing hypersonic vehicle. International Journal of Innovative Computing, Information and Control, 2011, 7(5A): 2269-2281

[12] Sigthorsson D O, Jankovsky P, Serrani A, Yurkovich S, Bolender M A, Doman D B. Robust linear output feedback control of an airbreathing hypersonic vehicle. Journal of Guidance,Control, and Dynamics, 2008, 31(4): 1052-1066

[13] Fiorentini L, Serrani A, Bolender M A, Doman D B. Nonlinear robust adaptive control of flexible air-breathing hypersonic vehicles. Journal of Guidance, Control, and Dynamics, 2009, 32(2): 401-416

[14] Lei Y, Cao C, Cliff E, Hovakimyan N, Kurdila A, Wise K. L1 adaptive controller for air-breathing hypersonic vehicle with flexible body dynamics. In: Proceedings of American Control Conference. 2009, 3166-3171

[15] Subbaram Naidu D, Banda S S, Buffington J L. Unified approach to H₂ and H∞ infinity optimal control of a hypersonic vehicle. In: Proceedings of American Control Conference. 1999, 2737-2741

[16] Chen J, Pan C P, Wu J H. Dynamic surface backingstepping control design for one hypersonic vehicle. In: Proceedings of the 2009 IEEE International Conference on Mechatronics and Automation. 2009, 4770-4774

[17] Gao D X, Sun Z Q. Fuzzy tracking control design for hypersonic vehicles via T-S model. Science China (Information Science), 2011, 54(3): 521-528

[18] Gunnarsson K S, Jacobsen J O. Design and simulation of a parameter varying controller for a fighter aircraft. In: Proceedings of the 2001 AIAA Guidance, Navigation, and Control Conference. 2001, AIAA-2001-4105

[19] Wang Q, Stengel R F. Robust nonlinear control of a hypersonic aircraft. Journal of Guidance, Control, and Dynamics, 2000, 23(4): 577-585

[20] Yee J-S, Yang G-H, Wang J L. Non-fragile H∞ flight controller design for a high performance aircraft. In: Proceedings of the American Control Conference. 2000, 1857-1861

[21] Chu H K, Deng M. Robust non-fragile H∞ control and simulation of aircraft lengthways system. Science Technology and Engineering, 2007, 7(10): 2233-2237 (in Chinese)

[22] Wei X K, del Re L. Gain scheduled H∞ control for air path systems of diesel engines using LPV techniques. IEEE Transactions on Control Systems Technology, 2007, 15(3): 406-415

[23] Rasmussen B P, Alleyne A G. Gain scheduled control of an air conditioning system using the Youla parameterization. IEEE Transactions on Control Systems Technology, 2010, 18(5): 1216-1225

[24] Saussi′eD, Saydy L, Akhrif O, B′erard C. Gain scheduling with guardian maps for longitudinal flight control. Journal of Guidance, Control, and Dynamics, 2011, 34(4): 1045-1059

[25] Ginter V J, Pieper J K. Robust gain scheduled control of a hydrokinetic turbine. IEEE Transactions on Control Systems Technology, 2011, 19(4): 805-817

[26] White A, Choi J, Nagamune R, Zhu G. Gain-scheduling control of port-fuel-injection processes. Control Engineering Practice, 2011, 19(4): 380-394

[27] Bolender M A, Doman D B. A non-linear model for the longitudinal dynamics of a hypersonic air-breathing vehicle. In: Proceedings of the 2005 AIAA Guidance, Navigation, and Control Conference. 2005, AIAA-2005-6255

[28] Li H Y, Si Y L, Wu L G, Hu X X, Gao H J. Guaranteed cost control with poles assignment for a flexible air-breathing hypersonic vehicle. International Journal of Systems Science, 2011, 42(5): 863-876

[29] Petres Z. Polytopic decomposition of linear parameter varying models by tensor-product model transformation. Ph.D. Thesis Booklet. Budapest: Budapest University of Technology and Economics, 2006

[31] Xie W. H₂ gain-scheduled state feedback for LPV system with new LMI formulation. IEE Proceedings —Control Theory and Applications, 2005, 152(6): 693-697

[32] de Souza C E, Trofino A. Gain-scheduled H₂ control of linear parameter varying systems using a parameteric Lyapunov function. In: Proceedings of the 43rd IEEE Conference on Decision and Control. 2004, 2936-2941

[33] Famularo D, Dorato P, Abdallah C T, Haddad W M, Jadbabaie A. Robust non-fragile LQ controller the static state feedback case. International Journal of Control, 2000, 73(2): 159-165

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg