Gain-scheduled H_2/H_∞ autopilot design with regional pole placement constraints: An LMI-based approach

Document Type : Article

Authors

Faculty of Electrical Engineering, Malek Ashtar University of Technology, Tehran, P.O. Box 15875-1774, Iran

10.24200/sci.2020.53269.3154

Abstract

In this paper, a gain-scheduled three loop autopilot is designed for a pursuit system which can guarantee the mixed H_2/H_∞ performance and time domain constraints. The gain-scheduled autopilot problem is converted into a static state feedback control for a Linear Parameter Varying (LPV) system and then a control method is proposed by following the Linear Matrix Inequalities (LMIs) approach to satisfy the mixed H_2/H_∞ performance with regional pole placement constraints without any constraints on system matrices. The final gain-scheduled controller is obtained by the interpolation of the finite number of fixed controllers in every vertex, guaranteeing the stability and performance of the LPV system. The simulation results demonstrate the efficiency of the proposed method for the three loop autopilot design.

Keywords


References
1.       Jackson, P. B. “Overview of missile flight control systems”, John Hopkins APL Technical Digest, 29 (1), pp. 9-24 (2010).
2.       Li, S. and Yang, J. “Robust autopilot design for bank-to-turn missiles using disturbance observers”, IEEE Transactions on Aerospace and Electronic Systems, 49(1), pp. 558- 579 (2013).
3.       Statement, I. P. “Pitch autopilot design for agile missiles with uncertain aerodynamic coefficients”, IEEE Transactions on Aerospace and Electronic Systems on aerospace and electronic systems,49(2), pp. 907–914 (2013).
4.       Reichert, R. T. “Dynamic scheduling of modern-robust-control autopilot designs for missiles”, IEEE Control Systems, 12(5), pp. 35-42 (1992).
5.       Biannic, J. M. and Apkarian, P. “Missile autopilot design via a modified LPV synthesis technique”, Aerospace Science and Technology, 3(3), pp. 153–160 (1999).
6.       Theodoulis, S., Seve, F., and Wernert, P. “Robust gain-scheduled autopilot design for spin-stabilized projectiles with a course-correction fuze”, Aerospace Science and Technology, 42, pp. 477–489 (2015).
7.       Shen, Y., Yu,  J., Luo, G., and et al. “Missile autopilot design based on robust LPV control”, Journal of Systems Engineering and Electronics, 28(3), pp. 536–545 (2017).
8.       Leith, D. J., Tsourdos, A., White, B. A., and et al. “Application of velocity-based gain-scheduling to lateral autopilot design for an agile missile”, Control Engineering Practice, 9(10), pp. 1079–1093 (2001).
9.       Mohammadpour, J. and Scherer, CW. Control of Linear Parameter Varying Systems with Applications. New York: springer, (2012).
10.     Shamma, M. A. J. “Guaranteed properties of gain scheduled control for linear parameter-varying plants”, Automatica, 27(3), pp. 559–564 (1991).
11.     Vesely , V. and Ilka, A. “Gain-scheduled PID controller design”, Journal of Process Control, 23(8), pp. 1141–1148 (2013).
12.     Ilka, A. and Vesely, V. “Discrete gain-scheduled controller design: Variable weighting approach”, Journal of Electrical Engineering, 65(2), pp. 116–120 (2014).
13.     Guo, Z., Yao, X., and Zhang, X. “Robust gain scheduled longitudinal autopilot design for rockets during the sustaining phase”, Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering, 230(10), pp. 1154–1163 (2016).
14.     Lhachemi, H., Saussié, D., and Zhu, G. “Handling hidden coupling terms in gain-sheduling control design: Application to a pitch-axis missile autopilot”, AIAA Guidance, Navigation, and Control Conference,pp. 1–21 (2016).
15.     Xiaofeng, S. and Yingmin, J. “Self-scheduled robust decoupling control with H∞ performance of hypersonic vehicles”, Systems & Control Letters, 70, pp. 38–48 (2014).
16.     Yang , S. M. and Huang, N. H. “Application of H∞ control to pitch autopilot of missiles”,  IEEE Transactions on Aerospace and Electronic Systems IEEE, 32(1), pp. 426–433 (1996).
17.     Veenman, J. and Scherer, C.W. “A synthesis framework for robust gain-scheduling controllers”, Automatica, 50(11), pp. 2799–2812 (2014).
18.     Behrouz, H., Mohammadzaman, I., and Mohammadi, A. “Robust static output feedback design with pole placement constraints for linear systems with polytopic uncertainties”, Transactions of the Institute of Measurement and Control, pp. 1–11 (2019).
19.     Hoffmann, C. and Werner, H. “A survey of linear parameter-varying control applications validated by experiments or high-fidelity simulations”, IEEE Transactions on Automatic Control systems technology, 23(2), pp. 416–433 (2015).
20.     Li, T., Zhang, S., Yang , H., and et al. “Robust missile longitudinal autopilot design based on equivalent-input-disturbance and generalized extended state observer approach”, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 229(6), pp. 1025–1042 (2015).
21.     Kurkcu, B. and Kasnakoglu, C. “Robust autopilot design based on a disturbance/uncertainty /coupling estimator”, IEEE Transactions on Control Systems Technology, 27(6), pp. 2622-2629 (2018).
22.     Dong, Y., Li, J., and Li, T. “Generalized extended state observer-based H∞ control design for a missile longitudinal autopilot”,  Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 230(12), pp. 2162–2178 (2016).
23.     Chen, B. S. and Zhang, W. “Stochastic H2/H∞ control with state dependent noise”, IEEE Transactions on Automatic Control, 49(1), pp. 45–57 (2004).
24.     Ibrir, S. and Sabir , A. “Dynamic-output stabilization and tracking of uncertain linear systems with mixed H2/H∞ performance”, Industrial Electronics and Applications, (2016).
25.     Lien, C. H., Yu, K. W., Lin, Y. F., and et al. “Robust reliable H∞ control for uncertain nonlinear systems via LMI approach”, Applied Mathematics and Computation, 198(1), pp. 453–462 (2008).
26.     Prempain, E. and Postlethwaite, I. “L2 and H2 performance analysis and gain-scheduling synthesis for parameter-dependent system”, Automatica, 44(8), pp. 2081–2089 (2008).
27.     Qingjiang , H., Sijun, Y., Yan, L., and et al. “An enhanced LMI approach for mixed H2/H∞ flight tracking control”, Chinese Journal of Aeronautics, 24, pp. 324–328 (2011).
28.     Rotondo, D., Ejjari, F., and Puig, V. “Robust state-feedback control of uncertain LPV systems: An LMI-based approach”, Journal of the Franklin Institute, 351(5), pp. 2781–2803 (2014).
29.     Scherer, C. W. “An efficient solution to multi-objective control problems with LMI objectives”, Systems & Control Letters, 40(1), pp. 43–57 (2000).
30.     Magni, J.F. “Multimodel eigenstructure assignment in flight-control design”, Aerospace Science and Technology, 3(3), pp. 141–151 (1999).
31.     Lee, C. H., Shin, M. H., and Chung, M. J. “A design of gain-scheduled control for a linear parameter varying system: an application to flight control”, Control Engineering Practice, 9(1), pp. 11–21 (2011).
32.     Lhachemi, H., Saussie, D., and Zhu, G. “Explicit hidden coupling terms handling in gain-scheduling control design via eigenstructure assignment”, Control Engineering Practice, 58, pp. 1–11 (2017).
33.     Wang, H., Lin, D., Wang , J., and et al. “An analytical design method for the missile two-loop acceleration autopilot”, System Simulation and Scientific Computing, pp. 57–65 (2012).
34.     Lee, C. H., Jun, B. E., and Lee, J. I. “Connections between linear and nonlinear missile autopilots via three-loop topology”, Journal of Guidance, Control, and Dynamics, 39(6), pp. 1424–1430 (2016).
35.     Nesline, W. and Zarchan, P. “Robust instrumentation configurations for homing missile flight control”, AIAA Guidance, Navigation, and Control, pp. 209–219 (1980).
36.     Mohamed, E. M. and Yan, L. “Design and comparison of two-loop with PI and three-loop autopilot for static unstable missile”, International Journal of Computer and Electrical Engineering, 8(1), pp. 1–11 (2016).
37.     Kim, J. H. and Whang, I. H. “Augmented three-loop autopilot structure based on mixed-sensitivity H∞ optimization”, Journal of Guidance, Control, and Dynamics, 41(3), pp. 748–753 (2018).
38.     Abd-Elatif, M. A., Qian, L., and Bo, Y. “Optimization of three-loop missile autopilot gain under crossover frequency constraint”, Defence Technology, 12(1), pp. 32-38 (2016).
39.     Mracek, C. P. and Ridgely, D. B. “Missile longitudinal autopilots: comparison of multiple three loop topologies”, AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, pp. 917–928 (2005).
40.     Defu, L., junfang, F., Zaikang, Q., and et al. “Analysis and improvement of missile three-loop autopilots”, System Engineering Electronic, 20(4), pp. 844–851 (2009).
41.     Qiu, W., Li, X. Q., and Kang, Q. Z. “Pole placement design with open-loop crossover frequency constraint for three-loop autopilot”, System Engineering Electronic (in China), 2, (2009).
42.     Zhou, K. “Essentials of robust control”, In Pearson (1999).
43.     Apkarian, P., Noll, D., and Rondepierre, A. “Mixed H2/H∞ control via nonsmooth optimization”, SIAM Journal on Control and Optimization, 47(3), pp. 1516–1546 (2008).
44.     Apkarian, P., Gahinets, P., and Becker, G. “Self-scheduled H∞ control of linear parameter-varying systems: a design example”, Automatica, 31(9), pp. 1251–1261 (1995).
45.     Scherer, C. and Weiland, S. “Linear matrix inequalities in control”, Lecture Notes, Dutch Institute for Systems and Control, Delft, The Netherlands(2000).
46.     Zipfel, P.H. “Modeling and simulation of aerospace vehicle dynamics”, In AIAA, Second Edition (2007).
47.     Nichols, R. A., Reichert, R. T., and Rugh, W. J. “Gain scheduling for H-infinity controllers: a flight control example”, IEEE Transactions on Control Systems Technology, 1(2), pp. 69 – 79 (1993).
48.     Dong, J. and Yang, G.-H. “Robust static output feedback control synthesis for linear continues systems with polytopic uncertainties”, Automatica, 49(6), pp. 1821–1829 (2013).
49.     Chang, X.-H., Park, J. H., and Zhou, J. “Robust static output feedback H∞ control design for linear systems with polytopic uncertainties”, Systems & Control Letters, 85, pp. 23–32 (2015).
50.     Ramos, D. C. W. and Peres, P. L. D. “An LMI condition for the robust stability of uncertain continuous-time linear systems”, IEEE Transactions on Automatic Control, 47(4), pp. 675–678 (2002).
51.     Pellanda, P. C., Apkarian , P., and Tuan, H. D. “Missile autopilot design via a multi-channel LFT / LPV control method”, International Journal of Nonlinear and Robust Control, 12(1), pp. 1–20 (2002).
52.     Zhou, K., Doyle, J. C., and Glover, K. “Robust and optimal control”, In Prentice Hall, New Jersey (1996).