## Smooth switching LPV controller design for LPV systems.(English)Zbl 1296.93079

Summary: This paper presents a method to design a smooth switching gain-scheduled Linear Parameter Varying (LPV) controller for LPV systems. The moving region of the gain-scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching, and one gain-scheduled LPV controller is assigned to each of the local subregions. For each switching subregion, a function interpolating two local LPV controllers associated with its neighborhood subregions is designed to satisfy the constraint of smooth transition of controller system matrices. The smooth switching controller design problem amounts to solving a feasibility problem which involves nonlinear matrix inequalities. To find a solution to the feasibility problem, an iterative descent algorithm which solves a series of convex optimization problems is proposed. The usefulness of the proposed controller design method is demonstrated with a control example of a flexible ball-screw drive system.

### MSC:

 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 93C05 Linear systems in control theory 93B40 Computational methods in systems theory (MSC2010)
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### References:

 [1] Apkarian, P.; Adams, R. J., Advanced gain-scheduling techniques for uncertain systems, IEEE Transactions on Control Systems Technology, 6, 1, 21-32, (1998) [2] Apkarian, P.; Gahinet, P., A convex characterization of gain-scheduled $$H_\infty$$ controllers, IEEE Transactions on Automatic Control, 40, 5, 853-864, (1995) · Zbl 0826.93028 [3] Bendtsen, J. D.; Stoustrup, J.; Trangbaek, K., Bumpless transfer between observer-based gain scheduled controllers, International Journal of Control, 78, 7, 491-504, (2005) · Zbl 1088.93007 [4] Bianchi, F. D.; Sanchez Pena, R. S., Interpolation for gain-scheduled control with guarantees, Automatica, 47, 1, 239-243, (2011) · Zbl 1209.93065 [5] Boyd, S.; Vandenberghe, L., Convex optimization, (2004), Chambridge University Press Cambridge · Zbl 1058.90049 [6] Chen, P., The design of smooth switching control with application to V/STOL aircraft dynamics under input and output constraints, Asian Journal of Control, 14, 2, 439-453, (2012) · Zbl 1286.93070 [7] Chen, P., Multi-objective control of nonlinear boiler-turbine dynamics with actuator magnitude and rate constraints, ISA Transactions, 52, 1, 115-128, (2013) [8] Chen, P., Wu, S., & Chuang, H. (2010). The smooth swtiching control for TORA system via LMIs. In The Proceedings of the 8th IEEE International conference on control and automation (pp. 1338-1343). Xiamen, China. [9] Edwards, C.; Postlethwaite, I., Anti-windup and bumpless-transfer schemes, Automatica, 34, 2, 199-210, (1998) [10] Gahinet, P.; Apkarian, P., A linear matrix inequality approach to $$H_\infty$$ control, International Journal of Robust and Nonlinear Control, 4, 4, 421-448, (1994) · Zbl 0808.93024 [11] Graebe, S. F.; Ahlen, A. L.B., Dynamic transfer among alternative controllers and its relation to anti-windup controller design, IEEE Transactions on Control Systems Technology, 4, 1, 92-99, (1996) [12] Hanifzadegan, M.; Nagamune, R., Switching gain-scheduled control of ball-screw drive systems, ASME Journal of Dynamic Systems, Measurement, and Control, 136, 1, 014503-1-014503-6, (2014) [13] Hencey, B.; Alleyne, A. G., A robust controller interpolation design technique, IEEE Transactions on Control Systems Technology, 8, 1, 1-10, (2010) [14] Hu, K.; Yuan, J., On switching $$H_\infty$$ controllers for nuclear steam generator water level: a multiple parameter-dependent Lyapunov functions approach, Annals of Nuclear Energy, 35, 10, 1857-1863, (2008) [15] Kinnaert, M., Delwiche, T., & Yamé, J. (2009). State resetting for bumpless switching in supervisory control. In Proceedings of the European control conference (pp. 2097-2102). Budapest, Hungary. [16] Liberzon, D., Switching in systems and control, (2003), Birkhäuser Boston · Zbl 1036.93001 [17] Lu, B.; Wu, F., Switching LPV control designs using multiple parameter-dependent Lyapunov functions, Automatica, 40, 11, 1973-1980, (2004) · Zbl 1133.93370 [18] Lu, B.; Wu, F.; Kim, S., Switching LPV control of an F-16 aircraft via controller state reset, IEEE Transactions on Control Systems Technology, 14, 2, 267-277, (2006) [19] (Mohammadpour, J.; Scherer, C. W., Control of linear parameter varying systems with applications, (2012), Springer New York) [20] Packard, A., Gain scheduling via linear fractional transformations, Systems & Control Letters, 22, 2, 79-92, (1994) · Zbl 0792.93043 [21] Postma, M.; Nagamune, R., Air-fuel ratio control of spark ignition engines using a switching LPV controller, IEEE Transactions on Control Systems Technology, 20, 5, 1175-1187, (2012) [22] Pour Safaei, F. R.; Hespanha, J. P.; Stewart, G., On controller initialization in multivariable switching systems, Automatica, 48, 12, 3157-3165, (2012) · Zbl 1255.93128 [23] Rugh, W. J.; Shamma, J. S., Research on gain-scheduling, Automatica, 36, 10, 1401-1425, (2000) · Zbl 0976.93002 [24] Shamma, J. S.; Athans, M., Analysis of gain scheduled control for nonlinear plants, IEEE Transactions on Automatic Control, 35, 8, 898-907, (1990) · Zbl 0723.93022 [25] Turner, M.; Walker, D., Linear quadratic bumpless transfer, Automatica, 36, 1089-1101, (2000) · Zbl 0960.93013 [26] White, A. P.; Zhu, G.; Choi, J., Linear parameter-varying control for engineering applications, (2013), Springer London · Zbl 1272.93004 [27] Yamé, J., & Kinnaert, M. (2004). Parametrization of linear controllers for bumpless switching in multi-controller schemes. In Proceedings of the AIAA guidance, navigation and control conference and exhibit (pp. 16-19). Providence, Rhode Island, USA. [28] Zaccarian, L.; Teel, A., The $$L_2$$ bumpless transfer problem for linear plants: its definition and solution, Automatica, 41, 7, 1273-1280, (2005) · Zbl 1115.93348
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