Abstract
A servo control with unknown system parameters and constraints imposed on the maximal tracking error is considered. The barrier Lyapunov functions approach is applied to assure the preservation of constraints in any condition. The system’s performance is examined for three methods of controller design based on: quadratic Lyapunov functions; on barrier Lyapunov functions if only position constraints are imposed; and on barrier Lyapunov functions if both position and velocity constraints are present. The tuning rules are discussed and several experiments demonstrating features of the proposed control and the influence of the parameters are presented.
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References
Grüne L, Pannek J (2011) Nonlinear model predictive control theory and algorithms. Springer, London
Dòria-Cerezo A, Acosta JA, Castaño ÁR, Fossas E (2014) Nonlinear state-constrained control. Application to the dynamic positioning of ships, In: IEEE conference on control applications (CCA), Juan Les Antibes, pp 911–916
Krstic M, Kanellakopoulos I, Kokotovic P (1995) Nonlinear and adaptive control design. Wiley, New York
Ngo K, Jiang Z (2005) Integrator backstepping using barrier functions for systems with multiple state constraints, In: Proceedings of the 44th IEEE conference on decision and control European control conference, pp 8306–8312
Tee KP, Ge SS, Tay EH (2009) Barrier Lyapunov functions for the output-constrained nonlinear systems. Automatica 45(4):918–927
Ren BB, Ge SS, Tee KP, Lee TH (2010) Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Trans Neural Netw 21(8):1339–1345
Tee KP, Ge SS (2010) Control of nonlinear systems with partial state constraints using a barrier Lyapunov function. Int J Control 84(12):2009–2023
Ren BB, Ge SS, Tee KP, Lee TH (2009) Adaptive control of electrostatic microactuator with bidirectional drive. IEEE Trans Contr Syst Technol 17(2):340–352
How BVE, Ge SS, Choo YS (2011) Control of coupled vessel, crane, cable, and payload dynamics for subsea installation operation. IEEE Trans Contr Sys Tech 19(1):208–220
Ioannou P, Fidan B (2006) Adaptive control tutorial. Society for industrial and applied mathematics, Philadelphia
Jastrzębski M, Kabziński J, Mosiołek P (2016) Adaptive motion control with state constraints using barrier Lyapunov functions. Przegląd Elektrotechniczny (Electr Rev) 92(4):112–116
Slotine JE, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliff
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Kabziński, J., Mosiołek, P., Jastrzębski, M. (2017). Adaptive Position Tracking with Hard Constraints—Barrier Lyapunov Functions Approach. In: Kabziński, J. (eds) Advanced Control of Electrical Drives and Power Electronic Converters. Studies in Systems, Decision and Control, vol 75. Springer, Cham. https://doi.org/10.1007/978-3-319-45735-2_2
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DOI: https://doi.org/10.1007/978-3-319-45735-2_2
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