Abstract
Based on the backstepping method, this paper proposes a robust control algorithm for nonlinear plants under parametric uncertainty and external bounded disturbances. The algorithm ensures tracking of the plant output to a smooth reference signal with a required accuracy in the steady-state mode. In comparison with the existing analogs, control system implementation requires only one filter of dimension coinciding with the plant relative degree and observers used for calculation of the stabilizing and basic control laws. This feature considerably simplifies the control scheme and calculation of its parameters. And finally, simulation results illustrating the performance of this scheme are given.
Similar content being viewed by others
References
Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complex Dynamic Systems), St. Petersburg: Nauka, 2000.
Khalil, H.K., Nonlinear Systems, New York: Prentice Hall, 2002, 3rd ed.
Khalil, H.K., Nelileinye sistemy (Nonlinear Systems), Izhevsk: NITs “Regulyarnaya i Khaoticheskaya Dinamika,” Inst. Komp. Issled., 2009.
Kokotovic, P.V., The Joy of Feedback: Nonlinear and Adaptive, IEEE Control Syst. Mag., 1992, vol. 12, no. 3, pp. 7–17.
Kanellakopoulos, I., Kokotovic, P.V., and Morse, A.S., Systematic Design of Adaptive Controllers for Feedback Linearizable Systems, IEEE Trans. Automat. Control, 1991, vol. 36, pp. 1241–1253.
Kokotovic, P.V., Kanellakopoulos, I., and Morse, A.S., Adaptive Feedback Linearization of Nonlinear System, in Foundation of Adaptive Control, Kokotovic, P.V., Ed., Berlin: Springer-Verlag, 1991, pp. 311–346.
Nikiforov, V.O., Adaptivnoe i robastnoe upravlenie s kompensatsiei vozmushchenii (Adaptive and Robust Control with Disturbances Compensation), St. Petersburg: Nauka, 2003.
Marino, R. and Tomei, P., Robust Stabilization of Feedback Linearizable Time-varying Uncertain Nonlinear Systems, Automatica, 1993, vol. 29, pp. 181–189.
Freeman, R.A. and Kokotovic, P.V., Design of “Softer” Robust Nonlinear Control Laws, Automatica, 1993, vol. 29, pp. 1435–1437.
Qu, Z., Robust Control of Nonlinear Uncertain Systems under Generalized Matching Condition, Automatica, 1993, vol. 29, pp. 985–998.
Zheng, Y. and Yang, Y., Adaptive Output Feedback Control for Class of Nonlinear Systems with Unknown Virtual Control Coefficients Signs, Adaptive Control Signal Process., 2007, vol. 21, no. 1, pp. 77–89.
Furtat, I.B., Modified Algorithm of Integrator Backstepping, Mekhatron. Avtomatiz. Upravlen., 2009, no. 10, pp. 2–7.
Furtat, I.B. and Tupichin, E.A., Control of Nonlinear Plant Based on Modified Robust Backstepping Algorithm, Proc. 2014 IEEE Int. Conf. Control Appl. (CCA), Part 2014 IEEE Multi-Conf. Syst. Control, Antibes, France, October 8–10, 2014, pp. 941–946.
Furtat, I.B. and Tupichin, E.A., Modified Robust Backstepping Algorithm for Plants with Time Delay, Proc. 6th Int. Congr. Ultra Modern Telecommunications and Control Syst. and Workshops (ICUMT), St.-Petersburg, October 6–8, 2014, pp. 541–545.
Tsykunov, A.M., Robust Control Algorithms with Compensation of Bounded Perturbations, Autom. Remote Control, 2007, vol. 68, no. 7, pp. 1213–1224.
Furtat, I., Fradkov, A., and Tsykunov, A., Robust Synchronization of Linear Dynamical Systems with Compensation of Disturbances, Int. J. Robust Nonlin. Control, 2014, vol. 24, no. 17, pp. 2774–2784.
Furtat, I.B., Robust Control for a Specific Class of Non-Minimum Phase Dynamical Networks, J. Comput. Syst. Sci. Int., 2014, vol. 53, no. 1, pp. 33–46.
Brusin, V.A., On a Class of Singularly Disturbed Adaptive Systems. I, Autom. Remote Control, 1995, vol. 56, no. 4, pp. 552–559.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.B. Furtat, E.A. Tupichin, 2016, published in Avtomatika i Telemekhanika, 2016, No. 9, pp. 70–83.
Rights and permissions
About this article
Cite this article
Furtat, I.B., Tupichin, E.A. Modified backstepping algorithm for nonlinear systems. Autom Remote Control 77, 1567–1578 (2016). https://doi.org/10.1134/S0005117916090058
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117916090058