Robust Error Feedback Sliding Mode Regulation of Nonlinear Systems (I)

Resumen: In this paper, the problem of nonlinear sliding mode (SM) regulation is addressed for nonlinear affine control system subject to unknown and unmodelled disturbance. In particular, the error feedback SM regulator problem is defined, taking the concepts related to the zero output tracking submanifold as a starting point. Applying the internal model concept to the time-invariant SM equation, the solvability conditions to the problem are derived. A proportional-integral (PI) nonlinear observer is proposed, and using the observer state, a sliding manifold on which the tracking error is ultimately bounded, is formulated. A SM control algorithm is proposed to ensure the designed manifold be attractive, achieving robustness with respect to allowed uncertainties. The effectiveness of the proposed method is demonstrated by the application to the Pendubot system.

¿Cómo citar?

Maximiliano Martin del Campo & Alexander G. Loukianov. Robust Error Feedback Sliding Mode Regulation of Nonlinear Systems (I). Memorias del Congreso Nacional de Control Automático, pp. 772-777, 2019.

Palabras clave

Control Discontinuo (modos deslizantes), Control de Sistemas No Lineales, Control Robusto

• Beale, S.R. and Shafai, B. (1988). Robust control system design with proportional integral observer. Proceedings of the 27th IEEE Conference on Decision and Control, 554–557.
• Bonivento, C., Marconi, L., and Zanasi, R. (2001). Output regulation of nonlinear systems by sliding mode. Automatica, 37(4), 535 – 542.
• Draˇzenovi´c, B. (1969). The invariance conditions in variable structure systems. Automatica, 5(3), 287 – 295.
• DZ, C., Tarn, T.J., and Spurgeon, S. (2001). On the design of output regulators for nonlinear systems. Systems & Control Letters, 43, 167–179.
• El-Ghezawi, O., Zinober, A., and Billings, S. (2007). Analysis and design of variable structure systems using a geometric approach. International Journal of Control, 38, 657–671.
• Elmali, H. and Olgac, N. (1992). Robust output tracking control of nonlinear mimo systems via sliding mode technique. Automatica, 28(1), 145 – 151.
• Govindaswamy, S., Floquet, T., and Spurgeon, S. (2014). Discrete time output feedback sliding mode tracking control forsystems with uncertainties. International Journal of Robust and Nonlinear Control, 24(15), 2098– 2118.
• Isidori, A. (1955). Nonlinear Control Systems. SpringerVerlag London, 3 edition.
• Jeong, H.S. and Utkin, V. (1999). Sliding mode tracking control of systems with unstable zero dynamics. 303– 327.
• Loukianov, A. and Utkin, V. (1981). Methods of reducing equations of dynamic systems to regular form. Automation and Remote Control, 42, 413–420.
• Loukianov, A.G., Dom´ınguez, J.R., and Castillo-Toledo, B. (2018). Robust sliding mode regulation of nonlinear systems. Automatica, 89, 241 – 246.
• Utkin, V., Guldner, J., and Shi, J. (2009). Sliding Mode Control in Electro-Mechanical Systems. Taylor & Francis Group, 2 edition. Utkin, V. and Utkin, A. (2014). Problem of tracking in linear systems with parametric uncertainties under unstable zero dynamics. Automation and Remote Control, 75, 1577–1592.
• Zheng, B. and Zhong, Y. (2013). Robust output regulation for a class of mimo nonlinear systems with uncertain exosystems. Journal of the Franklin Institute, 350.