Abstract
A family of continuous state feedback synthesis based on sliding mode control is analyzed using a Lyapunov approach, such that the compensation of growing perturbations together with state variables is shown. Robustness properties of a family of controllers, varying from the well known twisting sliding mode control law to the PD controller, are studied. A non-smooth Lyapunov function is proposed such that global finite-time stability of the origin is demonstrated and tuning rules for the control gains are obtained. Moreover, since the Lyapunov function is strict, an upper bound for the convergence time of the closed loop system can be estimated, in spite of the growing perturbations with respect to the state. To illustrate the performance and robustness properties of the feedback synthesis, experimental results are presented, using a one-link pendulum as a test bed.
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Recommended by Associate Editor Huaping Liu under the direction of Editor Fuchun Sun. This work was partially supported by IDSCEA, CONACyT and UPA under project FOMIX AGS-2012-01-207544. The authors would like to thank CICESE research center for providing the facilities and the equipment for the experimental setup.
Raúl Santiesteban-Cos was born in Mexico City on May 13, 1977. He received his Master’s degree in Applied Mathematics from Instituto Potosino de Investigación Científica y Tecnológica (IPICYT) and the Ph.D. degree in Electronics and Telecommunications, with orientation in instrumentation and control from Centro de Investigación Científica y de Educación Superior de Ensenada (CICESE), Baja California, Mexico, in 2004 and 2008, respectively. He is currently a Professor in the Department of Metal-Mechanics from Tecnológico Nacional de México since 2010. His research interests include nonlinear dynamics, mechanical systems, friction, sliding modes, and ordinary differential equation with inclusions.
Araceli Gárate-García was born in Mexicali, Mexico. She received her B.Eng. degree in electronics in the Mexicali Institute of Technology in 2003, her master’s degree in electronics and telecommunications from CICESE research center, Mexico, in 2006 and a Ph.D. Dual Degree from CICESE and the University of Nantes, France in 2011. Since 2011 she has been with the Polytechnic University of Aguascalientes (UPA) in the Department of Research and Postgraduate Studies. She is the head of the research group “Control, Automation and Instrumentation of Systems” at UPA. Her research focuses on algebraic methods of control theory, analysis and control of time-delay systems, symbolic computation and systems modelling.
Oscar Montaño-Godinez obtained his Master’s degree in Electronics and Telecommunications from CICESE, Mexico, in 2012, and received his Ph.D. degree in Robotics and Automation from l’Université de Nantes, France in 2016. He joined 2J Antennas USA, Corp in 2017. His research interests include analysis of nonlinear systems, applications to electromechanical systems, modeling and control of robotic manipulators and bipeds.
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Santiesteban-Cos, R., Gárate-García, A. & Montaño-Godinez, O. Stability analysis of a family of continuous state feedback synthesis: Theory and experiments. Int. J. Control Autom. Syst. 15, 1011–1019 (2017). https://doi.org/10.1007/s12555-014-0513-6
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DOI: https://doi.org/10.1007/s12555-014-0513-6