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Discrete-time chattering free exponentially stabilizing sliding mode scalar control via Lyapunov’s method

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Abstract

Linear time-invariant discrete-time plant, with no restrictions on the form of the state equation and with scalar control, is considered. The exponentially stabilizing state feedback control algorithm is developed by Lyapunov’s second method leading to the variable structure system with chattering free sliding modes. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspace S, in finite time and with prescribed velocity estimate. Inside the sliding subspace S, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, direct current (DC) servo motor, and simulation and experimental results are given. Also, it is compared with another already known algorithm from literature.

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Authors and Affiliations

  1. University of Belgrade, Mechanical Engineering Faculty, 16 Kraljice Marije, 11120, Belgrade 35, Serbia

    Zoran M. Bučevac & Radiša Ž. Jovanović

Authors
  1. Zoran M. Bučevac
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  2. Radiša Ž. Jovanović
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Corresponding author

Correspondence to Radiša Ž. Jovanović.

Additional information

Recommended by Associate Editor Shengyuan Xu under the direction of Editor Fuchun Sun.

Zoran Bučevac received his Ph.D. from the University of Belgrade (UB), Mechanical Engineering Faculty (MEF), Serbia, in 1985. He is with the same Faculty, MEF of UB since 1981 where he passed through all academic and professor titles. Now he is at position of full profesor for automatic control. Professor Buˇcevac spent visiting research school year 1985/86 at Electrical and Computer Engineering Dept. of University of Wisconsin- Madison, USA. His research interests are Lyapunov stability and tracking of discrete and digital systems in general, as well as of control systems, especially variable structure systems with sliding modes. Professor Buˇcevac was Head of the Department of Automatic Control, at MEF of UB, twice, 1996-98 and 2001-2003. He was President of scientific professional association "The Union of Serbia for systems, automatic control and measurements-SAUM", from 1992-2000.

Radiša Jovanović received his Ph.D. degree from the University of Belgrade, Faculty of Mechanical Engineering, Serbia, in 2011. He is currently an Assistant Professor in the Department of Automatic Control at Faculty of Mechanical Engineering, University of Belgrade, Serbia. His research interests include control theory and applications, nonlinear control systems, intelligent control, fuzzy control and neural networks.

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Bučevac, Z.M., Jovanović, R.Ž. Discrete-time chattering free exponentially stabilizing sliding mode scalar control via Lyapunov’s method. Int. J. Control Autom. Syst. 14, 698–705 (2016). https://doi.org/10.1007/s12555-014-0297-8

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  • DOI: https://doi.org/10.1007/s12555-014-0297-8

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