Applications of Sliding Mode Control by Nabil Derbel, Jawhar Ghommam, Quanmin Zhu

By Nabil Derbel, Jawhar Ghommam, Quanmin Zhu

This e-book offers crucial reviews and functions within the context of sliding mode keep watch over, highlighting the newest findings from interdisciplinary theoretical experiences, starting from computational set of rules improvement to consultant functions. Readers will tips on how to simply tailor the suggestions to deal with their advert hoc functions.

To make the content material as available as attainable, the booklet employs a transparent direction in each one paper, relocating from history to motivation, to quantitative improvement (equations), and finally to case studies/illustrations/tutorials (simulations, studies, curves, tables, etc.). although basically meant for graduate scholars, professors and researchers from similar fields, the ebook also will gain engineers and scientists from industry.

 

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Levantvosky, L. V. (1986). Higher order sliding modes in the binary control systems. Soviet Physics, Doklady, 31, 291–293. Emelyanov, S. , Utkin, V. , Taran, V. , Kostyleva, N. , Shubladze, A. , Ezerov, V. , et al. (1970). Theory of Variable Structure Control. Moscow (in russian): Nauka. Filippov, A. (1960). Equations différentielles à second membre discontinu. Journal de mathématiques, 51(1), 99–128. Fliess, M. (1990). Generalised controller canonical forms for linear and non-linear dynamics.

2011, 2012a, b; Chang and Chen 2000). In the case of the multivariable second order sliding mode control, the sliding functions vector is selected as follows (Mihoub et al. 2011): σ (k) = S(k) + βS(k − 1) = σ1 (k) . . 10) where β is an (m, m) diagonal matrix. The equivalent control law is obtained if the following relation is verified: σ (k + 1) = σ (k) = 0 Then, the expression of the equivalent control law can be calculated as: ueq (k) = (CB)−1 [−βS(k) − CAx(k)] The robustness is ensured by the addition of a discontinuous term udis (k) such as: ⎤ m1 sign(σ1 (k)) ⎥ ⎢ ..

The main idea behind SMC is to use a discontinuous control input to drive state trajectories towards desired sliding surface in finite time and maintain them on it. Nevertheless, the main drawback of the sliding mode control is the chattering phenomenon caused by the discontinuous part of the control law. The phenomenon of chattering is a harmful phenomenon and it often leads to undesirable results. Due to the development of computer and the use of digital control, discrete sliding mode control (DSMC) has become more important research in many theoretical and practical control systems (Gao et al.

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