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2021 | OriginalPaper | Buchkapitel

Integral Sliding Mode for Nonlinear System: A Control-Lyapunov Function Approach

verfasst von : Ankit Sachan, Herman Al Ayubi, Mohit Kumar Garg

Erschienen in: Advances in Machine Learning and Computational Intelligence

Verlag: Springer Singapore

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Abstract

This paper discusses a sophisticated control for nonlinear system in such a way that the state trajectories remain in predefined manifold and converges asymptotically. One of the solutions to the problem is by the use of generalized super-twisting control (GSTC) and control-Lyapunov function (CLF) where former renders to alleviate the disturbing term with continuous action such that state trajectories always remain in predefined manifold and latter brings the states to stable equilibrium point by the use of the priori Lyapunov function. These two approaches designed externally are independent to each other via integral sliding mode control (ISMC). The simulation results for the proposed algorithm is illustrated by a numerical example.

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Literatur
1.
Zurück zum Zitat V. Utkin,, J. Guldner, J. Shi, Sliding Mode Control in Electromechanical Systems. Boca Raton: CRC Press (2009) V. Utkin,, J. Guldner, J. Shi, Sliding Mode Control in Electromechanical Systems. Boca Raton: CRC Press (2009)
2.
Zurück zum Zitat V. Utkin, J. Shi, Integral Sliding Mode in Systems Operating Under Uncertainty Conditions, in Proceedings of the 35th IEEE Conference on Decision and Control, vol. 4. IEEE (1996), pp. 4591–4596 V. Utkin, J. Shi, Integral Sliding Mode in Systems Operating Under Uncertainty Conditions, in Proceedings of the 35th IEEE Conference on Decision and Control, vol. 4. IEEE (1996), pp. 4591–4596
3.
Zurück zum Zitat B. Yao, M. Tomizuka, Smooth robust adaptive sliding mode control of manipulators with guaranteed transient performance. J. Dyn. Syst. Meas. Contr. 118(4), 764–775 (1996)CrossRef B. Yao, M. Tomizuka, Smooth robust adaptive sliding mode control of manipulators with guaranteed transient performance. J. Dyn. Syst. Meas. Contr. 118(4), 764–775 (1996)CrossRef
4.
Zurück zum Zitat R. Matteo, D.M. Raimondo, A. Ferrara, L. Magni, Robust model predictive control with integral sliding mode in continuous-time sampled-data nonlinear systems. IEEE Trans. Autom. Control 56(3), 556–570 (2011)MathSciNetCrossRef R. Matteo, D.M. Raimondo, A. Ferrara, L. Magni, Robust model predictive control with integral sliding mode in continuous-time sampled-data nonlinear systems. IEEE Trans. Autom. Control 56(3), 556–570 (2011)MathSciNetCrossRef
5.
Zurück zum Zitat W.J. Cao, J.X. Xu, Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems. IEEE Trans. Autom. Control 49(8), 1355–1360 (2004)MathSciNetCrossRef W.J. Cao, J.X. Xu, Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems. IEEE Trans. Autom. Control 49(8), 1355–1360 (2004)MathSciNetCrossRef
6.
Zurück zum Zitat M. Defoort, T. Floquet, A. Kokosy, W. Perruquetti, Integral sliding mode control for trajectory tracking of a unicycle type mobile robot. Integrated Comput. Aided Eng. 13(3), 277–288 (2006)CrossRef M. Defoort, T. Floquet, A. Kokosy, W. Perruquetti, Integral sliding mode control for trajectory tracking of a unicycle type mobile robot. Integrated Comput. Aided Eng. 13(3), 277–288 (2006)CrossRef
7.
Zurück zum Zitat J.X. Xu, K. Abidi, Discrete-time output integral sliding-mode control for apiezomotor-driven linear motion stage. IEEE Trans. Ind. Electron. 55(11), 3917–3926 (2008)CrossRef J.X. Xu, K. Abidi, Discrete-time output integral sliding-mode control for apiezomotor-driven linear motion stage. IEEE Trans. Ind. Electron. 55(11), 3917–3926 (2008)CrossRef
8.
Zurück zum Zitat F. Castanos, L. Fridman, Analysis and design of integral sliding manifoldsfor systems with unmatched perturbations. IEEE Trans. Autom. Control 51(5), 853–858 (2006)CrossRef F. Castanos, L. Fridman, Analysis and design of integral sliding manifoldsfor systems with unmatched perturbations. IEEE Trans. Autom. Control 51(5), 853–858 (2006)CrossRef
9.
Zurück zum Zitat M. Rubagotti, A. Estrada, F. Castanos, A. Ferrara, L. Fridman. Integral sliding mode control for nonlinear systems with matched and unmatched perturbations. IEEE Trans. Autom. Control 56(11), 2699–2704 (2011) M. Rubagotti, A. Estrada, F. Castanos, A. Ferrara, L. Fridman. Integral sliding mode control for nonlinear systems with matched and unmatched perturbations. IEEE Trans. Autom. Control 56(11), 2699–2704 (2011)
10.
Zurück zum Zitat A. Levant, Sliding order and sliding accuracy in sliding modecontrol. Int. J. Control, 58(6), 1247–1263 (1993) A. Levant, Sliding order and sliding accuracy in sliding modecontrol. Int. J. Control, 58(6), 1247–1263 (1993)
11.
Zurück zum Zitat A. Chalanga, S. Kamal, B. Bandyopadhyay, Continuous Integral Slidingmode Control: A Chattering Free approach, in IEEE International Symposium on Industrial Electronics (2013), pp. 1–6 A. Chalanga, S. Kamal, B. Bandyopadhyay, Continuous Integral Slidingmode Control: A Chattering Free approach, in IEEE International Symposium on Industrial Electronics (2013), pp. 1–6
12.
Zurück zum Zitat S.P. Sadala, B.M. Patre, A new continuous sliding mode control approachwith actuator saturation for control of 2-DOF helicopter system. ISA Trans. 74, 165–174 (2018)CrossRef S.P. Sadala, B.M. Patre, A new continuous sliding mode control approachwith actuator saturation for control of 2-DOF helicopter system. ISA Trans. 74, 165–174 (2018)CrossRef
13.
Zurück zum Zitat Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. Theory, Methods Appl. 7(11), pp 1163–1173 (1983) Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. Theory, Methods Appl. 7(11), pp 1163–1173 (1983)
14.
Zurück zum Zitat E.D. Sontag, A universal construction of Artstein’s theorem on nonlinear stabilization. Syst. Control Lett. 13(2), 117–123 (1989)MathSciNetCrossRef E.D. Sontag, A universal construction of Artstein’s theorem on nonlinear stabilization. Syst. Control Lett. 13(2), 117–123 (1989)MathSciNetCrossRef
15.
Zurück zum Zitat Z.P. Jiang, Y. Lin, Y. Wang, Stabilization of Time-Varying Nonlinear Systems: A Control-Lyapunov Function Approach, in IEEE International Conference on Control and Automation (2007), pp. 404–409 Z.P. Jiang, Y. Lin, Y. Wang, Stabilization of Time-Varying Nonlinear Systems: A Control-Lyapunov Function Approach, in IEEE International Conference on Control and Automation (2007), pp. 404–409
16.
Zurück zum Zitat A. Shahmansoorian, B. Moshiri, A.K. Sedigh, S. Mohammadi, A new stabilizing control law with respect to a control-Lyapunov function and construction of control-Lyapunov function for particular nonaffine nonlinear systems. J. Dynam. Control Syst. 13(4), 563–576 (2007)MathSciNetCrossRef A. Shahmansoorian, B. Moshiri, A.K. Sedigh, S. Mohammadi, A new stabilizing control law with respect to a control-Lyapunov function and construction of control-Lyapunov function for particular nonaffine nonlinear systems. J. Dynam. Control Syst. 13(4), 563–576 (2007)MathSciNetCrossRef
17.
Zurück zum Zitat J.A. Moreno, A Linear Framework for the Robust Stability Analysis of a Generalized Super-Twisting Algorithm, in 6th International Conference on Electrical Engineering, Computing Science and Automatic Control (2009), pp. 1–6 J.A. Moreno, A Linear Framework for the Robust Stability Analysis of a Generalized Super-Twisting Algorithm, in 6th International Conference on Electrical Engineering, Computing Science and Automatic Control (2009), pp. 1–6
18.
Zurück zum Zitat G. Bitsoris, E. Gravalou, Comparison principle, positive invariance and constrained regulation of nonlinear systems. Automatica 31(2), 217–222 (1995)MathSciNetCrossRef G. Bitsoris, E. Gravalou, Comparison principle, positive invariance and constrained regulation of nonlinear systems. Automatica 31(2), 217–222 (1995)MathSciNetCrossRef
Metadaten
Titel
Integral Sliding Mode for Nonlinear System: A Control-Lyapunov Function Approach
verfasst von
Ankit Sachan
Herman Al Ayubi
Mohit Kumar Garg
Copyright-Jahr
2021
Verlag
Springer Singapore
DOI
https://doi.org/10.1007/978-981-15-5243-4_78

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