Abstract
In this paper, a continuous sliding mode algorithm for a system with relative degree three is presented. The studied mechanism is a class of nonlinear system with electro-mechanical actuators which includes both matched and unmatched bounded perturbations /uncertainties. The proposed homogeneous continuous control algorithm produces a continuous control signal ensuring finite time convergence of the states to the desired trajectory. Moreover, the control signal compensates the bounded perturbation in finite time, i.e. its value converges to the opposite value of the perturbation. The quality of the presented controller is proved via numerical simulations.
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References
Shevchenko, G.V.: A new 3 D.O.F. Numerical method for solving a nonlinear time-optimal control problem with additive control. Comput. Math. Math. Phys. 47(1), 1768–1778 (2007)
Utkin, V.: Sliding Modes in the Control and Optimization. Springer, Heidelberg (1992)
Ablameyko, S.V., Biryukov, A.S., Dokukin, A.A., D’yakonov, A.G., Zhuravlev, Y.I., Krasnoproshin, V.V., Obraztsov, V.A., Romanov, M.Y., Ryazanov, V.V.: Practical algorithms for algebraic and logical correction in precedent-based recognition problems. Comput. Math. Math. Phys. 54(12), 1915–1928 (2014)
Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding Mode Control and Observation. Birkhäuser Mathematics, Basel (2014)
Keshtkar, S., Poznyak, A.: Tethered space orientation via adaptive sliding mode. Robust Nonlinear Control 26(8), 1632–1646 (2016)
Utkin, V., Poznyak, A.: Adaptive sliding mode control with application to super-twist algorithm: equivalent control method. Automatica 49(1), 39–47 (2013)
Fridman, L., Moreno, J., Bandyopadhyay, B., Chalanga, A.: Continuous nested algorithms: the fifth generation of sliding mode controllers. In: Yu, X., Efe, O. (eds.) Recent Advances in Sliding Modes—Control to Intelligent Mechatronics. Studies in Systems, Decision and Control, vol. 24, pp. 5–35. Springer, Cham (2015)
Sanchez, T., Moreno, J.: A constructive Lyapunov function design method for a class of homogeneous systems. In: IEEE 53rd Annual Conference on Decision and Control, pp. 5500–5505. Los Angeles (2014)
Moreno, J., Negrete, D.Y., Torres-Gonzalez, V., Leonid, F.: Adaptive continuous twisting algorithm. Int. J. Control 89(9), 1798–1806 (2015)
Harib, K., Srinivasan, K.: Kinematic and dynamic analysis of Stewart platform-based on machine tool structures. Robotica 21, 541–554 (2003)
Kulikov, G.Y.: Solving the order reduction phenomenon in variable step size quasi-consistent nordsieck methods. Comput. Math. Math. Phys. 52(11), 1547–1564 (2012)
Kulikov, G.Y.: Method of fast expansions for solving nolinear differential equations. Comput. Math. Math. Phys. 54(1), 11–21 (2014)
Acknowledgments
Authors are grateful to CONACYT-Mexico and SIP-IPN for supporting part of this work through grants AEM-Conacyt 262887 and SIP20171092, respectively.
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Gutierrez, I., Hernandez-Martinez, E., Oropeza, A., Keshtkar, S. (2018). High-Order Sliding Mode Control for Solar Tracker Manipulator. In: Carvalho, J., Martins, D., Simoni, R., Simas, H. (eds) Multibody Mechatronic Systems. MuSMe 2017. Mechanisms and Machine Science, vol 54. Springer, Cham. https://doi.org/10.1007/978-3-319-67567-1_22
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DOI: https://doi.org/10.1007/978-3-319-67567-1_22
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