In order to deal with unmodeled dynamics in large vehicle systems, which have an ill condition of the state matrix, the use of model order reduction methods is a good approach. This article presents a new construction of the sliding mode controller for singularly perturbed systems. The controller design is based on a linear diagonal transformation of the singularly perturbed model. Furthermore, the use of a single sliding mode controller designed for the slow component of the diagonalized system is investigated. Simulation results indicate the performance improvement of the proposed controllers.
References
[1]
Alvarez-Gallegos, J. and Silva-Navarro, G. (1997) Two-Time Scale Sliding Mode Control for a Class of Nonlinear Systems. International Journal of Robust and Nonlinear Control, 7, 865-879. https://doi.org/10.1002/(SICI)1099-1239(199709)7:9%3C865::AID-RNC240%3E3.0.CO;2-0
[2]
De Leon-Morales, J., Alvarez-Leal, J.G., Castro-Linares, R. (1997) Speed and Position Control of Flexible Joint Robot Manipulator via a Nonlinear Control-Observer Scheme. Proceeding of the IEEE International Conference on Control Applications, Hartford, 5-7 October 1997, 312-317. https://doi.org/10.1109/CCA.1997.627565
[3]
Kokotovic, P., Khalil, H.K. and O’Reilly, J. (1999) Singular Perturbation Methods in Control, Analysis and Design. Society for Industrial and Applied Mathematics, Academic Press, Philadelphia. https://doi.org/10.1137/1.9781611971118
[4]
Naidu, D.S. (1988) Singular Perturbation Methodology in Control Systems. IEE Series Vol. 34, Peter Peregrinus.
[5]
Slotine, J.J. (1984) Sliding Controller Design for Non-Linear System. International Journal of Control, 40, 421-434. https://doi.org/10.1080/00207178408933284
[6]
Slotine, J.J. and Hong, S. (1986) Two Time Sliding Control of Manipulators with Flexible Joints. Proceeding of 1986 American Control Conference, Seattle, 18-20 June 1986, 805-810. https://doi.org/10.23919/ACC.1986.4789045
[7]
Heck, B.S. (1991) Sliding Mode Control for Singularly Perturbed Systems. International Journal of Control, 53, 985-1001. https://doi.org/10.1080/00207179108953660
[8]
Chow, J.H. and Kokotovic, P.V. (1976) A Decomposition of Near Optimum Regulators for System with Slow and Fast Modes. IEEE Transaction, 21, 701-705. https://doi.org/10.1109/TAC.1976.1101342
[9]
Phillips, R.G. (1983) The Equivalence of Time Scale Decomposition Techniques Used in the Analysis and Design of Linear Systems. International Journal of Control, 37, 1239-1257. https://doi.org/10.1080/00207178308933043
[10]
Narasimhamurthi, N. and Wu, F.F. (1977) On the Riccati Equation Arising from the Study of Singularly Perturbed Systems. Proceeding of Joint Automatic Control Conference, San Francisco, June 22-24 1977, 1244-1247.
[11]
Khasawneh, B., Sabra, M. and Zohdy, M.A. (2014) Paralleled DC-DC Power Converters Sliding Mode Control with Dual Stages Design. Journal of Power and Energy Engineering, 2, 1-10. http://dx.doi.org/10.4236/jpee.2014.22001
[12]
Hung, J.Y., Gao, W. and Hung, J.C. (1993) Variable Structure Control: A Survey. IEEE Transaction on Industrial Electronics, 40, 2-22. https://doi.org/10.1109/41.184817
[13]
Li, T.S. (1995) Composite Sliding Mode Control of Singularly Perturbation Systems. Proceeding of the American Control Conference, Seattle, 21-23 June 1995, 2248-2249.
[14]
Zohdy, M.A., Fadali, M.S. and Liu, J. (1995) Variable Structure Dynamic Output Feedback. Proceedings of 1995 American Control Conference, Seattle, 21-23 June 1995, 1518-1522. https://doi.org/10.1109/ACC.1995.521005
[15]
Jia, S., Jia, Y., Xu, S. and Hu, Q. (2018) Maneuver and Active Vibration Suppression of Free-Flying Space Robot. IEEE Transactions on Aerospace and Electronic Systems, 54, 1115-1134
[16]
Utkin, V.I. (1977) Variable Structure Systems with Sliding Mode. IEEE Transaction on Automatic Control, 22, 212-222. https://doi.org/10.1109/TAC.1977.1101446
[17]
Nair, S.V., Lakhekar, G.V., Panchade, V.M. (2016) Fuzzy Sliding Mode Control Approach for Two Time Scale System: Stability Issues. 2016 10th International Conference on Intelligent Systems and Control, Coimbatore, 7-8 January 2016, 1-8. https://doi.org/10.1109/ISCO.2016.7727081
[18]
Wang, Y., Gao, Y., Karimi, H.R., Shen, H. and Fang, Z. (2018) Sliding Mode Control of Fuzzy Singularly Perturbed Systems with Application to Electric Circuit. IEEE Transactions on Systems, Man, and Cybernetics, 48, 1667-1675. https://doi.org/10.1109/TSMC.2017.2720968
[19]
Zhang, Y., Zhao, Y. (2014) A Higher-Order Sliding Mode Controller Design for Spacecraft Attitude Tracking System. 2014 International Conference on Mechatronics and Control, Jinzhou, 3-5 July 2014, 1248-1251. https://doi.org/10.1109/ICMC.2014.7231752
