Przegląd reguł osiągania trybu ślizgowego w układach dyskretnych
Streszczenie
Stosując znane reguły osiągania trybu ślizgowego, rozpoczyna się działanie od określenia pożądanego przebiegu zmiennej ślizgowej. Następnie projektowany jest regulator gwarantujący, że zmienna ślizgowa układu będzie podążać za wybranym przebiegiem. Przewagą tej metody nad „klasycznym” sterowaniem ślizgowym jest zapewnienie lepszej kontroli nad dynamiką układu i spełnienie ograniczeń zmiennych stanu już podczas fazy osiągania trybu ślizgowego. W artykule przedstawiony zostanie przegląd prac naukowych dotyczących reguł osiągania trybu ślizgowego dla układów czasu dyskretnego. Wskazane i omówione zostaną różnice i podobieństwa między przebiegami stosowanymi przez badaczy.
Słowa kluczowe
dyskretne sterowanie ślizgowe, reguły osiągania trybu ślizgowego
Review of Discrete Time Sliding Mode Reaching Laws
Abstract
In the reaching law approach one first specifies the desired evolution of the sliding variable. Then, a sliding mode controller that ensures this evolution is derived. The main advantage of this method with respect to “classical” sliding mode control is better control of the system dynamics and state constraints during the reaching phase. In this paper, a review of recent results on discrete time reaching laws is presented. The differences and similarities between them are discussed.
Keywords
discrete sliding mode control, reaching laws
Bibliografia
- Bartoszewicz A., Discrete-time quasi-sliding-mode control strategies, ”IEEE Transactions on Industrial Electronics”, Vol. 45, No. 4, 1998, 633–637, DOI: 10.1109/41.704892.
- Bartoszewicz A., Remarks on ‘Discrete-time variable structure control systems’, “IEEE Transactions on Industrial Electronics”, Vol. 43, No. 1, 1996, 235–238.
- Bartoszewicz A., Adamiak K., Model reference discrete-time variable structure control, ”International Journal of Adaptive Control and Signal Processing”, Vol. 32, No. 10, 2018, 1440–1452, DOI: 10.1002/acs.2922.
- Bartoszewicz A., Latosiński P., Generalization of Gao’s reaching law for higher relative degree sliding variables, ”IEEE Transactions on Automatic Control”, Vol. 63, No. 9, 2018, 3173–3179, DOI: 10.1109/TAC.2018.2797193.
- Bartoszewicz A., Latosiński P., Reaching law for DSMC systems with relative degree 2 switching variable, ”International Journal of Control”, Vol. 90, No. 8, 2017, 1626–1638, DOI: 10.1080/00207179.2016.1216606.
- Bartoszewicz A., Latosiński P., Discrete time sliding mode control with reduced switching – a new reaching law approach, “International Journal of Robust and Nonlinear Control”, Vol. 26, No. 1, 2016, 47–68, DOI: 10.1002/rnc.3291.
- Bartoszewicz A., Latosiński P., Reaching law based discrete time sliding mode inventory management strategy, “IEEE Access”, Vol. 4, 2016, 10051–10058, DOI: 10.1109/ACCESS.2016.2633618.
- Bartoszewicz A., Leśniewski P., Reaching law-based sliding mode congestion control for communication networks, “IET Control Theory and Applications”, Vol. 8, No. 17, 2014, 1914–1920, DOI: 10.1049/iet-cta.2014.0503.
- Chakrabarty S., Bandyopadhyay B., Moreno J.A., Fridman L., Discrete sliding mode control for systems with arbitrary relative degree output, 14th International Workshop on Variable Structure Systems, 2016, 160–165, DOI: 10.1109/VSS.2016.7506909.
- Chakrabarty S., Bandyopadhyay B., A generalized reaching law with different convergence rates, “Automatica”, Vol. 63 2016, 34–37, DOI: 10.1016/j.automatica.2015.10.018.
- Chakrabarty S., Bandyopadhyay B., A generalized reaching law for discrete time sliding mode control, “Automatica”, Vol. 52, 2015, 83–86, DOI: 10.1016/j.automatica.2014.10.124.
- Chakrabarty S., Bandyopadhyay B., Bartoszewicz A., Discrete‐time sliding mode control with outputs of relative degree more than one, Recent Developments in Sliding Mode Control Theory and Applications, InTech, 2017, DOI: 10.5772/intechopen.68931.
- Chakrabarty S., Bartoszewicz A., Improved robustness and performance of discrete time sliding mode control systems, “ISA Transactions”, Vol. 65, 2016, 143–149, DOI: 10.1016/j.isatra.2016.08.006.
- Du H., Yang C., Li S., Non-smooth control-based reaching law for discrete-time sliding mode control, 14th International Workshop on Variable Structure Systems (VSS), 240–245, 2016, DOI: 10.1109/VSS.2016.7506923.
- Du H., Yu X., Chen M., Li S., Chattering-free discrete-time sliding mode control, “Automatica”, Vol. 68, 2016, 87–91, DOI: 10.1016/j.automatica.2016.01.047.
- Furuta K., Sliding mode control of a discrete system, “Systems & Control Letters”, Vol. 14, No. 2, 1990, 145–152, DOI: 10.1016/0167-6911(90)90030-X.
- Gao W., Hung J., Variable structure control of nonlinear systems: A new approach, IEEE Transactions on Industrial Electronics, Vol. 40, No. 1, 1993, 45–55, DOI: 10.1109/41.184820.
- Gao W., Wang Y., Homaifa A., Discrete-time variable structure control systems, IEEE Transactions on Industrial Electronics, Vol. 42, No. 2, 1995, 117–122, DOI: 10.1109/41.370376.
- Hou H., Yu X., Zhang Q., Huang J., Reaching law based sliding mode control for discrete time system with uncertainty, IEEE 27th International Symposium on Industrial Electronics, 2018, 1155–1160, DOI: 10.1109/ISIE.2018.8433844.
- Kurode S., Balajiwale S., Discrete sliding mode control of seeker scan loop using adaptive reaching law, IEEE International Conference on Control Applications, 2013, 704–709, DOI: 10.1109/CCA.2013.6662832.
- Kurode S., Bandyopadhyay B., Gandhi P., Discrete sliding mode control for a class of underactuated systems, Proc. 37th Annual Conference of the IEEE Industrial Electronics Society, 2011, 3936–3941, DOI: 10.1109/IECON.2011.6119952.
- Leśniewski P., Discrete time reaching law based sliding mode control: a survey, Proc. 22nd International Conference on System Theory, Control and Computing, 2018, 734–739, DOI: 10.1109/ICSTCC.2018.8540782
- Lin S., Zhang W., Controller designed via an adaptive reaching law for DSMC systems, IEEE Transactions on Circuits and Systems II: Express Briefs (Early Access), 2019, DOI: 10.1109/TCSII.2019.2907296.
- Liu B., Ding Z., Zhao H., Jin D., Active power filter DC bus voltage piecewise reaching law variable structure control, Mathematical Problems in Engineering, 2014.
- Ma H., Li Y., Multi-power reaching law based discrete-time sliding-mode control, IEEE Access, Vol. 7, 2019, 49822–49829, DOI: 10.1109/ACCESS.2019.2904103.
- Ma H., Li Y., Xiong Z., Discrete-time sliding-mode control with enhanced power reaching law, IEEE Transactions on Industrial Electronics, Vol. 66, No. 6, 2019, 3936–3941, DOI: 10.1109/TIE.2018.2864712.
- Ma H., Wu J., Xiong Z., A novel exponential reaching law of discrete-time sliding-mode control, IEEE Transactions on Industrial Electronics, Vol. 64, No. 5, 2017, 3840–3850, DOI: 10.1109/TIE.2017.2652390.
- Mehta A., Bandyopadhyay B., The design and implementation of output feedback based frequency shaped sliding mode controller for the smart structure, Proc. IEEE International Symposium on Industrial Electronics, 2010, 353–358, DOI: 10.1109/ISIE.2010.5637696.
- Mija S., Susy T., Reaching law based sliding mode control for discrete MIMO systems, Proc. IEEE International Conference on Control, Automation, Robotics and Vision, 2010, 1291–1296, DOI: 10.1109/ICARCV.2010.5707278.
- Milosavljević Č., General conditions for the existence of a quasisliding mode on the switching hyperplane in discrete variable structure systems, Automation and Remote Control, Vol. 46, No. 3, 1985, 307–314.
- Milosavljević Č., Peruničić-Draženović B., Veselić B., Mitić D., Sampled data quasi-sliding mode control strategies, Proc. IEEE Internernational Conference on Industrial Technology, 2006, 2640–2645, DOI: 10.1109/ICIT.2006.372711.
- Niu Y., Ho D.W.C., Wang Z., Improved sliding mode control for discrete-time systems via reaching law, IET Control Theory and Applications, Vol. 4, No. 11, 2010, 2245–2251, DOI: 10.1049/iet-cta.2009.0296.
- Perez M., Jimenez E., Camacho E.F., Design of an explicit constrained predictive sliding mode controller, IET Control Theory and Applications, Vol. 4, No. 4, 2010, 552–562, DOI: 10.1049/iet-cta.2009.0057.
- Qu S., Xia X., Zhang J., Dynamics of discrete-time sliding-mode-control uncertain systems with a disturbance compensator, IEEE Transactions on Industrial Electronics, Vol. 61, No. 7, 2014, 3502–3510, DOI: 10.1109/TIE.2013.2279369.
- Ren Y., Liu Z., Liu X., Zhang Y., A chattering free discrete-time global sliding mode controller for optoelectronic tracking system, Mathematical Problems in Engineering, 2013, DOI: 10.1155/2013/951492.
- Samantaray J., Chakrabarty S., Digital implementation of sliding mode controllers with DC-DC buck converter system, 15th International Workshop on Variable Structure Systems, 2018, 255–260, 10.1109/vss.2018.8460257.
- Utkin V.I., Variable structure systems with sliding modes, IEEE Transactions on Automatic Control, Vol. 22, No. 2, 1977, 212–222, DOI: 10.1109/TAC.1977.1101446.
- Veselić B., Peruničić-Draženović B., Milosavljević Č., Improved discrete-time sliding-mode position control using Euler velocity estimation, IEEE Transactions on Industrial Electronics, Vol. 57, No. 11, 2010, 3840–3847, DOI: 10.1109/TIE.2010.2042416.
- Viveknandan C., Prabhakar R. A redefined discrete quasi-sliding mode strategy, “International Journal of Recent Trends in Engineering”, Vol. 1, No. 3, 2009, 92–96.
- Xu Q., Du H.P., He B., Yan T.H., Li W.H., Sun S.S., A novel reaching law for sliding mode control of uncertain discrete-time systems, Mathematical Problems in Engineering, Vol. 2018, 2018, DOI: 10.1155/2018/6158492.
- Yazici I., Yaylaci E.K., Maximum power point tracking for the permanent magnet synchronous generator-based WECS by using the discrete-time integral sliding mode controller with a chattering-free reaching law, IET Power Electronics, Vol. 10, No. 13, 2017, 1751-1758, DOI: 10.1049/iet-pel.2017.0232.
- Zhao Y.X., Wu T., Ma Y., A double power reaching law of sliding mode control based on neural network, “Mathematical Problems in Engineering”, Vol., 2013, 2013, DOI: 10.1155/2013/408272.