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Discrete-time sliding mode output tracking control for a class of nonlinear perturbed systems. (English) Zbl 1525.93222

Summary: The output tracking problem for a class of sampled-data nonlinear systems exposed in nonlinear block controllable form is faced. This article considers both matched and unmatched perturbations. To formulate a desired sliding manifold on which the impact of unmatched perturbation is attenuated, the block control technique combined with the perturbation estimation, is implemented. A discrete-time sliding mode nonswitching controller is synthesized such that the closed-loop system state is driven toward a vicinity of the designed sliding manifold and stays there for all sampled time instants, avoiding chattering, and reducing the matched perturbation effect. The effectiveness of the proposed technique is confirmed by simulation.
{© 2020 John Wiley & Sons Ltd}

MSC:

93C55 Discrete-time control/observation systems
93B12 Variable structure systems
93B52 Feedback control
93B18 Linearizations
93C57 Sampled-data control/observation systems
93C73 Perturbations in control/observation systems
93C10 Nonlinear systems in control theory
Full Text: DOI

References:

[1] MonacoS, Normand‐CyrotD. The immersion under feedback of a multidimensional discrete‐time non‐linear system into a linear system. Int J Control. 1983;38(1):245‐261. https://doi.org/10.1080/00207178308933073. · Zbl 0566.93012 · doi:10.1080/00207178308933073
[2] MonacoS, Normand‐CyrotD. Nonlinear average passivity and stabilizing controllers in discrete time. Syst Control Lett. 2011;60(6):431‐439. https://doi.org/10.1016/J.SYSCONLE.2011.03.010. · Zbl 1225.93074 · doi:10.1016/J.SYSCONLE.2011.03.010
[3] MattioniM, MonacoS, Normand‐CyrotSD. Lyapunov stabilization of discrete‐time feedforward dynamics. Paper presented at: Proceedings of the IEEE 56th Annual Conference on Decision and Control (CDC); 2017:4272‐4277; Melbourne, Australia.
[4] UtkinV, GuldnerJ, ShiJ. Sliding Mode Control in Electro‐Mechanical Systems. 2nd ed.New York, NY: CRC Press; 2009.
[5] FurutaK. Sliding mode control of a discrete system. Syst Control Lett. 1990;14(2):145‐152. https://doi.org/10.1016/0167‐6911(90)90030‐X. · Zbl 0692.93043 · doi:10.1016/0167‐6911(90)90030‐X
[6] GaoW, WangY, HomaifaA. Discrete‐time variable structure control systems. IEEE Trans Ind Electron. 1995;42(2):117‐122. https://doi.org/10.1109/41.370376. · doi:10.1109/41.370376
[7] YuX, ChenG. Discretization behaviors of equivalent control based sliding‐mode control systems. IEEE Trans Autom Control. 2003;48(9):1641‐1646. https://doi.org/10.1109/TAC.2003.816970. · Zbl 1364.93132 · doi:10.1109/TAC.2003.816970
[8] WangB, YuX, ChenG. ZOH discretization effect on single‐input sliding mode control systems with matched uncertainties. Automatica. 2009;45(1):118‐125. https://doi.org/10.1016/j.automatica.2008.05.028. · Zbl 1154.93357 · doi:10.1016/j.automatica.2008.05.028
[9] NiuY, HoDWC, WangZ. Improved sliding mode control for discrete‐time systems via reaching law. IET Control Theory Appl. 2010;4(11):2245‐2251. https://doi.org/10.1049/iet‐cta.2009.0296. · doi:10.1049/iet‐cta.2009.0296
[10] AcaryV, BrogliatoB, OrlovYV. Chattering‐free digital sliding‐mode control with state observer and disturbance rejection. IEEE Trans Autom Control. 2012;57(5):1087‐1101. https://doi.org/10.1109/TAC.2011.2174676. · Zbl 1369.93122 · doi:10.1109/TAC.2011.2174676
[11] HuberO, AcaryV, BrogliatoB. Lyapunov stability and performance analysis of the implicit discrete sliding mode control. IEEE Trans Autom Control. 2016;61(10):3016‐3030. https://doi.org/10.1109/TAC.2015.2506991. · Zbl 1359.93091 · doi:10.1109/TAC.2015.2506991
[12] ChakrabartyS, BandyopadhyayB. A generalized reaching law for discrete time sliding mode control. Automatica. 2015;52:83‐86. https://doi.org/10.1016/j.automatica.2014.10.124. · Zbl 1309.93035 · doi:10.1016/j.automatica.2014.10.124
[13] FengY, XueC, YuX, HanF. On a discrete‐time quasi‐sliding mode control. Paper presented at: Proceedings of the 2018 15th International Workshop on Variable Structure Systems (VSS); July, 2018:251‐254; Graz, Austria.
[14] LevantA, LivneM. Uncertain disturbances attenuation by homogeneous multi‐input multi‐output sliding mode control and its discretisation. IET Control Theory Appl. 2015;9(4):515‐525. https://doi.org/10.1049/iet‐cta.2014.0342. · doi:10.1049/iet‐cta.2014.0342
[15] KochS, ReichhartingerM, HornM, FridmanL. Discrete‐time implementation of homogeneous differentiators. IEEE Trans Autom Control. 2020;65(2):757‐762. https://doi.org/10.1109/TAC.2019.2919237. · Zbl 1533.93433 · doi:10.1109/TAC.2019.2919237
[16] BartoszewiczA. Discrete‐time quasi‐sliding‐mode control strategies. IEEE Trans Ind Electron. 1998;45(4):633‐637. https://doi.org/10.1109/41.704892. · doi:10.1109/41.704892
[17] GoloG, MilosavljevicC. Robust discrete‐time chattering free sliding mode control. Syst Control Lett. 2000;41(1):19‐28. https://doi.org/10.1016/S0167‐6911(00)00033‐5. · Zbl 0985.93007 · doi:10.1016/S0167‐6911(00)00033‐5
[18] BartoszewiczA, LatosinskiP. Discrete time sliding mode control with reduced switching ‐ a new reaching law approach. Int J Robust Nonlinear Control. 2016;26(1):47‐68. https://doi.org/10.1002/rnc.3291. · Zbl 1333.93067 · doi:10.1002/rnc.3291
[19] DuH, YuX, ChenMZ, LiS. Chattering‐free discrete‐time sliding mode control. Automatica. 2016;68:87‐91. · Zbl 1334.93041
[20] DrakunovS, UtkinV. On discrete‐time sliding modes. IFAC Proc Vol. 1989;22(3):273‐278. https://doi.org/10.1016/S1474‐6670(17)53647‐2. · doi:10.1016/S1474‐6670(17)53647‐2
[21] Sira‐RamírezH, Aguilar‐OrduñaM, Zurita‐BustamanteE. On the sliding mode control of MIMO nonlinear systems: an input‐output approach. Int J Robust Nonlinear Control. 2019;29(3):715‐735. https://doi.org/10.1002/rnc.4320. · Zbl 1411.93051 · doi:10.1002/rnc.4320
[22] SharmaNK, JanardhananS. Optimal discrete higher‐order sliding mode control of uncertain LTI systems with partial state information. Int J Robust Nonlinear Control. 2017;27(17):4104‐4115. https://doi.org/10.1002/rnc.3785. · Zbl 1386.93068 · doi:10.1002/rnc.3785
[23] SharmaNK, JanardhananS. Discrete‐time higher‐order sliding mode control of systems with unmatched uncertainty. Int J Robust Nonlinear Control. 2019;29(1):135‐152. https://doi.org/10.1002/rnc.4377. · Zbl 1411.93047 · doi:10.1002/rnc.4377
[24] BartoliniG, FerraraA, UtkinV. Adaptive sliding mode control in discrete‐time systems. Automatica. 1995;31(5):769‐773. · Zbl 0825.93097
[25] BartoszewiczA, AdamiakK. Model reference discrete‐time variable structure control. Int J Adapt Control Signal Process. 2018;32(10):1440‐1452. https://doi.org/10.1002/acs.2922. · Zbl 1402.93073 · doi:10.1002/acs.2922
[26] SuWC, DrakunovSV, ÖzgünerÜ. An \(\mathcal{O} ( T^2 )\) boundary layer in sliding mode for sampled‐data systems. IEEE Trans Autom Control. 2000;45(3):482‐485. https://doi.org/10.1109/9.847728. · Zbl 0972.93039 · doi:10.1109/9.847728
[27] AbidiK, XuJX, XinghuoY. On the discrete‐time integral sliding‐mode control. IEEE Trans Autom Control. 2007;52(4):709‐715. https://doi.org/10.1109/TAC.2007.894537. · Zbl 1366.93091 · doi:10.1109/TAC.2007.894537
[28] BandyopadhyayB, FulwaniD. High‐performance tracking controller for discrete plant using nonlinear sliding surface. IEEE Trans Ind Electron. 2009;56(9):3628‐3637. https://doi.org/10.1109/TIE.2008.2007984. · doi:10.1109/TIE.2008.2007984
[29] HouH, ZhangQ. Novel sliding mode control for multi‐input‐multi‐output discrete‐time system with disturbance. Int J Robust Nonlinear Control. 2018;28(8):3033‐3055. https://doi.org/10.1002/rnc.4064. · Zbl 1391.93055 · doi:10.1002/rnc.4064
[30] LoukianovAG. Robust block decomposition sliding mode control design. Math Probl Eng. 2002;8(4‐5):349‐365. https://doi.org/10.1080/10241230306732. · Zbl 1059.93024 · doi:10.1080/10241230306732
[31] KrsticM, KokotovicPV, KanellakopoulosI. Nonlinear and Adaptive Control Design. 1st ed.New York, NY: John Wiley & Sons, Inc; 1995.
[32] IsidoriA. Nonlinear Control Systems. London, England: Springer; 1989.
[33] Zapata‐ZuluagaCC, LoukianovAG. Robust discrete‐time sliding mode controller for a class of nonlinear perturbed systems. Paper presented at: Proceedings of the 2018 IEEE Conference on Decision and Control (CDC); December, 2018:6754‐6759; Miami.
[34] ZhangC, YangJ, YanY, FridmanL, LiS. Semi‐global finite‐time trajectory tracking realization for disturbed nonlinear systems via higher‐order sliding modes. IEEE Trans Autom Control. 2019;65(5):2185‐2191. https://doi.org/10.1109/TAC.2019.2937853. · Zbl 1533.93706 · doi:10.1109/TAC.2019.2937853
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