This paper presents a robust controller design for a discrete linear system, dealing with internal and external disturbances. The main focus is to reduce chattering, minimize undesirable oscillations, and enhance robustness against disturbances using a new discrete sliding mode control. The novel approach involves replacing the classical Gao’s reaching law with a fractional order reaching law based on the Grunwald–Letnikov definition, leading to advantages like a simplified algorithm and improved performance against disturbances. The performances of the suggested method are evaluated through two simulation examples.
BartoszewiczALatosińskiMaP (2014) Reaching law-based sliding mode congestion control for communication networks. IET Control Theory & Applications8(17): 1914–1920.
2.
BartoszewiczALatosińskiMaP (2016) New switching and nonswitching type reaching laws for SMC of discrete time systems. IEEE Transactions on Control Systems Technology24(2): 670–677.
3.
BartoszewiczALatosińskiMaP (2017) Discrete time sliding mode control with reduced switching - a new reaching law approach. International Journal of Robust and Nonlinear Control26(1): 47–68.
4.
BartoszewiczALatosinskiP (2018) Generalization of Gao’s reaching law for higher relative degree sliding variables. IEEE Transactions on Automatic Control63(9): 3173–3179.
5.
BartoszewiczA (1998) Discrete-time quasi-sliding-mode control strategies. IEEE Transactions on Industrial Electronics45(4): 633–637.
6.
BenYazidYMehdiDNouriAS (2018) Discrete T–S fuzzy systems with time-varying delays: a new discrete sliding mode control approach. Transactions of the Institute of Measurement and Control40(7): 2332–2339.
7.
DehriKNouriSA (2021) A discrete repetitive adaptive sliding mode control for DC-DC buck converter. Part I: Journal of Systems and Control Engineering235(9): 1–11.
8.
GaoWWangYHomaifaA (1995) Discrete-time variable structure control systems. IEEE Transactions on Industrial Electronics42(2): 117–122.
9.
HaifengMYangminL (2019) Multi-Power Reaching Law Based Discrete-Time Sliding-Mode Control. IEEE Access.
10.
HaifengMYangminL (2020) Fractional order exponential type discrete-time sliding mode control. International Journal of Control, Automation and Systems18(2): 374–383.
11.
HaifengMChaoLYangL, et al. (2019a) Sliding mode control for uncertain discrete time systems based on fractional order reaching law. IET Control Theory & Applications13(13): 1963–1970.
12.
HaifengMYangminLXiongZ (2019b) Discrete-time sliding-mode control with enhanced power reaching law. IEEE Transactions on Industrial Electronics66(6): 4629–4638.
13.
KatarzynaABartoszewiczA (2022) Novel power-rate reaching law for quasi-sliding mode control. Energies15(5446): 1–14.
14.
KurodeSBandyopadhyayBGandhiP (2011) Discrete sliding mode control for a class of underactuated systems. In: Proccedings. 37th Annual Conference of the IEEE Industrial Electronics Society. IEEE, 3936–3941.
15.
MaHWuJXiongZ (2017) A novel exponential reaching law of discrete-time sliding-mode control. IEEE Transactions on Industrial Electronics64(5): 3840–3850.
16.
MartinSMartinHAntonellaF (2019) Discrete-time model reference adaptive sliding mode control for systems in state-space representation. In: Conference on Decision and Control (CDC). IEEE, 6007–6012.
17.
MohamedRRomdhaneHDehriK, et al. (2019) A discrete adaptive second order neuro sliding mode control for uncertain nonlinear system. In: International Conference on Sciences and Techniques of Automatic Control and Computer Engineering STA. IEEE, 518–523.
18.
JiNYanXGMaoZ, et al. (2021) Decentralised state feedback stabilisation for nonlinear interconnected systems using sliding mode control. International Journal of Systems Science53(5): 1017–1030.
19.
TahriFMessaoudABen AbdennourR (2021) a discrete interval observer for linear system: application on a real process. In: International Conference on Signal, Control and Communication. IEEE, 74—80.
20.
YaziciİYaylaciEK (2017) 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 Electronics10(13): 1751–1758.
21.
YuehengDXinggangYZehuiM, et al. (2022a) Decentralised output tracking of interconnected systems with unknown interconnections using sliding mode control. International Journal of Systems Science54(2): 283–294.
22.
YuehengDXinggangYZehuiM, et al. (2022b) Sliding mode based decentralized tracking control of underactuated four-body systems. In: Asian Control Conference. IEEE.
23.
YuehengDXinggangYZehuiM, et al. (2022c) System structure based decentralized sliding mode output tracking control for nonlinear interconnected systems. International Journal of Robust and Nonlinear Control33(3): 1407–2507.
24.
ZnidiADehriKNouriAS (2022a) Discrete indirect adaptive sliding mode control for uncertain Hammerstein nonlinear systems. Transactions of the Institute of Measurement and Control44(10): 1907–1921.
25.
ZnidiADehriKNouriAS (2022b) Discrete Adaptive second order sliding mode control for Uncertain Hammerstein Nonlinear systems. In: 19th International Multi-Conference on Systems, Signals and Devices (SSD). IEEE, 1241–1247.
