Abstract
This paper presents two sliding mode control (SMC) strategies for a magnetic levitation system. First, a state feedback-based discrete-time sliding mode controller (DSMC) is designed using an improved reaching law to counteract the matched uncertainties with reduced chattering. However, the disturbance rejection ability is compromised to some extent due to the quasi-sliding mode (QSM) motion of the state trajectory and the finite switching frequency. Next, to enhance the robustness without compromising the chattering reduction benefits of the state feedback-based DSMC, a robust multirate output feedback (MROF)-based DSMC strategy is proposed. This strategy utilizes a novel sliding surface, a modified reaching law, an integrated MROF-based state estimator, and an augmented nonlinear feedback linearization controller to reject the mismatched disturbances. With this technique, it is possible to realize the effect of full-state feedback with superior robustness features while preserving the properties of an ideal continuous-time SMC as much as possible. Quantitative and qualitative comparative analyses of the proposed controllers and different state-of-the-art control techniques are done using standard performance criteria. The simulation results and comparative studies demonstrate that the MROF-based DSMC performs much better than the other advanced control strategies in terms of superior disturbance rejection ability, better steady-state performance, smaller width of the QSM band, and reduced chatter under mismatched uncertainties. A rigorous stability analysis of the closed-loop system for the proposed controllers is performed using the Lyapunov stability theory. Furthermore, the benefits and drawbacks of some recently explored control strategies for a magnetic levitation system are elaborated.
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References
Abdelrahman AS, Sayeed J, Youssef MZ (2018) Hyperloop transportation system: analysis, design, control, and implementation. IEEE Trans Indust Electr 65(9):7427–7436. https://doi.org/10.1109/TIE.2017.2777412
El Hajjaji A, Ouladsine M (2001) Modeling and nonlinear control of magnetic levitation systems. IEEE Trans Indust Electr 48(4):831–838. https://doi.org/10.1109/41.937416
Yang ZJ, Tateishi M (2001) Adaptive robust nonlinear control of a magnetic levitation system. Automatica 37(7):1125–1131. https://doi.org/10.1016/S0005-1098(01)00063-2
Yang ZJ, Miyazaki K, Kanae S et al (2004) Robust position control of a magnetic levitation system via dynamic surface control technique. IEEE Trans Indust Electr 51(1):26–34. https://doi.org/10.1109/TIE.2003.822095
Bächle T, Hentzelt S, Graichen K (2013) Nonlinear model predictive control of a magnetic levitation system. Control Eng Pract 21(9):1250–1258. https://doi.org/10.1016/j.conengprac.2013.04.009
Wang J, Chen L, Xu Q (2022) Disturbance estimation-based robust model predictive position tracking control for magnetic levitation system. IEEE/ASME Trans Mech 27(1):81–92. https://doi.org/10.1109/TMECH.2021.3058256
Al-Muthairi NF, Zribi M (2004) Sliding mode control of a magnetic levitation system. Math Problems Eng 2004(2):93–107. https://doi.org/10.1155/S1024123X04310033
Boonsatit N, Pukdeboon C (2016) Adaptive fast terminal sliding mode control of magnetic levitation system. J Control Autom Electr Syst 27(4):359–367. https://doi.org/10.1007/s40313-016-0246-2
Pan J, Li W, Zhang H (2018) Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control. Int J Control Autom Syst 16(6):2878–2887. https://doi.org/10.1007/s12555-017-0616-y
Roy P, Roy BK (2020) Sliding mode control versus fractional-order sliding mode control: applied to a magnetic levitation system. J Control Autom Electr Syst 31(3):597–606. https://doi.org/10.1007/s40313-020-00587-8
Wang J, Zhao L, Yu L (2021) Adaptive terminal sliding mode control for magnetic levitation systems with enhanced disturbance compensation. IEEE Trans Indust Electr 68(1):756–766. https://doi.org/10.1109/TIE.2020.2975487
Yang J, Li S, Yu X (2013) Sliding-mode control for systems with mismatched uncertainties via a disturbance observer. IEEE Trans Indust Electr 60(1):160–169. https://doi.org/10.1109/TIE.2012.2183841
Yaseen H, Siffat S, Ahmad I et al (2022) Nonlinear adaptive control of magnetic levitation system using terminal sliding mode and integral backstepping sliding mode controllers. ISA Trans 126:121–133. https://doi.org/10.1016/j.isatra.2021.07.026
Young KD, Utkin VI, Ozguner U (1999) A control engineer’s guide to sliding mode control. IEEE Trans Control Syst Technol 7(3):328–342. https://doi.org/10.1109/87.761053
Gao W, Wang Y, Homaifa A (1995) Discrete-time variable structure control systems. IEEE Trans Indust Electr 42(2):117–122. https://doi.org/10.1109/41.370376
Niu Y, Ho DWC, Wang Z (2010) Improved sliding mode control for discrete-time systems via reaching law. IET Control Theory Appl 4(11):2245–2251. https://doi.org/10.1049/iet-cta.2009.0296
Bandyopadyay B, Janardhanan S (2006) Discrete-time sliding mode control: a multirate output feedback approach. In: Lecture notes in control and information sciences, vol 323. Springer-Verlag, Berlin https://doi.org/10.1007/11524083
Janardhanan S, Bandyopadhyay B (2007) Multirate output feedback based robust quasi-sliding mode control of discrete-time systems. IEEE Trans Autom Control 52(3):499–503. https://doi.org/10.1109/TAC.2006.890391
Zhang X, Ding F, Yang E (2019) State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors. Int J Adapt Control Signal Process 33(7):1157–1173. https://doi.org/10.1002/acs.3027
Ding F, Xu L, Meng D et al (2020) Gradient estimation algorithms for the parameter identification of bilinear systems using the auxiliary model. J Comput Appl Math 369(112):575. https://doi.org/10.1016/j.cam.2019.112575
Li M, Liu X (2020) Maximum likelihood least squares based iterative estimation for a class of bilinear systems using the data filtering technique. Int J Control Autom Syst 18(6):1581–1592. https://doi.org/10.1007/s12555-019-0191-5
Khalil HK (2002) Nonlinear Syst, 3rd edn. Prentice-Hall, Upper Saddle River
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P.V. developed the control concepts, wrote the proofs, performed the comparative analyses, and wrote and revised the manuscript from start to finish. V.B. served as an advisor and reviewed the manuscript.
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Vernekar, P., Bandal, V. Sliding mode control for magnetic levitation systems with mismatched uncertainties using multirate output feedback. Int. J. Dynam. Control 11, 2958–2976 (2023). https://doi.org/10.1007/s40435-023-01151-3
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DOI: https://doi.org/10.1007/s40435-023-01151-3