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An adaptive fuzzy sliding mode control under model uncertainties and disturbances: second-order non-linear system

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Abstract

Sliding mode control (SMC) is applied as an efficient strategy in controlling of the non-linear system which has some drawbacks. In this study, an adaptive non-linear SMC approach is employed in perturbed systems with disturbance in order to investigate several significant problems for sliding mode control and proposed solutions. For this aim, firstly, the adaptive gain parameter is obtained which leads to the reduction of overshoot of the manipulated variables and the proper control response. Secondly, a new parameter based on an estimation error is utilized in order to reject the improper effects of model uncertainties and disturbances. Thirdly, a new part is added to the control action, and the corresponding weight is obtained in order to overcome the chattering effect. The tuning parameters of the proposed control approach are developed based on artificial intelligence technique (i.e., fuzzy logic) in order to adapt to various conditions by varying during the system control process. The Lyapunov theory is utilized to demonstrate the stability of the designed controller. In order to test the effectiveness of the proposed controller, the underwater vehicle system is applied that has a second-order non-linear model with a single input–single output. The new control strategy is compared with three different SMC techniques. The results confirm that the efficiency of proposed scheme in terms of disturbance rejection capability, the proper control action response with reduced chattering effect in comparison with other SMC methods which presented in this paper.

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References

  1. Ravell DAM, Maia MM, Diez FJ (2018) Modeling and control of unmanned aerial/underwater vehicles using hybrid control. Control Eng Pract 76:112–122. https://doi.org/10.1016/j.conengprac.2018.04.006

    Article  Google Scholar 

  2. Hosen MA, Hussain MA, Mjalli FS, Khosravi A, Creighton D, Nahavandi S (2014) Performance analysis of three advanced controllers for polymerization batch reactor: an experimental investigation. Chem Eng Res Des 92(903):916. https://doi.org/10.1016/j.cherd.2013.07.032

    Article  Google Scholar 

  3. Han J, Yu S, Yi S (2019) Oxygen excess ratio control for proton exchange membrane fuel cell using model reference adaptive control. Int J Hydrog Energy 44:18425–18437. https://doi.org/10.1016/j.ijhydene.2019.05.041

    Article  Google Scholar 

  4. Van M (2019) An enhanced tracking control of marine surface vessels based on adaptive integral sliding mode control and disturbance observer. ISA Trans 90:30–40. https://doi.org/10.1016/j.isatra.2018.12.047

    Article  Google Scholar 

  5. Zhang H, Wang J, Shi Y (2013) Robust H∞ sliding-mode control for Markovian jump systems subject to intermittent observations and partially known transition probabilities. Syst Control Lett 62:1114–1124. https://doi.org/10.1016/j.sysconle.2013.09.006

    Article  MathSciNet  MATH  Google Scholar 

  6. Sinha A, Mishra RK (2018) Control of a non-linear continuous stirred tank reactor via event triggered sliding modes. Chem Eng Sci 187:52–59. https://doi.org/10.1016/j.ces.2018.04.057

    Article  Google Scholar 

  7. Çimen MA, Ararat O, Söylemez MT (2018) A new adaptive slip-slide control system for railway vehicles. Mech Syst Signal Process 111:265–284. https://doi.org/10.1016/j.ymssp.2018.03.050

    Article  Google Scholar 

  8. Rodríguez A, De León J, Fridman L (2008) Quasi-continuous high-order sliding-mode controllers for reduced-order chaos synchronization. Int J Non Linear Mech 43:948–961. https://doi.org/10.1016/j.ijnonlinmec.2008.07.007

    Article  Google Scholar 

  9. Li J, Zhang Q (2018) A linear switching function approach to sliding mode control and observation of descriptor systems. Automatica 95:112–121. https://doi.org/10.1016/j.automatica.2018.05.031

    Article  MathSciNet  MATH  Google Scholar 

  10. Feng Y, Zhou M, Zheng X, Han F, Yu X (2018) Full-order terminal sliding-mode control of MIMO systems with unmatched uncertainties. J Franklin Inst 355:653–674. https://doi.org/10.1016/j.jfranklin.2017.10.034

    Article  MathSciNet  MATH  Google Scholar 

  11. Deepika D, Narayan S, Kaur S (2019) Robust finite time integral sliding mode tracker for nth-order non-affine non-linear system with uncertainty and disturbance estimator. Math Comput Simulat 156:364–376. https://doi.org/10.1016/j.matcom.2018.09.006

    Article  MATH  Google Scholar 

  12. Mobayen S, Majd VJ, Sojoodi M (2012) An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems. Math Comput Simulat 85:1–10. https://doi.org/10.1016/j.matcom.2012.09.006

    Article  MathSciNet  MATH  Google Scholar 

  13. Cao WJ, Xu JX (2004) Non-linear integral-type sliding surface for both matched and unmatched uncertain systems. IEEE Trans Automat Contr 49:1355–1360. https://doi.org/10.1109/TAC.2004.832658

    Article  MATH  Google Scholar 

  14. Khan Q, Bhatti AI, Iqbal S, Iqbal M (2011) Dynamic integral sliding mode for MIMO uncertain non-linear systems. Int J Control Aut Syst 9:9151–9160. https://doi.org/10.1007/s12555-011-0120-8

    Article  Google Scholar 

  15. Suryawanshi PV, Shendge PD, Phadke SB (2016) A boundary layer sliding mode control design for chatter reduction using uncertainty and disturbance estimator. Int J Dyn Control 4:456–465. https://doi.org/10.1007/s40435-015-0150-9

    Article  MathSciNet  Google Scholar 

  16. Tahmane B, Kurode S (2018) Finite time state and disturbance estimation for robust performance of motion control systems using sliding modes. Int J Control 91:1171–1182. https://doi.org/10.1080/00207179.2017.1311026

    Article  MathSciNet  MATH  Google Scholar 

  17. Feng Y, Han F, Yu X (2014) Chattering free full-order sliding-mode control. Automatica 50:1310–1314. https://doi.org/10.1016/j.automatica.2014.01.004

    Article  MathSciNet  MATH  Google Scholar 

  18. Utkin V, Poznyak A, Orlov Y, Polyakov A (2020) Conventional and high order sliding mode control. J Fraklin Inst 357:10244–10261. https://doi.org/10.1016/j.jfranklin.2020.06.018

    Article  MathSciNet  MATH  Google Scholar 

  19. Lu X, Zhang X, Zhang G, Fan J, Jia S (2019) Neural network adaptive sliding mode control for omnidirectional vehicle with uncertainties. ISA Trans 86:201–214. https://doi.org/10.1016/j.isatra.2018.10.043

    Article  Google Scholar 

  20. Ayadi A, Smaoui M, Aloui S, Hajji S, Farza M (2018) Adaptive sliding mode control with moving surface: experimental validation for electropneumatic system. Mech Syst Signal Process 109:27–44. https://doi.org/10.1016/j.ymssp.2018.02.042

    Article  Google Scholar 

  21. Alsmadi YM, Utkin V, Haj-Ahmed MA, Xu L (2018) Sliding mode control of power converters: DC/DC converters. Int J Control 91:2472–2493. https://doi.org/10.1080/00207179.2017.1306112

    Article  MathSciNet  MATH  Google Scholar 

  22. Rahmani M, Rahman MH (2019) Adaptive neural network fast fractional sliding mode control of a 7- DOF exoskeleton robot. Int J Control Aut Syst 18:124–133. https://doi.org/10.1007/s12555-019-0155-1

    Article  Google Scholar 

  23. Govinda EK, Arunshankar J (2018) Control of non-linear two-tank hybrid system using sliding mode controller with fractional-order PI-D sliding surface. Comput Electr Eng 71:953–965. https://doi.org/10.1016/j.compeleceng.2017.10.005

    Article  Google Scholar 

  24. Zhu H, Shen J, Lee KY, Sun L (2020) Multi-model based predictive sliding mode control for bed temperature regulation in circulating fluidized bed boiler. Control Eng Pract 101:104484. https://doi.org/10.1016/j.conengprac.2020.104484

    Article  Google Scholar 

  25. Herrera M, Camacho O, Leiva H, Smith C (2020) An approach of dynamic sliding mode control for chemical processes. J Process Control 85:112–120. https://doi.org/10.1016/j.jprocont.2019.11.008

    Article  Google Scholar 

  26. Cargua-Sagbay D, Palomo-Lema E, Camacho O, Alvarez H (2020) Flash distillation control using feasible operating region: a sliding mode control approach. Ind Eng Chem Res 59:2013–2024. https://doi.org/10.1021/acs.iecr.9b05688

    Article  Google Scholar 

  27. Karami-Mollaee A, Tirandaz H, Barambones O (2019) Neural dynamic sliding mode control of non-linear systems with both matched and mismatched uncertainties. J Franklin Inst 356:4577–4600. https://doi.org/10.1016/j.jfranklin.2019.04.019

    Article  MathSciNet  MATH  Google Scholar 

  28. Mishra RN, Mohanty KB (2020) Development and implementation of induction motor drive using sliding-mode based simplified neuro-fuzzy control. Eng Appl Artif Intell 91:103593. https://doi.org/10.1016/j.engappai.2020.103593

    Article  Google Scholar 

  29. Sankar K, Jana AK (2018) Non-linear multivariable sliding mode control of a reversible PEM fuel cell integrated system. Energy Convers Manag 171:541–565. https://doi.org/10.1016/j.enconman.2018.05.079

    Article  Google Scholar 

  30. Shah DH, Patel DM (2019) Design of sliding mode control for quadruple-tank MIMO process with time delay compensation. J Process Control 76:46–61. https://doi.org/10.1016/j.jprocont.2019.01.006

    Article  Google Scholar 

  31. Weng YP, Gao XW (2017) Data-driven sliding mode control of unknown MIMO non-linear discrete-time systems with moving PID sliding surface. J Franklin Inst 354:6463–6502. https://doi.org/10.1016/j.jfranklin.2017.07.022

    Article  MathSciNet  MATH  Google Scholar 

  32. Zhao D, Zhu Q, Dubbeldam J (2015) Terminal sliding mode control for continuous stirred tank reactor. Chem Eng Res Des 94:266–274. https://doi.org/10.1016/j.cherd.2014.08.005

    Article  Google Scholar 

  33. Jokar H, Vatankhah H (2020) Adaptive fuzzy global fast terminal sliding mode control of an over-actuated fying robot. J Braz Soc Mech Sci Eng 42:166. https://doi.org/10.1007/s40430-020-2236-3

    Article  Google Scholar 

  34. Pan Y, Yang C, Pan L, Yu H (2018) Integral sliding mode control: performance, modification and improvement. IEEE Trans Ind Inform 14:3087–3096. https://doi.org/10.1109/TII.2017.2761389

    Article  Google Scholar 

  35. Sankar K, Jana AK (2018) Nonlinear multivariable sliding mode control of a reversible PEM fuel cell integrated system. Energy Convers Manag 171:541–565. https://doi.org/10.1016/j.enconman.2018.05.079

    Article  Google Scholar 

  36. Lu YS, Chen JS (1995) Design of a global sliding-mode controller for a motor drive with bounded control. Int J Control 62:1001–1019. https://doi.org/10.1080/00207179508921579

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Research Institute of Petroleum Industry (RIPI), P.O. Box: 14665-1998, Tehran, Iran

    Shokoufe Tayyebi

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Tayyebi, S. An adaptive fuzzy sliding mode control under model uncertainties and disturbances: second-order non-linear system. J Braz. Soc. Mech. Sci. Eng. 43, 533 (2021). https://doi.org/10.1007/s40430-021-03244-6

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