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Electrically Stimulated Lower Limb using a Takagi-Sugeno Fuzzy Model and Robust Switched Controller Subject to Actuator Saturation and Fault under Nonideal Conditions

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Abstract

Electrically stimulated lower limb systems contain higher order nonlinearities and uncertainties in their physical parameters. Takagi-Sugeno (TS) fuzzy models are used to model nonlinear systems. Techniques such as parallel distributed compensation (PDC) are dependent on the membership functions that constitute the TS fuzzy model. When the exact representation approach is used to electrical stimulation applications, the system’s performance under PDC control can be deteriorated, because the membership functions may be uncertain, besides a high computational cost be required to compute them. In this paper, we propose a robust switched control subject to actuator saturation and fault (RSwASF) that effectively handles system uncertainties and nonidealities, such as fatigue, spasms, tremor, and muscle recruitment. Control techniques based on TS fuzzy modeling (PDC and robust PDC), as well as other approaches, such as sliding-mode control, backstepping, super-twisting, gain-scheduling, and proportional-integral-derivative (PID) control were compared to RSwASF through the root-mean-squared error (RMSE). The results indicate that RSwASF minimizes the influence of the parametric uncertainties and presents the lowest RMSE for healthy and paraplegic individuals.

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Acknowledgements

This study was financed in part by the CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil) - Finance Code 001; by the Brazilian National Council for Scientific and Technological Development (CNPq) under research fellowships 309.872/2018-9 and 312.170/2018-1. The authors would like to thank Enago for English language review.

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Authors and Affiliations

  1. Control and Automation Laboratory, Federal University of Technology - Paraná (UTFPR), Marcilio Dias St., 635., Apucarana, PR, Brazil

    Willian Ricardo Bispo Murbak Nunes

  2. Department of Control and Automation Engineering, Federal Institute of Education, Science and Technology of Paraná (IFPR), Dr. Tito Ave., 801, Jacarezinho, PR, Brazil

    Uiliam Nelson Lendzion Tomaz Alves

  3. Instrumentation & Biomedical Engineering Laboratory, São Paulo State University (UNESP), Prof. José Carlos Rossi Ave., Ilha Solteira, SP, 1370, Brazil

    Marcelo Augusto Assunção Sanches & Aparecido Augusto de Carvalho

  4. Control Research Laboratory, São Paulo State University (UNESP), Prof. José Carlos Rossi Ave., Ilha Solteira, SP, 1370, Brazil

    Marcelo Carvalho Minhoto Teixeira

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Nunes, W.R.B.M., Alves, U.N.L.T., Sanches, M.A.A. et al. Electrically Stimulated Lower Limb using a Takagi-Sugeno Fuzzy Model and Robust Switched Controller Subject to Actuator Saturation and Fault under Nonideal Conditions. Int. J. Fuzzy Syst. 24, 57–72 (2022). https://doi.org/10.1007/s40815-021-01115-9

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