Robust T-S Fuzzy Control of Electrostimulation for Paraplegic Patients considering Norm-Bounded Uncertainties

Márcio Roberto Covacic,Ruberlei Gaino,Aparecido Augusto De Carvalho,Marcelo Carvalho Minhoto Teixeira,Anderson Ross Biazeto,Maxwell Simões Mineo,Marcelo Augusto Assunção Sanches,Rodrigo Cardim,Edvaldo Assunção,Henrique Shuiti Fujimoto

doi:10.1155/2020/4624657

Abstract

This manuscript presents a Takagi–Sugeno fuzzy control for a mathematical model of the knee position of paraplegic patients using functional electrical stimulation (FES). Each local model of the fuzzy system is represented considering norm-bounded uncertainties. After obtaining the model of FES with norm-bounded uncertainties, the fuzzy control strategy is designed through the solution of linear matrix inequalities (LMIs) using the conditions available in the literature, which consider these norm-bounded uncertainties. The strategy considers decay rate and constraints on the input signal. The model is simulated in the Matlab environment using the numerical parameters measured by experimental tests from a paraplegic patient.

Highlights

Several researchers have used functional electrical stimulation (FES) to restore some motion activities of people with injured spinal cord [1]
We present a Takagi–Sugeno nonlinear system with the aim of controlling the position of the leg of a paraplegic patient. e controller was designed in order to change the angle of the knee joint from 0° to 30° when electrical stimulation is applied in the quadriceps muscle
E authors considered the leg mathematical model proposed by Ferrarin and Pedotti [1], with the parameter values given in [2, 3]. e parameters B, J, τ, and G of the shank-foot complex model have the nominal values given in [2, 3], but with a 20% tolerance range around these nominal values, that is, these values are in the range between 80% and 120% of their nominal values. e minimum and the maximum values of the nonlinear term f􏽥21(x1) are computed considering the angle variation from 0° to 60°, that

Summary

Introduction

Several researchers have used functional electrical stimulation (FES) to restore some motion activities of people with injured spinal cord [1]. E controller was designed in order to change the angle of the knee joint from 0° to 30° when electrical stimulation is applied in the quadriceps muscle. For the case studied in this manuscript, with two local models and four uncertain parameters, the control design methods that consider polytopic uncertainty analysis require the solution of a set of 49 LMIs, while, for the norm-bounded uncertainty analysis, only 4 LMIs are required. The proposal for the knee position control design of paraplegic patients with functional electrical stimulation (FES) considers that the parameters of the mathematical model of the system are uncertain, whose uncertainties are bounded in norm. To the authors’ knowledge, the Takagi–Sugeno (T-S) fuzzy control considering norm-bounded uncertainties, applied to the knee joint movement of the paraplegic patient, was not published yet

Results

Discussion

Conclusion