Resumo Sistemas de controle em malha fechada têm sido utilizados para movimentar músculos e articulações dos membros inferiores de pacientes paraplégicos, por meio de estimulação elétrica funcional (Functional Electrical Stimulation -FES

This paper presents the design and simulation results considering the use of functional electrical stimulation to control the leg position of paraplegic patients. The plant is described by a nonlinear system using Takagi-Sugeno fuzzy models and a closed-loop control is presented. A transfer function represents the mathematical model related to the muscle torque and the electrical stimulation pulse width. Considering that, during the operation, the leg position is between 0 • and 60 • , then two fuzzy regulators were designed, assuming that the state vector is available or using an observer when only the output is available. This design was based on the Lyapunov stability theory and Linear Matrix Inequalities (LMIs). The simulation results show that the proposed procedures are efficient and offer good results for this control problem. Finally, new conditions regarding the design of the output tracking control, using a suitable nonlinear transformation for the description of the plant in an adequate form, is presented.

Introduction: A methodology was developed for implementing closed-loop control algorithms and for evaluating the behavior of a system, considering certain component restrictions used in laboratory implementation. Methods:Mathematical functions representing a model of the biological system were used for knee extension/fl exion movements. A Proportional Integral Derivative (PID) controller and another one using the root locus method were designed to control a patient's leg position by applying functional electrical stimulation (FES). The controllers were simulated in Matlab and ISIS Proteus. After the simulations were performed, the codes were embedded in a microcontroller, and tests were conducted on a paraplegic volunteer. To the best of the authors' knowledge, this is the fi rst time that ISIS Proteus software resources have been used prior to implementing a closed-loop system designed to control the leg position of patients. Results: This method obviates the application of initial controller tests directly to patients. The response obtained in the experiment with a paraplegic patient complied with the specifi cations set in terms of the steady-state error, the settling time, and the percentage overshoot.The proposed procedure was successfully applied for the implementation of a controller used to control the leg position of a paraplegic person by electrical muscle stimulation. Conclusion: The methodology presented in this manuscript can contribute to the implementation of analog and digital controllers because hardware limitations are typically not taken into account in the design of controllers.

In this manuscript, a method for designing Takagi-Sugeno (T-S) fuzzy discrete-time regulators based on linear matrix inequalities (LMIs) is proposed to control the variation of the knee joint angle movement of paraplegic patients through electrical stimulation. A simple method for discretizing nonlinear systems described by T-S fuzzy models is used. The control strategy is applied for a paraplegic volunteer and a healthy one. The results and analysis show that the controlled system attended the design specifications for small values of the sample time considered for the discretization.

A proposal for the knee position control design of paraplegic patients with functional electrical stimulation (FES) using control systems and considering norm-bounded uncertainties is presented. A state-space representation of the knee joint model of the paraplegic patient with its nonlinearity is also demonstrated. The use of linear matrix inequalities (LMIs) in control systems with norm-bounded uncertainties for asymptotic stability is analyzed. The model was simulated in the Matlab environment. The matrix of state space feedback was obtained through LMIs.