Robust Control of the Knee Joint Angle of Paraplegic Patients considering Norm-Bounded Uncertainties

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 K of state space feedback was obtained through LMIs

Controle automático com estrutura variável utilizando sistemas ERP e LMI

Propõem-se novas condições, em termos de Desigualdades Lineares Matriciais (em inglês, Linear Matrix Inequalities, LMI), para a resolução do seguinte problema, classificado como síntese Estritamente Real Positiva (ERP): dada uma planta linear invariante no tempo, com o número de saídas maior ou igual ao número de entradas, encontre uma matriz constante de realimentação da saída K e uma matriz constante em série com a saída F para que o sistema controlado seja ERP. Então, com base neste resultado, um novo projeto baseado em LMI para o Controle com Estrutura Variável (CEV) com realimentação da saída de plantas dinâmicas incertas é apresentado. O método considera as seguintes especificações do projeto: distúrbios casados ou não-linearidades da planta, restrições na saída, taxa de decaimento e, finalmente, incertezas da planta não casadas. O método é aplicado em alguns exemplos. As contribuições principais desta dissertação são: a generalização do método de projeto para plantas com o mesmo número de entradas e saídas e a proposta de um novo método de projeto para plantas com o número de saídas maior que o número de entradas.We propose new Linear Matrix Inequalities (LMI) conditions for the following problem, called Strictly Positive Real (SPR) synthesis: given a linear time-invariant plant, with the number of outputs greater or equal to the number of inputs, find a constant output feedback matrix K and a constant output tandem matrix F for the controlled system to be SPR. Then, taking into account this result, a new LMI based design for output Variable Structure Control (VSC) of uncertain dynamic plants is presented. The method considers the following design specifications: matched disturbances or nonlinearities of the plant, output constraints, decay rate and, finally, unmatched plant uncertainties. The method is applied in some examples. This dissertation presents a more general design method for the case where the plant has the same number of inputs and outputs and it proposes a new design method for the case where the plant has more outputs than inputs.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Análise de estabilidade de sistemas incertos através do critério de Routh.

O Critério de Estabilidade de Routh é uma ferramenta simples e útil para a análise da estabilidade de sistemas de controle. Neste trabalho, é proposto um método para o estudo da estabilidade de sistemas incertos dx(t)/dt=(Ao+aDA)x(t), utilizando o Critério de Estabilidade de Routh na análise dos autovalores de Ao+aDA. O método determina a faixa de valores de a que garante a estabilidade assintótica do sistema. Uma aplicação análoga para sistemas com realimentação negativa do tipo dx(t)/dt=(A-BKC)x(t), com K=kI, também é proposta

Síntese de sistemas estritamente reais positivos através do critério de routh-hurwitz

Given a linear time-invariant plant Gol(s) with one input and q outputs, where q > 1, a method based on the Routh-Hurwitz Stability Criterion is proposed to obtain a constant tandem matrix F ∈ ℝq, such that FGOl(s) is a minimumphase system. From this solution, the system FGol(s) is represented in state space by {A, B, FC} and a constant output feedback matrix K0 ∈ ℝ is obtained such that the feedback system {A - BK0C, B, FC} is Strictly Positive Real (SPR). The proposed procedure offers necessary and sufficient conditions for both problems. Initially, the general case, with a generic q, is analyzed. Following, the particular cases q = 2 and q = 3 are studied

Modelo Fuzzy Takagi-Sugeno para controle do ângulo de articulação do joelho de pacientes paraplégicos

Neste trabalho foi elaborado o controle em malha fechada, por meio de estimulação elétrica funcional, para o movimento da perna de um paciente paraplégico. Isto é feito utilizando modelos fuzzy Takagi-Sugeno, os quais resolvem classes de sistemas não lineares. O problema é descrito por desigualdades matriciais lineares (LMI) atendendo a especificações, tais como estabilidade segundo o teorema de Lyapunov, taxa de decaimento e restrição no sinal de entrada. Este controle foi projetado para variar o ângulo de articulação do joelho na faixa de 0º a 45°, mediante a estimulação elétrica no músculo quadríceps. O sinal de realimentação é relacionado ao ângulo de articulação do joelho, estabilizando-o em 45º

Realimentação derivativa e modelo fuzzy Takagi-Sugeno paracontrole da articulação do joelho de pacientes paraplégicos com o uso de acelerômetros

Feedback control systems have been used to move the muscles and joints of the limbs of paraplegic patients. The feedback signal, related to the knee joint angle, can be obtained by using an electrogoniometer. However, the use of accelerometers can help the measurements due the facility of adhering these devices to the skin. Accelerometers are also very suitable for these applications due their small dimensions and weight. In this paper a new method for designing a control system that can vary the knee joint angle using Functional Electrical Stimulation (FES) is presented, as well as a simulation with parameters values available in the literature. The nonlinear control system was represented by a Takagi-Sugeno fuzzy model and the feedback signals were obtained by using accelerometers. The design method considered all plant nonlinearities and was efficient and reliable to control the leg position of a paraplegic patient with the angle of the knee ranging from 0° to 30°, considering electric stimulation at the quadriceps muscle. The proposed method is viable and offers a new alternative for designing control systems of the knee joint angle using more comfortable sensors for the patients

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

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

Digital controller design considering hardware constraints: application in a paraplegic patient

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/flexion 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 first 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 specifications 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.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES