CONTROL OF THE ANGLE OF THE KNEE JOINT USING ERP SYSTEMS, CONSIDERING UNCERTAINTY IN THE PLANT

• DOI: https://doi.org/10.22533/at.ed.3174192401079

• Palavras-chave: ERP Systems, LMI, Polytopic Uncertainties, Electrostimulation.

• Keywords: ERP Systems, LMI, Polytopic Uncertainties, Electrostimulation.

• Abstract:

  In this work, a controller was designed based on the study of conditions in terms of Linear Matrix Inequalities, (in English, Linear Matrix Inequalities, LMIs), for the synthesis of Strictly Real Positive Systems (ERP), with applications aimed at control with variable structure, in order to apply the conditions obtained in a mathematical model for controlling the knee joint angle of paraplegic patients through electrical stimulation. In the project carried out, time-varying polytopic uncertainties were considered in the plant. Thus, the ERP synthesis was based on a Lyapunov V (x) = xT P0(α)x, and matrix P0(α) depends on the uncertainties present in the system, with α having a limited rate of variation. The conditions obtained were used in the mathematical model for controlling the electrical stimulation of a paraplegic patient, associated with a dynamic compensator, the use of which is necessary to obtain a system. Matlab software was used to solve the LMIs, as well as to simulate the systems with the results obtained. However, feasible solutions to the problem were found only in the case where the rate of variation of α is zero. The project developed was extremely important for learning, enabling the understanding of Lyapunov's stability theory with time-varying uncertainties, as well as the modeling and construction of controllers.