SUMMARY OF A STRICTLY POSITIVE REAL SYSTEM FOR CONTROLLING A WHEELCHAIR MODEL USING A PARAMETER-DEPENDENT LYAPUNOV FUNCTION

• DOI: https://doi.org/10.22533/at.ed.13176326270312

• Palavras-chave: ERP System. Lyapunov Function. Wheelchair. Polytopic Uncertainties. Linear Matrix Inequalities (LMIs).

• Keywords: ERP System. Lyapunov Function. Wheelchair. Polytopic Uncertainties. Linear Matrix Inequalities (LMIs).

• Abstract:

  The objective of this undergraduate research project was to synthesize the controller for a breath- and suction-controlled wheelchair model, described in Mazo et al. (1995), using the Strictly Positive Real (ERP) method and considering polytopic uncertainties in the system plant with random noise at the input, via Linear Matrix Inequalities (LMIs) and a Lyapunov function V(x) = xT  P(α) x, where the matrix P(α) depends on the polytopic uncertainties present in the model. To carry out the proposed work, Matlab software was used both to perform the calculations necessary for the synthesis of the ERP system and to conduct simulations of the synthesized system, applied to the wheelchair model. The results obtained were satisfactory, achieving a strictly positive-definite system of the plant model through the LMIs and also good results in the system simulations regarding a sinusoidal input, presenting short stabilization times of the plant parameters with respect to time. Throughout this work, it was possible to gain extensive knowledge of advanced and modern control techniques, widely used in the context of contemporary control engineering, which have proven to be highly effective and capable of stabilizing systems with a high degree of complexity.