Procedimento de projeto de controladores robustos para conversores de potência por meio de otimização por enxame de partículas

Abstract

This master thesis provides as contribution a design procedure, based on particle swarm optimization and Kharitonov’s Theorem, to obtain fixed gains for robust controllers for power converters with parametric uncertainties. Firstly, a transfer function model of the converter with uncertain parameters is used and included in a polytopic model. In the sequence, the transfer function of the controller is chosen, and its fixed coefficients are considered as the decision variables of an optimization problem. An objective function is then used to map each vector of controller coefficients to a real positive value, considering the criteria phase margin, crossover frequency, gain margin, overshoot, steady state error and amplitude of the control signal, for the vertices of the polytopic model. A penalty factor based on the Kharitonov’s Theorem is included in the objective function. A search space for the coefficients of the controller is systematically defined as a hyper-rectangle, based on the positivity of the coefficients of the characteristic polynomial, and the particle swarm optimization algorithm is then employed to search for the coefficient vector of the controller that minimizes the proposed objective function. To prove the ability to find robust controllers for applications in power electronics, the proposed procedure is used to obtain PID controllers for a Buck converter and PI controllers for a permanent magnet synchronous motor, ensuring good regulation of the output variables in both applications. Experimental results for the permanent magnet synchronous motor confirm the practical viability of the proposed procedure, with superior performance compared to gains obtained by a function specialized for PID design. The proposed procedure can be considered as an alternative to analytical methods and to trial and error designs, allowing to reduce the time demanded in human-machine interaction in order to design controllers that meet multiple objectives and constraints of interest in practice.