Desenvolvimento de um algoritmo utilizando os métodos de NewtonRaphson e de Levenberg-Marquardt para a sintonia de controladores PID com base em critérios de desempenho.

Abstract

This work proposes a new tuning technique for PID controllers to control SISO LTI processes, based on performance criteria in the time domain. This procedure is carried out through the application of the Newton-Raphson and the Levenberg-Marquardt iterative methods to solve the nonlinear set of equations that describe how close the step response parameters are to the desired ones. Therefore, an algebraic development was conducted to determine the jacobian of the performance functions with respect to the controller coefficients, allowing the implementation of the aforementioned numerical methods. Numerical simulations of the proposed algorithm were performed in the software MATLAB for three transfer functions of different orders. The results demonstrated the feasibility of using this tuning algorithm, as long as certain restrictions on the transfer function of the process are obeyed, and a performance comparison between the two numerical methods showed the advantages and disadvantages of each one. In addition, it was shown that the convergence rate of the methods can be amplified when the performance parameters of the initial response curve are relatively close to the desired ones, suggesting that a prior tuning by already established techniques increases the chances of success of the algorithm.