Evaluación y análisis comparativo de las estrategias de sintonización, optimización y aproximación de controladores de orden fraccionario aplicados a sistemas mecatrónicos.

Abstract

A comparative evaluation of the performance of the different fractional order PID controllers (FOPID) applied to FODPT processes was performed, the process used in this study is a DC motor. Four steps are used in the design procedure of FOPID controllers: tuning methods, optimization algorithms, performance indexes and approximation algorithms. In each of these stages there is a variety of methodologies and algorithms, which makes the design of a FOPID controller applied to a particular process complex. For the comparative analysis four (4) tuning methods were used: Ziegler-Nichols, Amstrom-Hagglund (AMIGO), Chien-Hromes-Reswick (CHR) and Cohen Coon (CC); In addition, (3) Nelder-Mead optimization algorithms (NM), the internal point (IP) and the sequential quadratic programming algorithm (SQP) were applied; With respect to the phase of approximation of fractional order to whole order, three (3) algorithms were used: Crone, Matsuday Carlson; and finally to quantify the performance of the tuning method and used four (4) error rates: ISE, IAE, ITSE and ITAE. As a result of this work, 180 FOPID controllers were generated, of which it is shown that, when applying the ZN tuning algorithm, together with the SQP optimization algorithm, selecting the ITAE performance metric and the Matsuda approximation algorithm, it becomes in the optimal communication of strategies applied to the design of FOPID controllers. The closed loop simulation between this controller and the process gave us the best results in the temporal response, an elongation percentage of 1.07% was obtained and an establishment time of 1.3 milliseconds. Finally, it is recommended to use the plant identified by the PID Tuner tool, this first-order model with delay time has better simulation results in the temporal parameters with respect to the other models.