Aplicações de controladores FOPID na engenharia mecatrônica

Abstract

FOPID controllers come from the PID controller’s generalization by fractional calculus formulations and therefore have a greater tuning capacity compared to traditional controllers. Therefore, this paper sought out to realize a case study survey in the mechatronics engineering context comparing PID and FOPID controllers’ performance. For the process control scope, the FOMCON toolbox was used, what allowed inserting fractional powers in transfer functions. Then, utilizing the evolutionary algorithm PSO to search for parameters for performance index minimization, simulations were executed for a level control system, for a stirred tank heating system and for a unknown system’s SOPDT approximation. While for robotics systems, manipulator robots’ kinematics and dynamics configurations of two, four and six degrees of freedom were modeled. As computed torque was the law applied in these systems, in time domain, numerical problems from GrünwaldLetnikov numerical fractional derivative formulations were corrected by adaptative memory approach. The simulations outcome confirmed the hypothesis that FOPID controllers’ flexibility results in a better or at least equivalent performance in comparison to PID. Thus, it was shown that FOPID is able to provide a degree of improvement in performance index for each analyzed system.