Identificação e controle de sistemas de ordem fracionária, estudo de caso aplicada a um sistema térmico

Abstract

The need to model nature has always been a great challenge to man. Describing natural phenomena in mathematical models has been challenging throughout history in the area of systems identification. Currently, there is a multitude of methods and rules to be followed when it comes to real systems such as thermal systems, among others. Having as main objective the one of obtaining the control under the identified system, modifying their behavior efficiently, with the lowest cost and possibly human intervention. However, it is not possible to identify a system with 100% accuracy, what is achieved is an approximate model of the studied dynamics. In this work, identification methods based on fractional calculations applied to fractional-order systems are investigated. The thermal plant studied is composed of a 250 Watt ultraviolet lamp driven by a dimmer that is controlled through a microcontroller. The data obtained in a power range are collected in an open loop in the time domain. With the stored data, the plant is identified according to the non-recursive or batch least-squares model, offline mode, in which an adjustment of the plant’s response curve is investigated, minimizing by mean quadratic error function. After identifying the system, a controller of the typePIμDλisproposed for the control in all power ranges from 10% in the range of 20% to 80%. As result, good performance of the controller was obtained, proving the efficiency of the identification of the studied system.