An Experimental Tuning Approach of Fractional Order Controllers in the Frequency Domain

Isabela Birs,Silviu Folea,Cristina Muresan,Eva Dulf,Ovidiu Prodan

doi:10.3390/app10072379

Isabela Birs, Silviu Folea + Show 3 more

Open Access

https://doi.org/10.3390/app10072379

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Journal: Applied Sciences	Publication Date: Mar 31, 2020
Citations: 12	License type: CC BY 4.0

Affiliation: Technical University of Cluj-Napoca

Abstract

Fractional calculus has been used intensely in recent years in control engineering to extend the capabilities of the classical proportional–integral–derivative (PID) controller, but most tuning techniques are based on the model of the process. The paper presents an experimental tuning procedure for fractional-order proportional integral–proportional derivative (PI/PD) and PID-type controllers that eliminates the need of a mathematical model for the process. The tuning procedure consists in recreating the Bode magnitude plot using experimental tests and imposing the desired shape of the closed loop system magnitude. The proposed method is validated in the field of active vibration suppression by using an experimental set-up consisting of a smart beam.

Highlights

When subjected to the task of improving the performance of a physical process, classical control theory tackles the issue using two steps: mathematically modeling the dynamics of the process and tuning a suitable controller for the identified model.Several alternatives have been developed for controller tuning based on information gained from the experimental response of the process
It is important to emphasize that the efficiency of the obtained fractional-order controller lies in a stable, robust, closed-loop system that reduces the effect of the vibration on the process
The oscillation amplitude is reduced by 75% with the fractional-order proportional derivative (PD) and by 80% with the fractional-order PID controller

Summary

Introduction

When subjected to the task of improving the performance of a physical process, classical control theory tackles the issue using two steps: mathematically modeling the dynamics of the process and tuning a suitable controller for the identified model. One of the popular methods for tuning fractional-order controllers is by imposing frequency domain constraints such as the gain crossover frequency, phase margin, sensitivity, and complementary sensitivity [11]. From the obtained information regarding the output amplitude, phase and the derivative slope, a fractional-order PD controller is determined. The tuning of the fractional-order controller is based on an optimization routine that considers the frequency response magnitude values obtained experimentally. From an engineer’s point of view, the presented fractional-order controller tuning procedure consists of two steps: The first one implies performing several experiments on the vibration platform, reading the vibration amplitude and experimental approximation of the resonant peak. The novelty of the presented study is asserted in determining optimal fractional-order controller parameters based solely on the experimental response of the process. The obtained controllers are validated by analyzing disturbance rejection capabilities

Proposed Tuning Method

Experimental Platform

Optimization Guidelines

Fractional-Order PID Tuning

Robustness Analysis

Findings

Conclusions