Generalizing Hybrid Integrator-Gain Systems Using Fractional Calculus

Conference paper (2022)

Authors

S. Ali Hosseini Sharif University of Technology
Mohammad Saleh Tavazoei Sharif University of Technology
Luke F. Van Eijk ASM Pacific Technology
S. Hassan HosseinNia Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering
Research Group
Mechatronic Systems Design (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2022 S. Ali Hosseini, Mohammad Saleh Tavazoei, Luke F. Van Eijk, S. Hassan HosseinNia
DOI: https://doi.org/10.1109/CCTA49430.2022.9966184
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Published Date

2022

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Precision and Microsystems Engineering

Research Group

Mechatronic Systems Design

Abstract

The Hybrid Integrator-Gain System (HIGS) has recently gained a lot of attention in control of precision motion systems. HIGS is a nonlinear low pass filter/integrator with a 52° phase advantage over its linear counterpart. This property allows us to avoid the limitations typically associated with linear controllers, like the waterbed effect and Bode's gain-phase relation. In this paper, we generalize HIGS by replacing the involved integer-order integrator by a fractional-order one to adapt the phase lead from 0° (linear low pass filter) to 52° (HIGS). To analyze this filter in the frequency domain, the describing function of the proposed filter, i.e., the fractional-order HIGS, is obtained using the Fourier expansion of the output signal. In addition, this generalized HIGS is implemented in a PID structure controlling a double integrator system to validate the performance of the proposed filter in the time domain, in which by changing the fractional variable from zero to one, the output varies from the response of a linear control system to a nonlinear one.

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