Generalizing Hybrid Integrator-Gain Systems Using Fractional Calculus

TL;DR

This paper introduces a fractional-order generalization of Hybrid Integral Gain Systems (HIGS), enhancing phase control in nonlinear filters, and validates its effectiveness in a PID-controlled double integrator system.

Contribution

It extends HIGS by incorporating fractional calculus, allowing adjustable phase lead, and provides analysis and validation in control system applications.

Findings

Fractional HIGS offers tunable phase lead from 0° to 52°.

The fractional-order filter improves control performance in simulations.

The approach bridges linear and nonlinear control responses.

Abstract

The Hybrid Integral Gain Systems (HIGS) has recently gained a lot of attention in the control of precision motion systems. HIGS is a nonlinear low pass filter with a 52 degree 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 phase gain relation. In this paper, we generalize HIGS via replacing the involved integer order integrator with a fractional order one to adapt the phase lead from 0 degree (linear low pass filter) to 52 degree (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 changing the fractional variable from zero to one, the output varies from the response of a nonlinear control system to a linear one.