  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.
