  Professor Utkin in his discussion paper proposed an example showing that the
amplitude of chattering caused by the presence of parasitic dynamics in systems
governed by First-Order Sliding-Mode Control (FOSMC) is lower than the obtained
using Super-Twisting Algorithm (STA). This example served to motivate this
research reconsidering the problem of comparison of chattering magnitude in
systems governed by FOSMC that produces a discontinuous control signal and by
STA that produces a continuous one, using Harmonic Balance (HB) methodology.
With this aim the Averaged Power (AP) criteria for chattering measurements is
revisited. The STA gains are redesigned to minimize amplitude or AP of
oscillations predicted by HB. The comparison of the chattering produced by
FOSMC and STA with redesigned gains is analyzed taking into account their
amplitudes, frequencies and values of AP allowing to conclude that: (a) for any
value of upperbound of disturbance and Actuator Time Constant (ATC) there exist
a bounded disturbance for which the amplitude and AP of chattering produced by
FOSMC is lower than the caused by STA; (b) if the upperbound of disturbance and
upperbound of time-derivative disturbance are given, then for all sufficiently
small values of ATC the amplitude of chattering and AP produced by STA will be
smaller than the caused by FOSMC; (c) critical values of ATC are predicted by
HB for which the parameters, amplitude of chattering and AP, produced by FOSMC
and STA are the same. Also the frequency of self-exited oscillations caused by
FOSMC is always grater than the produced by STA.
