where h is the sample time, i is the imaginary unit, !n is
the disturbance frequency in radians and n and n are
tuning parameters related to the disturbance mitigation
and convergence rates, respectively. Cð!nÞ ¼ Gp ei!n
1
is the inverse of the discrete process model at the given
frequency. For nonsquare processes, an optimal
approximation of the inverse process in the leastsquares
sense is obtained by using the pseudo-inverse
Cð!nÞ ¼ GT
p ei!n
Gp ei!n
n o1
GT
p ei!n
. The pseudoinverse
approach is indeed very applicable to processes
with more outputs than inputs. However, for processes
with more inputs than outputs, the inverse involved in
the derivation becomes singular, resulting in a very
unpredictable and poor control performance thereof.
This becomes evident in the time-domain performance
analyses in Section 4, where the controller fails to provide
any mitigation for MISO system subject to two
sinusoidal disturbances. Regardless of the obvious
problems, this is the approach utilized in this study as
it is the form often suggested in the literature, although
it is most likely supposed to be applied only to SIMO
systems, where it makes sense. Also, as the control