3.2. Input disturbance cancellation
This control approach is based on a mixture of optimal
feedback and feedforward control strategies, which was
originally presented by Sievers and von Flotow (1988)
and later revised with some modifications by Bittanti
et al. (1996). In this method, the disturbance dynamics
are described by a filter driven by white noise, resulting
in colored (sinusoidal) disturbance. The point of excitation
for the disturbance is chosen at the process input.
This choice is readily justified for SISO systems, where
any sinusoidal signal at the process output can be
moved to the process input simply by altering the
phase and amplitude of the signal correspondingly.
This approach can be extended also for the MIMO
processes regardless of the fact that the set of possible
input signals providing the corresponding output signals
is not necessarily unique. However, when being
applied to the nonsquare processes, there is a strong
likelihood of potential problems. In essence, there are
two possible occurrences. First, if the number of outputs
is smaller than the number of inputs, there are
excess degrees of freedom for the choice of the sinusoidal
inputs, resulting in nonunique and possibly overparameterized
solutions. The second and the worst case
occurs when the number of inputs is less than the
number of outputs, enabling the possibility of output
signals that cannot be expressed with the input signals.
Such a scenario occurs when the components of the
true disturbance at the process output do not result in
exactly the same signal when filtered through the