Correspondences Between Input Estimation and Feedforward
International Journal of Control,
vol 48, pp 1723-1734, October 1988.
The problem of estimating the input to a linear system is known
as deconvolution. Feedforward control is the use of measurements
of disturbances in the control of a dynamic system.
These two problems seem to have little in common, but they
are here shown to be closely related.
A correspondence between MMSE input estimation (deconvolution)
and LQG feedforward control is discussed from a polynomial point
Optimal estimation and feedforward control filters are
derived from a spectral factorization and a polynomial equation.
Simple loop transformations are used for transforming one
problem into the other.
The close relationship can not
in this paper be explained by the well-known
duality between optimal state estimation and
Instead, it is related to the fact that both the problems
discussed are open loop.
They can be seen as two interpretations of
one underlying design problem.
Several other open-loop problems can be described in this
- Related publications:
Paper in IJC 1993,
where duality is actually demonstrated
for more general problem formulations.
Paper in Automatica 1988,
on LQG feedforward controller design using polynomial equations.
Paper in IEEE Trans. ASSP 1989,
on deconvolution filter design using polynomial equations.