Correspondences Between Input Estimation and Feedforward Control

Mikael Sternad and Anders Ahlén

International Journal of Control, vol 48, pp 1723-1734, October 1988.

Outline:

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.

Abstract:

A correspondence between MMSE input estimation (deconvolution) and LQG feedforward control is discussed from a polynomial point of view. 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 feedback control. 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 framework.

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.