LQG-Optimal Feedforward Regulators

Mikael Sternad and T Söderström

Automatica, vol 24, pp 557-561, July 1988.

Outline:

Disturbances which act on a process can sometimes be measured and used by a controller. The use of such disturbance measurement feedforward can lead to large performance improvements, as compared to the use of feedback only. The paper presents the optimal structure and design of scalar LQG control laws which utilize feedforward based on ARMA models of the measurable disturbances.

Abstract:

A polynomial LQG approach to the design of feedforward regulators is presented. Given a linear system and possibly a prespecified feedback, optimal feedforward filters for non-minimum phase systems can be calculated in a simple way. An infinite horizon criterion including a filtered input signal is minimized. This makes it possible to include frequency-dependent trade-offs between input energy and disturbance rejection in the design.

The achievable feedforward control performance turns out to be unaffected by the choice of feedback, if the optimal regulator structure is used. This suggests a simple way of optimizing combined feedback and feedforward regulators: a main output feedback is first optimized with respect to unmeasurable disturbances. The feedforward link is then optimized with respect to the measurable disturbance.

Related publications:

Paper in IJC 1991, on adaptive scalar LQG combined feedback and feedforward control.
Book chapter on multivariable LQG feedforward and adaptive LQG control.
Paper in IJC 1993, on the duality between feedforward control and deconvolution.
Paper in Automatica 1993 which includes the robust design of scalar feedforward filters.
PhD Thesis by Kenth Öhrn 1996, with robust design of multivariable feedforward filters.