Two-degree-of-freedom ℓ2-optimal tracking with preview

Abstract

A simple SISO two-degree-of-freedom pole-placement design method is presented that provides ℓ2-optimal tracking of a given reference signal. The closed-loop pole locations are first chosen by the system designer. The closed-loop zeros are then placed in an optimal fashion by a computationally inexpensive algorithm to achieve asymptotic tracking with an optimal transient response. The preview approach, which has become a common method for dealing with systems which have non-minimum phase behavior, can then optionally be used to further improve the transient behavior for both minimum phase and non-minimum phase systems. Unlike previous results based on the preview approach, the solution presented here takes into consideration the closed-loop pole dynamics, and is ℓ2 optimal with respect to all other two-degree-of-freedom preview controllers with the same closed-loop poles. A simple solution to the H2 model matching problem, where the design parameter Q is not rational, but polynomial, is the heart of the solution method.