Parameterization of frequency weighting for a two-stage linear quadratic regulator based design

The purpose of this paper is to parametrize a class of LQ frequency weightings and the associated dynamic controllers and to utilize the available freedom in a controller design methodology. A two-stage methodology is described. In the first stage, an acceptable solution to the conventional LQ problem is obtained, utilizing established guidelines for the selection of constant cost matrices to achieve satisfactory closed-loop performance and an acceptable reference spectrum for the design model. In the second stage, frequency weighting is introduced to produce controller parameterizations which retain a part or all of the reference spectrum to preserve the desired dynamics associated with the design model and make the controller more robust with respect to the differences between the design model and the actual system.