Frequency-shaped cost functionals - Extension of linear-quadratic-Gaussian design methods

Abstract

The linear-quadratic-Gaussian method for feedback control design is extended to include frequency-shaped weighting matrices in the quadratic cost functional. This extension provides a means to meet classical design requirements with automated computational procedures of modern control theory. A design algorithm to optimize frequency-shaped cost functional requires definition of new states and the solution of a modified linearquadratic-Gaussian problem. Four examples are presented to demonstrate frequency shaping methodology: 1) aircraft in lateral wind, 2) an industrial crane, 3) vibration control in helicopters, and 4) a system with truncated modes.