Eigenvalue assignment optimization for stable and unstable systems

Abstract

A method for designing linear quadratic regulators (LQR) which meet performance specifications with minimal control-signal amplitude is developed. A non-derivative search routine is used to find a smaller gain vector which places the closed-loop eigenvalues in a specific sector-type region. The method may be used to specify arbitrary damping and settling-time characteristics for both stable and unstable systems. In this paper, controllers are designed for example systems to demonstrate the use of the method. The method is shown to yield smaller gain vectors than a previous method, and may be expanded to address more complicated design problems.