Optimal Regulator with the Desired Low-Pass Property Achieved by the Third-Order Lag Elements

Abstract

We have proposed a synthesis method of the linear quadratic regulator (LQR) with the desired low-pass property achieved by the second-order lag elements. However, a synthesis method of the LQR with the property attained by the higher order lag elements has never been proposed. In this letter, the LQR with the desired low-pass property achieved by the third-order lag elements is studied. The basic design idea is based on the fact that feedback control law can be reduced to the problem which solves a quartic algebraic equation.