Continuous-Time Quadratic Regulators and Pseudo-Continuous-Time Quadratic Regulators with Pole Placement in a Specific Region

摘要

A linear quadratic regulator is developed, for optimally placing the closed-loop poles of multivariable continuous time systems within the common region of an open sector, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, without explicity utilizing the eigenvalues of the open-loop systems. Also, a pseudo-continuous-time state-space method is developed, for finding the linear sub-optimal quadratic regulator which suboptimally places the closed loop poles of multivariable discrete time systems within a common region of a circle, and the logarithmic spiral in the complex z-plane. An illustrative example is presented to demonstrate the effectiveness of the proposed procedures. Keywords: Computer aided design, Optimal control, Control systems, Closed-loop systems, Matrix algebra, Reprints.