Extension of ILQ Method to Non-Minimum Phase Systems for the Design of Optimal Servo Systems

Abstract

ILQ (Inverse Linear Quadratic) method is a new design method for control systems which utilizes the result of the inverse problem of optimal regulator. This method is more effective when it is applied to the design of an optimal servo system. It is called “ILQ optimal servo system”. The existing theory has assumed the minimum phase condition for the plant. But this condition can be relaxed to a class of MIMO non- minimum phase systems which includes all SISO systems. This paper describes an extension of this theory to such a class of systems and at the same time it shows this extension is an achievable limit. In the extension, proofs of “analytical description of optimal gains” and “asymptotic property of a closed loop transfer function matrix” which are the basic properties of ILQ optimal servo system, are performed in a way different from the past papers. This paper also contains a numerical example to illustrate the effectiveness of this method for the non-minimum phase plant.