Digital Controller Design for Analog Systems Represented by Multiple Input–Output Time-Delay Transfer Function Matrices with Long Time Delays

Abstract

This paper presents a digital controller design methodology for multivariable analog systems represented by minimally realizable multiple input–output time-delay transfer function matrices with long time delays. First, the analog transfer function matrix with multiple input–output time delays is minimally realized and represented by a delay-free state-space model and a multiple output-delay function. For a specific multiple time-delay transfer function matrix with complex poles, a minimal realization scheme is newly proposed. Then the minimized delay-free state-space model is utilized for linear quadratic regulator (LQR) design. Furthermore, the designed analog LQR is digitally redesigned via a predictive state-matching method for finding a low-gain digital controller from the pre-designed high-gain analog controller. For implementation of the digitally redesigned controller, a digital observer is constructed for the multiple time-delay system with long time delays. An illustrative example is given to demonstrate the effectiveness of the proposed method.