Discretization of Continuous-Time Controllers Based on the Hilbert-Schmidt Norm of the Sampled-Data Frequency Response

Abstract

This paper is concerned with new discretization methods of continuous-time controllers taking account of the intersample behavior of the resulting sampled-data systems. We first state how to evaluate the controller discretization error based on the Hilbert-Schmidt norm of the sampled-data frequency response, and introduce what we call the desirable frequency response of the discretized controller. We then show that the desirable frequency response can be determined in a closed form in terms of the state-space representations of the original continuous-time controller and the frequency-domain weight. We further discuss some important properties of the desirable frequency response, whereby we propose a heuristic method for controller discretization. We further propose a more sophisticated method, and the effectiveness of these proposed methods is demonstrated by numerical examples. The relationship of the proposed methods with (as well as difference and advances from) similar existing studies are clarified from the viewpoint of the modern theory on the frequency response of sampled-data systems, and the roles and choice of the frequency-domain weight are discussed for better recovery of control performance.