Impact of sampling time on tustin digitization

Abstract

This paper investigates the impact of sampling time on Tustin digitization. A Q-matrix representation for the digitized system via Tustin transformation is first proposed. It is shown that Tustin transformation is a special case of the higher-order integrator approaches to digitize a continuous system. Pole-variation loci is then introduced to describe the trajectories of poles of the digitized system using Tustin transformation when sampling time is varied from zero to infinity. With new theorems derived in this paper, the pole-variation loci can be easily sketched. Sampling time of any point on the pole-variation loci of the digitized system can be determined by the angle of the vector drawn from the origin to the designated pole location. System dynamics of the digitized system can then be estimated from the sampling time, which determines the pole locations.