Performance comparison of digital implementation of analog systems

A new controller discretization approach, the generalized bilinear transformation (GBT), is proposed in [1]. Given an analog controller K, GBT generates a class of digital controllers K_gbt parameterized by alpha isin (-infin, infin). A geometric interpretation of GBT is first presented. Secondly, when the original analog feedback system is stable, a method is proposed to find the value of the parameter alpha which provides upper bound of the sampling period guaranteeing closed-loop stability of the resulting sampled-data system. Thirdly, it is shown that step-tracking is preserved if the closed-loop sampled-data system is stable. Finally, two examples are used to demonstrate the strength of our digitization approach.