Noninvertible Digital Transfer Functions Arising From Minimum Phase Analog Process Models

Abstract

Current approaches to discrete model reference adaptive control (MRAC) [1–6] require the inverse of the discretized process model to achieve the desired model following. The objective of this paper is to illustrate that the step-invariant transformation of a minimum phase, physical analog process model (based upon a machine tool position controller) leads to a nonminimum phase discrete-time model and thus precludes the possibility of obtaining a stable inverse for the discrete-time process model. This example illustrates the shortcomings of applying discrete MRAC to higher-order processes and indicates the need for alternative MRAC approaches which do not require the adaptive cancellation of process zeros.