Characterization and compensation of discrete-time non-minimum-phase systems for precision tracking control

The objective of this study is to characterize the unstable zeros of discrete-time non-minimum-phase systems and to compensate the gain and phase errors induced by unstable zeros for tracking control. These two objectives are attempted via examining the frequency response of unstable zeros. The gain error and phase shift induced by unstable zeros are first presented. It is well known that they are undesirable and cannot be cancelled directly via the method of pole-zero cancellation. Through investigating the characteristics of unstable zeros, a systematic approach is then given to compensate the gain and phase errors induced by unstable zeros. Using this approach, both a simple tracking control method and a precision tracking control method are proposed. The design procedure is presented and the design formulae are given. Simulation results are presented to illustrate the effectiveness of the proposed methods.