Analysis and comparison of three discrete-time feedforward model-inverse control techniques for nonminimum-phase systems

Noncollocated sensors and actuators, and/or fast sample rates with plants having high relative degree, can lead to nonminimum-phase (NMP) discrete-time zero dynamics that complicate the control system design. In this paper, we examine three stable approximate model-inverse feedforward control techniques, the nonminimum-phase zeros ignore (NPZ-Ignore), the zero-phase-error tracking controller (ZPETC), and the zero-magnitude-error tracking controller (ZMETC), which have frequently been used for NMP systems. We analyze how the discrete-time NMP zero locations in the z-plane affect the success of the NPZ-Ignore, ZPETC, and ZMETC model-inverse techniques. We also examine the use of low-pass filters with the three model-inversion techniques. Experimental results on the x direction of an AFM piezoscanner are provided to support the discussions. Tips on the use of these three model-inversion discrete-time feedforward methods are presented throughout the paper.