In previous work, we evaluated the performance of two control architectures applied to atomic force microscopes (AFM) [1]. Experimental results in [1] indicated that the closed-loop-injection (FFCLI) architecture outperformed the plant-injection (FFPI) architecture when using a specific model-inversion feedforward technique for the tracking of a raster pattern. Empirical work suggested that a nontraditional variation upon the experimentally inferior FFPI architecture may allow it to track a raster pattern at a performance level in the neighborhood of the FFCLI architecture. This variation is manifested as additional delay inserted in the feedforward control system. An online adaptive technique is used to determine the required amount of additional delay. Experimental results show that the performance level of the FFCLI architecture and the adaptive-delay FFPI architecture are comparable.

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 nonmimimum-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 lowpass filters with the three model-inversions techniques. Experimental results on the x direction of an AFM piezoscanner are provided to support the discussions. Finally, tips on the use of these three model-inversion discrete-time feedforward methods are presented throughout the paper. 1

Abstract—We evaluate the performance of two combined feedforward/feedback control architectures applied to the raster scan of a piezo-based positioning system. Empirical work suggests that a nontraditional variation upon the feedforward plantinjection (FFPI) architecture may allow it to track a raster pattern at a higher performance level in the neighborhood typical of the feedforward closed-loop-injection (FFCLI) architecture. This variation is manifested as additional delay inserted in the feedforward control system rather than a unity-gain filter constructed from plant parameters. An online adaptive technique is used to determine the required amount of additional delay. Experimental results show that the performance level of the adaptive-delay FFPI architecture is comparable with the FFCLI architecture or better. Two key benefits to the algorithm include reduced computational load and an adaptation calculation that does not require knowledge of plant parameters. This method can be applied to piezo-based positioning systems including atomic force microscopes (AFMs), other scanning probe microscopes (SPMs), probe-based data storage systems or other systems in which raster tracking is a critical control objective. Additionally, if the goal is to track other trajectories (including those that are not repetitive), the converged results of the algorithm can be used after a brief raster-motion calibration phase. I.