banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Feedforward control of a closed-loop piezoelectric translation stage for atomic force microscope
Rent this article for


Image of FIG. 1.
FIG. 1.

(a) Block diagram of a typical feedback control system showing the control input , direct-acting disturbances , and sensor noise . The physical system is represented by and the control algorithm by . (b) Feedforward prefilter modifies the input signal from to , which is then substituted for the control signal in the closed-loop system in (a). The closed-loop system of (a) is represented in (b) by the block .

Image of FIG. 2.
FIG. 2.

Measured frequency response (solid lines) of loaded and unloaded translation stage, overlaid with fits (dashed lines) to the loaded response by three different models (two, four, and six poles). (a) Magnitude response of the Bode plot. (b) Phase response.

Image of FIG. 3.
FIG. 3.

Pole-zero plot of the system , showing how the prefilter “cancels out” poles of the system with zeros and then adds new poles at higher frequencies. The crosses indicate poles; the circles, zeros.

Image of FIG. 4.
FIG. 4.

Signal flow in the design of an acausal feedforward filter, using the second-order model. The light-shaded boxes represent dynamics that are coded on computer. The dark-shaded box represents the physical system, including its analog closed-loop control.

Image of FIG. 5.
FIG. 5.

Collage showing time series of measured stage responses using the two-pole dynamical model and its associated prefilter . Dotted-line triangular waveform represents the desired stage response . Dashed lines represent the signal fed to the stage. Solid lines represent the measured sensor signal. (a) Normal stage operation; (b) causal feedforward algorithm; (c) acausal feedforward algorithm. The phase shifts in the stage response observed in (a) and (b) are removed in (c). (Use the vertical dotted line as a reference.)

Image of FIG. 6.
FIG. 6.

AFM images of a calibration grating. All images are taken at 40 Hz , scanning to the left. The white vertical dashed lines indicate the “turnaround” point in the image, with the distance to the right side of the image proportional to the phase lag. (a) Image taken by the scanner in its normal mode, without feedforward. (b), (d), (f): Images taken with causal feedforward filters of second, fourth, and sixth orders, respectively. (c), (e), (g): Same, with acausal filters.

Image of FIG. 7.
FIG. 7.

AFM images of calibration grating. (a) “Standard” image, 1 Hz, without feedforward. (b)–(d) Images taken with a fourth-order feedforward filter, at indicated scan rates. All images are scanned over a area.


Generic image for table
Table I.

Phase shift (degrees) produced by different types of filters.

Generic image for table
Table II.

Average spacing of dots measured on images with different types of causal filters, compared to actual spacing and that expected without feedforward.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Feedforward control of a closed-loop piezoelectric translation stage for atomic force microscope