A Modified Positive Velocity and Position Feedback scheme with delay compensation for improved nanopositioning performance

TLDR: In this article, a controller design to compensate the effects of time delay in a flexure-based piezoelectric stack driven nanopositioner is presented. And a theoretical model which takes into account the dependence between the sampling time and the delay introduced is proposed.

Abstract: This paper presents a controller design to compensate the effects of time delay in a flexure-based piezoelectric stack driven nanopositioner. The effects of the time delay in flexure nanopositioners is illustrated and identified by means of experimentally obtaining the frequency response of the system. Moreover, a theoretical model which takes into account the dependence between the sampling time and the delay introduced is proposed. The proposed control design methodology not only accommodates for time delay but also ensures the robust stability and allows its application to systems with a larger delay than other schemes proposed previously. Limitations and future work are discussed.

Figures

Figure 8. Root contours of the closed-loop system controlled with the traditional PVPF when the changing parameter is the delay of the system (Circle of radius ωn indicated in dashed line)

Figure 9. Root contours of the closed-loop system controlled with the modified PVPF scheme scheme designed considering a nominal value of delay τ = 351 µs (indicated with crosses). The arrows in the figure indicate the moving direction of the poles when the actual delay of the plant is increased

Figure 3. FRF of the experimental platform and the secondorder model (including time delay), measured from the input to output displacements

Figure 2. A two-axis serial kinematic nanopositioner, designed at the EasyLab, University of Nevada, Reno, driven by two PiezoDrive 200V Linear amplifiers, with position measured by a Microsense 4810 capacitive sensor

Figure 7. Evolution of the closed-loop poles of the experimental platform for delay in the range [0,600] µs. The position of the poles for a delay of 351 µs is indicated with crosses and diamonds.

Figure 4. Magnitude and phase response of the nanopositioning platform measured from input to output displacement for different sampling rates. Plots in blue are experimental results and plots in green are simulated results including time delay