Robust broadband nanopositioning: fundamental trade-offs, analysis, and design in a two-degree-of-freedom control framework

Abstract

This paper studies and analyses fundamental trade-offs between positioning resolution, tracking bandwidth, and robustness to modeling uncertainties in two-degree-of-freedom (2DOF) control designs for nanopositioning systems. The analysis of these systems is done in optimal control setting with various architectural constraints imposed on the 2DOF framework. In terms of these trade-offs, our analysis shows that the primary role of feedback is providing robustness to the closed-loop device whereas the feedforward component is mainly effective in overcoming fundamental algebraic constraints that limit the feedback-only designs. This paper presents (1) an optimal prefilter model matching design for a system with an existing feedback controller, (2) a simultaneous feedforward and feedback control design in an optimal mixed sensitivity framework, and (3) a 2DOF optimal robust model matching design. The experimental results on applying these controllers show a significant improvement, as high as 330% increase in bandwidth for similar robustness and resolution over optimal feedback-only designs. Other performance objectives can be improved similarly. We demonstrate that the 2DOF freedom design achieves performance specifications that are analytically impossible for feedback-only designs.

Robust damping PI repetitive control for nanopositioning

“…As can be seen, the actual response of the first vibration mode is well approximated by the second-order model (3). There are higher order modes in the system, and the second 1 Mainly determined by the material, amount of polarization, and the driving voltage amplitude (as the amount of deflection generated changes with voltage amplitude due to hysteresis).…”

“…Compared to regular PI control, the proposed PI controller introduces damping, increases the bandwidth, and reduces the overall noise level due to feedback. The proposed PI controller utilizes the instrumentation already present in the signal chain, and provides a very low complexity control solution which is on par with more complex control schemes, such as controllers based on H ∞ synthesis [3], although the latter can in principle provide higher bandwidth by attempting to control higher frequency dynamics. Additionally, the integral action helps to minimize the tracking error due to hysteresis and creep nonlinearities inherent in the piezoactuator.…”

Fast Scanning and Fast Image Reconstruction in Atomic Force Microscopy

“…Most of the research pertaining to this new impetus has been in increasing the bandwidths of single cantilever devices such as AFM to enable new studies in biology, material science and physics. New devices, modes of operations, and control techniques have been proposed to obtain higher bandwidths [6][7][8][9][10][11].…”

Low-order continuous-time robust repetitive control: Application in nanopositioning

“…In contrast, any linear control law without a periodic signal model will not achieve the same level of performance for periodic signals and any change in plant dynamics will also lead to a different closed-loop response [8]. Examples of such control laws applied to nanopositioning systems can be found in [9,10,11,12,13,14,15].…”