A Modified Polynomial-Based Controller for Enhancing the Positioning Bandwidth of Nanopositioners

Polynomial-based damping techniques such as Positive Position Feedback (PPF) and Positive Velocity and Position Feedback (PVPF) have been applied successfully to a number of lightly damped systems to overcome resonance-induced vibration issues. These control designs exhibit several advantages such as substantial damping performance, relative ease of design and adequate robustness in the presence of plant parameter uncertainties. Their formulation is based on the well-known pole-placement technique where damping is achieved by pushing the poles of the close-loop system arbitrarily away from the jω axis and in to the left-half plane. Current designs result in changing the real part of the poles while keeping the imaginary part unaltered; thus keeping the resonant frequency of the closed-loop, damped system unchanged, compared to the original undamped, open-loop system. In this work, we present a pole-placement technique which results not only in the substantial damping of the resonance but also in shifting the system resonance to a substantially higher frequency. This result is beneficial to a number of systems such as nanopositioners employed in Scanning Probe Microscopes, where maximizing the positioning bandwidth is a major goal and the achievable bandwidth is severely limited by the resonant frequency of the positioner.