Discrete-time Integral Resonant Control of Negative Imaginary Systems: Application to a High-speed Nanopositioner

TL;DR

This paper introduces a discrete-time integral resonant control method for negative imaginary systems, demonstrating its effectiveness in stabilizing high-speed nanopositioners through FPGA implementation at high sampling rates.

Contribution

It presents a novel discrete-time IRC approach that overcomes limitations of continuous-time methods and applies it successfully to a high-speed nanopositioner.

Findings

Discrete-time IRC has a step-advanced NI property.

Successfully stabilizes a sampled NI system.

Effective FPGA implementation at 1.25 MHz sampling rate.

Abstract

We propose a discrete-time integral resonant control (IRC) approach for negative imaginary (NI) systems, which overcomes several limitations of continuous-time IRC. We show that a discrete-time IRC has a step-advanced negative imaginary property. A zero-order hold-sampled NI system can be asymptotically stabilized using a discrete-time IRC with suitable parameters. A hardware experiment is conducted where a high-speed flexure-guided nanopositioner is efficiently damped using the proposed discrete-time IRC with the discrete-time controller being implemented in FPGA hardware at the sampling rate of 1.25 MHz.