Structured {\mu}-Synthesis for Nanopositioners under Payload-Induced Uncertainties: Minimising Conservatism for Robust Performance

TL;DR

This paper presents a structured {b5}-synthesis approach that reduces conservatism in robust control design for nanopositioners with payload-induced uncertainties, improving performance while managing complexity.

Contribution

It introduces a novel uncertainty modeling framework with multiple uncertainty blocks and applies structured mixed-{b5} synthesis to nanopositioners, enhancing robustness and reducing conservatism.

Findings

Reduced conservatism in uncertainty models.

Improved robust performance of nanopositioners.

Trade-offs between model complexity and computational effort.

Abstract

Most systems exhibit significant variability in their dynamics, including variations in system parameters and large high-frequency dynamic uncertainties. Traditional uncertainty modelling techniques consolidate all such variations into a single uncertainty block, often yielding overly conservative representations of the true plant behaviour. This paper introduces an uncertainty modelling framework that employs multiple structured and unstructured uncertainty blocks to reduce this conservatism. The methodology is evaluated for an industrial piezoelectric nanopositioner subject to payload-induced variations, using uncertainty models of differing complexity. A bandpass controller is synthesised via structured mixed-{\mu} synthesis, and the resulting designs are compared in terms of conservatism of the uncertainty model, robust performance, and computational effort.