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-μ synthesis, and the resulting designs are compared in terms of conservatism of the uncertainty model, robust performance, and computational effort.

AbstractPiezoelectric nanopositioning systems exhibit low damping and resonance modes that are highly sensitive to loading conditions, resulting in performance degradation under payload variations. Conventional damping and robust control methods typically address these challenges separately, overlooking the coupling between damping and tracking dynamics as well as the influence of higher-order resonant modes. This paper proposes a dual-loop control framework that integrates active damping with mixed-sensitivity H∞ synthesis to achieve robust reference tracking and disturbance rejection under large resonance frequency variations. A Non-Minimum-Phase Resonant Controller (NRC) is implemented in the inner loop to suppress the dominant resonance and reduce system uncertainty. Generalized plant formulation and systematic weighting design guidelines of arbitrary order are developed to explicitly incorporate higher-order modes in the outer loop H∞ synthesis. The proposed approach is validated through simulations and experiments on an industrial piezoelectric nanopositioning system, demonstrating improved robustness and precision across the full payload range.