H-Infinity Robust Dynamic Decoupling for Precision Motion Systems: an LMI Approach

In multi-axis precision positioning systems, the plant dynamics are typically decoupled into single-input, single-output (SISO) channels to enable a decentralized controller structure. However, static decoupling often fails to provide sufficient decoupling performance in the mid-to-high frequency range, which limits the system’s performance. Dynamic decoupling has been demonstrated as a promising tool for addressing cross-coupling effects while preserving the use of SISO feedback and feedforward controllers. However, existing model-based dynamic decoupling approaches cannot offer sufficient robustness with respect to model uncertainties. While data-driven methods have been developed, they often lack a stability guarantee and cannot be used for hardware-control co-optimization purposes. This paper proposes a novel model-based dynamic decoupling controller synthesis method for precision motion systems with model uncertainties explicitly considered through a robust ${{\mathcal{H}}_\infty }$ optimization, which can be transformed into linear matrix inequalities (LMI) for solving. Simulation using a lightweight three-axis precision motion system is presented for evaluation.