H-infinity-based Selective Inversion of Nonminimum-phase Systems for Feedback Controls

Stably inverting a dynamic system model is fundamental to subsequent servo designs. Current inversion techniques have provided effective model matching for feedforward controls. However, when the inverse models are to be implemented in feedback systems, additional considerations are demanded for assuring causality, robustness, and stability under closedloop constraints. To bridge the gap between accurate model approximations and robust feedback performances, this paper provides a new treatment of unstable zeros in inverse design. We provide first an intuitive pole-zero-map-based inverse tuning to verify the basic principle of the unstable-zero treatment. From there, for general nonminimum-phase and unstable systems, we propose an optimal inversion algorithm that can attain model accuracy at the frequency regions of interest while constraining noise amplification elsewhere to guarantee system robustness. Along the way, we also provide a modern review of model inversion techniques. The proposed algorithm is validated on motion control systems and complex high-order systems.

Journal article