Unified Feedforward Control Framework for Disturbed Nonminimum Phase Systems: The Koopman-Type Inverse Operator Approach

Feedforward control is essential for precise output tracking in non-minimum phase systems, and stable inversion has been proposed to address input instability caused by unstable internal dynamics. However, this approach demands an accurate mathematical model, limiting its effectiveness in the presence of model uncertainties and especially in cases without a model. While data-driven control can enhance performance in these scenarios, it often fails to achieve precise tracking under input stabilitty conditions. To address these challenges, this paper introduces a unified feedforward control framework using the Koopman-type inverse operator for output tracking for disturbed non-minimum phase systems. This framework extends the applicability of the stable inversion method from model-available scenarios to model-unavailable scenarios. Besides other data-driven control approaches, it enables precise output tracking while ensuring the stability of the input, without necessitating additional design constraints. It features two novel algorithms that maintain a consistent controller structure while varying only in parameter determination methods. The convergence properties of the proposed algorithms are rigorously analyzed, and their effectiveness is verified through piezoelectric ceramic positioning experiments.