Precision Tracking for Nonminimum Phase LPTV Systems via a Lifted Time Stable Inversion

Feedforward control demonstrates the capacity of precision tracking in applications, typically necessitating the solution of the inverse model. For nonminimum phase systems with unstable internal dynamics, the inverse model yields unbounded inputs, impeding the implementation of the feedforward control method. Existing stable inversion leverages noncausal input and initial state transition to achieve exact tracking with an infinite time preview of the output. However, a limited preview window results in tracking errors, and the existence of the optimal transition relies on the invertibility of the Grammian matrix. Recently, a novel stable inversion based on lifting time systems has been introduced. It enables finite-time precision tracking without an infinite preview window and exhibits significant application potential, though confined to linear time-invariant systems. From the perspective of the lifted system, this article addresses the stable inversion problem in finite time for multivariate linear periodic time-varying systems leveraging the equivalence between the linear periodic time-varying system and its lifted system. Simulation is designed to validate the effectiveness of the results.