Frequency-based NMPC for Flexible Systems with Parametric Resonance

Many mechatronic systems, especially nonlinear oscillatory systems with variable structures, are prone to parametric resonance caused by time-varying characteristics. This paper addresses the vibration damping problem of a flexible nonlinear system with parametric resonance studied on a stacker crane with a variable load. It tackles the related challenges of established approaches for both feedforward and feedback. Accordingly, this paper proposes a novel scheme of nonlinear model predictive control (NMPC). In particular, it addresses parametric resonance explicitly and exploits the Parseval theorem to enforce specific requirements on relevant frequencies. Recursive feasibility and stability are guaranteed by using an appropriate invariant set. In addition, experimental validation is performed to demonstrate the significant advantages of the proposed NMPC scheme over two established vibration damping control approaches. Copyright (c) 2022 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)