Active vibration control of nonlinear flexible structures via reduction on spectral submanifolds

TL;DR

This paper introduces a novel spectral submanifold-based reduction method for real-time active vibration control of complex nonlinear flexible structures, transforming high-dimensional problems into manageable linear control tasks.

Contribution

It develops a spectral submanifold reduction framework that enables real-time optimal control of large-scale nonlinear flexible structures, demonstrated on an aircraft wing model.

Findings

Effective vibration suppression demonstrated on complex models

Reduction from high-dimensional to low-dimensional control problems

Potential for real-time implementation in engineering structures

Abstract

Large amplitude vibrations can cause hazards and failure to engineering structures. Active control has been an effective strategy to suppress vibrations, but it faces great challenges in the real-time control of nonlinear flexible structures. Here, we present a control design framework using reductions on aperiodic spectral submanifolds (SSMs) to address the challenges. We formulate high-dimensional nonlinear optimal control problems to suppress the vibrations and then use the SSM-based reductions to transform the original optimal control problems into low-dimensional linear optimal control problems. We further establish extended linear quadratic regulators to solve the reduced optimal control problems, paving the road for real-time active control of nonlinear flexible structures. We demonstrate the effectiveness of our control design framework via a suite of examples with increasing complexity, including a finite element model of an aircraft wing with more than 130,000 degrees of freedom.