Modal-based nonlinear model predictive control for 3D very flexible structures
File(s)
Accepted version
Author(s)
Artola, Marc
Wynn, Andrew
Palacios, Rafael
Type
Journal Article
Abstract
In this paper a novel NMPC scheme is derived, which is tailored to the underlying structure of the intrinsic description of geometrically exact nonlinear beams (in which velocities and strains are primary variables). This is an important class of PDE models whose behaviour is fundamental to the performance of flexible structural systems (e.g., wind turbines, High-Altitude Long-Endurance aircraft). Furthermore, this class contains the much-studied Euler-Bernoulli and Timoshenko beam models, but has significant additional complexity (to capture 3D effects and arbitrarily large displacements) and requires explicit computation of rotations in the PDE dynamics to account for orientation-dependent forces such as gravity. A challenge presented by this formulation is that uncontrollable modes necessarily appear in any finite dimensional approximation to the PDE dynamics. We show, however, that an NMPC scheme can be constructed in which the error introduced by the uncontrollable modes can be explicitly controlled. Furthermore, in challenging numerical examples exhibiting considerable deformation and nonlinear effects, it is demonstrated that the asymptotic error can be made insignificant (from a practical perspective) usingour NMPC scheme and excellent performance is obtained evenwhen applied to a highly resolved numerical simulation of thePDEs. We also present a generalisation of Kelvin-Voigt dampingto the intrinsic description of geometrically-exact beams. Finally,special emphasis is placed on constructing a framework suitablefor real-time NMPC control, where the particular structure ofthe underlying PDEs is exploited to obtain both efficient finite-dimensional models and numerical schemes.
Date Issued
2021-04-06
Date Acceptance
2021-03-29
Citation
IEEE Transactions on Automatic Control, 2021, 67 (5)
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
67
Issue
5
Copyright Statement
© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Sponsor
Commission of the European Communities
Identifier
https://ieeexplore.ieee.org/document/9397328
Grant Number
765579
Subjects
Industrial Engineering & Automation
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Publication Status
Published online
Date Publish Online
2021-04-06