Towards Automated Model Order Reduction and Feedback Control for Nonlinear Finite Element Models

Spanning applications from microsystems to passenger jets, finite element (FE) models play a crucial role in the design of a wide range of technical products. However, such models are not suited for applications at system-level or in control due to their large scale. While several schemes to obtain models and controllers based on FE models exist, they either require high-level access to the FE software, create black-box models without physical interpretation, or require specialist knowledge. This paper outlines a workflow to generate highly efficient models and appropriate controllers for nonlinear FE models at the push of a button. In a first step, model order reduction via proper orthogonal decomposition creates an accurate surrogate model of drastically smaller dimension. Nonlinearities are handled via the trajectory piecewise linear approximation (TPWL), maximizing compatibility with commercial FE software by exclusively relying on data produced by regular solutions. Complementing TPWL, gain-scheduling is deployed to establish a precise controller. The proposed workflow is demonstrated for a tunable prism, showcasing its efficacy.