Observer-Based State Feedback Controller for a Mindlin Plate Model in port-Hamiltonian framework

TL;DR

This paper extends observer-based state-feedback control to 2-D boundary-controlled Mindlin plates within the port-Hamiltonian framework, ensuring stability through structure-preserving discretization and controllability analysis.

Contribution

It generalizes a control methodology from 1-D to 2-D systems, introduces a structure-preserving discretization, and guarantees closed-loop stability for Mindlin plates.

Findings

Successfully discretized the 2-D model using finite differences on staggered grids.

Designed positive real observer-based controllers ensuring system stability.

Numerical simulations confirm the effectiveness of the proposed control approach.

Abstract

This paper generalises an early lumped observer-based state-feedback (OBSF) control design methodology, originally developed for one-dimensional (1-D) boundary-controlled port-Hamiltonian systems, to a two-dimensional (2-D) boundary-controlled Mindlin plate. To this end, the 2-D port-Hamiltonian Mindlin plate model is first introduced and then discretized using a structure-preserving finite-difference method on staggered grids. A controllability decomposition is subsequently applied to identify the controllable modes of the discretized model. Furthermore, the state-feedback and observer gains are designed so that the OBSF controller is strictly positive real. This guarantees the stability of the closed-loop system when the finite-dimensional OBSF controller is interconnected with the 2-D boundary-controlled Mindlin plate. Numerical simulations are finally presented to illustrate the effectiveness of the proposed method.