Energy-optimal control of adaptive structures

TL;DR

This paper introduces an energy-optimal control method for adaptive structures that leverages port-Hamiltonian models to achieve vibration damping efficiently and with proven stability, improving resource use over traditional methods.

Contribution

It proposes a novel energy-optimal control strategy based on port-Hamiltonian structure, with proven uniqueness and stability, advancing adaptive structure control techniques.

Findings

Optimal control is uniquely determined even on singular arcs.

The control exhibits a turnpike property ensuring long-term stability.

Numerical evaluation confirms the controller's efficiency.

Abstract

Adaptive structures are equipped with sensors and actuators to actively counteract external loads such as wind. This can significantly reduce resource consumption and emissions during the life cycle compared to conventional structures. A common approach for active damping is to derive a port-Hamiltonian model and to employ linear-quadratic control. However, the quadratic control penalization lacks physical interpretation and merely serves as a regularization term. Rather, we propose a controller, which achieves the goal of vibration damping while acting energy-optimal. Leveraging the port-Hamiltonian structure, we show that the optimal control is uniquely determined, even on singular arcs. Further, we prove a stable long-time behavior of optimal trajectories by means of a turnpike property. Last, the proposed controller's efficiency is evaluated in a numerical study.