# Vibration control of a class of flexible mechanical systems with output constraints based on partial differential equations

## TL;DR

This paper presents a new control method using PDEs and BLF to suppress vibrations in flexible mechanical systems, ensuring stability and safety.

## Contribution

A novel robust control scheme using PDEs and BLF for vibration suppression in flexible systems with output constraints.

## Key findings

- The proposed control strategy effectively damps vibrations and rotations in flexible mechanical systems.
- The system output remains within predefined safety limits despite environmental disturbances.
- Comparative simulations confirm the method's effectiveness in handling unforeseen disturbances.

## Abstract

Vibration suppression in flexible mechanical systems (FMSs) significantly enhances the precision and stability of equipment, extending its operational life. This technology is extensively applied across various sectors, including aerospace, robotics, and precision manufacturing. This paper introduces a robust control scheme leveraging a Partial Differential Equations (PDEs) model and Barrier Lyapunov Function (BLF), applied through backstepping technology to manage a flexible mechanical system modeled as an Euler-Bernoulli beam with a centrally attached rigid body. The control laws we have formulated are designed to effectively dampen vibrations and rotations, thereby ensuring system stability despite the presence of environmental disturbances. Throughout the control process, the system output consistently stays within the predefined safety limits. Comparative simulations further validate the effectiveness of the proposed control strategy, showing that it can effectively counteract unforeseen disturbances while ensuring that the output remains within the specified constraints.