Modeling and stabilization of a rotating mechanical system with elastic plates

TL;DR

This paper develops a mathematical model for a rotating mechanical system with elastic plates, deriving coupled nonlinear equations and designing a feedback control law to ensure system stability.

Contribution

It introduces a novel modeling approach for a rigid body with Kirchhoff plates and constructs a dissipative feedback control law for stabilization.

Findings

Derived coupled nonlinear equations of motion

Represented the system as an abstract differential equation in a Hilbert space

Designed a feedback control law ensuring dissipativity and stability

Abstract

A mechanical system consisting of a rigid body and attached Kirchhoff plates under the action of three independent controls torques is considered. The equations of motion of such model are derived in the form of a system of coupled nonlinear ordinary and partial differential equations. The operator form of this system is represented as an abstract differential equation in a Hilbert space. A feedback control law is constructed such that the corresponding infinitesimal generator is dissipative.