Physics

Nonlinear system

Mathematics

Boundary (topology)

Structural engineering

Partial differential equation

Engineering

Mathematical analysis

Boundary value problem

Artificial intelligence

Vibration

Control (management)

Computer science

Quantum mechanics

Differential equation

Wing

Control theory (sociology)

Ordinary differential equation

Lyapunov function

IEEE/ASME Transactions on Mechatronics

A boundary control approach is used to control a two-link rigid-flexible wing in this article. Its design is based on the principle of bionics to improve the mobility and the flexibility of aircraft. First, a series of partial differential equations (PDEs) and ordinary differential equations (ODEs) are derived through the Hamilton's principle. These PDEs and ODEs describe the governing equations and the boundary conditions of the system, respectively. Then, a control strategy is developed to achieve the objectives including restraining the vibrations in bending and twisting deflections of the flexible link of the wing and achieving the desired angular position of the wing. By using Lyapunov's direct method, the wing system is proven to be stable. The numerical simulations are carried out with the finite difference method to prove the effectiveness of designed boundary controllers.

Dynamical Modeling and Boundary Vibration Control of a Rigid-Flexible Wing System