Stability (learning theory)

Physics

Finite element method

Nonlinear system

Deflection (physics)

Mathematics

Boundary (topology)

Structural engineering

Machine learning

Engineering

Mathematical analysis

Boundary value problem

Artificial intelligence

Vibration

Control (management)

Galerkin method

Turbine

Computer science

Quantum mechanics

Bounded function

Control theory (sociology)

Lyapunov function

Classical mechanics

Mechanical engineering

Uniform boundedness

IEEE Transactions on Automatic Control

This article studies a vibration and disturbance rejection problem of a wind turbine tower under exogenous perturbations. The tower dynamics is captured by a nonhomogeneous Euler–Bernoulli beam model. The dissipativity of the system is realized by a boundary feedback control solution with a multivalued symbolic function. A Lyapunov-based stability analysis is established to assess the deflection of the tower is uniformly bounded even subject to exogenous disturbances. The extended Filippov framework and Galerkin approximation scheme are introduced to tackle the existence of the solution to the system with a discontinuous control input. Simulation results demonstrate the performance of the proposed control scheme.

Boundary Feedback Control of a Nonhomogeneous Wind Turbine Tower With Exogenous Disturbances