Active disturbance rejection boundary control of Timoshenko beam with tip mass. (September 2018) - Tavasoli, Ali
Abstract: In this paper, the active disturbance rejection control (ADRC) is utilized to stabilize the vibration of perturbed Timoshenko beam model with tip mass. The boundary control design is based on a hybrid PDE–ODE model, and is accompanied with designing a high-gain extended state observer (ESO) that is used to estimate the boundary disturbances. By transforming the model into the appropriate state space, the semigroup theory is employed to prove the well-posedness of the closed-loop system. To this end, it is proved by a frequency domain method that the semigroup generated by the system operator is exponentially stable, which allows to conclude the boundedness of perturbed closed-loop system response. The stability of the closed-loop system is further analyzed using the Lyapunov approach. Simulation results are presented to illustrate the efficacy of the suggested method. Highlights: The dynamic model is a hybrid system including PDEs and ODEs. The tip mass dynamics is used to estimate boundary disturbances. The control law consists of a linear feedback part and the estimation of disturbances. The semigroup theory and frequency domain method show the system is well-posed. The Lyapunov theory demonstrates the stability of the closed-loop system.