Modeling and vibration suppression based on Nussbaum function for beam bridge with unknown control directions and unknown nonlinear time-varying actuator faults

Abstract

In this paper, the modeling of the beam bridge system with in-domain control and the vibration suppression under unknown control directions, unknown nonlinear time-varying actuator faults and external disturbances are studied. The beam bridge with fixed ends can be regarded as Euler Bernoulli beam, which is a typical distributed parameter system. Firstly, the partial differential equation (PDE) model of the beam bridge is established according to Hamilton principle. Then, an adaptive in-domain control scheme based on Nussbaum function is designed on the PDE model to eliminate the vibration of the beam bridge. It is proved theoretically that all closed-loop signals are uniformly bounded under this control law, and the vibration of the system asymptotically converges to zero. The simulation results also prove the effectiveness of the proposed control scheme. What’ more, the modeling and control scheme presented in this paper can be applied to a class of systems similar to beam bridges, such as vibration suppression of the main beam of an overhead crane bridge.