PDE modelling and vibration control of overhead crane bridge with unknown control directions and parametric uncertainties

In this study, problems of the partial differential equation (PDE) modelling and vibration control design are first resolved for an overhead crane bridge system, which is regarded as a Timoshenko beam with an attached rigid body. With the established infinite-dimensional PDE model, a Nussbaum function-based adaptive control approach is developed in order to settle out parametric uncertainties of the system with unknown control directions. Under the proposed control method, states of the overhead crane bridge are globally bounded and finally converge to an adjustable region of zero. The stability of the closed-loop overhead crane bridge system is analysed by employing Lyapunov's direct method. The effectiveness of the developed control strategy is verified through the simulation results.