Modeling and vibration control for a nonlinear three-dimensional flexible moving string system with input quantization and event-triggering

In this article, modeling and vibration control issues are addressed for a nonlinear three-dimensional flexible moving string system with input quantization and event-triggering. The flexible string with a payload takes the bridge crane as a moving carrier. The system models are established by Hamilton's principle, including a group of partial differential equations and ordinary differential equations. Logarithmic and hysteretic quantizers are both adopted to compare quantitative effects, and then the quantized control input signals are processed effectively to further relieve communication burdens by event-triggering, which is based on the fixed threshold strategy. The proposed control scheme can drive the cart to the desired position and suppress the vibration of the three-dimensional flexible string. The uniform ultimate boundedness of the closed-loop system is proved via the Lyapunov direct method. Finally, numerical simulations are carried out to verify the control effect.