Vibration control of nonlinear three-dimensional length-varying string with input quantization

This article studies the stability problem for a three-dimensional string with variable length in the case of input quantization. A nonlinear partial differential equation model is used to depict the dynamic characteristics of the length-varying flexible string with distributed variable parameters. The control signals are effectively mapped from a continuous region to a discrete set of numerical signals before being transmitted through communication channels using quantizers. With no information about quantizers, the vibration of the string is eliminated under the proposed adaptive quantized control despite of the actuator degradation, and the stability of the closed-loop system is demonstrated based on the Lyapunov’s direct method. Simulation results are supplied to show the effectiveness of the presented control strategy.