Consensus tracking and vibration control for multiple single-link flexible manipulators with input signal quantization

This study examines consensus tracking and vibration control of a multiagent system consisting of multiple single-link flexible manipulators with input signal quantization. The dynamics of each flexible manipulator are described by fourth-order partial differential equations (PDEs). A logarithmic quantizer with changeable parameters is adopted to quantize control inputs, and adaptive laws are designed to compensate for the effect caused by quantization. A distributed adaptive boundary control protocol is proposed based on the PDE model to ensure all manipulators track the desired angular position and eliminate vibrations without knowledge of quantizer parameters. The proposed control protocol is proven to ensure the uniformly bounded stability of the closed-loop system. Simulations are carried out under three cases to illustrate the effectiveness of the designed strategy.