Multi-Rate Analysis and Design of Visual Feedback Digital Servo-Control System

This paper addresses the analysis and design of digital motion control system with machine vision as a feedback measurement in the servo loop. The camera vision is modeled as a discrete time-delayed sensor. A multirate formulation is proposed based on the fact that vision update rate is slower than the digital servo-control update rate and is analyzed through the lifting technique which converts the periodic time varying multirate system to a time invariant one. Some interesting properties of this specific multirate system are found and are utilized in control system design. An 1-7 norm optimal control problem is formulated to minimize the maximum time domain error, which has direct connection to camera field of view and mechanical tolerance. A numerical example is given to demonstrate the presented methods.