Feedback synchronization: a relaxation of tracking

Tracking is concerned with driving the response of a system to follow a desired time trajectory. Many applications, however, are interested in following a desired trajectory that is indexed by some other index variable instead of time, such as thickness or length along a specified curve. When the time evolution of this index variable is fixed, then such a performance objective is equivalent to tracking. Frequently, however, one can affect the evolution of this index variable, adjusting process parameters such as machine speed, growth rate, etc. This extra degree of freedom introduces a new performance objective of synchronizing the system response with the time evolution of this index variable. Exploiting this degree of freedom in the feedback design can have a significant impact on tracking performance while explicitly trading off notions of product quality and throughput. This paper uses the feedback control of epitaxy, a critical process for the manufacture of compound semiconductor devices, to demonstrate feedback synchronization as a new approach to these inherently nonlinear problems