Stability and performance analysis of mixed product run-to-run control

Run-to-run control has been widely used in batch manufacturing processes to reduce variations. However, in batch processes, many different products are fabricated on the same set of process tool with different recipes. Two intuitive ways of defining a control scheme for such a mixed production mode are (i) each run of different products is used to estimate a common tool disturbance parameter, i.e., a “tool-based” approach, (ii) only a single disturbance parameter that describe the combined effect of both tool and product is estimated by results of runs of a particular product on a specific tool, i.e., a “product-based” approach. In this study, a model two-product plant was developed to investigate the “tool-based” and “product-based” approaches. The closed-loop responses are derived analytically and control performances are evaluated. We found that a “tool-based” approach is unstable when the plant is non-stationary and the plant-model mismatches are different for different products. A “product-based” control is stable but its performance will be inferior to single product control when the drift is significant. While the controller for frequent products can be tuned in a similar manner as in single product control, a more active controller should be used for the infrequent products which experience a larger drift between runs. The results were substantiated for a larger system with multiple products, multiple plants and random production schedule.