Optimal product quality control design in a semi-batch reactive crystallization process: An input authority profile based approach

For a sufficiently repeatable batch or semi-batch process, a central end-point quality-control task is to determine a time-varying input profile that improves final product quality while satisfying operating constraints such as a fixed total feed. Such a profile may be adjusted within a batch using online measurements or revised between batches using information from completed runs. This work proposes the notion of input-authority, a perturbation-based diagnostic that quantifies the relative leverage of different feed-profile time windows on a terminal objective using constant-sum feed redistributions and relative terminal-cost changes. The utility of this diagnostic is demonstrated on a semi-batch BaSO4 reactive crystallization test bed with particle size distribution (PSD)-based terminal CQAs. The authority test reveals strong early-stage authority and negligible late-stage authority. The implemented authority-guided secant-type B2B update is compared with a multiphase subspace identification (MPSSID)-based data-driven MPC design. When authority is concentrated in the early stage, within-batch feed-profile adjustments may have little effect if they can only be implemented after informative measurements become available. B2B updating can instead revise the early-stage recipe before the next run. In the demonstrated process, it achieved better end-point quality. These results illustrate how authority profiling can serve as a practical pre-screening tool for choosing between within-batch MPC and B2B recipe updating in fixed-total-feed batch and semi-batch processes.