(183b) Modeling and Monitoring of Batch Processes in Relative Time

Batch processes are widely used in many industries. Typically, raw materials are combined in a suitable batch vessel before a chemical, physical or biological transformation take place, resulting in the end product. In many cases the control of the batch process is recipe driven and not adjusted to accommodate raw material variation, changes in uncontrollable factors, etc. to ensure the best possible end product quality. Real time control of a batch process saves the industry money and resource due to less rework and rejects, as well as the opportunity for real time quality assurance of the end product.

 There are some solutions available for batch monitoring and control but typically they are assuming equal lengths of batches, i.e. the batch starts at the same chemical or biological time t₀ and has the same number of time points for all batches. Obviously this is resulting in problems if the batches do not meet these criteria. Alternative approaches to handle uneven batch lengths include replacing time with a maturity index or using dynamic time warping. In both these approaches complications can occur if the first measurement does not coincide with the true t₀ and the batch evolution is non-linear, which is often the case.

In this presentation, a better approach accommodating both uneven batch lengths and unknown true t₀ is proposed. The approach is based on projections in the score space so all control options used in MSPC are valid and available.