A Smooth Formulation for Maximum On-Specification Production in Campaign Continuous Manufacturing
Volume Title: 1
1Department of Chemical Engineering, AmirKabir University of Technology (Tehran Polytechnic)
2Department of Chemical Engineering, AmirKabir University of Technology
Campaign continuous manufacturing (CCM), i.e. continuous processes with a short operational window, is gaining attention in the pharmaceutical industry as an alternative to the traditional batch-wise manufacturing. A major challenge in CCM is how to meet stringent product quality specifications during the operation, in which the startup and shutdown phases constitute a large portion of the process, making the quality specifications even harder to meet. The optimal operation of CCM was discussed in a recent publication, where an optimization problem for maximizing the on-specification production was also formulated. However, the formulation was potentially nondifferentiable due to its hybrid discrete-continuous nature, and required rather complicated remedies to ensure differentiability before the problem could be solved by gradient-based optimization algorithms. In this work, the same problem of maximizing on-specification production in CCM is addressed by proposing a much simpler formulation, in which the discrete events are approximated by smooth functions. Therefore, the proposed formulation lends itself to conventional gradient-based algorithms, and can solve optimal CCM problems reliably as demonstrated in the case studies.
Dynamic optimization; Hybrid dynamic systems; Smooth approximation; Sigmoid function; Pharmaceutical manufacturing