Our group recently defined two novel data-driven modeling methodologies: The Design of Dynamic Experiments (DoDE) and the Dynamic Response Surface Methodology (DRSM). These two methods enable the quick and efficient d...
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Our group recently defined two novel data-driven modeling methodologies: The Design of Dynamic Experiments (DoDE) and the Dynamic Response Surface Methodology (DRSM). These two methods enable the quick and efficient data-driven modeling of processes with a partial understanding of their inner workings. They generalize the Design of Experiments (DoE) and the Response Surfaces Methodology (RSM). DoDE allows time-varying inputs, and DRSM models time-varying process outputs. In this paper, we combine the above data-driven tools and partial knowledge of a batch polymerization process to develop an integrated data and knowledge-driven model. The optimization objective is to minimize the process’s batch time while producing the same product quality, increasing productivity. The process knowledge incorporated into the model consists of material and energy balances in which we lack a quantitative description of the rate phenomena, such as reaction or mass/heat transfer rates. The optimization is evolutionary; initially, targeting small improvements through constrained extrapolations around the normal operating conditions. Then, we build the first models and use such models to design the next set of experiments that meet our specifications. This cycle of running experiments and updating the models is repeated until an optimum is reached. After three cycles, we succeeded in reducing the batch time by 26%, while producing acceptable product.
We consider the problem of periodic trajectory design for single-output systems which may be subject to periodic external disturbances. We show how trajectories optimizing a possibly nonquadratic and nonconvex polynom...
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We consider the problem of periodic trajectory design for single-output systems which may be subject to periodic external disturbances. We show how trajectories optimizing a possibly nonquadratic and nonconvex polynomial performance objective can be found by using the frequency-domain description of the plant by converting the problem to a polynomial optimization problem (POP) in the Fourier coefficients of the external input signals. The method is suited for distributed-parameter systems, since the system transfer functions are not required to be rational; the computational complexity of the method depends on the order of the polynomial nonlinearities in the performance objective as well as the number of required harmonics, but is independent of the underlying system dimension.
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