Experimental Validation of Robust Process Design and Control Based on Gaussian Mixture Densities∗

In this contribution, the effects of different degrees of uncertainty description are investigated experimentally using an exothermic chemical reaction with safety constraint on the temperature. For that purpose, two robust trajectories are designed that respect the artificially created uncertainties of the experiments either coarsely using a single multivariate normal distribution (1GMD) or in a more detailed fashion using a Gaussian mixture density (GMD) consisting of 32 multivariate normal densities (32GMD). For the optimization, the uncertainties are propagated using the unscented transformation. Both trajectories were run 71 times in an open-loop manner. The more detailed trajectory (32GMD) leads to a 9 % higher yield without increasing the risk of constraint violation. Furthermore, many experimental realizations of two robust closed-loop process control schemes are being compared. They differ again only in the degree of the underlying uncertainty description. Although the frequent corrections of the controller marginalize the advantage of a more detailed stochastic process prediction, the 4GMD-controller still allows for 3 % more educt conversion compared to the 1GMD-controller.