Robuste modellgestützte Prozessführung auf Basis von Gauß'schen Mischdichten am Beispiel der Bray-Liebhafsky-Reaktion und der autotrophen Kultivierung von Ralstonia eutropha H16

Technical processes are continuously required to be more efficient. This development is driven by an increasing shortage of resources as well as market liberalisation leading to more competition and financial pressure. The efficiency can be increased by new reaction pathways or improved process components. This theses, however, focuses on methods of process design and control to reach this goal. The definition of efficiency that usually refers to the amount of product per educt, time, and/or energy is here supplemented by the expected production variance, which arises from uncertain model parameters and initial conditions. Therefore, the process can be designed with respect to a low variation of product, which is often referred to as quality by design. This is especially beneficial in highly cross-linked production facilities with many depending downstream processes. The incorporation of statistical information in process design and control requires methods, which allow for the prediction of uncertainties according to the nonlinear process model. The complete probabilistic representation of the process states over time also allows for an improved process observation and a better compliance of safety constraints. Thus, safety margins can be better exploited, which generally leads to increased productivity. The propagation of normally distributed input variables through the nonlinear model equations can be simulated using the Unscented Transformation (UT). It is based on an approximation of 2 order and describes the development of the state variables with a single normal distribution. If the input uncertainties, however, are reformulated using several normal distributions along one or more input dimensions a Gaussian mixture density (GMD) is created. By applying the UT to each component of the GMD, the probabilistic description of the state variables can be improved due to the higher local resolution provided by the individual GMD components. Therefore, also higher order statistical information like skewness and kurtosis can be captured, leading to improved state estimates in an observer framework or to more accurately predicted confidence bounds in nonlinear process design and control. Therefore, the first part thoroughly discusses the UT and shows how it can be applied to GMDs. After the introduction of the Maximum Likelihood Estimation for the data-driven identification of model parameters, theMaximum A Posteriori Estimation is presented, from which the Extended-Kalman-Filter framework is derived. Using the UT the Sigma-PointKalman-Filter is introduced, expanded to parameter-depending measurement equations and finally formulated using GMDs. The concept of using the UT for process design and control is well known and also the use of GMDs has been discussed in theory. In this theses, however, the GMD-based robust process control is applied to a chemical and later to a biological process. While the chemical process has been fully automated allowing for hundreds of process runs for the statistical verification of the probabilistic framework, the biological process is used as a proof of concept representing more complex applications.