Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty

Optimal experimental design for parameter identification and model selection

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2014René Schenkendor

Aplicação de controle não-linear para veículos marítimos e produção de petróleo

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Pós-Graduação em Sistemas Mecatrônicos, Departamento de Engenharia Mecânica, 2014.O desenvolvimento de sistemas de controle vem abrangendo cada vez mais diferentes operações em campos de petróleo a fim de contornar os desafios recentes da indústria petrolífera. Nesta dissertação, uma abordagem de controle não-linear baseada na teoria de planicidade diferencial é apresentada em torno de questões práticas relacionadas ao posicionamento dinâmico de veículos marítimos e ao problema de otimização de produção em reservatórios sujeitos ao fenômeno do cone de água ou de gás. Dentro desse contexto, dois principais problemas na área de controle são discutidos: planejamento de trajetória e rastreamento de trajetória. A partir da noção de sistemas diferencialmente planos, esses problemas podem ser definidos em relação a um sistema linear controlável equivalente na forma canônica de Brunovsky, reduzindo os esforços no desenvolvimento da lei de controle ao se comparar a técnicas tradicionais da teoria de controle não-linear. Adicionalmente, como essa propriedade não é verificada em todos os sistemas dinâmicos abordados nesse manuscrito, conceitos de sistemas liouvilianos e de entradas planas são apresentados com o objetivo de adaptar sistemas não-diferencialmente planos de tal forma que estratégias de controle baseadas na planicidade diferencial possam ser utilizadas. A partir da modelagem matemática existente na literatura e da teoria de planicidade diferencial, esse trabalho descreve o projeto de controladores de rastreamento de trajetória para os seguintes sistemas: navio de superfície, veículo subaquático autônomo e o comportamento dinâmico da superfície livre em reservatórios sujeitos ao fenômeno do cone 2D. Para um conjunto de trajetórias de referência, os resultados obtidos através de simulações numéricas e testes experimentais avaliam a performance dos controladores mesmo na presença de perturbações externas. _______________________________________________________________________________________ ABSTRACTControl design is increasingly encompassing different operations in oil fields aiming to circumvent the recent challenges in oil and gas industry. In this work, a nonlinear control approach based on differential flatness theory is presented around practical issues concerning dynamic positioning of marine vehicles and optimization of oil production in reservoir subject to the phenomenon of water and gas coning. Within this context, two main problems in control theory are discussed here: motion planning and trajectory tracking. From the notion of differentially flat systems, these problems can be defined in relation to an equivalent controllable linear system in Brunovsky canonical form, reducing efforts on control law design over traditional techniques of nonlinear control theory. Additionally, as this property is not verified in all dynamic systems addressed in this manuscript, concepts of liouvillian systems and flat inputs are presented in order to adapt non-differentially flat systems so that control strategies based on differential flatness can be used. Based on the mathematical modeling from the existing literature and differential flatness theory, this manuscript describes the trajectory tracking control design for the following nonlinear systems: surface vessels, autonomous underwater vehicle and dynamic behavior of the free surface in reservoirs subject to the phenomenon of 2D cone. For a set of reference trajectories, the results obtained from numerical simulations and experimental tests evaluate the control performance, including in the presence of external disturbances

Conditions for the existence of a flat input

We introduce the concept of an affine flat input to a non-linear system with a given output function. This approach can be seen as dual to the search for a flat output of a control system with given input. Our results provide a necessary and sufficient condition for the existence of a flat input in the SISO case, which also allows to construct of the vector field associated to the flat input. In addition, a relation between the flat input vector field and non-linear observer design is discussed. A population model is used to illustrate the construction of a flat input.status: publishe