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Abstract

Model Predictive Control (MPC) is a well-established technique for process control. It is based on a dynamical model that is used to predict and optimize the behavior of a dynamical process. In fixed sampling intervals, measurements of the controlled process are carried out and they are embedded into a parametric Optimal Control Problem (OCP). The solution of this OCP is used to generate an optimal feedback control answer, which is applied to the process. This methodology enables the controller to react to disturbances in an optimal manner. In this thesis, we focus on MPC schemes, which consider Ordinary Differential Equation (ODE) or Differential Algebraic Equation (DAE) models, and employ the multiple shooting discretization for the arising OCPs.

One of the main challenges of MPC is the computational complexity of the arising OCPs. The Real-Time Iteration (RTI) is a well-established approach to reduce the computational demand by exploiting the similarities of subsequent OCPs. The Multi-Level Iteration (MLI) is an extension of the RTI scheme that aims at a further reduction of the computational cost by reusing simulation data. For this, it defines a hierarchy of update formulas with an increasing computational complexity, but also with stronger convergence properties. These update formulas state individual MPC schemes, but they can also be executed in parallel. In this thesis, we review the current methodologies and describe how the individual levels can be combined to holistic schemes. We propose a novel scheduling algorithm that is especially tailored to applications with high sampling frequencies.

Accurate state estimation is a vital prerequisite for fast feedback control methods such as MPC. For efficient process control, it is of great importance that the estimation process is carried out as fast as possible to provide the feedback mechanism with precise information and enable fast reactions in case of disturbances. Moving Horizon Estimation (MHE) is a model-based methodology for online state estimation, which builds upon dynamic optimization. The model is fitted to a limited number of past measurements in order to predict to current state. The methodology has structural similarities to MPC and thus, the RTI can be applied to reduce the computational effort of MHE schemes, too. We present a new method to apply the MLI update formulas to the RTI for MHE (RTI-MHE) in order to increase feedback rates.

Therefore, we propose a reformulation of the MHE problems that does not only allow the application of MHE update formulas, but also their parallel evaluation. The algorithmic developments in this thesis are driven by the need for new control concepts for Microgrids (MGs). The energy transition leads to an increasing number of Renewable Energy Resources (RES), which are characterized by a high volatility, and their efficient integration poses a rising challenge. MGs are considered a key-technology to incorporate RES into the utility grid, because they allow to cluster provider and consumer of electrical energy locally as a single controllable unit. However, the control of MGs is challenging itself and current control approaches reach their limits due to the rising penetration of RES and the fast electrical system dynamics. In this thesis, we summarize the control structure of MGs and introduce full transient models for the networks dynamics as well as for the most import components. The goal of this thesis is to investigate the applicability of MPC to MG control. To prove the efficacy of the proposed mathematical methods, we demonstrate their capabilities in challenging load scenarios for realistically sized MGs in numerical experiment