Title: From system model to optimal control - A tool chain for the efficient solution of optimal control problems
Authors: Manuel Gräber, Jörg Fritzsche and Wilhelm Tegethoff
Abstract:Based on a specific application example - the thermal management system of an internal combustion engine - a toolchain is presented for formulating and solving of nonlinear optimal control problems. Starting from graphical modeling of the thermal management system with the Modelica library TIL, the model is exported to the standardized model exchange format Functional Mock-up Interface (FMI). Furthermore, it is imported to the optimal control software package MUSCOD-II. Python is used as scripting language for the problem formulation, the numerical solution and the processing of results. By using FMI as an interface, models from any simulation and modeling tools can be used if there is an FMI model export and the models fulfill certain mathematical requirements (smoothness).
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Title: Nonlinear Model Predictive Control of a Thermal Management System for Electrified Vehicles using FMI
Authors: Torben Fischer, Tom Kraus, Christian Kirches and Frank Gauterin
Abstract:Energy-efficient thermal management systems for Emobility help to decrease energy consumption and increase range. Due to transient external conditions and the increasing system complexity, optimization-based control approaches are required in order to harness the full potential of such systems. In (Fischer et al., 11th Int. Modelica Conf, 2015), we have presented a model-based development cycle for a thermal management system in Emobility to this end. In this article, we build upon this work to describe the use of this model within a nonlinear model predictive control (NMPC) approach. The main benefits of using an advanced optimization-based control system in this application are a) the ability to control the battery temperature and the cabin temperature simultaneously, b) the increased energy efficiency achieved by exploiting the predictive character of the optimizationbased control approach, c) the possibility to include operational limits as constraints in the optimization problems and d) the fast reaction to disturbances or model parameter changes. We evaluate the merit of the proposed advanced control system by way of a comparison to conventional PID controller.
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Title: Defining and Solving Hybrid Optimal Control Problems with Higher Index DAEs
Authors: Radoslaw Pytlak, Damian Suski, Tomasz Tarnawski and Tomasz Zawadzki
Abstract:The paper deals with optimal control problems defined for hybrid systems described by higher index DAEs. We present a prototype solution that supports the whole process from defining such problem to solving it and presenting results. Problem’s definition is done with Dynamic Optimization Modeling Language (DOML) which is based directly on Modelica. The proposed numerical procedure for solving the problems of interest has the following features: 1) it is based on the appropriately defined adjoint equations formulated for the discretized equations being the result of the numerical integration of system equations by an implicit Runge–Kutta method; 2) initialization for higher index DAEs is performed with the help of Pantelides’ algorithm; 3) it does not require the system to be transformed to ODEs (through differentiation of some algebraic equations). The paper presents numerical examples related to hybrid systems described by index three DAEs, showing the validity of the proposed approach. All software components needed to carry out the computations, i.e. the code editor, compiler, numerical libraries and GUI for presenting results are prepared as parts of a combined platform: Interactive Dynamic Optimization Server (IDOS).
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