Fredrik Magnusson

Toolbox for development and validation of grey-box building models for forecasting and control

As automatic sensing and information and communication technology get cheaper, building monitoring data becomes easier to obtain. The availability of data leads to new opportunities in the context of energy efficiency in buildings. This paper describes the development and validation of a data-driven grey-box modelling toolbox for buildings. The Python toolbox is based on a Modelica library with thermal building and Heating, Ventilation and Air-Conditioning models and the optimization framework in JModelica.org. The toolchain facilitates and automates the different steps in the system identification procedure, like data handling, model selection, parameter estimation and validation. To validate the methodology, different grey-box models are identified for a single-family dwelling with detailed monitoring data from two experiments. Validated models for forecasting and control can be identified. However, in one experiment the model performance is reduced, likely due to a poor information content in the identification data set.

A framework for nonlinear model-predictive control using object-oriented modeling with a case study in power plant start-up

In t his paper, nonlinear model predictive control (NMPC) is applied to the start-up of a combined-cycle power plant. An object-oriented first-principle model library expressed in the high-level language Modelica has been written for the plant and used to set up the simulation and optimization models. The NMPC optimization problems are both encoded, using a high-level notation, and solved in the open-source framework JModelica.org. The results demonstrate the effectiveness of the framework and its high-level description. It bridges the gap between an intuitive physical modeling format and state of the art numerical optimization algorithms. Promising closed-loop control results are shown for plant start-up when the NMPC model contains parametric errors and the simulation model, corresponding to the real plant, is subject to disturbances.

Hierarchical predictive control for ground-vehicle maneuvering

This paper presents a hierarchical approach to feedback-based trajectory generation for improved vehicle autonomy. Hierarchical vehicle-control structures have been used before-for example, in electronic stability control systems, where a low-level control loop tracks high-level references. Here, the control structure includes a nonlinear vehicle model already at the high level to generate optimization-based references. A nonlinear model-predictive control (MPC) formulation, combined with a linearized MPC acting as a backup controller, tracks these references by allocating torque and steer commands. With this structure the two control layers have a physical coupling, which makes it easier for the low-level loop to track the references. Simulation results show improved performance over an approach based on linearized MPC, as well as feasibility for online implementations.

Dynamic Multi-Objective Optimization of Batch Chromatographic Separation Processes

This contribution presents a novel offline dynamic multi-objective optimization framework for high-pressure liquid chromatographic (HPLC) processes in batch elution mode. The framework allows for optimization of general elution trajectories parametrized with piecewise constant control signals. It is based on a simultaneous method where both the control and state variables are fully discretized in the temporal domain, using orthogonal collocations on finite elements, and the state variables are discretized in the spatial domain, using a finite volume weighted essentially non-oscillatory (WENO) scheme. The resulting finite dimensional nonlinear program (NLP) is solved using a primal-dual interior point method and automatic differentiation techniques. The advantages of this open-loop optimal control methodology are highlighted through the solution of a challenging ternary complex mixture separation problem for a hydrophobic interaction chromatography (HIC) system. For a bi-objective optimization of the target component productivity and yield, subject to a purity constraint, the set of Pareto solutions generated with general elution trajectories showed considerable improvement in the productivity objective when compared to the Pareto set obtained using conventional linear elution trajectories.

Discretized multi-level elution trajectory: A proof-of-concept demonstration

Biomolecular and pharmaceutical downstream processing is dominated by chromatographic separation, which is associated with high product quality, low capacity and high costs. The separation can be optimized to minimize the costs while achieving a high purity. This paper presents an experimental validation of a discretized multi-level elution (DiME) trajectory, implemented on commercially available chromatography equipment. The tertiary protein separation of ribonuclease A, cytochrome C and lysozyme was used as a case study. A mechanistic model was calibrated using step and linear gradient experiments. The model was simulated together with the state sensitivities with respect to model parameters, which was used in the Levenberg-Marquardt algorithm to fit the model response to the experimental data. The model was used to solve the dynamic optimization problem of maximizing the yield of cytochrome C given a 95% purity requirement, 1000s processing time and 50 salt concentration levels in the elution trajectory. The model was spatially discretized using finite volumes and temporally discretized using direct collocation. The corresponding non-linear programming problem was solved with IPOPT. Once the optimal salt trajectory was found it was experimentally implemented on an ÄKTA Pure using an OPC interface. The optimal trajectory was analyzed in-line by UV absorbance measurements and off-line by analysis of collected fractions. The results presented in this study show the successful experimental realization of DiME trajectories and how to use model calibration, optimization and control to realize DiME trajectories for any chromatography separation problem.

Symbolic elimination in dynamic optimization based on block-triangular ordering

We consider dynamic optimization problems for systems described by differential-algebraic equations (DAEs). Such problems are usually solved by discretizing the full DAE. We propose techniques to symbolically eliminate many of the algebraic variables in a preprocessing step before discretization. These techniques are inspired by the causalization and tearing techniques often used when solving DAE initial value problems. Since sparsity is crucial for some dynamic optimization methods, we also propose a novel approach to preserving sparsity during this procedure. The proposed methods have been implemented in the open-source JModelica.org platform. We evaluate the performance of the methods on a suite of optimal control problems solved using direct collocation. We consider both computational time and probability of solving the problem in a timely manner. We demonstrate that the proposed methods often are an order of magnitude faster than the standard way of discretizing the full DAE, and also significantly increase probability of successful convergence.