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In this work, a method for reducing the number of degrees of freedom in online optimal dynamic experiment design problems for systems described by differential equations is proposed. The online problems are posed such that only the inputs which extend an operation policy resulting from an experiment designed offline are optimized. This is done by formulating them as multiple experiment designs, considering explicitly the information of the experiment designed offline and possible time delays unknown a priori. The performance of the method is shown for the case of the separation of isopropanolol isomers in a Simulated Moving Bed plant.
Forschungsbericht 2017
(2017)
A nonlinear state observer is designed for a thermal energy storage with solid/liquid phase change material (PCM). Using a physical 2D dynamic model, the observer reconstructs transient spatial temperature fields inside the storage and estimates the stored energy and the state of charge. The observer has been successfully tested with a lab-scale latent heat storage with a single pass tube bundle and the phase change material located in a shell around each tube. It turns out that the observer robustly tracks the real process data with as few as four internal PCM temperature sensors. © 2017 Elsevier Ltd. All rights reserved.
We present a novel derivative-based parameter identification method to improve the precision at the tool center point of an industrial manipulator. The tool center point is directly considered in the optimization as part of the problem formulation as a key performance indicator. Additionally, our proposed method takes collision avoidance as special nonlinear constraints into account and is therefore suitable for industrial use. The performed numerical experiments show that the optimum experimental designs considering key performance indicators during optimization achieve a significant improvement in comparison to other methods. An improvement in terms of precision at the tool center point of 40% to 44% was achieved in experiments with three KUKA robots and 90 notional manipulator models compared to the heuristic experimental designs chosen by an experimenter as well as 10% to 19% compared to an existing state-of-the-art method.
We propose a method for an efficient optimization of experimental designs, using a combination of discrete adjoint computations, Taylor arithmetic and matrix calculus. Compared to the state of the art of using finite differences or the forward mode of automatic differentiation, our proposed approach leads to a reduction of the relative temporal complexity from linear to constant time in the number of control variables and measurement weights. We demonstrate that the advantageous complexity results are not only of theoretical nature, but lead to significant speedups in practice as well. With our implementation we are very close to the theoretical bound of the cheap gradient principle. We present one academic (spatially discretized heat equation) and two industrial application examples (biochemical process/Diesel-oxidation catalysis process) where we achieve speedups that range between 10 and 100. In addition to our core results, we also describe an efficient adjoint approach for the treatment of differential algebraic equations and present adjoint formulas for constrained least-squares problems.
The adaptive input design (also called online redesign of experiments) for parameter estimation is very effective for the compensation of uncertainties in nonlinear processes. Moreover, it enables substantial savings in experimental effort and greater reliability in modeling.
We present theoretical details and experimental results from the real-time adaptive optimal input design for parameter estimation. The case study considers separation of three benzoate by reverse phase liquid chromatography. Following a receding horizon scheme, adaptive D-optimal input designs are generated for a precise determination of competitive adsorption isotherm parameters. Moreover, numerical techniques for the regularization of arising ill-posed problems, e.g. due to scarce measurements, lack of prior information about parameters, low sensitivities and parameter correlations are discussed. The estimated parameter values are successfully validated by Frontal Analysis and the benefits of optimal input designs are highlighted when compared to various standard/heuristic input designs in terms of parameter accuracy and precision.