In this paper, a new framework for model order reduction of LTI parametric systems is introduced. After generating and reducing several local original models in the parameter space, a parametric reduced-order model is calculated by interpolating the system matrices of the local reduced models. The main task is to find compatible system representations with optimal interpolation properties. Two approaches for this purpose are presented together with several numerical simulations.Zusammenfassung In diesem Beitrag wird ein neuer Rahmen zur Modellordnungsreduktion parametrischer LZI-Systeme vorgestellt. Er sieht zunächst die Reduktion des Originalmodells in einigen Stützstellen des Parameterraums vor. Anschließend wird ein reduziertes parametrisches System generiert, indem die Systemmatrizen der lokalen Reduktionen durch geeignete Transformationen kompatibel gemacht und interpoliert werden. Hierfür werden zwei alternative Verfahren beschrieben, deren Eigenschaften an drei numerischen Testfällen dargestellt werden.
This dissertation delivers a contribution to the field of order reduction of large-scale nonlinear models of electromagnetic devices. In particular, it enables applying model order reduction techniques to an important class of electromagnetic devices that contain moving components and materials with nonlinear magnetic properties. Such devices include among others rotating electrical machines, electromagnetic valves, electromagnetic solenoids, and electromechanical relays.The presented methods exploits the trajectory piecewise linear (TPWL) approach in approximating the nonlinear dependency of materials properties on the applied magnetic field. Additionally, the model nonlinearity that is caused by the movement of the device components is handled using a novel approach that updates the electromagnetic (EM) field model permanently according to the new components positions.The order of the large-scale electromagnetic field model is reduced by approximating the original electromagnetic field distribution by a linear combination of few virtual field distributions that are found using the proper orthogonal decomposition (POD) approach.The challenge of selecting the number and the position of the linearization points in the TPWL model is tackled using a new approach that considers the change in the magnetic properties of the device materials among all the simulated state-vectors.The new presented methods are extended to enable generating parametric reduced order models of moving nonlinear EM devices. Such models enable a fast and accurate prediction of the behavior of the EM device and its variations that result from changing the values of its design parameters. Additionally, several algorithms for generating an optimal reduction subspace of the parametric model are presented and compared.Finally, an approach for overcoming the challenge of generating reduced order models of EM devices while considering the strong influence of their power electronics driving circuits is introduced and applied to the example of a rotating electrical machine coupled to a power electronics driving circuit.The new methods presented in this work are validated by applying them on the examples of three industrial devices. An electrical transformer, an electromagnetic valve, and a rotating electrical machine.
DEDICATIONTo my parents, my wife, and my daughter.
ACKNOWLEDGMENTS
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.