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This chapter presents a so-called extended model-reduction technique for linear delay differential equations. The presented technique preserves the infinite-dimensional nature of the system and facilitates the preservation of properties such as system parameterizations (uncertainties). It is proved in this chapter that the extended model-reduction technique also preserves stability properties and provides a guaranteed a-priori bound on the reduction error. The reduction technique relies on the solution of matrix inequalities that characterize controllability and observability properties for time delay systems. This work presents conditions on the feasibility of these inequalities, and studies the applicability of the extended model reduction to a spatio-temporal model of neuronal activity, known as delay neural fields. Lastly, it discusses the relevance of this technique in the scope of model reduction of uncertain time delay systems, which is supported by a numerical example.

Für die Fertigung von Mikro- und Präzisionsbauteilen, beispielsweise Spinndüsen oder Kühlluftbohrungen, wurde ein neuartiges aktives Spannsystem zur Positionierung entwickelt. Der entwickelte Prototyp ist in der Lage, Winkelabweichungen von ± 0,57° mit einer Genauigkeit von 0,5 Winkelsekunden zu kompensieren. Dazu werden hochgenaue Piezomotoren, kapazitive Wegsensoren und Festkörpergelenke genutzt. Die Werkstücke werden über ein pneumatisch betätigtes Nullpunktspannsystem aufgenommen. Für einen Test unter realen und praxisnahen Bedingungen wurde der entwickelte Prototyp in ein hybrides Bearbeitungszentrum integriert und anschließend der Einfluss von Positionsunsicherheiten auf die Bearbeitungsergebnisse untersucht. Die verwendete Maschine vereint die Mikrofunkenerosion mit der Laserbearbeitung Der Fachbeitrag beschreibt den mechanischen Aufbau des Prototyps, die Montage und Justierung.

In this paper, we discuss the present and future needs of the electronics industry with regard to model order reduction. The industry has always been one of the main motivating fields for the development of MOR techniques, and continues to play this role. We discuss the search for provably passive methods, as well as passivity enforcement methods that are currently being developed. Structure preservation is another important research topic, for which new concepts are being developed. This also holds for the calculation of delays in long interconnect lines, a topic that leads to an entirely new type of methods. Topics that are still in their infancy are model order reduction for parameterized and nonlinear problems. We will discuss what the needs of the industry are in all of these fields, show specific applications and what has been achieved so far. The paper is meant as a guideline for future research, not as a detailed survey of existing methods.

This paper discusses model reduction of electrical circuits based on a port-Hamiltonian representation. It is shown that by the use of the Kalman decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits the port-Hamiltonian structure. Energy and co-energy variable representations for port-Hamiltonian systems are defined and the reduction procedures are used for both representations. These exact reduction procedures motivate two approximate reduction procedures that are structure preserving for general port-Hamiltonian systems, one reduction procedure is called the effort-constraint reduction methods. The other procedure is structure preserving under a given condition. A numerical example illustrating the model reduction of a ladder network as a port-Hamiltonian system is considered.

Oscillators are used in many integrated RF circuits. Since their behavior is highly nonlinear, full system simulation can be expensive. Furthermore, the behavior of an oscillator can be (un)intendedly perturbed by that of other components and oscillators. We apply a method to build nonlinear phase macromodels of voltage controlled oscillators and show how these can be used to predict the behavior of oscillators under perturbation. Model order reduction techniques are used to decrease simulation times. Numerical results for realistic design illustrate the proposed approach.

A framework for model reduction and synthesis is presented, which enables the re-use of reduced order models in circuit simulation. Two synthesis techniques are considered for obtaining the circuit representation (netlist) of the reduced model: (1) by means of realizing the reduced transfer function and (2) by unstamping the reduced system matrices. For both methods, advantages and limitations are discussed. Especially when model reduction exploits structure preservation, we show that using the model as a current-driven element is possible, and allows for synthesis without controlled sources. The presented framework serves as a basis for reduction of large parasitic R/RC/RCL networks.

In organic apple growing protective applications with copper, sulphur or lime sulphur are used for apple scab control. Protective applications have to be repeated when new leaves unfold. The timing of protective sprays depends on the weather forecast. If forecasted infection conditions fail to appear, treatments were for nothing. With curative control agents available, the number of treatments could be reduced. In greenhouse trials we tested control agents for their protective and curative efficiency against apple scab after artificial inoculation of potted apple trees. Applications were done 2 hours before inoculation, 5 hours after inoculation on wet leaves, 5 hours after inoculation during simulated rainfall or 24 hours after inoculation on wet or dry leaves. The optimal time of application differed between the preparations tested. Vitisan and OmniProtect had their highest activity when sprayed curative 24 hours after inoculation. Combinations were found, which revealed a high efficiency against apple scab from 2h before to 24 hours after inoculation. In a field trial apple scab was effectively controlled by curative applications of OmniProtect.