Zusammenfassung Der deutsche Pavillon bei der Weltausstellung EXPO 2010 in Shanghai zeigte als seine Hauptattraktion ein großes interaktives Pendel. Das wichtigste Element dieses Pendels ist eine Kugel mit einem Durchmesser von 3 m, die mit ca. 400.000 LEDs bestückt ist. Die Kugel ist mithilfe einer dünnen Stange und einem Kardan-Gelenk an einem Kreuztisch aufgehängt und liefert den Zuschauern eine Licht-und Bewegungsshow. Dabei führt das Pendel sowohl große ebene Schwingungen als auch Kreisbewegungen aus, während die Bewegungen des Kreuztisches harten Beschränkungen unterliegen. In diesem Beitrag werden die hierfür entwickelten Regelungskonzepte vorgestellt und deren Wirksamkeit anhand von Experimenten gezeigt.Summary The German Pavilion on the World Exhibition EXPO 2010 in Shanghai showed a big pendulum as its main attraction. The pendulum consists of a sphere with 3 m diameter which is equipped with about 400 000 LEDs and used as a projection screen. The sphere is mounted via a long bar at an electrically driven crosstable and provide a motion and light show. Thereby, the sphere performs large circular and pendular motions, while the crosstable can only perform very small motions. In this paper the control design is presented. The efficiency of this control system is shown by experimental results.

In many cases, the design of a tracking controller can be significantly simplified by the use of a 2-degrees of freedom (DOF) control structure, including a feedforward control (i.e., the inversion of the nominal system dynamics). Unfortunately, the computation of this feedforward control is not easy if the system is nonminimum-phase. Important examples of such systems are flexible multibody systems, such as lightweight manipulators. There are several approaches to the numerical computation of the exact inversion of a flexible multibody system. In this paper, the singularly perturbed form of such mechanical systems is used to give a semianalytic solution to the tracking control design. The control makes the end-effector to even though not exactly, but approximately track a certain trajectory. Thereby, the control signal is computed as a series expansion in terms of an overall flexibility of the bodies of the multibody system. Due to the use of symbolic computations, the main calculations are independent of given parameters (e.g., the desired trajectories), such that the feedforward control can be calculated online. The effectiveness of this approach is shown by the simulation of a two-link flexible manipulator.

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The German Pavilion on the World Exhibition EXPO 2010 in Shanghai showed an interactive 3D-pendulum as one of its main attractions. The pendulum consists of a sphere with 3 m diameter which is equipped with several hundred thousand LEDs and used as a projection screen. The sphere is mounted via a long bar at an electrically driven crosstable which is used for the excitation of the pendulum. The crosstable is located in a theater-like building where the visitors can follow the show. Thereby, the sphere performs large circular and pendular motions, while the crosstable can only perform very small motions. Also during some parts of the show the sphere should move in a certain way which is obtained by interpreting the visitors' action as a physical excitation. In this paper the system and control design are discussed and experimental results are presented.

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