Problems (Monadologie) und der Theodi zee in der Philosophie und Theologie wurde er berühmt. Er s... more Problems (Monadologie) und der Theodi zee in der Philosophie und Theologie wurde er berühmt. Er stand mit zahlreichen internationalen Gelehrten seiner Zeit in Kontakt, war auch politisch eine // Vorwort 8 // Hamburger Akademievorträge 1 / Gottfried Wilhelm Leibniz einflussreiche Persönlichkeit und Initiator und erster Präsident einer Gelehrten-Gesellschaft, nämlich der Kurfürstlich Bran den burgischen Sozietät der Wissenschaften, der Vorläuferin der heutigen Berlin-Brandenburgischen Akademie der Wissenschaften. Leibniz verfasste wichtige Beiträge für die Natur-und Technik wissenschaften und legte die mathematische Grundlage für binäre Rechen maschinen. Er sorgte als Leiter der Herzog-August-Bibliothek in Wolfen büttel dafür, dass dort der erste alphabetische Katalog angelegt wurde, und war Pionier der Windkraft und weiterer Ingenieurleistungen sowie ganz lebenspraktischer Einrichtungen für das Gemeinwohl, wie zum Beispiel einer Brandkasse. Um solche, zum Teil zwar weniger bekannte, aber bis heute aktuelle Facetten von Leibniz' Schaffen und Wirken geht es auch in den Kapiteln dieses Bandes. Mit der bereits erwähnten Brandkasse und mit Leibniz' Studien zur Versicherungs-und Finanzmathematik befasst sich Eberhard Knobloch in seinem Beitrag. Wie sehr Leibniz die moderne Geschichts forschung durch Quellenstudium geprägt hat, legt Nora Gädeke dar. Über Leibniz' objektbezogenes Denken, seine lebenslange Betonung der Wichtigkeit von Kunstkammern, berichtet Horst Bredekamp, und last but not least macht Thomas Sonar im letzten Kapitel des Bandes den Ver such einer ausgewogenen Beurteilung des berühmt-berüchtigten "Pri o ri tätsstreites" zwischen Newton und Leibniz. Allen Autoren gilt mein Dank für ihre Vorträge und deren Ausarbeitung zu Beiträgen in diesem Band. Organisiert wurde die sehr erfolgreiche Vorlesungsreihe von der Akademie-Arbeitsgruppe "Wissenschaftsgeschichte", allen voran von ihrer Sprecherin Edwin J. Kreuzer / Vorwort // 9 Karin Reich, der ich dafür an dieser Stelle ganz be son ders danken möchte. Mein Dank geht auch an die Natur wissen schaft lerin und Malerin Bärbel Jürgens. Eine kleine Ausstellung ihrer Bilder begleitete die gesamte Vorlesungsreihe in den Baseler Hof Sälen. Zu unserer großen Freude hat sie uns ihre Werke zu Leibniz auch für die Illustration dieses Bandes zur Verfügung gestellt. In ihren Bildern verbindet sie, an geregt durch wissenschaftsgeschichtliche Studien an der Hamburger Uni versität, Kunst und Mathematik. Seit 1990 widmet sie sich neben ihrem Beruf als Chemikerin intensiv der Malerei. Fasziniert besonders von der Vielseitigkeit des Universalgenies Leibniz visualisiert sie seine mathe ma tischen, technischen und philosophischen Überlegungen puzzleartig durch Bearbeitung alter Gemälde in Siebdrucktechnik auf Leinwand und Papier. Dank gebührt auch Elke Senne für die umfangreiche redaktionelle Betreuung des Bandes. Und schließlich möchte ich auch Hamburg University Press, dem Verlag der Staats-und Universitätsbibliothek Hamburg Carl von Ossietzky, nament lich Tobias Buck und Isabella Meinecke, sowie der Grafikerin Christine Klein, Büro für Gestaltung, danken. Sie haben uns bei der technischen und optischen Gestaltung dieser neuen Publikationsreihe vor dem Hintergrund der Entwicklung einer Open-Access-Strategie für die Akademie und ihrer Einbindung in die "Digitale Stadt" der Freien und Hansestadt Hamburg ganz wesentlich und stets hilfreich beratend unterstützt.
In this paper an automated numericalsymbolical analysis concept for dynamic systems in engineerin... more In this paper an automated numericalsymbolical analysis concept for dynamic systems in engineering mechanics is outlined. Besides the computerized generation of symbolic equations of motion, the subsequent analysis is also performed by means of computer algebra in combination with well-established numerical methods.
In applied mathematics and mechanical engineering we normally think of numerical calculations if ... more In applied mathematics and mechanical engineering we normally think of numerical calculations if computers are involved. Although simulations by means of numerical methods are powerful tools for investigations in mechanics, they do have drawbacks, e.g. finite precision, errors generated when evaluating expressions. General global results or proofs of theoretical results cannot be obtained from simulations.
The nonlinear dynamic responses of moored crane vessels to regular waves are investigated experim... more The nonlinear dynamic responses of moored crane vessels to regular waves are investigated experimentally and theoretically. The main subject of interest are nonlinear phenomena like bifurcations and the existence of multiple attractors. In the experimental part of the work, a moored model of a crane vessel has been excited by regular waves in a wave tank. A special mechanism has been developed to model the nonlinear behavior of real mooring systems. The theoretical part of the work concerns the mathematical modeling of the floating cranes. Two mathematical models of different levels of complexity are presented. Two different tools are used to systematically determine the responses of the systems to periodic forcing of waves. Firstly, the path-following techniques in combination with numerical integration of equations of motion applied to a full nonlinear model give insight into the dynamics in time domain. Secondly, the multiple scales method allows for an analytical investigation of simplified nonlinear models in frequency domain. Many results of computations for two crane vessels, barge and ship, are presented. Special attention is paid to oscillations near the frequencies of primary resonances and to subharmonic motions. An excellent agreement is found between the results of time-domain and frequency-domain analysis. The computational examples chosen correspond to the models used not only in the present experiments but in the experiments of others as well. The results presented in the work allow us to draw several important conclusions concerning the dynamic behavior of floating cranes during offshore operations. Both the developed models and the analytical tools can be used to identify the limits of the operating range of floating cranes.
Monitoring missions in confined underwater environments such as nuclear storage ponds or industry... more Monitoring missions in confined underwater environments such as nuclear storage ponds or industry tanks call for highly maneuverable fully autonomous micro underwater robots. In this work, we target this challenging scenario with the new low-cost open-source HippoCampusX platform. We present a modular software and hardware architecture which is easily adaptable to mission specific requirements. Our system is part of the PX4-environment [1] and constitutes PX4’s first underwater extension including a SITL simulation. We conduct a series of experiments to demonstrate HippoCampus’ agile maneuvering capabilities and validate the derived dynamic model.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
Container cranes belong to the class of underactuated systems for which the design of control law... more Container cranes belong to the class of underactuated systems for which the design of control laws is a challenging task. We study the stabilization of certain modes of a crane system using a method of averaging. Based on the local approximation to the system dynamics by a second order Taylor series expansion, the effects of nonlinear couplings are exploited to steer degrees of freedom, for which no linear actuation is available. Rotations of the load about the vertical axis are analyzed and a control method is derived and tested experimentally.
Underactuated mechanical systems are frequently encountered in several industrial and real-world ... more Underactuated mechanical systems are frequently encountered in several industrial and real-world applications such as robotic manipulators with elastic components, aerospace vehicles, marine vessels, and overhead container cranes. The design of accurate controllers for this kind of mechanical system can become very challenging, especially if a high level of uncertainty is involved. In this paper, an adaptive fuzzy inference system is combined with a sliding mode controller in order to enhance the control performance of uncertain underactuated mechanical systems. The proposed scheme can deal with a large class of multiple-input-multiple-output underactuated systems subject to parameter uncertainties, unmodeled dynamics, and external disturbances. The convergence properties of the resulting intelligent controller are proved by means of a Lyapunov-like stability analysis. Experimental results obtained with an overhead container crane demonstrate not only the feasibility of the proposed scheme, but also its improved efficacy for both stabilization and trajectory tracking problems.
This paper presents an intelligent controller for uncertain underactuated nonlinear systems. The ... more This paper presents an intelligent controller for uncertain underactuated nonlinear systems. The adopted approach is based on sliding mode control and enhanced by an artificial neural network to cope with modeling inaccuracies and external disturbances that can arise. The sliding surfaces are defined as a linear combination of both actuated and unactuated variables. A radial basis function is added to compensate the performance drop when, in order to avoid the chattering phenomenon, the sign function is substituted by a saturation function in the conventional sliding mode controller. An application of the proposed scheme is introduced for an inverted pendulum, in order to illustrate the controller design method, and numerical results are presented to demonstrate the improved performance of the resulting intelligent controller.
Almost all offshore structures have to be modeled as multibody systems. Only ships or single pont... more Almost all offshore structures have to be modeled as multibody systems. Only ships or single pontoons can be modeled as a single rigid body. The dynamic behavior of the multibody system is significantly influenced by fluid-structure interactions. So far, most available methods for analyzing these interactions are restricted to single bodies, small wave amplitudes and body motions, or both. In the present paper a two-dimensional boundary integral approach with fully nonlinear boundary conditions on the free surface is used to simulate the behavior of elastically coupled floating multibody systems in gravity waves. This method will be applied to analyze the dynamics of two floating bodies moored to a quay. The results of numerical simulations for selected configurations are shown.
Vorspann: Der 3D-Druck erobert die Entwicklungsabteilungen, weil er eine schnelle und flexible Fe... more Vorspann: Der 3D-Druck erobert die Entwicklungsabteilungen, weil er eine schnelle und flexible Fertigung von Prototypen ermöglicht. Wie bei jedem Fertigungsverfahren gibt es auch bei generativen Fertigungsverfahren „Best-Prac- tices”. Während allgemeine Richtlinien zum 3D-Druck- gerechten Konstruieren einen guten allgemeinen Überblick bieten, fehlen bislang Konstruktionsrichtlinien für die Dichtheit der gedruckten Teile. Einflussfaktoren wie Druck oder auch die Materialeigenschaften beeinflussen die Dichtheit eines Systems aus 3D-gedruckten Komponenten. Dieser Beitrag stellt eine Vorgehensweise für das 3D-Druck-gerechte Konstruieren vor, um 3D-gedruckte Systeme und Module zu dichten. Die Methoden werden anhand eines Mikro-Autonomen-Unterwasserfahrzeugs aufgezeigt.
The importance of remotely operated underwater vehicles for construction, inspection, and mainten... more The importance of remotely operated underwater vehicles for construction, inspection, and maintenance of off-shore structures has been continuously increasing in the recent years. Especially oil prospecting in water depths inaccessible for human divers (>300m) needs unmanned vehicles. For a great variety of tasks a robust positioning control of the vehicle is required. This control is complicated not only due to nonlinearities involved in the system including the umbilical and parameter uncertainties [1,7] but also because of the lack of precise position information. The positioning problem can be split into two domains: the region far from the structure, where the navigation from the basis ship to the structure takes place and the region close to the structure, where the position of the vehicle relative to the structure must be kept for a task to be performed.
Problems (Monadologie) und der Theodi zee in der Philosophie und Theologie wurde er berühmt. Er s... more Problems (Monadologie) und der Theodi zee in der Philosophie und Theologie wurde er berühmt. Er stand mit zahlreichen internationalen Gelehrten seiner Zeit in Kontakt, war auch politisch eine // Vorwort 8 // Hamburger Akademievorträge 1 / Gottfried Wilhelm Leibniz einflussreiche Persönlichkeit und Initiator und erster Präsident einer Gelehrten-Gesellschaft, nämlich der Kurfürstlich Bran den burgischen Sozietät der Wissenschaften, der Vorläuferin der heutigen Berlin-Brandenburgischen Akademie der Wissenschaften. Leibniz verfasste wichtige Beiträge für die Natur-und Technik wissenschaften und legte die mathematische Grundlage für binäre Rechen maschinen. Er sorgte als Leiter der Herzog-August-Bibliothek in Wolfen büttel dafür, dass dort der erste alphabetische Katalog angelegt wurde, und war Pionier der Windkraft und weiterer Ingenieurleistungen sowie ganz lebenspraktischer Einrichtungen für das Gemeinwohl, wie zum Beispiel einer Brandkasse. Um solche, zum Teil zwar weniger bekannte, aber bis heute aktuelle Facetten von Leibniz' Schaffen und Wirken geht es auch in den Kapiteln dieses Bandes. Mit der bereits erwähnten Brandkasse und mit Leibniz' Studien zur Versicherungs-und Finanzmathematik befasst sich Eberhard Knobloch in seinem Beitrag. Wie sehr Leibniz die moderne Geschichts forschung durch Quellenstudium geprägt hat, legt Nora Gädeke dar. Über Leibniz' objektbezogenes Denken, seine lebenslange Betonung der Wichtigkeit von Kunstkammern, berichtet Horst Bredekamp, und last but not least macht Thomas Sonar im letzten Kapitel des Bandes den Ver such einer ausgewogenen Beurteilung des berühmt-berüchtigten "Pri o ri tätsstreites" zwischen Newton und Leibniz. Allen Autoren gilt mein Dank für ihre Vorträge und deren Ausarbeitung zu Beiträgen in diesem Band. Organisiert wurde die sehr erfolgreiche Vorlesungsreihe von der Akademie-Arbeitsgruppe "Wissenschaftsgeschichte", allen voran von ihrer Sprecherin Edwin J. Kreuzer / Vorwort // 9 Karin Reich, der ich dafür an dieser Stelle ganz be son ders danken möchte. Mein Dank geht auch an die Natur wissen schaft lerin und Malerin Bärbel Jürgens. Eine kleine Ausstellung ihrer Bilder begleitete die gesamte Vorlesungsreihe in den Baseler Hof Sälen. Zu unserer großen Freude hat sie uns ihre Werke zu Leibniz auch für die Illustration dieses Bandes zur Verfügung gestellt. In ihren Bildern verbindet sie, an geregt durch wissenschaftsgeschichtliche Studien an der Hamburger Uni versität, Kunst und Mathematik. Seit 1990 widmet sie sich neben ihrem Beruf als Chemikerin intensiv der Malerei. Fasziniert besonders von der Vielseitigkeit des Universalgenies Leibniz visualisiert sie seine mathe ma tischen, technischen und philosophischen Überlegungen puzzleartig durch Bearbeitung alter Gemälde in Siebdrucktechnik auf Leinwand und Papier. Dank gebührt auch Elke Senne für die umfangreiche redaktionelle Betreuung des Bandes. Und schließlich möchte ich auch Hamburg University Press, dem Verlag der Staats-und Universitätsbibliothek Hamburg Carl von Ossietzky, nament lich Tobias Buck und Isabella Meinecke, sowie der Grafikerin Christine Klein, Büro für Gestaltung, danken. Sie haben uns bei der technischen und optischen Gestaltung dieser neuen Publikationsreihe vor dem Hintergrund der Entwicklung einer Open-Access-Strategie für die Akademie und ihrer Einbindung in die "Digitale Stadt" der Freien und Hansestadt Hamburg ganz wesentlich und stets hilfreich beratend unterstützt.
In this paper an automated numericalsymbolical analysis concept for dynamic systems in engineerin... more In this paper an automated numericalsymbolical analysis concept for dynamic systems in engineering mechanics is outlined. Besides the computerized generation of symbolic equations of motion, the subsequent analysis is also performed by means of computer algebra in combination with well-established numerical methods.
In applied mathematics and mechanical engineering we normally think of numerical calculations if ... more In applied mathematics and mechanical engineering we normally think of numerical calculations if computers are involved. Although simulations by means of numerical methods are powerful tools for investigations in mechanics, they do have drawbacks, e.g. finite precision, errors generated when evaluating expressions. General global results or proofs of theoretical results cannot be obtained from simulations.
The nonlinear dynamic responses of moored crane vessels to regular waves are investigated experim... more The nonlinear dynamic responses of moored crane vessels to regular waves are investigated experimentally and theoretically. The main subject of interest are nonlinear phenomena like bifurcations and the existence of multiple attractors. In the experimental part of the work, a moored model of a crane vessel has been excited by regular waves in a wave tank. A special mechanism has been developed to model the nonlinear behavior of real mooring systems. The theoretical part of the work concerns the mathematical modeling of the floating cranes. Two mathematical models of different levels of complexity are presented. Two different tools are used to systematically determine the responses of the systems to periodic forcing of waves. Firstly, the path-following techniques in combination with numerical integration of equations of motion applied to a full nonlinear model give insight into the dynamics in time domain. Secondly, the multiple scales method allows for an analytical investigation of simplified nonlinear models in frequency domain. Many results of computations for two crane vessels, barge and ship, are presented. Special attention is paid to oscillations near the frequencies of primary resonances and to subharmonic motions. An excellent agreement is found between the results of time-domain and frequency-domain analysis. The computational examples chosen correspond to the models used not only in the present experiments but in the experiments of others as well. The results presented in the work allow us to draw several important conclusions concerning the dynamic behavior of floating cranes during offshore operations. Both the developed models and the analytical tools can be used to identify the limits of the operating range of floating cranes.
Monitoring missions in confined underwater environments such as nuclear storage ponds or industry... more Monitoring missions in confined underwater environments such as nuclear storage ponds or industry tanks call for highly maneuverable fully autonomous micro underwater robots. In this work, we target this challenging scenario with the new low-cost open-source HippoCampusX platform. We present a modular software and hardware architecture which is easily adaptable to mission specific requirements. Our system is part of the PX4-environment [1] and constitutes PX4’s first underwater extension including a SITL simulation. We conduct a series of experiments to demonstrate HippoCampus’ agile maneuvering capabilities and validate the derived dynamic model.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
Container cranes belong to the class of underactuated systems for which the design of control law... more Container cranes belong to the class of underactuated systems for which the design of control laws is a challenging task. We study the stabilization of certain modes of a crane system using a method of averaging. Based on the local approximation to the system dynamics by a second order Taylor series expansion, the effects of nonlinear couplings are exploited to steer degrees of freedom, for which no linear actuation is available. Rotations of the load about the vertical axis are analyzed and a control method is derived and tested experimentally.
Underactuated mechanical systems are frequently encountered in several industrial and real-world ... more Underactuated mechanical systems are frequently encountered in several industrial and real-world applications such as robotic manipulators with elastic components, aerospace vehicles, marine vessels, and overhead container cranes. The design of accurate controllers for this kind of mechanical system can become very challenging, especially if a high level of uncertainty is involved. In this paper, an adaptive fuzzy inference system is combined with a sliding mode controller in order to enhance the control performance of uncertain underactuated mechanical systems. The proposed scheme can deal with a large class of multiple-input-multiple-output underactuated systems subject to parameter uncertainties, unmodeled dynamics, and external disturbances. The convergence properties of the resulting intelligent controller are proved by means of a Lyapunov-like stability analysis. Experimental results obtained with an overhead container crane demonstrate not only the feasibility of the proposed scheme, but also its improved efficacy for both stabilization and trajectory tracking problems.
This paper presents an intelligent controller for uncertain underactuated nonlinear systems. The ... more This paper presents an intelligent controller for uncertain underactuated nonlinear systems. The adopted approach is based on sliding mode control and enhanced by an artificial neural network to cope with modeling inaccuracies and external disturbances that can arise. The sliding surfaces are defined as a linear combination of both actuated and unactuated variables. A radial basis function is added to compensate the performance drop when, in order to avoid the chattering phenomenon, the sign function is substituted by a saturation function in the conventional sliding mode controller. An application of the proposed scheme is introduced for an inverted pendulum, in order to illustrate the controller design method, and numerical results are presented to demonstrate the improved performance of the resulting intelligent controller.
Almost all offshore structures have to be modeled as multibody systems. Only ships or single pont... more Almost all offshore structures have to be modeled as multibody systems. Only ships or single pontoons can be modeled as a single rigid body. The dynamic behavior of the multibody system is significantly influenced by fluid-structure interactions. So far, most available methods for analyzing these interactions are restricted to single bodies, small wave amplitudes and body motions, or both. In the present paper a two-dimensional boundary integral approach with fully nonlinear boundary conditions on the free surface is used to simulate the behavior of elastically coupled floating multibody systems in gravity waves. This method will be applied to analyze the dynamics of two floating bodies moored to a quay. The results of numerical simulations for selected configurations are shown.
Vorspann: Der 3D-Druck erobert die Entwicklungsabteilungen, weil er eine schnelle und flexible Fe... more Vorspann: Der 3D-Druck erobert die Entwicklungsabteilungen, weil er eine schnelle und flexible Fertigung von Prototypen ermöglicht. Wie bei jedem Fertigungsverfahren gibt es auch bei generativen Fertigungsverfahren „Best-Prac- tices”. Während allgemeine Richtlinien zum 3D-Druck- gerechten Konstruieren einen guten allgemeinen Überblick bieten, fehlen bislang Konstruktionsrichtlinien für die Dichtheit der gedruckten Teile. Einflussfaktoren wie Druck oder auch die Materialeigenschaften beeinflussen die Dichtheit eines Systems aus 3D-gedruckten Komponenten. Dieser Beitrag stellt eine Vorgehensweise für das 3D-Druck-gerechte Konstruieren vor, um 3D-gedruckte Systeme und Module zu dichten. Die Methoden werden anhand eines Mikro-Autonomen-Unterwasserfahrzeugs aufgezeigt.
The importance of remotely operated underwater vehicles for construction, inspection, and mainten... more The importance of remotely operated underwater vehicles for construction, inspection, and maintenance of off-shore structures has been continuously increasing in the recent years. Especially oil prospecting in water depths inaccessible for human divers (>300m) needs unmanned vehicles. For a great variety of tasks a robust positioning control of the vehicle is required. This control is complicated not only due to nonlinearities involved in the system including the umbilical and parameter uncertainties [1,7] but also because of the lack of precise position information. The positioning problem can be split into two domains: the region far from the structure, where the navigation from the basis ship to the structure takes place and the region close to the structure, where the position of the vehicle relative to the structure must be kept for a task to be performed.
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Papers by Edwin Kreuzer