Applications of the local state-space form of constrained mechanical systems in multibody dynamics and robotics

This thesis explores several areas in dynamics which can be viewed as applications of the local state-space form of a mechanical system. The simulation of mechanical systems often involves the solution of differential algebraic equations (DAEs). DAEs occur in every mechanism containing kinematic loops. Such systems can be found in a wide range of areas including the aerospace, automotive, construction, and farm equipment industries. The numerical treatment of DAEs is a topic which is relatively recent and continues to be studied. One can regard DAEs as ordinary differential equations (ODEs) on certain invariant manifolds after index reduction. Thus, the numerical solutions of the DAEs can be obtained through integration of their underlying ODEs. In certain circumstances, difficulties may occur since the numerical solutions of the underlying ODE can drift away from the invariant manifold. In this thesis, the underlying ODEs are locally transformed into ODEs of minimal dimension via local parameterizations of the invariant manifold. By their nature, such ODEs are local and implicit, but their solutions do not suffer from the drift phenomenon. Since the states of these minimal ODEs are independent, they are known as a local state-space form of the equations of motion. This work focuses on generalizing the application of the local state-space form and applying it towards problem areas in multibody dynamics and robotics. The first application of the local state-space form is in deriving a formulation of dynamics called the Singularity Robust Null Space Formulation. This formulation utilizes several aspects of the singular value decomposition for an approach which is efficient, does not fail at singularities, and is better suited than most near singularities. The second application area in this work is the study of the linearized mechanical system. Since the linearized model is also useful in optimization and implicit integration problems, an efficient recursive algorithm for its construction is derived. The algorithm appeals to a formulation of the dynamics found in robotics to ease in a coherent derivation

Numerical Methods for Scenario Tree Nonlinear Model Predictive Control

In this thesis we propose new methods in the field of numerical mathematics and stochastics for a model-based optimization method to control dynamical systems under uncertainty. In model-based control the model-plant mismatch is often large and unforeseen external influences on the dynamics must be taken into account. Therefore we extend the dynamical system by a stochastic component and approximate it by scenario trees. The combination of Nonlinear Model Predictive Control (NMPC) and the scenario tree approach to robustify with respect to the uncertainty is of growing interest. In engineering practice scenario tree NMPC yields a beneficial balance of the conservatism introduced by the robustification with respect to the uncertainty and the controller performance. However, there is a high numerical effort to solve the occuring optimization problems, which heavily depends on the design of the scenario tree used to approximate the uncertainty. A big challenge is then to control the system in real-time. The contribution of this work to the field of numerical optimization is a structure exploiting method for the large-scale optimization problems based on dual decomposition that yields smaller subproblems. They can be solved in a massively parallel fashion and additionally their discretization structure can be exploited numerically. Furthermore, this thesis presents novel methods to generate suitable scenario trees to approximate the uncertainty. Our scenario tree generation based on quadrature rules for sparse grids allows for scenario tree NMPC in high-dimensional uncertainty spaces with approximation properties of the quadrature rules. A further novel approach of this thesis to generate scenario trees is based on the interpretation of the underlying stochastic process as a Markov chain. Under the Markovian assumption we provide guarantees for the scenario tree approximation of the uncertainty. Finally, we present numerical results for scenario tree NMPC. We consider dynamical systems from the chemical industry and demonstrate that the methods developed in this thesis solve optimization problems with large scenario trees in real-time

Froth across the Universe Dynamics and Stochastic Geometry of the Cosmic Foam

A review on the properties and dynamical origin and nature of the cosmic foam, the tenuous space-filling frothy network permeating the interior of the Universe. We discuss the properties of this striking and intriguing pattern, describing its observational appearance, and seeking to elucidate its dynamical origin and nature. An extensive discussion on the gravitational formation and dynamical evolution of weblike patterns puts particular emphasis on the formative role of the generic anisotropy of the cosmic gravitational force fields. These tidal fields play an essential role in shaping the pattern of the large scale cosmic matter distribution. Special attention is put on a geometrical and stochastic framework for a systematic evaluation of its fossil information content on the cosmic structure formation process. Its distinct geometric character and the stochastic nature provides the cosmic web with some unique and at first unexpected properties. The implications for galaxy clustering are discussed on the basis of its relevant branch of mathematics, stochastic geometry. Central within this context are Voronoi tessellations, which have been found to represent a surprisingly versatile model for spatial cellular distributions.Comment: Invited review, Proceedings 2nd Hellenic Cosmology Workshop, eds. M. Plionis, S. Cotsakis, I. Georgantopoulos, Kluwer, 153 pages, 56 figures. Full resolution version available at http://www.astro.rug.nl/~weygaert/tim1publication/weyhellas2001.ps.g

Iowa State University, Courses and Programs Catalog 2014–2015

The Iowa State University Catalog is a one-year publication which lists all academic policies, and procedures. The catalog also includes the following: information for fees; curriculum requirements; first-year courses of study for over 100 undergraduate majors; course descriptions for nearly 5000 undergraduate and graduate courses; and a listing of faculty members at Iowa State University.https://lib.dr.iastate.edu/catalog/1025/thumbnail.jp

Modelling of power electronics controllers for harmonic analysis in power systems

The research work presented in this thesis is concerned with the modelling of this new generation of power electronics controllers with a view to conduct comprehensive power systems harmonic analyses. An issue of paramount importance in this research is the representation of the self-commutated valves used by the controllers addressed in this work. Such a representation is based on switching functions that enable the realization of flexible and comprehensive harmonic models. Modularity is another key issue of great importance in this research, and the model of the voltage source converter is used as the basic building block with which to assemble harmonic models of actual power systems controllers. In this research the complex Fourier series in the form of operational matrices was used to derive the harmonic models. Also, a novel methodology is presented in this thesis for conducting transient analysis of electric networks containing non-linearities and power electronic components. The methodology is termed the extended harmonic domain. This method is based on the use of time-dependent Fourier series, operational matrices, state-space representation and averaging methods. With this method, state-space equations for linear circuit, non-linear circuits, and power electronics controllers models are obtained. The state variables are the harmonic coefficients of x(t) instead of x(t) itself. The solution of the state-space equations gives the dynamic response of the harmonic coefficients of x(t). Moreover, a new harmonic power flow methodology, based on the instantaneous power flow balance concept, the harmonic domain, and Newton-Raphson method, is developed and explained in the thesis. This method is based on the instantaneous power balance as opposed to the active and reactive power balance, followed by traditional harmonic power flow methods. The power system and the power electronics controllers are modelled entirely in the harmonic domain

Interjurisdictional Competition and Public-Sector Modernisation - Theory and Empirics

This dissertation analysis the consequences of interjurisdictional competition for a mobile tax base for the efficiency of the public sector and the growth potential of a jurisdiction.Diese Dissertation untersucht die Konsequenzen des Standortwettbewerbs um eine mobile Steuerbasis für die Effizienz der öffentlichen Verwaltung und das Wachstumspotential einer Volkswirtschaft oder einer Region