Modeling of Electromechanical Systems

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33 1 Page 2. CONTENTS CONTENTS 4 Electromechanical Systems 34 4.1 Introduction . . . . .

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Modeling of Electromechanical Systems
Werner Haas, Kurt Schlacher and Reinhard Gahleitner Johannes Kepler University Linz, Department of Automatic Control and Control Systems Technology Altenbergerstr.69, A—4040 Linz, email: RichODL@mechatronik.uni-linz.ac.at December 20, 2000

Contents
1 Motivation 2 Mechanical Systems 2.1 Derivation of the Lagrange Equations . . . . . 2.1.1 Example I . . . . . . . . . . . . . . . . . 2.1.2 Example II . . . . . . . . . . . . . . . . 2.2 Variational Principle and Lagrange’s Equations 2.3 State Functions . . . . . . . . . . . . . . . . . . 2.3.1 Example I . . . . . . . . . . . . . . . . . 2.3.2 Example II . . . . . . . . . . . . . . . . 2.4 Energy of Mechanical Systems . . . . . . . . . 2.5 Legendre Transformations . . . . . . . . . . . . 2.6 Case Studies . . . . . . . . . . . . . . . . . . . 2.6.1 Atwood’s Machine . . . . . . . . . . . . 2.6.2 Car and Beam . . . . . . . . . . . . . . 2.6.3 Double Pendulum . . . . . . . . . . . . 2.6.4 Bead and Hoop . . . . . . . . . . . . . . 2.6.5 Ball on a Wheel . . . . . . . . . . . . . 2.6.6 Two dimensional truck model . . . . . . 3 Electrical Systems 3.1 Energy and Coenergy of Simple Devices 3.1.1 Static terminals . . . . . . . . . . 3.1.2 Dynamic Devices . . . . . . . . . 3.1.3 Example . . . . . . . . . . . . . . 3.2 Equations of Motion of Simple Networks 3.2.1 Example I . . . . . . . . . . . . . 3.2.2 Example II, Cuk—Converter . . . 3.3 The Energy of Electrical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 5 8 9 9 11 13 15 15 16 17 17 18 18 18 18 18 19 20 20 22 24 24 27 28 33

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