Modelica Hybrid Modeling and Efficient Simulation

Modelica is an object-oriented language for modeling of large and heterogeneous physical systems. Typical applications include mechatronic models in automotive and aerospace applications involving mechanical, electrical and hydraulic subsystems as well as control systems. Modeling of an ideal diode and Coulomb friction is discussed to illustrate the unique hybrid features of Modelica. The language has been designed to allow tools to generate efficient code automatically. Approaches supported by the Dynamic Modeling Laboratory Dymola from Dynasim are presented. Real-time simulation of an automatic gearbox is discussed to demonstrate the power of symbolic manipulation. A gearbox is inherently hybrid, since the structure varies during each gearshift. Friction is also an important phenomenon. It takes Dymola only a few seconds to translate a Modelica model of an automatic gearbox with 11 switching elements into efficient simulation code. A 500 MHz DEC alpha processor from dSPACE evaluates one Euler step including a possible mode switch in less than 0.18 ms.