Course objectives

The course is aimed to deepen the concepts of dynamic modelling and simulation, and to explain the architecture of the most popular relevant software tools. To be more specific, the course is aimed to provide students with the skills needed to address problems of modeling and simulation of complex engineering systems. The first part will be dedicated to illustrate the causal approach to modeling, on which probably the most widespread simulation tool is based: Simulink. The second part of the course will be devoted to introducing the acausal approach, based on object oriented programming concepts, languages and tools. In particular, in this second part, the characteristics of the modeling language Modelica will be illustrated, now standard "de facto" for the modular, multi domain modelling, as well as the architecture of its most widespread interpreter: Dymola. The characteristics of the simulation environments will be illustrated in reference to some application cases.

Course plan

Lessons

1. Introduction.
2. Causal approach.
2.1 ODE systems.
2.2 Theorem of global existence and uniqueness of an IVP: hypothesis.
2.3 Theorem of global existence and uniqueness of an IVP: thesis.
2.4 Numerical integration and stability of the solution of an IVP.
2.5 Elementary methods.
2.5.1 Forward Euler method.
2.5.2 Consistency and convergence.
2.5.3 0-stability of the forward Euler method.
2.5.4 Region of absolute stability.
2.5.5 Stiffness.
2.5.6 Backward Euler method.
2.5.7 Newton method.
2.5.8 Trapezoid method.
2.5.9 Midpoint methods.
2.6. Managing discontinuities.
2.7 Local error and tolerances.
2.8 Methods of step size selection.
2.9 Higher order methods.
2.9.1 General formulation of Runge Kutta methods.
2.9.2 Accuracy, 0-stability and absolute stability regions of Runge-Kutta methods.
2.9.3 Adams-Bashforth methods.
2.9.4 Adams-Moulton methods.
2.9.5 BDF methods.
2.9.6 0-stability of multistep methods.
2.9.7 Absolute stability of multistep methods.
3. Acausal approach.
3.1 DAE systems.
3.2 Index: examples.
3.3 DAE systems with constant coefficients.
3.4 Index and numerical integration.
3.5 General definition of index.
3.6 Hessenberg forms.
3.7 Coordinate partitioning method.
3.8 BDF methods for DAE systems.
3.9 Runge Kutta methods for DAE systems.
4. Introduction to the Modelica language.
4.1 Classes, connectors, inheritance.
4.2 Algorithms, functions and event models.
4.3 Packages.
5 Modelica code translation.
5.1 Hybrid DAE system.
5.2 Structural analysis.
5.2.1 Bipartite graphs.
5.2.2 Duff Algorithm.
5.2.3 Pantelides theorem.
5.2.4 BLT reordering.
5.2.5 Sargent and Westerberg algorithm.
5.2.6 Algorithm Tarjan (notes).
5.2.7 Tearing.

Exercises

All exercises will be carried out in a computer laboratory.

1. Matlab and elementary methods.
2. Introduction to Simulink.
2.1 Model of discontinuous friction: stick-slip and hunting motion.
2.2 Model of continuous friction: stick-slip and hunting motion.
2.3 Simulation of a double pendulum.
2.4 Simulation of a brushless motor.
3. Introduction to Dymola.
3.1 Simulation of a brushless motor in Dymola.
3.2 Multibody Library.
3.2.1 Simulation of a machine tool in Dymola.

Other informations

Teacher
Prof. FERRETTI Gianni
Tel. 02 2399 3682 or 0372 567745 - E-mail: gianni.ferretti@polimi.it
Course web site
https://beep.metid.polimi.it/

The evaluation will be written, possibly supplemented by an oral examination at the discretion of the teacher.