The goal of the course is to teach you how to build control-oriented mathematical models of complex dynamic systems. The focus will be on modeling techniques that can glue together subsystems from diverse physical domains. We will show that the concept of energy (or power), which is universally valid across physical domains, is the right tool for combining electrical, mechanical, hydraulic, pneumatic, thermal and thermodynamic systems. Some of the methods presented in this course will be at least partially useful in the domains where the concept of energy is not so useful such as socio-economic systems. In total we will introduce three groups of modeling techniques, which are based on the concept of energy. Analytical methods based on the Lagrangean and Hamiltonian functions well known from the studies in theoretical physics and/or mechanics, object-oriented modeling as an alternative to the more widespread block-oriented modeling, and last but not least an intuitive graphical techniques known as bond graph modeling. Whichever methodology is followed to create the mathematical model, of of the ways to analyze it is a numerical simulation, that is, numerical solution of the corresponding differential or differential-algebraic equations. In this course we will be exposed to the basics of numerical techniques for differential and differential-algebraic equations with the objective to understand the basic issues such as approximation errors, numerical stability and suitability of the common methods for different classes of models.
1.) Overview of formats of mathematical models of dynamical systems; partially a recap and partially new
2.) Basic concepts and components for modeling using bond graphs. Simple examples for electrical, mechanical and hydraulic systems
3.) Modeling simple systems using bond graphs; adding causal strokes and extracting a signal model from a bond graph
4.) Obtaining state-space quations from causal bond graphs; further examples of modeling using bond graphs; reductions of bond graphs
5.) Introduction to the Lagrange methodology
6.) Using Lagrange methodology to model multibody mechanical systems
7.) Examples of modeling and simulation projects from industry.
8.) Software for modeling and simulation of dynamic systems
9.) Hybrid dynamic systems
10.) Thermal systems modeled using bond graphs
11.) Algorithms and concepts of numerical simulation of dynamical systems
12.) Algorithms and concepts of numerical simulation of dynamical systems
13.) Modeling distributed parameter systems using bond graphs
The exercises will be dedicated to the work on assigned projects.