# Modeling and simulation of dynamic systems (MSD)

The goal of the course is to learn together 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, electromagnetic, pieozoelectric, mechanical, hydraulic, pneumatic, thermal, thermofluidic 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 or biological systems, in which the role of energy in coupling the subsystems is taken over information. We will go through three groups of modeling techniques, which are based on energy. First, analytical methods based on the Lagrangian and Hamiltonian functions well known from the studies in theoretical physics and/or mechanics. Second, object-oriented modeling (OOM) as an alternative to the more widespread block-oriented modeling that you know from Simulin. And, above all, an intuitive graphical techniques known as (power) bond graph modeling. Whichever methodology is used to create a mathematical model, one of the ways to analyze the model is through 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.