Basics in Dynamical System Modelling

Abstract

In this chapter, we propose a graded approach to modelling, and we recall some principles that allow the design of mathematical models for a large class of dynamical systems. A mathematical model is a first step on the path leading to the design of a control law. In practice, a control law is an algorithm which is adapted to a mathematical representation of the system to be controlled. We intend to provide the readers with tools allowing to obtain such a representation, and we refer them to specialized literature on the subject for complements. Due to their importance, we first describe mathematical expressions of balance equations in § 1.2, together with general principles to obtain additional phenomenological laws. Basic laws and principles of Physics are discussed in § 1.3, and applications in solid mechanics, fluid mechanics and electricity are provided in § 1.4.