
SC4092: 
Modelling and Nonlinear Systems Theory 
ECTS: 
4 
Responsible Instructor: 
Dr.ing. D. Jeltsema 
Contact Hours / Week x/x/x/x: 
0/4/0/0 
Education Period: 
2 
Start Education: 
2 
Exam Period: 
2, 3 
Course Language: 
English 
Expected prior knowledge: 
Linear algebra, calculus, linear systems and control theory. Basic knowledge of electrical and mechanical is helpful. 
Course Contents: 
Based on the analogies between the physical laws and energy flows of electrical, mechanical, hydraulical, and thermal components, a systematic modelings approach is developed to describe the dynamic behavior of a large class of physical systems. The resulting nonlinear differential equations are represented as nonlinear state space models and are used to study various qualitative aspects. The first fundamental topic to be treated is concerned with the study of the system"s internal behavior via Lyapunov stability theory. The extension of Lyapunov stability theory to systems with inputs and outputs will be accomplished by the introduction of the concept of dissipative systems. The two main examples of dissipative systems are passive systems and nonlinear control systems having finite inputoutput L2induced norm. Important results, such as the smallgain theorem, are highlighted and implications towards the stability analysis of largescale physical systems, as well as to the robustness of stability with respect to unmodeled dynamics are discussed. Another main topic concerns the extension of the controllability and observability concepts to nonlinear control systems. The key ingredients to analyze controllability of a nonlinear system are the socalled Lie brackets of the associated system vector fields. Observability can be analyzed by considering the (repeated) Lie derivatives of the output mapping with respect to the system vector fields. The necessary mathematical preliminaries are introduced during the lectures. In the last part of the course, the problem of transforming a nonlinear control system by feedback transformations and the choice of state space coordinates into a linear control system is discussed. It turns out that for controllable systems an elegant ‘if and only if’ condition can be given, stated in terms of the involutivity of certain Lie bracket expressions of the system vector fields. Applications with respect to control problems such as tracking of desired output trajectories will be provided. All topics will be illustrated by examples from various application domains, in particular actuated mechanical systems (robotics), electrical circuits (power converters), mechatronics (electric and magnetic transducers), hydraulic systems (interconnected tanks) and process (heat exchanger) systems. 
Study Goals: 
The purpose of the course is to introduce the students to basic concepts and results in physical modeling and the theory of nonlinear control systems. After successful completion of the course, the student is able to  construct models of systems from the knowledge of physics, with an emphasize on the internal energy of the system.  write models of systems described by differential and algebraic equations in a control systems form.  distinguish between linear and nonlinear systems properties.  decide when to apply the linear and when to apply the nonlinear theory.  determine several stability properties for nonlinear systems.  apply dissipativity and passivity concepts for stabilization and to analyze inputoutput stability.  determine controllability and observability properties for nonlinear systems.  design linearizing feedback transformations. 
Education Method: 
Lectures, instructions, self study assignments, discussion forum. 
Literature and Study Materials: 
Reader + hand outs 
Assessment: 
Case study + homeworks + written exam 
