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Instructors: Prof. Dr. Ansgar Trächtler
Event type:
Lecture
Org-unit: Maschinenbau
Displayed in timetable as:
NL
Hours per week:
2
Language of instruction:
German
Min. | Max. participants:
- | -
Requirements and recommendations:
Control Engineering, Advanced Control Engineering
Aim of the event:
The lecture is to impart the fundamentals of the analysis of nonlinear systems. On the basis of a classification of dynamical systems and related examples, different analysis methods for the computation of phenomena occurring in nonlinear systems will be dealt with. The stability features of such systems will be dealt with extensively. Thus, we are going to impart an understanding of the behaviour of nonlinear systems and present the mathematical aspects of dealing with these systems.
Target group:
Mechanical engineering
Techno-mathematics,
Information science in engineering,
Master
Contents:
1. Introduction
- Definition of nonlinear systems, types of system equations
- Typical features of these systems
- Description and classification of typical nonlinearities
2. Common analysis methods
- Linearization around operating points, step-by-step linear approximations
- Digital simulation, exact solutions
3. System representation in the phase plane
- Features and construction of the phase plane
- Trajectories of linear systems
- Singular trajectories
4. Harmonic linearization
- Derivation and computation of the description function
- Stability of oscillatory states in nonlinear control loops
- Transfer behaviour, step phenomena in nonlinear control loops
- Harmonic balance, considerations of energy
5. Stability concept in nonlinear systems
- Introduction and analysis
6. Stability on a small scale
- Methods of local linearization
- 1st Lyapunov method
7. Stability on a large scale
- 2nd Lyapunov method, Lyapunov functions, transmission behaviour
- Autonomous linear systems
- Design of nonlinear controllers by means of the 2nd Lyapunov method
Contact person:
Julia Timmermann
Literature:
O. Föllinger: Nichtlineare Regelungen
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