Nonlinear Control Systems

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Lecture-No.:

105221 / L.104.52280 / L.104.52480

Type of course:

Lecture (2 SWS)

Schedule:

The event takes place in the winter term.

Current schedule of events will be announced in Paul.

Target group:

Students of mechanical engineering, technomathematics, industrial computer sciences, Master.

Requirements / foundation:

Control Engineering, Advanced Control Engineering (formerly Control Engineering 2)

Content:

Introduction

  • Definition of nonlinear systems, types of system equations
  • Typical features of these systems
  • Description and classification of typical nonlinearities

Common analysis methods

  • Linearization around operating points, step-by-step linear approximations
  • Digital simulation, exact solutions

System representation in the phase plane

  • Features and construction of the phase plane
  • Trajectories of linear systems
  • Singular trajectories

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

Stability concept in nonlinear systems

  • Introduction and analysis

Stability on a small scale

  • Methods of local linearization
  • 1st Lyapunov method

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

Objectives:

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.

Text books / further reading:

  • Otto Föllinger: "Nichtlineare Regelungen"