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Analysis of nonlinear systems with the describing function method

Analysis of nonlinear systems with the describing function method

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The describing function (DF) is one method for the analysis of nonlinear systems. The main idea is to study the ratio between a sinusoidal input applied to the system and the fundamental harmonic component of the output. The DF allows the extension of the Nyquist stability criterion to nonlinear systems for detection of limit cycles, namely the prediction of limit cycle amplitude and frequency.

Chapter Contents:

  • 10.1 Fundamentals
  • 10.1.1 List of symbols
  • 10.1.2 The describing function
  • 10.1.3 Describing functions of common nonlinearities
  • 10.1.4 Nonlinear systems analysis
  • 10.2 Solved problems
  • 10.3 Proposed problems
  • 10.4 Describing function method using computer packages
  • 10.4.1 MATLAB
  • 10.4.2 SCILAB
  • 10.4.3 OCTAVE

Inspec keywords: nonlinear systems; stability

Other keywords: describing function method; fundamental harmonic component; limit cycle amplitude; DF method; nonlinear systems; Nyquist stability criterion

Subjects: Stability in control theory; Nonlinear control systems

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