Construct · 1 fields · 2 citations

describing function: a standalone construct

One name. One construct. A landmark on the map.

● anchor · standalone: control theory Nearest construct by meaning·not indexed
describingfunction1 CONSTRUCTDescribing functionSLOTINE · QUASI-LINEAR

A single standalone construct; nearby constructs are located against it in the Collider. Tap a field for its definition, unit, and measures.

Nonlinear control

Treat a nonlinearity as a gain that depends on amplitude

A describing function is an approximate, amplitude-dependent gain that stands in for a static nonlinearity: assuming a sinusoidal input, it is the complex ratio of the fundamental component of the output to the input, letting a nonlinear element be analysed with the frequency-response tools of linear control. Slotine and Li's Applied Nonlinear Control and Khalil's Nonlinear Systems present the method and its central use: predicting the amplitude and frequency of limit cycles from the intersection of the describing function with the linear loop. The referent is this quasi-linear approximation technique, judged by how well its limit-cycle predictions match the true nonlinear behaviour.[1][2]

Unit
The amplitude-dependent complex gain approximating the nonlinearity
Recovery means
Not applicable
Measured by
Applied by locating intersections of the negative-reciprocal describing function with the loop frequency response to predict limit-cycle amplitude and frequency

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Nearby constructs

limit cycle3 fields · 4 citationsinvariant · one construct, three systemsamplitude4 fields · 4 citationsjingle · one word, four constructscomplex4 fields · 4 citationsjingle · one word, four constructs

References

  1. Slotine, J.-J. E., & Li, W. (1991). Applied nonlinear control. Prentice Hall. ISBN 9780130408907
  2. Khalil, H. K. (2002). Nonlinear systems (3rd ed.). Prentice Hall. ISBN 9780130673893

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