Nichols plot

The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols.Allen Stubberud, Ivan Williams, and Joseph DeStefano, ''Shaums Outline Feedback and Control Systems'', McGraw-Hill, 1995, ch. 17 It plots the phase response versus the response magnitude of a transfer function for any given frequency, and as such is useful in characterizing a system's frequency response.

Use in control design

Given a transfer function,

:$G(s) = \frac$

with the closed-loop transfer function defined as,

:$M(s) = \frac$

the Nichols plots displays $20 \log_(, G(s), )$ versus $\arg(G(s))$. Loci of constant $20 \log_(, M(s), )$ and $\arg(M(s))$ are overlaid to allow the designer to obtain the closed loop transfer function directly from the open loop transfer function. Thus, the frequency $\omega$ is the parameter along the curve. This plot may be compared to the Bode plot in which the two inter-related graphs - $20 \log_(, G(s), )$ versus $\log_(\omega)$ and $\arg(G(s))$ versus $\log_(\omega)$) - are plotted.

In feedback control design, the plot is useful for assessing the stability and robustness of a linear system. This application of the Nichols plot is central to the quantitative feedback theory (QFT) of Horowitz and Sidi, which is a well known method for robust control system design.

In most cases, $\arg(G(s))$ refers to the phase of the system's response. Although similar to a Nyquist plot, a Nichols plot is plotted in a Cartesian coordinate system while a Nyquist plot is plotted in a Polar coordinate system.

See also

* Hall circles
* Bode plot
* Nyquist plot
* Transfer function

References

External links

Mathematica function for creating the Nichols plot

{{DEFAULTSORT:Nichols Plot
Plots (graphics)
Signal processing
Classical control theory