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The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols.cite-ref-1[1]cite-ref-2[2]cite-ref-3[3] 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

• See also

• References

• External links

Given a transfer function,

G ( s ) = Y ( s ) X ( s ) {\displaystyle G(s)={\frac {Y(s)}{X(s)}}}

with the closed-loop transfer function defined as,

M ( s ) = G ( s ) 1 + G ( s ) {\displaystyle M(s)={\frac {G(s)}{1+G(s)}}}

the Nichols plots displays 20 log 10 ⁡ ⁡ ( | G ( s ) | ) {\displaystyle 20\log _{10}(|G(s)|)} versus arg ⁡ ⁡ ( G ( s ) ) {\displaystyle \arg(G(s))} . Loci of constant 20 log 10 ⁡ ⁡ ( | M ( s ) | ) {\displaystyle 20\log _{10}(|M(s)|)} and arg ⁡ ⁡ ( M ( s ) ) {\displaystyle \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 ω ω {\displaystyle \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 10 ⁡ ⁡ ( | G ( s ) | ) {\displaystyle 20\log _{10}(|G(s)|)} versus log 10 ⁡ ⁡ ( ω ω ) {\displaystyle \log _{10}(\omega )} and arg ⁡ ⁡ ( G ( s ) ) {\displaystyle \arg(G(s))} versus log 10 ⁡ ⁡ ( ω ω ) {\displaystyle \log _{10}(\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 ) ) {\displaystyle \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.

• Hall circles

• Bode plot

• Nyquist plot

• Transfer function

cite-note-11. ↑ Isaac M. Howowitz, Synthesis of Feedback Systems, Academic Press, 1963, Lib Congress 63-12033 p. 194-198

cite-note-22. ↑ Boris J. Lurie and Paul J. Enright, Classical Feedback Control, Marcel Dekker, 2000, ISBN 0-8247-0370-7 p. 10

cite-note-33. ↑ Allen Stubberud, Ivan Williams, and Joseph DeStefano, Shaums Outline Feedback and Control Systems, McGraw-Hill, 1995, ISBN 0-07-017052-5 ch. 17

• Mathematica function for creating the Nichols plot