Nichols plot

The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols.

Given a transfer function,

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

with the closed-loop transfer function defined as,

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

the Nichols plots displays ${\displaystyle 20\log _{10}(|G(s)|)}$ versus ${\displaystyle \arg(G(s))}$. Loci of constant ${\displaystyle 20\log _{10}(|M(s)|)}$ and ${\displaystyle \arg(M(s))}$ are overlaid to allow the designer to obtain the closed loop transfer function directly from the open loop transfer function. Thus, the frequency ${\displaystyle \omega }$ is the parameter along the curve. This plot may be compared to the Bode plot in which the two inter-related graphs - ${\displaystyle 20\log _{10}(|G(s)|)}$ versus ${\displaystyle \log _{10}(\omega )}$ and ${\displaystyle \arg(G(s))}$ versus ${\displaystyle \log _{10}(\omega )}$) - are plotted.

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