Nichols plot

A Nichols plot.

TheNichols plotis aplotused insignal processingandcontrol design,named after American engineerNathaniel B. Nichols.

Use in control design

Given atransfer function,

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

with theclosed-loop transfer functiondefined as,

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

the Nichols plots displays$20\log _{10}(|G(s)|)$versus$\arg(G(s))$.Loci of constant$20\log _{10}(|M(s)|)$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 theBode plotin which the two inter-related graphs -$20\log _{10}(|G(s)|)$versus$\log _{10}(\omega )$and$\arg(G(s))$versus$\log _{10}(\omega )$) - are plotted.

Infeedback 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 thequantitative 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 aNyquist plot,a Nichols plot is plotted in aCartesian coordinate systemwhile a Nyquist plot is plotted in aPolar coordinate system.

See also

• Hall circles
• Bode plot
• Nyquist plot
• Transfer function

External links

• Mathematica function for creating the Nichols plot