Nichols plot

A Nichols plot.

The Nichols plot is a plot used in signal processing and control design .

Use in Control Design

Given a transfer function,

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

with the closed-loop transfer function defined 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 the Bode plot in 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. Note that the decibel convention shown above, $20*log_{10}$ is not unique; another convention sometimes used is $10*log_{10}$.

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.

See also

• Nyquist plot
• Transfer function