Nichols plot

A Nichols plot.

A Nichols plot is a plot used in signal processing and control design . Given a transfer function, $G(s)={\frac {Y(s)}{X(s)}}$, and a closed loop transfer function defined as, $M(s)={\frac {G(s)}{(1+G(s))}}$ , the Nichols chart plots $20*log_{10}(|G(s)|)$ on the y-axis versus $arg(G(s))$ on the x-axis. Loci of constant $10*log_{10}(|M(s)|)$ 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 convention $20*log_{10}$ is shown, but another convention sometimes used is $10*log_{10}$.

This plot is also used in closed loop control systems. In these systems the plot is useful for assessing the stability and robustness of the system. This application of the Nichols plot is central to the Quantitative feedback theory (QFT) of Horowitz and Sidi, a well known method for robust control system design.

See also

• Nyquist plot
• Transfer function