Nichols plot

A Nichols plot.

The Nichols plot is a plot used in signal processing and control design ^{[1] [2] [3]}.

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 20log ₁₀( | G(s) | ) versus arg(G(s)). Loci of constant 20log 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 ω is the parameter along the curve. This plot may be compared to the Bode plot in which the two inter-related graphs - 20log ₁₀( | G(s) | ) versus log ₁₀(ω) and arg(G(s)) versus log ₁₀(ω)) - are plotted. Note that the decibel convention shown above, 20log ₁₀ is not unique; another convention sometimes used is 10log 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

References

1. ^ Isaac M. Howowitz, Synthesis of Feedback Systems, Academic Press, 1963, Lib Congress 63-12033 p. 194-198
2. ^ Boris J. Lurie and Paul J. Enright, Classical Feedback Control, Marcel Dekker, 2000, ISBN 0-8247-0370-7 p. 10
3. ^ Allen Stubberud, Ivan Williams, and Joseph DeStefano, Shaums Outline Feedback and Control Systems, McGraw-Hill, 1995, ISBN-10: 0070170525 ch. 17