science

Nichols plot

Nichols plot is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nichols plot rather than just read about it. In short: The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols.

Key takeaways

Nichols plot belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Nichols plot to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Nichols plot from memory before moving on to harder problems.

Reference excerpt

The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols. It plots the phase response versus the response magnitude of a transfer function for any given frequency, and as such is useful in characterizing a system's frequency response.

Use in control design Given a transfer function,

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

with the closed-loop transfer function defined as,

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

the Nichols plots displays 20 log 10 ⁡ ( | G ( s ) | ) {\displaystyle 20\log _{10}(|G(s)|)} versus arg ⁡ ( G ( s ) ) {\displaystyle \arg(G(s))} . Loci of constant 20 log 10 ⁡ ( | M ( s ) | ) {\displaystyle 20\log _{10}(|M(s)|)} and arg ⁡ ( M ( s ) ) {\displaystyle \arg(M(s))} (so-called Hall circles) are overlaid to allow the designer to obtain the closed loop transfer function directly from the open loop transfer function. Thus, the frequency ω {\displaystyle \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 ) | ) {\displaystyle 20\log _{10}(|G(s)|)} versus log 10 ⁡ ( ω ) {\displaystyle \log _{10}(\omega )} and arg ⁡ ( G ( s ) ) {\displaystyle \arg(G(s))} versus log 10 ⁡ ( ω ) {\displaystyle \log _{10}(\omega )} ) - are plotted. 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. In most cases, arg ⁡ ( G ( s ) ) {\displaystyle \arg(G(s))} refers to the phase of the system's response. Although similar to a Nyquist plot, a Nichols plot is plotted in a Polar coordinate system while a Nyquist plot is plotted in a Cartesian coordinate system.

See also Hall circles Bode plot Nyquist plot Transfer function

References

External links Mathematica function for creating the Nichols plot

Illustrations

Worked examples

Example 1 — a first encounter with Nichols plot

Start with the simplest possible case. Write down what Nichols plot claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nichols plot before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nichols plot ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nichols plot

In research: Nichols plot appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Nichols plot in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Nichols plot is common in secondary-school and first-year university syllabi. It links to neighbouring topics Classical control theory, Plots (graphics), Signal processing, so understanding it makes those chapters shorter.
In everyday life: Look for Nichols plot outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Nichols plot in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Nichols plot means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Nichols plot out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Nichols plot in simple terms?

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

Why does Nichols plot matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Nichols plot?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Nichols plot.