# Is the Nyquist plot useful in actual electrical engineering?

I am currently doing a course on linear control theory, and we are covering Nyquist Plot to study phase and gain margin.

I find myself unable to appreciate this concept. One, the proof of the Nyquist criterion is very non-intuitive to me, something about encircling the origin however many times. Secondly, it is almost never used outside of a course on basic control theory in any other courses I have taken so far. I have asked the teaching assistants for the course and they told me they have never seen any application of the Nyquist plot in real life or in their personal research.

I quickly looked up some potential applications on the Nyquist plot on databases such as IEEE Explore. From 1948 - 2018, only 272 instances where Nyquist plot was used in a published paper

Similarly for Nyquist Diagram

And we are only talking about papers, which are theoretical in nature, and very few of these papers go on to become a useful engineering hardware. Not to say many of these papers are extremely low quality.

By comparison, the much later concept of Linear Matrix Inequality (also used in control theory - which we are not taught) is cited over ten-thousand times.

Some commenter also said that my search result for LMI is biased, because it is more like a math property than a control tool, which may include papers that are not control related. How about "model predictive control"?

I can't help but wonder whether or not the Nyquist plot is even that useful in modern electrical engineering.

Sure, if I wanted to design a circuit with a single capacitor and a single inductor, I could potentially use the Nyquist plot to set the parameters to ensure stability. But in the era of supercomputers, GPUs, CPU with billions of transistors, this entire concept seems to be out-of-date and to put it bluntly, useless.

Has anyone seen a Nyquist plot in the design of an actual control system such as a humanoid robot? For a swarm of quadrocopters? Have anyone used a Nyquist plot in the design of self-driving cars, or rover to Mars? It seems that what we are taught in school have not caught up with real world applications.

Can someone please point to some realistic application of the Nyquist plot and the Nyquist stability criterion (if any)?

• not sure what your question is but Nyquist plots are beyond useful
– user16222
Commented Apr 9, 2018 at 23:11
• Stability margin, frequency response
– user16222
Commented Apr 9, 2018 at 23:18
• That they do not appear in the title or the abstract, but could nonetheless be used inside the papers? Commented Apr 10, 2018 at 0:48
• "Superposition principle" returns 365 results (817 if you search for "superposition" and "principle"). Should we deduce that the superposition principle is almost not used at all? Commented Apr 10, 2018 at 0:54
• My point is that they do not show up because they do not put those words in the title and the abstract. Go to the Advanced search page, and you'll discover that if you search the text you'll find some 25 thousand references for nyquist plots ieeexplore.ieee.org/search/… Commented Apr 10, 2018 at 1:03

(1) The Nyquist plot demonstrates why it is the LOOP GAIN which matters (as far as stability is concerned)

(2) It is the Nyqist plot which explains WHY we have something like a stability limit (application of Cauchy`s residuen theorem)

(3) The stability criteria based on the BODE plot are derived from the Nyquist plot (separate drawing of magnitude and phase)

(4) Only the Nyquist plot shows why we have something like "conditional" stability (open loop transfer function with a pol in the right half plane)

(5) In addition to the phase resp. gain margin we have another margin (combination of both): Vector margin. This margin can be definded and explained only on the basis of the Nyquist plot.

(6) We need the Nyquist plot to find the point (the frequency) where negative feedback turns into positive feedback.

If you plan to master Control Systems that are a lot more complicated than an Op Amp or a SMPS, then you will want to master Nyquist Stability Criteria. But you may not have to do it now, but when someone pays you to use. But then you may not have the time to learn it then, due to time pressures, so if you like it, learn it now.

• Maybe you can link to Brian Douglas in your answer as his videos are extremely helpful in covering the basics of control system theory and you already provided material by him? Personally I think it would add value to the answer. Commented Apr 10, 2018 at 8:30
• I did include the link already. Commented Apr 10, 2018 at 14:44
• but here are more google.com/… Commented Apr 10, 2018 at 14:47

The transfer function of a "system" can be used to generate: -

• A Bode plot (amplitude and phase versus frequency)
• A Nyquist plot (Complex amplitude and phase)

Either can be used to predict the same things except I tend to see real Nyquist plots with missing information i.e. sometimes notes are not added that tell you that a particular "nuance" of the diagram is at such and such a frequency. This can be frustrating.

For this reason I shy away from them and stick with the Bode plot because it expresses everything to me that a Nyquist plot should and also, I prefer working directly with numeric values of: -

• Phase Margin
• Gain Margin

Both of which are directly extractable from the Bode plot.

From 1948 - 2018, only 272 instances where Nyquist plot was used in a published paper

It doesn't surprise me at all but, it would be interesting to compare this with a search for use of bode plots over the same period.

I understand your question as I also use the same reductio ad absurdum technique to stimulate debate. Clearly a Nyquist plot doesn't define the operational characteristics of the 2 million lines of C code for (Mars) Curiosity.

But do can you think of a way of using a billion transistor GPU to double the voltage of a 1MHz sinusoidal small signal? Might stable op amps be more appropriate? And would a simple inductor capacitor arrangement be suitable to smooth the power to your inappropriately specified GPU?

“Small moves, Roy. Small moves.”

• What do you mean by reductio ad absurdum? The Nyquist plot is a graphical method for determining the stability of a system. Do engineers not care about stability when they design transistor circuits or Mars rovers? If they do, and I expect that they do, where are the applications of Nyquist plot for this purpose? Commented Apr 10, 2018 at 0:21
• In searching for system integrity, for systems that do not fail even after 10 years on Mars, understanding the fundamentals ----- the various knobs and levers, and how system degradation may flow over the years ----- and picking operating conditions with high robustness requires a subtle competence. Commented Apr 10, 2018 at 3:47
• even though the models of battery life failed to reach computed lifespan on Mars Commented Apr 10, 2018 at 14:46