# Nyquist Criterion: Determine Order of Open Loop Transfer Function W(s)

• stefaneli
In summary, the possibility of using the Nyquist criterion to determine the difference between the order of numerator and denominator of open loop transfer function W(s) is uncertain due to the complexity of the system. However, one possible way to investigate this is by plotting Nyquist charts for different examples and analyzing the changes in the plot as poles and zeros are introduced. A free Nyquist plotter is available online for this purpose. Ultimately, more research and experimentation is needed to fully understand this concept.
stefaneli
I was wondering if it's possible to know the difference between order of numerator and order of denumerator of open loop transfer function W(s) using Nyquist criterion ('stable' poles/zeros are bothering me; basically is there a way to find out a number of poles and zeros of W(s))? I hope I've explained my problem good enough...Any help is appreciated.:)

Perhaps if you plot the Nyquist chart for some examples you concoct you might be able to answer this. Start off with a few poles, then introduce a zero midway between the poles and see what changes on the Nyquist plot, and so on. (Bear in mind that each pole contributes at most 90 degrees of lag.) If you search online I bet you'll find a free Nyquist plotter.

I'm not pretending to know the answer; but that's how I would go about investigating it. Good luck!

Here's a basic free plotter. Having played around with it, I don't think Nyquist alone is going to help with what you asked. http://www.facstaff.bucknell.edu/mastascu/eControlHTML/Problems/Freq/Interactive/Freq6NyquistP01Int.htm

## 1. What is the Nyquist Criterion?

The Nyquist Criterion is a mathematical tool used to determine the order of an open loop transfer function by analyzing its frequency response.

## 2. How does the Nyquist Criterion work?

The Nyquist Criterion involves plotting the frequency response of the open loop transfer function on a complex plane and examining the behavior of the plot as the frequency approaches infinity. The number of encirclements around the -1 point on the plot can determine the order of the transfer function.

## 3. Why is it important to determine the order of an open loop transfer function?

Determining the order of an open loop transfer function is important because it can provide valuable information about the system's stability and performance. It can also help in designing appropriate control strategies for the system.

## 4. Can the Nyquist Criterion be used for any type of transfer function?

Yes, the Nyquist Criterion can be used for any open loop transfer function, whether it is a single-input single-output (SISO) or a multiple-input multiple-output (MIMO) system.

## 5. Are there any limitations to using the Nyquist Criterion?

Yes, the Nyquist Criterion assumes that the open loop transfer function is stable and that its frequency response can be plotted on a complex plane. It may not be applicable for systems with unstable or non-linear transfer functions.

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