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

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SUMMARY

The discussion centers on using the Nyquist criterion to determine the order of the numerator and denominator of an open loop transfer function W(s). Participants suggest plotting the Nyquist chart to visualize the impact of poles and zeros on system stability. It is established that each pole contributes a maximum of 90 degrees of lag, which is crucial for analyzing the system's behavior. A free Nyquist plotter is recommended for practical experimentation.

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  • Understanding of open loop transfer functions in control systems
  • Familiarity with the Nyquist criterion and its application
  • Basic knowledge of poles and zeros in transfer functions
  • Experience with plotting and interpreting Nyquist charts
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  • Explore the use of Nyquist plotters for control system analysis
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  • Investigate the effects of varying pole and zero configurations on Nyquist plots
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Control system engineers, students studying feedback systems, and anyone involved in analyzing the stability of open loop transfer functions using the Nyquist criterion.

stefaneli
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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.:)
 
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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
 

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