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Design >> Analog Design >> how to understand pole at RHP
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Message started by Jacki on Feb 19^th, 2018, 1:19am

Title: how to understand pole at RHP
Post by Jacki on Feb 19^th, 2018, 1:19am

Hi,

If we look at the basic transfer function of a linear system, calculate the magnitude and phase, we can get any real pole (either at LHP or at RHP) will decrease the amplitude by -20dB/dec in the bode plot, but the phase shift the one at LHP is -90, and at RHP is +90. From here, we can see to stabilize a system, a pole at RHP is good.
But if we look at the time domain, pole at RHP will oscillate (of course t->infinite, and frequency ->0), and definitely it is not good for a stable system.
Can anybody show me how to plot a bode plot with a RHP pole, and how to understand it physically? How to generate a RHP pole?
Thank you.

Title: Re: how to understand pole at RHP
Post by kabir_fakir on Feb 19^th, 2018, 3:35am

Jacki wrote on Feb 19^th, 2018, 1:19am:

Hi,

Can anybody show me how to plot a bode plot with a RHP pole, and how to understand it physically? How to generate a RHP pole?
Thank you.

I always understand poles/zero by the root locus. You can also think of zero as the RHP. RHP behaves the same as zero behaves in the system.
Here is very nice handout from the MIT
http://web.mit.edu/2.14/www/Handouts/PoleZero.pdf
Have a look to understand the behaviour of poles/zero in time domain as well in the frequency domain.
And if you wanted to generate the RHP then its equivalent to saying to have a transfer function with a zero. You can make any transfer function with help of resistor and cap in cadence or can directly do in MATLAB.

Hope it will help you.

Title: Re: how to understand pole at RHP
Post by Jacki on Feb 19^th, 2018, 3:45am

Hello kabir_fakir,

Thank you for your reply. Actually my question is based on the link you post. I am just a bit confused how to understand the pole at RHP in both frequency and time domain. If we only consider the real pole, definitely the amplitude of the transfer function will decrease by -20dB/dec, but in time domain it will rise (for conjugate poles at RHP, it will oscillator). That's why I am curious how the plot of pole at RHP looks like.

Title: Re: how to understand pole at RHP
Post by kabir_fakir on Feb 19^th, 2018, 4:24am

Here is the nice animation which shows how the pole location(from LHP to RHP) in s-domain corresponds to the time domain response.
https://www.youtube.com/watch?v=PybGMXKTp7c

I am pretty much sure you can plot this in MATLAB or in control system tool.
Is that what you were looking for?

Moreover, for more deeper understanding in fequency domain,with illustration follow this link. He explanation is quite lucid.
https://www.youtube.com/watch?v=8jNjVkoZQCU

All the best.

Title: Re: how to understand pole at RHP
Post by A Kumar R on Feb 20^th, 2018, 3:54am

Hi Jacki,

Can you please let me know what kind of systems can generate a pole in the right hand plane?

Title: Re: how to understand pole at RHP
Post by nrk1 on Feb 23^rd, 2018, 9:04am

There are two parts in the response to a linear system. 1) Steady-state response, and 2) Natural response. What you plot in the Bode plot is the sinusoidal steady-state response. i.e. change in magnitude and phase that a sinusoidal input undergoes. For LHP and RHP pole at the same frequency, the magnitude of this will be the same and the phase will be of opposite polarity. The natural response of an LHP pole eventually dies out and you see the steady-state response. The natural response of an RHP pole blows up and overwhelms the steady-state response.

Title: Re: how to understand pole at RHP
Post by Jacki on Feb 28^th, 2018, 11:30pm

Hi kabir_fakir, thank you for your link, I will look at them in details later.
Hi nrk1, thank you for your explanation, now I think I get the point, not confused. The pre-condition to consider the bode plot is very important.

Title: Re: how to understand pole at RHP
Post by deba on Mar 1^st, 2018, 4:30am

If there are RHP poles, the closed loop stability should be analyzed using Nyquist criteria. As mentioned BODE plot is only for analyzing sinusoidal steady state response.

Title: Re: how to understand pole at RHP
Post by Jacki on Mar 11^th, 2018, 5:52am

Hi deba,

Thank you very much. I forgot the basic condition. For a system with a pole on RHP, it will not be used in the bode plot.

Title: Re: how to understand pole at RHP
Post by subtr on Mar 20^th, 2018, 11:54pm

Have you seen how a back to back connected inverter works? From the mid point, a small differential input will cause the whole system to switch to one direction. That's the example of a simple real pole at RHP. The real part of the pole being in the right hand side causes the output to bloat.