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PID speed control

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@AndyClegg wrote: 

The sample time should be at very most 0.2x the time constant (*) of the response you want get, but as a guideline I would always aim for 0.04x just so that it can be negligible. (*) - note time constant here is for first order response, so for a more general system rise time = 4 x time constant.

 


Dear Andy, 

 

I am very interested in your statement here which might be the solution of a problem I am facing now.  I hope you can give me some advising. 

 

The sample time should be at very most 0.2x the time constant (*) of the response you want get.

 

I wonder where do you get this coefficient of 0.2? Is it based on your past experiences or theoretical derivation?

 

for a more general system rise time = 4 x time constant.

May I know how do you obtain this coefficient of 4?

 

Based on what you said, rise time is 100x sample rate, may I interpret it as the controller needs to iterate 100 times to make the output reach the desired value? 

 

Looking forward to your reply. 

 

Best Regards,

Jake

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If you sample too slowly it can degrade the closed loop perfomance from the nominal continuous time response - the sampling introduces extra phase shift that can destabilise a control loop. The sample time being at least 5 x faster than system time constant to ensure the sampling doesn't degrade performance significantly. This is more a guideline though I am sure you coud define an exact figure based on a continuous to discrete transformation (s to z).

As noted I woud always try to make sample time x25 faster if you want to ensure the effect of the sample time is negligble.

 

For a first order system it can be regarded as being in steady state after 4 time constants (it will be about 96% of way there, so not exact). Rise time is usualy defined as time it takes to get from 10-90%, so that could also be about 4 time constants - again not exact but close enough for most tuning requirements.

 

Consultant Control Engineer
www-isc-ltd.com
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hi can you show, diagram block from labview pls

 

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@Silver_Shaper wrote:

Dear Andy and Gerd,

Sorry for keeping this post open for the long duration. 

I have finally done with my PID Speed control and please find the result in the image (sorry for bad quality - its captured in mobile). I am happy with the rise time, overshoot, undershoot, step response (not shown here), ramp response and oscillation/quantization errors.

 

Thanks for all your help and suggestions. I am closing this post. KudosSmiley HappySmiley Happy


It's good Forum etiquette to engage with the community to communicate the actual solution since we were willing to engage with the problem. It's a give and take. Others may well profit from the actual solution you found, turning your post into a source of information rather than a request for help.

 

Please post a description of HOW you solved the problem so that others can share in the outcome.

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