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I have a robotic system I'm controlling with Arduino, is there an heuristic way to determine a proper sampling time for my PID controller? Considering I have some other things to compute on my sketch that require time, but of course a good sampling time is crucial.

Basically I have a distance sensor that needs to detect at a constant rate an object that is moving, sometimes slow, sometimes fast. I don't have a good model of my system so I can't actually tell the physical frequency of the system.

Gian Mauro Musso
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    It really depends on what it is your PID is controlling and how fast that device responds to changes. For instance, controlling a heater you can get away with sampling periods in the order of seconds. – Majenko Nov 28 '15 at 13:07
  • Look up Nyquist frequency. Essentially you just need to worry about how the frequency of your system relates to the sampling frequency. If you want to control something to respond in 0.1 s and you are sampling at 1 Hz, then you won't get a good response (in fact, it will likely become unstable). As Majenko's comment mentions, figure out what response time you want for your controller, then choose an appropriate sampling frequency that is say 10 times the desired frequency (so if you want 0.1 s response time, then use 100 Hz). – Brian Lynch Dec 04 '15 at 01:30

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In order to properly sample a system you need to be sampling at least as fast as the Nyquist rate, which is twice as fast as the response rate of the system, preferably faster. You can do a lot of math to find out how fast is fast enough (I suggest Ogata), or go with the rule of thumb, 5-10x the system frequency.

Since you are detecting the rate that an object is moving, you need to sample it fast enough to see it move no more than the minimum you care about.

As an example, lets say your maximum rate is 100mm/s, and you want an accuracy of 1mm.

In this case, to see the object move no more than 1mm, you would need to sample at 2 x (max speed / accuracy) = 2 x (100mm/s / 1mm) or 200Hz minimum, and preferably you would be sampling at 500-1000Hz per the rule of thumb.

Mark Booth
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carmiac
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    Welcome to robotics carmiac. I presume that you mean Katsuhiko Ogata, but you might want to edit your answer to mention the specific book you are referring to. – Mark Booth Dec 04 '15 at 11:38
  • Thank you for your answer! I was familiar with the Nyquist rate, I was looking for a tecnique to sample a phisical system with no mathematical model and you gave me a good explanation. – Gian Mauro Musso Dec 04 '15 at 19:30
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A simple rule of thump is based on the rise time that you want to achieve. This is basically the time that the final system needs to change form one position to another.

A reasonable choice is a value between 5 and 100 samples within the desired rise time.

The concrete choice may be influenced by a bunch of factors, for example:

  • Method of the controller design
  • available computing power
  • existing disturbances

For a little overview check my article https://www.imt.ch/en/insight/saving-computing-power-with-the-right-choice-of-sampling-time/

Sebastian Süss
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