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Digital PID implementation - considerations

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banh

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site:www.edaboard.com pid+z transform

when implementing PID using microcontroller, there are a few methods, esp. for differentiation and integration.

what are the methods of differentiation ( for e.g. D[n] = e[n]-e[n-1] or e[n]-2[n-1]+e[n-2], etc.) and what are their pros & cons?

what are the methods of integration (summing all errors, or I[n] = I[n-1]+t0*e[t], etc.) and what are their pros & cons ?
 

as far as i know, those that you mentioned are the standard way of implementing differentiation and integration in Digital PID algorithms. Mostly the question in PID or the challenge there is to determine the gain for the integral, derivative, and pro terms.
 

As far as I know, there is only one standard form for implementing differentiators and integrators. But in digital control, we usually find the overall transfer function, then use the inverse Z-transform to get the difference equations.

banh said:
what are the methods of differentiation ( for e.g. D[n] = e[n]-e[n-1] or e[n]-2[n-1]+e[n-2], etc.) and what are their pros & cons?
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The 2nd form is simply a double differentiator (without consideration for the differential gain of course). You can work it out yourself.
 

oh yes, i noticed again the 2nd form of differentiation is double. for differentiation -> noise is amplified. double differentiation -> more noise?
 

I worked through the inverse Z-transform for a digital PID. Hope it will help you.
 

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