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Numeric derivation and integration

Numeric derivation and integration

Numeric derivation and integration

I'm looking for a discrete form of derivation and integration to use in a PLC program. I tried with the classic form af these operations but I encountered difficulties in defining time constants for them (Td,Tm, Ti)

RE: Numeric derivation and integration

Suggestion: Please, would you clarify "derivation"? (Derivation of what? Or perhaps "differentiation"?)

RE: Numeric derivation and integration

You are experiencing difficulties because differention and integration are not meant to be used in disrete quantities. They are operations that are used in continous quantities.

RE: Numeric derivation and integration

Thank You for the answers. I'll try to be more speciffic: I have to write the discrete differentiation and integrative for inputs wich are aqiered at a constant sample time. For the derivative I use for the moment the centered discrete differentiation formula. But I need to know how the difference between the time constants I use (1-10 sec) and the sample time (about 5 millisec) influence the result of the operation.

RE: Numeric derivation and integration

Suggestion: Some PLC are programmed in C or C+ or C++ or similar languages. The discrete form of differentiation, i.e. differences, and integration in discrete form are usually done over the Z-transform or Modified Z-transform. The direct discrete integration over inverse differences is usually not applied. The discrete integration is performed in Z-space (image space) and then the results are inverted into original or time domain space. The discrete machines (PC, PLC, discrete automata) are operating in Z-space using discrete (numerical) integrators and discrete (numerical) differentiators.
1. Eliahu I. Jury "Sampled-Data Control Systems," John Wiley  Sons, Inc., 1958
2. E.I. Jury "Theory and Application of the Z-Transform Method," John Wiley & Sons, 1964
for differences and antidifferences

RE: Numeric derivation and integration

Thank's again. After I made the translation  from the Laplace form of the transfer function in the time domain, as an intermediar step, I used afterwards the Z-transform. I will reconsider the whole algoritm again.

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