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# Numeric derivation and integration

## Numeric derivation and integration

(OP)
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

(OP)
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.
References:
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
Visit
http://www.webpearls.com/hypergeo/hgf_l08.html
for differences and antidifferences

### RE: Numeric derivation and integration

(OP)
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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