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[SP500]

I've been trying to find out how the Kc', Ti ' and Td' values (constants of PID function integration with trapezium rule) can be determined knowing Kc, Ti and Td (constants of PID function integration with rectangular rule). I've attached a copy of the problem I've been trying to solve.

 

I found a book saying that all that has to be done is equate the coefficients of En , En-1 and En-2, which is exactly what I have been trying to do. What i've done is multiply out all the terms, and then gather the terms En, En-1 and En-2 for both of the above equations and then equated them, but this doesn't work out.

Attached Files

•  Tuning Constant Derivation.png   241.87KB   1 downloads

Edited by SP500, 16 April 2017 - 06:03 AM.