Why Integral part uses forward difference, Derivative part uses backward difference to discretisize PID controller?
Most textbooks only say this without why. I really want to know the reason. Thank you.

 

Qiuqiuaaa... before you fall into a state of math oblivion, like some of Control.Com's pony-tailed members, I suggest you read the book, "Calculus and Pizza", by Clifford A. Pickover.

Regards, Phil Corso

 

My guess is that many practical design books (written by practical people) use that approximation of the D and I parts because are of easy understanding and very straight forward to implement in a computer based control. Other better approximations are not as easy, not well understood by many people and with more deep mathematical basis. By the way PID is easy and discrete PID is still easy to understand using backwards difference based algorithms.

 

because the integral part has the same sign as proportional part, but
the derivative part has inverse sign. The derivative part works against the
proportional part. The more velocity, the more counteraction.
So,
- (PV - SP) = SP - PV

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All the best, Vladimir E. Zyubin