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PID Math

Created by: Dkrills at: 8/26/2022 12:07 PM (2 Replies)

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8/26/2022 12:07 PM	Rate (0)
Dkrills Regular Member Joined: 7/28/2022 Last visit: 9/27/2022 Posts: 14 Rating: (0)	I know this isnt the proper place to post but just wanted to ask about PID math so I understand PID's better. I understand that for the Proportional part of its just the gain*(setpoint-process value). My question come with the integral The equation is My question is the integral always taken from time 0 to current time? What is e of (e dt)? Ti is the reset time correct? How does the integral output eventually become steady when the integral goes to zero? I've heard people say there's memory of some sort but i dont see how that is in equation? D

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9/6/2022 7:33 AM	Rate (0)
jacek d Platinum Member Joined: 9/23/2005 Last visit: 9/5/2025 Posts: 5112 Rating: (768)	Dkrills My question is the integral always taken from time 0 to current time? It's just a convention. Time = 0 is when you start integration, not when the Big Bang happed. Dkrills What is e of (e dt)? e (error) = setpoint - process value Dkrills Ti is the reset time correct? Yes. Dkrills How does the integral output eventually become steady when the integral goes to zero? It's not an integral which goes to 0, it's integrated function which does this. Dkrills I've heard people say there's memory of some sort but i dont see how that is in equation? Because you are looking at some math symbols which do not tell you how to calculate it numerically.
	Regards, Jacek What is confusing you is the fact that you never see a number but always its digit representation. So you end up thinking that the number is the representation. - Andrej Bauer Any claims against me - based on whatever legal reason - resulting from the use of any code and/or ideas presented on this forum shall be excluded. #StayWithUkraine
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9/8/2022 12:14 PM	Rate (0)
hdhosseini Diamond Expert Joined: 1/28/2009 Last visit: 8/31/2025 Posts: 6874 Rating: (1368)	Dear users, The basic concept of numeric Integral calculation is simple. We need a cyclic program execution in constant intervals dt(OB3X) , read the current value of signal in interest e(error in this example). We form a rectangle and calculate the area of the rectangle: Segment area:= edt; We easily accumulate the current segment area with the total SUM and that will be approximate area under the curve or integral from starting point up to now. The memory* of system behavior is hidden in the integral value. In a real PID application , normally Integral value is positive because error is positive for most of operation and in order to make Integral zero we need to experience a relatively long overshoot that is not pleasant for most of process industry applications. Please keep mind that output of PID controller is summation of P_PART,I_PART and D_PART. Integration Time (Ti) forms the weight that I_PART plays in PID output calculation. Bigger Ti makes the response sluggish because I_PART has less contribution and needs time to accumulate. I hope it helps, hdhosseini Attachment Riemann_Integration.jpg (873 Downloads)
	Last edited by: hdhosseini at: 09/08/2022 12:24:36 Demo Channel on Youtube
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