Ulrich
That is correct, none of these simple code blocks form a controller.
This is just a block of code that could be used for the PI gain function of
a controller.
In a complete controller the input to this gain block would typically come
from a pre-filter,
and the prefilter's input from the error difference between the setpoint and
the feedback, etc.
I wanted to keep the math as simple as possible by only including this
section of code.
My question was does the math in these four blocks of code all provide the
same exact input to output function.
What the code is being used for is not really relevant to the answer.
simple example:
Does the code X = 3Y have the same input to output function as X = 4 + 2 +
(1+2) *Y - 6?
Just because they look different does not mean they are different.
The question was meant to be a simple math exercise like does 3y = (1+2)y?
The answer does not need any high level math or depend on the value of y or
what the code is being used for.
ws
*******************
----- Original Message -----
From: "Ulrich Bangert" <df...@ulrich-bangert.de>
To: "'Discussion of precise time and frequency measurement'"
<time-nuts@febo.com>
Sent: Thursday, April 17, 2014 1:14 AM
Subject: Re: [time-nuts] PI Math question
Warren,
the job of a controller, regardless of P, PI od PID, is to minimize the
error between a process value and its setpoint. Since I see no setpoint
value in any of your versions my 50 ct is that none of them really
incorporates a controller at all and that for this reason the question
whether they produce the same output is close to being irrelevant.
Best regards
Ulrich
-----Ursprungliche Nachricht-----
Von: time-nuts-boun...@febo.com
[mailto:time-nuts-boun...@febo.com] Im Auftrag von WarrenS
Gesendet: Mittwoch, 16. April 2014 18:50
An: Discussion of precise time and frequency measurement
Betreff: [time-nuts] PI Math question
A question to the math time-nuts
With the values of K1, K2 & K3 constant,
and the initial state of I#1, I#2 and Last_Input all zero
assuming there is no rounding, clipping or overflow in the
math and that if I've made any obvious dumb typo errors, that
they are corrected,
Given this PID type of controller;
D = (Input - Last_Input))
Last_Input = Input
I#1 = I#1 + (K1 * Input)
I#2 = I#2 + (K2 * D)
Output = I#1 + I#2 + (K3 * Input)
Is the above Input to Output's transfer function any
different than any of
the following more simplified versions of PI controllers?
Or asked another way, if each of the four codes are given the
exact same
input string and same K Gains, will the difference between
any of their outputs ever be non zero?
a)
D = Input - Last_Input
Last_Input = Input
I#1 = I#1 + (K1 * Input) + (K2 * D)
Output = (K3 * Input) + I#1
b)
D = (Input - Last_Input)
Last_Input = Input
Output = Output + (K1 * Input) + (K2 + K3) * D
a)
I#1 = I#1 + (K1 * Input)
Output = I#1 + ((K2 + K3) * Input)
ws
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