[time-nuts] PI Math question

[Ulrich Bangert]

Warren,

I understand your message as an afterwards try to put some sense in your
original question, but if you write

> D = (Input - Last_Input)

then this clearly denotes the differential part of a PID controller (with
the multiplication with the coefficient for the differential part coming
later)

If you add now

> 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.

saying that "input is something complete different then I fear that this
discusion is drifting into complete nonsense because if "Input" denotes an
entity which contains an error signal in any form then

> D = (Input - Last_Input)

is something that is ill defined and has nothing to do with the differential
part of a PID controller.  

> I wanted to keep the math as simple as possible...

Good idea but if simplification creates something wrong then the
simplification has gone one step to far.

Best regards

Ulrich

 

> -----Ursprungliche Nachricht-----
> Von: time-nuts-bounces at febo.com 
> [mailto:time-nuts-bounces at febo.com] Im Auftrag von WarrenS
> Gesendet: Donnerstag, 17. April 2014 11:54
> An: Discussion of precise time and frequency measurement
> Betreff: Re: [time-nuts] PI Math question
> 
> 
> 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" <df6jb at ulrich-bangert.de>
> To: "'Discussion of precise time and frequency measurement'" 
> <time-nuts at 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-bounces at febo.com 
> [mailto:time-nuts-bounces at 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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