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: [email protected] > [mailto:[email protected]] 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 > > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to > https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
