[time-nuts] Fury - Rubidium

J. Forster jfor at quik.com
Wed Jul 28 01:36:18 UTC 2010


> I read the article on PID on Wikipedia last night.  I do not fully
> understand it, but I see/learning some of the relationship.

Here's a very quick primer:

Consider a very simple control position servo loop:


Pos. Input --- + (SUM)--- PID --- AMP > --- MOTOR ===== Output Pos
                   |-                               ||
                   |                               POS Sensor
                   |                                 |
                   -----------------------------------


If you put an upwards step into the Pos Input the output of the SUM goes
up. This is applied to the AMP via the PID network and the MOTOR stasrts
up, turning the output shaft. As the Output shaft turns, the position
sensor output rises. That subtracts from the commanded position in the
SUM, reducing the AMP input.

Thats how the P = Proportional signal drives the loop to null.

However, in order for the motor to turn some non-zero voltage needs to be
applied. As the SUM output approaches zero the motor drive ceases and the
loop never reaches null. So the I = Integral term is added. If the loop
stops just shy of null, the SUM output will not be zero. The I Integrator
takes the near-null voltage and integrates it (Vsum dT) which will
eventually rise sufficiently to drive the motor to null.

However, the motor does not stop instantly when the SUM reaches zero
because of inertia, so it overshoots. So the D = Derivative term
(dVsum/dT)is added in to cut the motor drive as the loop approaches null.

Note, in general the I term is destabilizing and the D term is
stabilizing, as long as you are considering frequencies below where the
othy components have significant phase shift.

FWIW,

-John

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