Bill Hawkins bill at iaxs.net
Tue May 11 07:29:11 UTC 2010

```Bob,

I'd expect the PID output to change instantly with error. The equation is
roughly:

OUT = previous integrated error + gain * (error + current error/integral
time constant
+ delta error * derivative time constant)
where multiply or divide occurs before addition, as controlled by
parentheses.

Then previous integrated error = new output.

The time constants are relative to the sampling time of the PID algorithm.

Like all integrals, something has to set the initial value.

Damping is a function of gain and time constants. Either a high gain or a
short
integral time will cause the output to oscillate, as will a long derivative
time.

How are you calculating damping?

Bill Hawkins

-----Original Message-----
From: time-nuts-bounces at febo.com [mailto:time-nuts-bounces at febo.com] On
Behalf Of Bob Camp
Sent: Monday, May 10, 2010 7:22 PM
To: Discussion of precise time and frequency measurement
Subject: [time-nuts] Lying to Lady Heather

Hi

I've spent some time lying to Lady Heather, with some interesting results:

1) Classical control loop theory would suggest that damping should be fairly
close to 1 for reasonable operation. Greater than 10 should be highly
damped. Less than 0.1 should ring quite a bit. The TBolt doesn't seem to
work this way. You can go to << 0.1 and still have a stable response to a
step. You can go out to > 100 and not get a "lazy" response to a step. You
can get to a point that it will ring, but it's down < 0.001. Obviously the
TBolt and I read different books.

2) In a PID setup, you would have control on each coefficient. With the
TBolt setup the "gain" seems to be the only way to impact the D part of the
PID. You can watch the DAC output as you increase the gain. The swing of the
DAC responding to the GPS pps jumping will decrease as you increase the gain
number. It sounds backwards, but it makes sense. With "correct" gain, each
time there is a step in the GPS PPS, the DAC immediately changes, no matter
what the damping or time constant. Again, seems strange, but that's the way
it works.

3) Time Constant does seem to slow down the "integrator" in the PID.

On a very stable unit - watch the DAC voltage. It's climbing up and down
like crazy on a second to second basis. It's reasonable to believe that the
OCXO is more stable than GPS at one second. The DAC should be fairly quiet
second to second. DAC LSB's are around 1 ppt. That's around (like a factor
or 3 or 5) the stability of the OCXO at 1 second. One or two LSB per second
might make sense. Anything 5 or 10X  than that is mostly noise that you
simply don't need.

Tell the unit enough lies (like gain = -60) and sure enough the DAC slows
down and hops 1 LSB every so often. When GPS is stable it will stay in one
state for 10's of seconds. Even with 10 ns hops in the GPS, it still stays
down in the 1 to 2 LSB range. That's *got* to be more stable.

Why is this good - nice as a frequency standard.

Why this is bad - TBolt pps does not track GPS PPS very closely. Not good
for E911 service.

Bottom line - there's lots of ways to optimize a TBolt.

Bob
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