[time-nuts] (no subject)

[Magnus Danielson]

Cash,

Typically a PLL loop uses a PI loop-filter, making it a PI-control 
system with a steered integrator in the form of the oscillator. Many 
other control systems prefer to use the PID controller, and Bob found 
that there is a D factor in there.

The factors at hand is:

P = Proportinal
I = Integrate
D = Diffrentiate

If you have the reference phase phi_ref and the oscillator output phase 
of phi_out, the detected phase difference Vd is

Vd = Kd * (phi_ref - phi_out)

The oscillator steering is Vf can then be formulated as

VD = Vd - Vd_prev
Vd_prep = Vd
VI = VI + I*Vd
Vf = D*VD + P*Vd + VI

Thus, the D factor steers how much of the time-derivate of the phase 
goes into the frequency steering. The P factor steers the phase and the 
I factor the amount of integrated signal.

A loop in stable condition will have the integrator force Vd to be 
around zero, so VI will hold the frequency correction needed. The I will 
scale how quickly it will "learn" this frequency. The P will scale the 
AC part of Vd for dynamics, typically you set the damping.
The D factor can play an important part in the track-in process and the 
dynamics of that.

A key factor is the sample-time T. I and D needs to be scaled with T to 
get the same behavior for alternate values sampling periods.

Cheers,
Magnus

On 01/25/2015 12:35 AM, Cash Olsen wrote:
> Bob,
>
> I am relatively new to the list and still learning the jargon and
> concepts. You wrote: "There does appear to be a D in the TBolt loop.
> For what ever reason, that’s not a changeable value. The D does scale
> with the time constant."
>
> Could you or one of the other members elaborate on the what is meant
> by "D" above. Does it have anything to do with a flat spot in the
> loop?
>