Orbit during ramp

 

Hi Thijs,

please excuse my lengthy e-mail. Maybe I can answer some of you questions:
> what this Smith Predictor actually is : [..]
The 'Smith Predictor' (SP) is an _option_ and only required once we intend to
operate those feedback at possible rates of 25 or 50 Hz.
Yes, you are right, if we use a SP the derivative (and proportional) term of
the PID provide are in principle redundant. I didn't spend too much time on
these advanced topics (SP, ramp rate limiter) in order keep the talk simple.

(NB: Actually, Jorg predicted that just mentioning 'Smith Predictor' will lead
to discussions -- well well -- think he was right, as usual ;-)

For early startup for the sake of simplicity we intend to use a simple PID (or
just integral) control only. However, the feedback controller is designed to
execute an arbitrary transfer function with as many 'poles' and 'zeros' as
required. The PID is just one of the possible and best understood choices
that (we thought) will likely get the biggest acceptance by people that
operate the feedbacks other than Jorg and me. The fact that the derivate part
of the PID is foreseen does not mean that the derivative gain has to be used
at all. The derivative part is only required if high integral gains and no SP
is used.

We considered also a state-space design for the controller, but dropped it
because it is not flexible enough when dealing with disabling erroneous BPMs
and CODs.

> 2/ 'The squeeze was considered as less critical, since one could slow it
> down or divide
> it into more and smaller steps, which is less obvious for the snapback.'
>
> Slowing down the ramp rate (though still ramping at dB/dt/B constant)
> would certain help
> in case of the snap back and the feedback loop will require much less
> voltage from the power
> converters. Also, we can play with the amplitude of the snapback via
> degaussing.
> I would be very interested to see what the maximum ramp rate would be in
> either case, assuming we
> have fully operational tune/orbit/chromaticity loops operational.

We do not hit any ramp rate limitations during the decay or snap-back. The
magnets and power converters were designed to operate at 7 TeV. In principle,
at 7 TeV the slowest (cryogenic) magnet can generate/compensate an orbit
drift of up to 20 um/s. This corresponds to a maximum drift compensation of
more than 300 um/s at 450 GeV.
Using the baseline dipole ramp and field model predictions (e.g. LPR 172, LPR
854), one can find that the maximum orbit drift at the start of the ramp is
less than about 20 um/s. Hence, these drifts are not an issue with respect to
the controllability point of view. Similar applies for tune and chromaticity.
I added a plot showing the ramp induced orbit r.m.s. perturbations due to
snapback and decay of the persistent currents. Ground motion predictions,
which are slow, are in the slides.

The only issue concerning the controllability might be during the squeeze
assuming a worst case misalignment of 0.5 mm r.m.s. of the quadrupoles. The
gross movement due to the off-centre beam inside the quadrupoles can be as
large as 30 mm (the simulation results are in the slides as well). These high
orbit drifts are found in the insertion quadrupoles. This can however largely
be minimised if we do a k-modulation and adjustment of the orbit inside the
to be squeezed insertions. Comparing the 30 mm in 20 minutes would yield a
drift rate of about 25 um/s, which is slightly above what the correctors can
do. The actual drift rate depends on how much time we spend per squeezing
step. Anyway this drift rate is mitigated by the fact that the 30 mm occurs
at the insertion quadrupoles with large beta-functions where the cods can
create more than 20 um/s @ 7 TeV.
This may be an issue with respect to controllability but can however to a
large extend be minimised by a proper alignment of the insertion quadrupoles
- if they are really that badly aligned. The alignment targets from the
survey group are 0.2 mm r.m.s. globally and 0.1 mm r.m.s. within 10
neighbouring magnets.

The real issue is whether the total feedback bandwidth is sufficient, that is
whether we can detect these drifts (shouldn't be a problem) and whether the
calibration is sufficient. In any case, we can trade a less good calibration
with a higher sampling frequency: going from 10 to 25 to 50 Hz makes a
difference wrt. the achievable bandwidth. That's the reason why 'Franklin et
al.' state that the feedback frequency should be at least 20-30 times
(ideally 40 times) larger than the bandwidth of the actuators, so that
calibrations, discretisation and other things are less of an issue. More
explicit: If we run the feedbacks at maximum 10 Hz one should not expect a
bandwidth of more than 0.25 Hz, which is sufficient for most effects (ramp
etc.). Higher frequencies are only required _if_ we detect that the noise
spectrum differs from the one we know.


> 3/ "Afterwards, the feedback could immediately be operated, with a low
> integral gain at 0.1-1 Hz."
>
> It would be interesting to see what gain we can get at higher
> frequencies and what the real
> noise spectrum in the LHC will be as perturbations at higher frequencies
> can drive the loops
> unstable and we would need to reduce the gain.
Part of you questions concerning expected high frequency perturbations are
answered in the AB report: CERN-AB-2005-087
Most of the perturbation sources are not an issue for feedbacks. Two
candidates where I am not sure yet are quadrupole oscillations due to
cryogenics (an issue at RHIC: 300 um) and the 'air-duct' in IR7. However,
this will essentially be only measurable with beam.

I didn't want to go into too much detail during that presentation. If you
want, since these are very technical questions, we could meet for a coffee or
tea?

Cheers,
Ralph