1. Fk. Bordry AB/PO Ability of the converter s to follow the reference function (static, dynamics) I1 I2 I3 Static part is covered by the static definition : accuracy, reproducibility (see session 7) Dynamic part comes from : - timing error - lagging error in the regulation Tracking error between I1 and I2 Iref Tracking 11th Chamonix workshop - 18th January 2001

2. Fk. Bordry AB/PO I I ref Dynamics : - Measurement and command must be synchronised : timing (1ms) - Lagging error : # Iref => I : regulation loop are designed with no lagging error independent of the load time constant Dynamics : - Measurement and command must be synchronised : timing (1ms) - Lagging error : # Iref => I : regulation loop are designed with no lagging error independent of the load time constant Power Converter + Circuit T1/S R Ts ADC Digital controller DAC Ts B Magnet F(s) = 1/(1+Ts) # I => B : time constant (T : vacuum chamber, beam screen…) must be known (could be corrected by control) Measurement campaign : test benches and String 2. Tracking : dynamics

3. Fk. Bordry AB/PO The curve marked feed-forward uses the knowledge of the transfer functions as established on the test benches. This correction compensates well the difference in the high field saturation, but leaves a substantial deviation at low and intermediate field. This deviation is mostly due to a systematic measurement artefact. Irrespective of its nature however, and because this is a systematic effect, the deviation is well corrected by iteration on the measured B2/B1 ratio as shown by the curves marked feed-back. In this case the tracking error on the B2/B1 ratio is definitely inside the range to be achieved for the tune feed-back system to lock, and in fact quite close to the range necessary to maintain the maximum allowed tune variation to within 3 × 10 -3 as dictated by the nominal LHC performance. The optimised current ramp was sent unchanged in a second cycle, with the aim to verify the reproducibility of the ramp. The result demonstrates that the reproducibility is excellent. The ratio B2/B1 for the focussing quadrupole plotted as a function of the dipole field along the reference current ramp. Tracking at String 2

4. 20 ppm Accuracy after calibration  B/B ultimate =  I/I ultimate = 20ppm  B = 9 * 20 10 -6 = 1.8 10 -4 T  B/B o = 3.3 10 -4 Orbit excursion :  X = D x.  B/B o = ~ 0.7 mm Tracking between the 8 main dipole converters 3 8 7 2 4 5 1 6 Could be corrected with a pilot run and new cycle => reproducibility 10 ppm reproducibility Orbit excursion :  X = D x.  B/B o = ~ 0.35 mm ”It would be better with 5 ppm ” Oliver Brüning (  X < 180  m) Could be corrected with a pilot run and new cycle => reproducibility 10 ppm reproducibility Orbit excursion :  X = D x.  B/B o = ~ 0.35 mm ”It would be better with 5 ppm ” Oliver Brüning (  X < 180  m) 11th Chamonix workshop - 18th January 2001

5. Fk. Bordry AB/PO Power Converter Tolerances for LHC Precision Control

6. Tracking between the dipole and quadrupole converters 20 ppm Accuracy  B/B ultimate =  I/I ultimate = 20ppm  B = 9 * 20 10 -6 = 1.8 10 -4 T  B/B o = 3.3 10 -4 Energy error in the machine leads to a tune change :  Q =  nat.  p/p o =  nat.  B/B o = 100 * 3.3 10 -4 = 0.032 Tuning quadrupoles can correct up to  Q = 0.3 20 ppm Accuracy  B/B ultimate =  I/I ultimate = 20ppm  B = 9 * 20 10 -6 = 1.8 10 -4 T  B/B o = 3.3 10 -4 Energy error in the machine leads to a tune change :  Q =  nat.  p/p o =  nat.  B/B o = 100 * 3.3 10 -4 = 0.032 Tuning quadrupoles can correct up to  Q = 0.3 Tracking between the main quadrupole converters small  beating : no problem

8. Fk. Bordry AB/PO –Accuracy Long term setting or measuring uncertainty taking into consideration the full range of permissible changes* of operating and environmental conditions. * requires definition –Reproducibility Uncertainty in returning to a set of previous working values from cycle to cycle of the machine. –Stability Maximum deviation over a period with no changes in operating conditions. Accuracy, reproducibility and stability are defined for a given period –Accuracy Long term setting or measuring uncertainty taking into consideration the full range of permissible changes* of operating and environmental conditions. * requires definition –Reproducibility Uncertainty in returning to a set of previous working values from cycle to cycle of the machine. –Stability Maximum deviation over a period with no changes in operating conditions. Accuracy, reproducibility and stability are defined for a given period Glossary Precision Precision is qualitative. Accuracy is quantitative. I Nominal I Meas. ± Accuracy ppm * I Nominal half an hour Cycle 1 Cycle 2Cycle 3 One day max I B1 I B2 I B3 11th Chamonix workshop - 18th January 2001

9. Fk. Bordry AB/PO Accuracy Long term setting or measuring uncertainty taking into consideration the full range of permissible changes* of operating and environmental conditions. LHC : The accuracy is defined by default for a period of one year. The accuracy is expressed in ppm of I Nominal. If the one year accuracy is too large, a calibration process should be executed more often (e.g every month) LHC : The accuracy is defined by default for a period of one year. The accuracy is expressed in ppm of I Nominal. If the one year accuracy is too large, a calibration process should be executed more often (e.g every month) * For LHC :Engineering Specifications General parameters for equipment installed in the LHC (e.g.  T = ±2 o C in UAs) (LHC-PM-ES-0002.00) Main parameters of the LHC 400/230 V distribution system (LHC-EM-ES-0001) I Nominal I Meas. ± Accuracy ppm * I Nominal

10. Fk. Bordry AB/PO Reproducibility LHC : The reproducibility is defined by default for a period of one day without any intervention affecting the calibrated parts (e.g. DCCT, ADC) The reproducibility is expressed in ppm of I Nominal. Cycle 1 Cycle 2 Cycle 3 One day max I B1 I B2 I B3 I B2 = I B1 ± (Reproducibility pmm. I nominal ) I B3 = I B2 ± (Reproducibility pmm. I nominal ) Uncertainty in returning to a set of previous working values from cycle to cycle of the machine.

11. Fk. Bordry AB/PO Stability Maximum deviation over a period with no changes in operating conditions. LHC : The stability is defined by default for a period of half an hour The stability is expressed in ppm of I Nominal. ± Stability ppm. I Nominal half an hour Time in Minutes -40 -20 0 20 40 0 60120180240 -2 0 1 2 Current offset in Milliamps Current offset in ppm of 20 kA I 0 = 16000 Amps