Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Orbit feedback robustness testsand

System identification for FACET

Jürgen Pfingstner29th of February 2012

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Outline

1. Orbit feedback robustness1. Static accelerator imperfections2. Controller parameter errors3. Conclusions

2. System identification at FACET1. Principle2. Algorithms3. Results4. Conclusions

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

1. Orbit feedback robustness

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Orbit feedback system for ML and BDS

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

1.1 Static accelerator imperfections

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Static RF errors

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Static QP strength errors

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Actuator scaling errors

30% error

=> 0.5% lumi. loss

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

BPM scaling errors

1% error

=> 0.5% lumi. loss

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

1.2 Controller parameter errors

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Errors in the used orbit response matrix due to ground motion (input/output directions)

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Controller gain variations Δfi

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Gain factors fi

• Smooth distribution of the fi

would be preferable for the

robustness

• Why are some patterns that

create small BPM readings

so important?

Mode 189

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Investigation of mode 189

SF1, SD0

SD4, SF5, SF6

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

1.) Effect of the mode:• Luminosity loss via beam size

growth in y plane, due to a correlation x’y

• Corresponds to coupling from the x to the y plain in the FD

-> Sextupoles

2.) Possible explanation:• Setup

• General sextupole kick

• Angel y without sextupoles

• Angle with sextupoles

• Angle with sextupoles and kick in between them[-I]

S1 S2

x1 x2 -x2 x3

Uncorrected geometric aberrations

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Possible future work

1.) Orbit feedback:

• Robustness improvement by searching in a measured response matrix for the mode 189 and

a. Assign a high gain to itb. Correct the problem with

a different system, e.g. tuning knobs.

1.) Tuning (from discussion with Andrea, Daniel):

• Maybe a possibility to use BPM readings as

a tuning signal instead of luminosity

• Maybe also other effects at the IP can be

assigned to a BPM pattern

• Correlation studies could be interesting

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

2. System identification at FACET

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

2.1 Principle

Real-world system R(t)

Estimation algorithm

y(t)u(t)

... Input data (actuators)

… Output data (BPM readings)

… real-world system (accelerator)

… estimated system

• Goal:

Fit the model system in some sense to the real

system,

using u(t) and y(t)

• Ingredients

• Model assumption

• Estimation algorithm

• System excitation

Excitation

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

2.2 Algorithms• Model:

• Task: Find R from many known measurements yk and excitations uk .

• Least squares solution: (pseudo-inverse)

• LS calculation can be modified for recursive calculation (RLS):

• Modified RLS can “forget” older values to learn time-

changing systems.

• Derivatives (easier to calculate)

- Stochastic approximation (SA)

- Least Mean Square (LMS)

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

2.3 Results

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Excitation level vs. emittance growth

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

RLS no noise, 63 corr.

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

RLS with noise, 63 corr.

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

RLS only one corrector, noise

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

RLS more excitation with noise

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

2.4 Conclusions

• Full orbit response matrix R cannot be identified in acceptable time with an parasitical excitation

• Reasons:

1) Low BPM resolution

2) Slow actuator dynamics

• Alternative scenarios

1) Identification of a subset of correctors with higher excitation.

This could be helpful to get necessary information for BBA

2) Identification of only 1 or 2 correctors for diagnostics purposes

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

Thank you for your attention!

Jürgen Pfingstner Orbit feedback robustness and system identification for FACET

LMS and SA algorithm, noise, 190 corr., Δεx=2%