Closed orbit correction at synchrotrons for symmetric and near-symmetric lattices

Mirza, Sikander M.; Singh, Rahul; Forck, P.; Klingbeil, Harald

doi:10.1103/physrevaccelbeams.22.072804

Cited by 8 publications

(6 citation statements)

References 24 publications

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“…The resulting quadrupole settings variation during a typical dipole magnets ramp (10 T/s) of SIS18 is shown in Fig. 4 into a continuous ORM variation with time [14] as evident from the variation of the highest singular values of the ORMs during the ramp plotted for both planes in Fig. 4 (bottom), although the design (set) tune remains the same.…”

Section: Simulationsmentioning

confidence: 99%

“…System interconnection for the application of small gain theorem. a theoretical comparison between SGT and spectral radius condition discussed in inequality 11 based upon following assumptions: 1) we consider circulant or block-circulant ORMs (a scenario which exists for FAIR synchrotrons and also some synchrotron light sources [14]) for which the spectral radius is equal to the H ∞ norm i.e. the highest singular value σ.…”

Section: B Comparison To Small Gain Theoremmentioning

confidence: 99%

“…The elements of the diagonal matrix S Θ called singular values, σ i are the characteristic of the matrix R Θ and their inverses act as the controller gain for each mode (column) of the orthogonal matrices U Θ , V Θ . For the symmetric and the near-symmetric arrangements of BPMs and corrector magnets, a DFT-based diagonalization and inversion method is recently discussed in the context of closed orbit correction [14] as an alternate to SVD resulting in a sparse representation for changing lattices. These special matrices will be utilized in this report for deriving exact relations due to their favourable properties.…”

Section: Introductionmentioning

confidence: 99%

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Performance of the closed orbit feedback systems with spatial model mismatch

Mirza

Singh

Forck

et al. 2020

Phys. Rev. Accel. Beams

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Closed orbit feedback (COFB) systems used for the global orbit correction rely on the pseudo-inversion of the orbit response matrix (ORM). A mismatch between the model ORM used in the controller and the actual machine ORM can affect the performance of the feedback system. In this paper, the typical sources of such model mismatch such as acceleration ramp ORM variation, intensity-dependent tune shift and beta beating are considered in simulation studies. Their effect on the performance and the stability margins are investigated for both the slow and fast regimes of a COFB system operation. The spectral radius stability condition is utilized instead of the small gain theorem to arrive at the theoretical limits of COFB stability and comparisons with simulations for SIS18 of GSI and experiments at the Cooler synchrotron (COSY) in the Forschungzentrum J ülich (FZJ) are also presented.

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Section: Simulationsmentioning

confidence: 99%

Section: B Comparison To Small Gain Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Performance of the closed orbit feedback systems with spatial model mismatch

Mirza

Singh

Forck

et al. 2020

Phys. Rev. Accel. Beams

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“…There may be different reasons that feedback systems have not generally exploited these existing symmetries (one exception is [14]). Firstly, the matrices involved in the feedback systems have around 100,000 elements and recognizing these symmetries by by inspection is not straightforward.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Exploitation in Orbit Feedback Systems of Synchrotron Storage Rings

Kempf,

Goulart,

Duncan

et al. 2020

Preprint

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Structural symmetries in the storage ring of synchrotrons are intentionally created during the design phase of the magnetic lattices, but they are not considered in the design of control algorithms that stabilize the beam of accelerated particles. The choice of control algorithm, however, is limited by the speed requirements of the synchrotron. Standard control algorithms for synchrotrons are based on a singular value decomposition (SVD) of the orbit response matrix. SVD controllers neither exploit the structural symmetries nor exhibit any speed advantages. Based on the periodicity and the reflection properties of the betatron function, we show that these structural symmetries are inherited by the orbit response matrix. We show that the resulting block-circulant and centrosymmetric properties of the matrix can be used for different computationally efficient decompositions of the controller. We also address the case of broken symmetry due to odd placements of magnets and monitors. Our efficient decomposition could enable the use of more advanced control techniques for synchrotrons, such as control algorithms that require real-time optimization. These advanced control techniques could in turn increase the quality of research in synchrotron light sources.

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“…The contributions of the work presented in this chapter can be summarized below, while some of them are also published in [79].…”

Section: Summary and Contributionsmentioning

confidence: 99%

Closed orbit feedback system for the fast ramping hadron synchrotrons

Mirza¹

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The realization of a fast and robust closed orbit feedback (COFB) system for the on-ramp orbit correction at SIS18 synchrotron of FAIR project is reported in this thesis. SIS18 has some peculiar behaviors including on-ramp optics variation, very short lengths of the ramps (200 ms to 1 s) and a cycle-to-cycle variation of beam parameters. The realized fast COFB system being robust against above mentioned features of SIS18 is a first of its kind and the course to its realization led to some novel contributions in the field of closed orbit correction. A new method relying on the discrete Fourier transform (DFT)-based decomposition of the orbit response matrix (ORM) has been introduced, exploiting the symmetry in the arrangement of beam position monitors (BPMs) and the corrector magnets in the synchrotrons. A nearest-circulant approximation has also been introduced for synchrotrons having slight deviation from the symmetry, making the method applicable to a vast majority of synchrotrons. Moreover, the performance and the stability analysis of COFB systems in the presence of ORM mismatch between the synchrotron and the feedback controller is presented. The COFB systems are divided into slow and fast regimes and a new stability criterion consistent with measurements, is introduced. The practicality of the criterion is verified experimentally at COSY Jülich and is used for the analysis of various sources of ORM mismatch at SIS18. The commissioning of the SIS18 COFB system is also reported in detail which relies on Libera Hadron as the main hardware resource for the controller implementation. The on-ramp orbit correction is demonstrated for the horizontal plane of SIS18, for the disturbance rejection up to 600 Hz.

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Closed orbit correction at synchrotrons for symmetric and near-symmetric lattices

Cited by 8 publications

References 24 publications

Performance of the closed orbit feedback systems with spatial model mismatch

Performance of the closed orbit feedback systems with spatial model mismatch

Symmetry Exploitation in Orbit Feedback Systems of Synchrotron Storage Rings

Closed orbit feedback system for the fast ramping hadron synchrotrons

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