Symmetry Exploitation in Orbit Feedback Systems of Synchrotrons for Computational Efficiency

Kempf, Idris; Goulart, Paul J.; Duncan, Stephen R.; Rehm, Guenther

doi:10.1109/tns.2021.3052553

Cited by 5 publications

(5 citation statements)

References 24 publications

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“…The number of actuators will be increased from 173 to 396 for Diamond-II, which will significantly increase the computational complexity of the algorithm and further slow down the controller. However, in contrast to the current system the DLS-II system will have a block-circulant and centrosymmetric symmetry, which can be exploited to increase the computational speed of the controller by a factor of 10 [8].…”

Section: Discussionmentioning

confidence: 99%

“…In most synchrotrons the monitors and magnets are placed in repeated patterns around the storage ring. These patterns produce a circulant and centrosymmetric structure in R [8]. In contrast to the modal decomposition, which requires the outputs and inputs to be multiplied by dense matrices, the symmetric transformations can be carried out using the computationally efficient Fast Fourier Transformation (FFT).…”

Section: Symmetriesmentioning

confidence: 99%

“…In contrast to the modal decomposition, which requires the outputs and inputs to be multiplied by dense matrices, the symmetric transformations can be carried out using the computationally efficient Fast Fourier Transformation (FFT). In our previous work, we have shown how these symmetries can be exploited for cross-directional [8] and MPC [3] to increase the computational speed of the controller and reduce the memory requirements. These symmetries stand out in the DLS-II orbit response matrix, but have been corrupted in the current orbit response matrix after adding modifications in anticipation DLS-II.…”

Section: Symmetriesmentioning

confidence: 99%

“…where variables with a hat denote estimated quantities and the state-space system (5) has been combined with the disturbance model (8).…”

Section: State and Disturbance Observermentioning

confidence: 99%

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Model Predictive Control for Electron Beam Stabilization in a Synchrotron

Kempf¹,

Goulart²,

Duncan³

2021

Preprint

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Electron beam stabilization in a synchrotron is a disturbance rejection problem, with hundreds of inputs and outputs, that is sampled at frequencies higher than 10 kHz. In this feasibility study, we focus on the practical issues of an efficient implementation of model predictive control (MPC) for the heavily ill-conditioned plant of the electron beam stabilization problem. To obtain a tractable control problem that can be solved using only a few iterations of the fast gradient method, we investigate different methods for preconditioning the resulting optimization problem and relate our findings to standard regularization techniques from crossdirectional control. We summarize the single-and multi-core implementations of our control algorithm on a digital signal processor (DSP), and show that MPC can be executed at the rate required for synchrotron control. MPC overcomes various problems of standard electron beam stabilization techniques, and the successful implementation can increase the stability of photon beams in synchrotron light sources.

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Section: Discussionmentioning

confidence: 99%

Section: Symmetriesmentioning

confidence: 99%

Section: Symmetriesmentioning

confidence: 99%

“…where variables with a hat denote estimated quantities and the state-space system (5) has been combined with the disturbance model (8).…”

Section: State and Disturbance Observermentioning

confidence: 99%

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Model Predictive Control for Electron Beam Stabilization in a Synchrotron

Kempf¹,

Goulart²,

Duncan³

2021

Preprint

Self Cite

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“…Symmetry exploitation and the DFT-based decomposition of the ORM can be applied as an alternate to the SVD for modern synchrotrons and light sources. Even a recent effort has already been reported to utilize the computational benefits of symmetry exploitation for the Diamond-II COFB system [96].…”

Section: Discussionmentioning

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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