Feedback Systems, Tuning
Paper Title Page
MOC3O01 Comprehensive Fill Pattern Control Engine: Key to Top-Up Operation Quality 1
  • T. Birke, F. Falkenstern, R. Müller, A. Schälicke
    HZB, Berlin, Germany
  Funding: Work supported by BMBF and Land Berlin.
At the light source BESSY II numerous experiments as well as machine development studies benefit from a very flexible and stable fill pattern: standard operation mode comprises a multibunch train for the average users, a purity controlled high current camshaft bunch in a variable length ion clearing gap for pump/probe experiments and a mechanical pulse picking chopper, three high current bunches for femto second slicing opposite to the gap and a specific bunch close to the end of the ion clearing gap for resonant excitation pulse picking. The fill pattern generator and control software is based on a state machine. It controls the full chain from gun timing, linac pulse trains, injection and extraction elements as well as next shot predictions allowing triggering the next DAQ cycle. Architecture and interplay of the software components as well as implemented functionality with respect to hardware control, performance surveillance and reasoning of next actions, radiation protection requirements are described.
slides icon Slides MOC3O01 [3.687 MB]  
MOC3O02 PIDTUNE: A PID Autotuning Software Tool on UNICOS CPC 1
  • E. Blanco Vinuela, B. Bradu, R. Marti Martinez
    CERN, Geneva, Switzerland
  • R. Mazaeda, L. de Frutos, C. de Prada
    University of Valladolid, Valladolid, Spain
  PID (Proportional, integral and derivative) is the most used feedback control algorithm in the process control industry. Despite its age, its simplicity in terms of deployment and its efficiency on most of industrial processes allow this technique to still have a bright future. One of the biggest challenges in using PID control is to find its parameters, the so-called tuning of the controller. This may be a complex problem as it mostly depends on the dynamics of the process being controlled. In this paper we propose a tool that is able to provide the engineers a set of PID parameters in an automated way. Several auto-tuning methods, both in open and close loop, are selectable and others can be added as the tool is designed to be flexible. The tool is fully integrated in the UNICOS framework and can be used to tune multiple controllers at the same time.  
slides icon Slides MOC3O02 [2.788 MB]  
MOC3O03 Automatic FEL Optimization at FERMI 1
  • G. Gaio, M. Lonza
    Elettra-Sincrotrone Trieste S.C.p.A., Basovizza, Italy
  FERMI is a seeded Free Electron Laser (FEL) located in Trieste, Italy. The machine setup and optimization is a non-trivial problem due to the high sensitivity of the FEL process to several machine parameters. In particular, the electron bunch trajectory and its spatial overlap with the seed laser beam represent one of the key aspects to optimize and then preserve during machine operation. In order to ease the FEL tuning and to guarantee a long term stability of the photon beam, a software process integrated into the feedback systems performs automatic trajectory optimization of both the seed laser and the electron beams. The algorithm implementation, the results and the operational issues are presented.  
slides icon Slides MOC3O03 [8.957 MB]  
MOC3O04 System Identification and Robust Control for the LNLS UVX Fast Orbit Feedback 1
  • D.O. Tavares
    LNLS, Campinas, Brazil
  • D.R. Grossi
    Sao Paulo University, São Carlos Campus, São Carlos, Brazil
  This paper describes the optimization work carried out to improve the performance of the LNLS UVX fast orbit feedback system. Black-box system identification techniques were applied to model the dynamic behavior of BPM electronics, orbit correctors, communication networks and vacuum chamber eddy currents. Due to the heterogeneity on the dynamic responses among several units of those subsystems, as well as variations on the static response matrix due to accelerator optics changes during operation, robust control techniques were employed to achieve appropriate closed-loop performance and robustness.  
slides icon Slides MOC3O04 [3.792 MB]  
MOC3O05 NSLS-II Fast Orbit Feedback System 1
  • Y. Tian, W.X. Cheng, L.R. Dalesio, J.H. De Long, K. Ha, L. Yu
    BNL, Upton, Long Island, New York, USA
  • W.S. Levine
    UMD, College Park, Maryland, USA
  This paper presents the NSLS-II fast orbit feedback (FOFB) system, including the architecture, the algorithm and the commissioning results. A two-tier communication architecture is used to distribute the 10kHz beam position data (BPM) around the storage ring. The FOFB calculation is carried out in field programmable gate arrays (FPGA). An individual eigenmode compensation algorithm is applied to allow different eigenmodes to have different compensation parameters. The system is used as a regular tool to maintain the beam stability at NSLS-II.  
slides icon Slides MOC3O05 [10.087 MB]  
MOC3O06 The Laser Megajoule Facility: The Computational System PARC 1
  • S. Vermersch
    CEA, LE BARP cedex, France
  The Laser MegaJoule (LMJ) is a 176-beam laser facility, located at the CEA CESTA Laboratory near Bordeaux (France). It is designed to deliver about 1.4 MJ of energy to targets, for high energy density physics experiments, including fusion experiments. The assembly of the first line of amplification (8 beams) was achieved in October 2014. A computational system, PARC has been developed and is under deployment to automate the laser setup process, and accurately predicts the laser energy and temporal shape. PARC is based on the computer simulation code MIRO. For each LMJ shot, PARC determines the characteristics of the laser injection system required to achieve the desired main laser output, provide parameter checking needed for all equipment protections, determines the required diagnostic setup, and supplies post-shot data analysis and reporting. This paper presents the first results provided by PARC. It also describe results obtained with the PARC demonstrator during the first experiments conducted on the LMJ facility.  
slides icon Slides MOC3O06 [4.980 MB]  
MOC3O07 Low Level RF Control Implementation and Simultaneous Operation of Two FEL Undulator Beamlines at FLASH 1
  • V. Ayvazyan, S. Ackermann, J. Branlard, B. Faatz, M.K. Grecki, O. Hensler, S. Pfeiffer, H. Schlarb, Ch. Schmidt, M. Scholz, S. Schreiber
    DESY, Hamburg, Germany
  • A. Piotrowski
    FastLogic Sp. z o.o., Łódź, Poland
  The Free-Electron Laser in Hamburg (FLASH) is a user facility delivering femtosecond short radiation pulses in the wavelength range between 4.2 and 45 nm using the SASE principle. The tests performed in the last few years have shown that two FLASH undulator beamlines can deliver FEL radiation simultaneously to users with a large variety of parameters such as radiation wavelength, pulse duration, intra-bunch spacing etc. FLASH has two injector lasers on the cathode of the gun to deliver different bunch trains with different charges, needed for different bunch lengths. Because the compression settings depend on the charge of bunches the low level RF system needs to be able to supply different compression for both beamlines. The functionality of the controller has been extended to provide intra-pulse amplitude and phase changes while maintaining the RF field amplitude and the phase stability requirements. The RF parameter adjustment and tuning for RF gun and accelerating modules can be done independently for both laser systems. Having different amplitudes and phases within the RF pulse in several RF stations simultaneous lasing of both systems has been demonstrated.  
slides icon Slides MOC3O07 [4.640 MB]  
A Model-Based Approach to Motion Control Design at the Australian Synchrotron  
  • N. Afshar
    ASCo, Clayton, Victoria, Australia
  • C. Glover, P. Kappen, P. Martin, E.L. Shepherd
    SLSA, Clayton, Australia
  • M. Stephenson
    ANSTO, Menai, New South Wales, Australia
  The sophistication and flexibility of versatile motion controllers often implies complex and potentially difficult configuration and tuning processes. This demands highly specialised engineering and system management efforts to meet performance requirements and process maintainability. To address these challenges, a model-based approach is used to provide a framework for generalising and formulating motion control systems which classifies applications and suggests optimum motor configuration and tuning based on design inputs and specifications. The framework also includes a dynamic Simulink® model which models the GeoBrick® and the PMAC configuration, stepper/servo motors, mechanical stages, encoders and cabling. This model is used for tuning and validating configurations with modeled motors, load conditions, encoders, etc. at design time prior to purchases. The model and framework developed has been applied successfully to more than 110 motion axes at different beamlines to design or upgrade motion controllers resulting in highly improved reliability and performance. Configuration management, deployment and commissioning processes are significantly improved at the same time.  
slides icon Slides MOM312 [4.657 MB]  
MOPGF066 Synchronized Ramping of Magnet Power Supplies for Streamlined Operation at Energy Recovery Linac (ERL) and Electron Lens (e-Lens) 1
  • P. K. Kankiya, J.P. Jamilkowski, T. Samms
    BNL, Upton, Long Island, New York, USA
  Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DE-SC0012704 with the U.S. Department of Energy.
Synchronous ramping of an assembly of magnets is critical for operation of beam in an accelerator. Magnet currents must remain within the operational limits to avoid dis-alignment of electron beam. In order to comply with the design specifications of ERL and ELENS project , two different software control mechanisms have been developed. The ramp profile is automated and maintained by tracking current in all dipole magnets at ERL and superconducting solenoid magnets at ELENS. This mechanism speeds up operations and adds a level of protection. The purpose of this application is to reduce unnecessary interlocks of the personnel protection system. This paper will describe the power supply arrangement, communication mechanism and the state machine algorithm used for feedback and control. A report on operating experience will be presented.
poster icon Poster MOPGF066 [1.966 MB]  
PARC : An Automated Laser Setup System for the Laser MegaJoule Facility  
  • J-P. Airiau, S. Vermersch
    CEA, LE BARP cedex, France
  The LMJ* is a 176 beams laser facility, located at the CEA** CESTA laboratory near Bordeaux. It is designed to deliver 1.4 MJ of energy to the target, for high density physics experiment, including fusion experiments. PARC determines the characteristics of the injection laser system, provides parameters checking for equipment protection, calculates the required diagnostic setup, and supplies post-shot data analysis and reporting. The CEA has developed a generic platform including a client/server software using the computational power of a cluster and a smart interface with the Control Command System (CCS). The software compiles and generates runnable sequences composed of heterogeneous simulation modules. PARC uses the configuration data from CCS to parametrize simulation models, executes prediction computation, returns each beam laser setup to CCS and compares simulation and measured data. It finally recalibrates the prediction models like a standard feedback system. This paper firstly describes PARC architecture and the communication protocol with the CCS. Secondly, an execution sequence from the generation process to the execution on the cluster is outlined.
*LMJ: Laser MegaJoule**CEA: French Atomic Energy Commission
MOPGF077 Drift Control Engines Stabilize Top-Up Operation at BESSY II 1
  • T. Birke, F. Falkenstern, R. Müller, A. Schälicke
    HZB, Berlin, Germany
  Funding: Work supported by BMBF and Land Berlin.
Full stability potential of orbit and bunch-by-bunch-feedback controlled top-up operation becomes available to the experimental users only if the remaining slow drifts of essential operational parameters are properly compensated. At the light source BESSY II these are the transversal tunes as well as the path length and energy. These compensations are realized using feedback control loops together with supervising state machines. Key to the tune control is a multi-source tune determination algorithm. For the path length correction empirical findings are utilized. All involved software systems and data-paths are sketched.
poster icon Poster MOPGF077 [2.003 MB]  
MOPGF079 European XFEL Cavities Piezoelectric Tuners Control Range Optimization 1
  • W. Cichalewski, A. Napieralski
    TUL-DMCS, Łódź, Poland
  • J. Branlard, Ch. Schmidt
    DESY, Hamburg, Germany
  The piezo based control of the superconducting cavity tuning has been under the development over last years. Automated compensation of Lorentz force detuning of FLASH and European X-FEL resonators allowed to maintain cavities in resonance operation even for high acceleration gradients (in range of 30 MV/m). It should be emphasized that cavity resonance control consists of two independent subsystems. First of all the slow motor tuner based system can be used for slow, wide range mechanical tuning (range of hundreds of kHz). Additionally the piezo tuning system allows for fine, dynamic compensation in a range of ~1 kHz. In mentioned pulse mode experiments (like FLASH), the piezo regulation budget should be preserved for in-pulse detuning control. In order to maintain optimal cavity frequency adjustment capabilities slow motor tuners should automatically act on the static detuning component at the same time. This paper presents work concerning development, implementation and evaluation of automatic superconducting cavity frequency control towards piezo range optimization. FLASH and X-FEL dedicated cavities tuning control experiences are also summarized.  
poster icon Poster MOPGF079 [0.932 MB]  
MOPGF080 Control System of RF Stations for NICA Booster 1
  • G.A. Fatkin, A.M. Batrakov, I.V. Ilyin, M.Yu. Vasilyev
    BINP SB RAS, Novosibirsk, Russia
  • G.A. Fatkin
    NSU, Novosibirsk, Russia
  NICA (Nuclotron based Ion Collider fAcility) is an accelerator complex, which is being built in JINR (Dubna, Russia). The system described in this paper is controlling the RF stations of booster, the first element of the NICA complex. The two devices are parts of the Control System: Intellectual Controller and Tester module. The first one is designed for precise measurement of magnetic field, generation of the acceleration frequency in accordance with measured field and control RF power and pre-amplifiers. Intellectual Controller is a real-time feed-forward system with 20 ums loop time. It is based on ARM microcontroller and bare-metal control programs are used to reach maximum performance. Approaches that were used to achieve maximum performance are elaborated and presented in this paper. The second part of system - Tester is a simulator for tuning and checking the RF stations before start of operations or in absence of real accelerator. The achieved accuracy in chain 'magnetic field' - 'acceleration frequency' is better than 5*10-5. Plans on feedback incorporation to stabilize ion beam behavior via frequency and phase tuning are discussed.  
poster icon Poster MOPGF080 [15.316 MB]  
MOPGF087 TPS Booster Tune Measurement System 1
  • P.C. Chiu, Y.-S. Cheng, K.T. Hsu, K.H. Hu, C.Y. Liao
    NSRRC, Hsinchu, Taiwan
  The TPS is a state-of-the-art synchrotron radiation facility featuring ultra-high photon brightness with extremely low emittance. Its Booster has 6 FODO cells which include 7 BD dipoles with 1.6 m long and 2 BH dipoles with 0.8 m long in each cell. After magnetization of stainless steel vacuum chamber of the booster were identified and then dismantled, annealed, and re-installed, the electron beam energy of the Taiwan Photon Source (TPS) in the booster ring has ramped to 3 GeV in a week. The booster tune correction during ramping is one of the main reasons why the booster commissioning progress is so fast. In this paper the summarized the booster tune monitor system will be summarised  
MOPGF088 Integrating the Measuring System of Vibration and Beam Position Monitor to Study the Beam Stability 1
  • C.H. Huang, Y.-S. Cheng, P.C. Chiu, K.T. Hsu, K.H. Hu, C.Y. Liao
    NSRRC, Hsinchu, Taiwan
  For a low emittance light source, beam orbit motion needs to be controlled within submicron for obtaining a high quality light. Magnets vibration especially quadruples will be one of the main sources to destroy the beam stability. In order to study the relationship between vibration and beam motion, it is highly desirable to use a synchronous data acquisition system which integrates measurement of vibration and beam position monitor systems especially for the coherence analysis. For a larger vibration such as earthquakes are also deleterious to beam stability or even make the beam trip due to the quench of superconducting RF cavity. A data acquisition system integrated with an earthquake detector is also quite necessary to show and archive the data on the control system. The data acquisition systems of vibration and earthquake measurement system are summarized in this report. The relationship between the beam motion and magnets vibration will also study here.  
poster icon Poster MOPGF088 [0.499 MB]  
MOPGF090 Control of Fast-Pulsed Power Converters at CERN Using a Function Generator/Controller 1
  • R. Murillo-Garcia, Q. King, M. Magrans de Abril
    CERN, Geneva, Switzerland
  The electrical power converter group at CERN is responsible for the design of fast-pulsed power converters. These generate a flat-top pulse of the order of a few milliseconds. Control of these power converters is orchestrated by an embedded computer, known as the Function Generator/Controller (FGC). The FGC is the main component in the so-called RegFGC3 chassis, which also houses a variety of purpose-built cards. Ensuring the generation of the pulse at a precise moment, typically when the beam passes, is paramount to the correct behaviour of the accelerator. To that end, the timing distribution and posterior handling by the FGC must be well defined. Also important is the ability to provide operational feedback, and to configure the FGC, the converter, and the pulse characteristics. This paper presents an overview of the system architecture as well as the results obtained during the commissioning of this control solution in CERN's new Linac4.  
poster icon Poster MOPGF090 [8.193 MB]  
MOPGF091 White-Rabbit Based Revolution Frequency Program for the Longitudinal Beam Control of the CERN PS 1
  • D. Perrelet, Y. Brischetto, H. Damerau, A.V. Villanueva
    CERN, Geneva, Switzerland
  • D. Oberson
    HEIA-FR, Fribourg, Switzerland
  • M.V. Sundal
    IST, Lisboa, Portugal
  The measured bending field of the CERN Proton Synchrotron (PS) is received in real-time by the longitudinal beam control system and converted into the revolution frequency used as set-point for beam phase and radial loops. With the renovation of the bending field measurement system the transmission technique is changed from a differential sequence of pulses, the so-called B-train, to a stream of Ethernet frames based on the White Rabbit protocol. The packets contain field, its derivative and auxiliary information. A new frequency program for the conversion of the bending field into the revolution frequency, depending also on parameters like radius of the accelerator and the particle type, has been developed. Instead of storing large conversion tables from field to frequency for fixed parameters, the frequencies are directly calculated in programmable logic (FPGA). In order to reduce development time and keep flexibility, the conversion is processed in real-time in the FPGA using Xilinx floating-point primitives mapped by a higher level tool Simulink System Generator. Commissioning with beam of the new frequency program in the PS is progressing.
Authors: D. Perrelet, Y. Brischetto, H. Damerau, D. Oberson, M. Sundal, A. Villanueva
poster icon Poster MOPGF091 [0.991 MB]  
MOPGF092 Integration of the TRACK Beam Dynamics Model to Decrease LINAC Tuning Times 1
  • C.E. Peters, C. Dickerson, F. Garcia, M.A. Power
    ANL, Argonne, Illinois, USA
  Funding: This work is supported by the U.S. DOE, Office of Nuclear Physics, contract No. DE-AC02-06CH11357.  This research used resources of ANLs ATLAS facility, which is a DOE Office of Science User Facility
The Accelerator R&D Group within the Argonne National Laboratory (ANL) Physics Division maintains a beam dynamics model named TRACK. This simulation code has the potential to assist operators in visualizing key performance parameters of the Argonne Tandem Linear Accelerating System (ATLAS). By having real-time access to visual and animated models of the particle beam transverse and longitudinal phase spaces, operators can more quickly iterate to a final machine tune. However, this effort requires a seamless integration into the control system, both to extract initial run-time information from the accelerator, and to present the simulation results back to the users. This paper presents efforts to pre-process, batch execute, and visualize TRACK particle beam physics simulations in real-time via the ATLAS Control System.
poster icon Poster MOPGF092 [2.199 MB]  
MOPGF093 Real-time Beam Loading Compensation for Single SRF Cavity LLRF Regulation 1
  • I. Rutkowski, M. Grzegrzólka
    Warsaw University of Technology, Institute of Electronic Systems, Warsaw, Poland
  • Ł. Butkowski, Ch. Schmidt
    DESY, Hamburg, Germany
  • M. Kuntzsch
    HZDR, Dresden, Germany
  Stable and reproducible generation of a photon beam at Free Electron Lasers (FELs) necessitates a low energy spread of the electron beam. A low level radio frequency (LLRF) control system stabilizes the RF field inside accelerating modules. An electron beam passing through the cavity induces a drop in the actual stored field proportional to the charge, the cavity shunt impedance, and the bunch repetition rate. The feedback loop compensates for the perturbation after the accelerating gradient drops. Due to the digital loop delay and limited bandwidth of the closed loop system, this disturbance induces control errors which can increase beam energy spread. An open-loop controller uses information obtained from the beam diagnostic systems accounting in real-time for fluctuations of the beam current. This paper describes the bunch charge detection scheme, its implementation, as well as results of the tests performed on the ELBE (Electron Linac for beams with high Brilliance and low Emittance) radiation source at the HZDR (Helmholtz-Zentrum Dresden-Rossendorf) facility.  
poster icon Poster MOPGF093 [4.046 MB]  
Automatic Tuning of an Optical Notch Filter for Stochastic Cooling  
  • A.O. Sidorin, N. Shurkhno, G.V. Trubnikov
    JINR, Dubna, Moscow Region, Russia
  Longitudinal stochastic cooling of the beam in High Energy Storage Ring of the FAIR project and in the heavy ion collider of the NICA project is planned to be realized using the filter method. An unique optical notch filter was developed in cooperation between JINR and FZJ. The tuning of the filter is one of the most time consumption procedures. The automatic system developed for the tuning of the filter is described.  
MOPGF097 Architecture of Transverse Multi-Bunch Feedback Processor at Diamond 1
  • M.G. Abbott, G. Rehm, I.S. Uzun
    DLS, Oxfordshire, United Kingdom
  We describe the detailed internal architecture of the Transverse Multi-Bunch Feedback processor used at Diamond for control of multi-bunch instabilities and measurement of betatron tunes. Bunch by bunch selectable control over feedback filters, gain and excitation allows fine control over feedback, allowing for example the single bunch in a hybrid or camshaft fill pattern to be controlled independently from the bunch train. It is also possible to excite all bunches at a single frequency while simultaneously sweeping the excitation for tune measurement of a few selected bunches. The single frequency excitation has been used for continuous measurement of the beta-function. A simple programmable event sequencer provides support for up to 7 steps of programmable sweeps and changes to feedback and excitation, allowing a variety of complex and precisely timed beam characterisation experiments including grow-damp measurements in unstable conditions and programmed bunch cleaning. Finally input and output compensation filters allow for correction of front end and amplifier phasing at higher frequencies.  
poster icon Poster MOPGF097 [0.247 MB]  
MOPGF099 Upgraded Control System for LHC Beam-Based Collimator Alignment 1
  • G. Valentino, G. Baud, M. Gąsior, S. Jackson, L.K. Jensen, J. Olexa, S. Redaelli, J. Wenninger
    CERN, Geneva, Switzerland
  In the Large Hadron Collider (LHC), over 100 movable collimators are connected to a three-tier control system which moves them to the required settings throughout the operational cycle from injection to collision energy. A dedicated control system was developed to align the collimators to the beam during machine commissioning periods and hence determine operational settings for the active run. During Long Shutdown 1, the control system was upgraded to allow beam-based alignments to be performed using embedded beam position monitors in 18 newly installed collimators as well as beam loss monitors. This paper presents the new collimation controls architecture for LHC Run II along with several modifications in the Java-based application layer.  
poster icon Poster MOPGF099 [1.414 MB]  
MOPGF175 A Unified Approach to the Design of Orbit Feedback with Fast and Slow Correctors 1
  • S. Gayadeen, M.T. Heron, G. Rehm
    DLS, Oxfordshire, United Kingdom
  A unified control design is proposed to simultaneously determine control actions for both fast and slow arrays of correctors used for orbit feedback. By determining the interaction of the spatial subspaces of each array of correctors, spatial modes which require both fast and slow correctors can be identified. For these modes, a mid-ranging control technique is proposed to systematically allocate control action for each corrector. The mid-ranging control technique exploits the different dynamic characteristics of the correctors to ensure that the two arrays of actuators work together and avoid saturation of the fast correctors. Simulation results for the Diamond Storage Ring are presented.  
poster icon Poster MOPGF175 [0.995 MB]  
MOPGF177 Robust Stability Analysis of Orbit Feedback Controllers 1
  • S. Gayadeen, M.T. Heron, G. Rehm
    DLS, Oxfordshire, United Kingdom
  Closed loop stability of electron orbit feedback controllers is affected by mismatches between the accelerator model and the real machine. In this paper, the small gain theorem is used to express analytical criteria for closed loop stability in the presence of spatial uncertainty. It is also demonstrated how the structure of the uncertainty models affects the conservativeness of the robust stability results. The robust stability criteria are applied to the Diamond Light Source electron orbit controller and bounds on the allowable size of spatial uncertainties which guarantee closed loop stability is determined.  
poster icon Poster MOPGF177 [1.023 MB]  
MOPGF178 Uncertainty Modelling of Response Matrix 1
  • S. Gayadeen, M.T. Heron, G. Rehm
    DLS, Oxfordshire, United Kingdom
  Electron orbit feedback controllers are based on the inversion of the response matrix of the storage ring and as a result, mismatches between the accelerator model and the real machine can limit controller performance or cause the controller to become unstable. In order to perform stability analysis tests of the controller, accurate uncertainty descriptions are required. In this paper, BPM scaling errors, actuator scaling errors and drifts in tune are considered as the main sources of spatial uncertainties and because most electron orbit feedback systems use Singular Value Decomposition (SVD) to decouple the inputs and outputs of the system, the uncertainty can be expressed in terms of this decomposition. However SVD does not allow the main sources of uncertainty to be decoupled so instead, a Fourier-based decomposition of the response matrix is used to decouple and model the uncertainties. In this paper, both Fourier and SVD uncertainty modelling methods are applied to the Diamond Light Source storage ring and compared.  
poster icon Poster MOPGF178 [1.465 MB]