{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:02:52Z","timestamp":1760230972082,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2022,8,19]],"date-time":"2022-08-19T00:00:00Z","timestamp":1660867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002301","name":"the Estonian Research Council","doi-asserted-by":"publisher","award":["PRG658"],"award-info":[{"award-number":["PRG658"]}],"id":[{"id":"10.13039\/501100002301","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Control applications targeting fast industrial processes rely on real-time feasible implementations. One of such applications is the stabilization of an electron bunch arrival time in the context of a linear accelerator. In the past, only the electric field accelerating the electron bunches was actively controlled in order to implicitly stabilize the accelerated electron beam. Nowadays, beam properties are specifically measured at a target position and then stabilized by a dedicated feedback loop acting on the accelerating structures. This dedicated loop is usually referred to as a beam-based feedback (BBF). Following this, the control system of the electron linear accelerator for beams with high brilliance and low emittance (ELBE) is planned to be upgraded by the BBF, and the problem of implementing a designed control algorithm becomes highly relevant. In this work, we propose a real-time feasible implementation of a high-order H2 regulator based on a field-programmable gate array (FPGA). By presenting simulation and synthesis results made in hardware description language (HDL) VHDL, we show that the proposed digital solution is fast enough to cover the bunch repetition rates frequently used at ELBE, such as 100 kHz. Finally, we verify the implementation by using a dedicated FPGA testbench.<\/jats:p>","DOI":"10.3390\/s22166236","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T01:56:40Z","timestamp":1661133400000},"page":"6236","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Real-Time Regulation of Beam-Based Feedback: Implementing an FPGA Solution for a Continuous Wave Linear Accelerator"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9560-0487","authenticated-orcid":false,"given":"Andrei","family":"Maalberg","sequence":"first","affiliation":[{"name":"Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8145-5837","authenticated-orcid":false,"given":"Michael","family":"Kuntzsch","sequence":"additional","affiliation":[{"name":"Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2167-6280","authenticated-orcid":false,"given":"Eduard","family":"Petlenkov","sequence":"additional","affiliation":[{"name":"Department of Computer Systems, Tallinn University of Technology, 19086 Tallinn, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,19]]},"reference":[{"key":"ref_1","unstructured":"Schlarb, H. (2005, January 16\u201320). Techniques for Pump-Probe Synchronisation of Fsec Radiation Pulses. Proceedings of the Particle Accelerator Conference, Knoxville, TN, USA."},{"key":"ref_2","unstructured":"Pfeiffer, S., Branlard, J., Hoffmann, M., and Schmidt, C. (July, January 30). Advanced LLRF System Setup Tool for RF Field Regulation of SRF Cavities. Proceedings of the 19th International Conference on RF Superconductivity, Dresden, Germany."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2326","DOI":"10.1109\/TNS.2021.3096757","article-title":"MicroTCA.4-Based Low-Level RF for Continuous Wave Mode Operation at the ELBE Accelerator","volume":"68","author":"Zenker","year":"2021","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Maalberg, A., Kuntzsch, M., and Petlenkov, E. (2022, January 8\u201310). Regulation of the Linear Accelerator ELBE Exploiting Continuous Wave Mode of a Superconducting RF Cavity. Proceedings of the American Control Conference, Atlanta, GA, USA.","DOI":"10.23919\/ACC53348.2022.9867172"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S1367-5788(02)80010-4","article-title":"H2-optimization\u2014Theory and applications to robust control design","volume":"26","author":"Kwakernaak","year":"2002","journal-title":"Annu. Rev. Control"},{"key":"ref_6","unstructured":"Skogestad, S., and Postlethwaite, I. (2005). Multivariable Feedback Control: Analysis and Design, John Wiley & Sons, Ltd.. [2nd ed.]."},{"key":"ref_7","unstructured":"Pfeiffer, S., Schmidt, C., Bock, M.K., Schlarb, H., Jalmuzna, W., Lichtenberg, G., and Werner, H. (2012, January 20\u201325). Fast Feedback Strategies for Longitudinal Beam Stabilization. Proceedings of the 2012 International Particle Accelerator Conference, New Orleans, LA, USA."},{"key":"ref_8","unstructured":"Koprek, W., Behrens, C., Bock, M.K., Felber, M., Gessler, P., Schlarb, H., Schmidt, C., Schulz, S., Steffen, B., and Wesch, S. (2010, January 23\u201327). Intra-train Longitudinal Feedback for Beam Stabilization at FLASH. Proceedings of the 32nd International Free Electron Laser Conference, Malm\u00f6, Sweden."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Rezaeizadeh, A., Schilcher, T., and Smith, R. (2015, January 15\u201318). MPC based Supervisory Control Design for a Free Electron Laser. Proceedings of the 54th Conference on Decision and Control, Osaka, Japan.","DOI":"10.1109\/CDC.2015.7402452"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"052802","DOI":"10.1103\/PhysRevAccelBeams.19.052802","article-title":"Adaptive robust control of longitudinal and transverse electron beam profiles","volume":"19","author":"Rezaeizadeh","year":"2016","journal-title":"Phys. Rev. Accel. Beams"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1109\/TNS.2021.3067598","article-title":"Online Detuning Computation and Quench Detection for Superconducting Resonators","volume":"68","author":"Bellandi","year":"2021","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_12","unstructured":"L\u00f6hl, F. (2009). Optical Synchronization of a Free-Electron Laser with Femtosecond Precision. [Ph.D. Thesis, University of Hamburg]."},{"key":"ref_13","unstructured":"Bock, M.K. (2013). Measuring the Electron Bunch Timing with Femtosecond Resolution at FLASH. [Ph.D. Thesis, University of Hamburg]."},{"key":"ref_14","unstructured":"Kuntzsch, M., Zenker, K., Maalberg, A., Schwarz, A., Czwalinna, M.K., and Kral, J. (2022, January 12\u201317). Update of the Bunch Arrival Time Monitor at ELBE. Proceedings of the 13th International Particle Accelerator Conference, Bangkok, Thailand."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1109\/TNS.2017.2687981","article-title":"FPGA-Based RF and Piezocontrollers for SRF Cavities in CW Mode","volume":"64","author":"Rybaniec","year":"2017","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"082004","DOI":"10.1103\/PhysRevAccelBeams.21.082004","article-title":"Digital low level rf control system for the International Linear Collider","volume":"21","author":"Wibowo","year":"2018","journal-title":"Phys. Rev. Accel. Beams"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"032003","DOI":"10.1103\/PhysRevAccelBeams.21.032003","article-title":"Real-time cavity simulator-based low-level radio-frequency test bench and applications for accelerators","volume":"21","author":"Qiu","year":"2018","journal-title":"Phys. Rev. Accel. Beams"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"104601","DOI":"10.1103\/PhysRevAccelBeams.24.104601","article-title":"Real-time artificial intelligence for accelerator control: A study at the Fermilab Booster","volume":"24","author":"Herwig","year":"2021","journal-title":"Phys. Rev. Accel. Beams"},{"key":"ref_19","unstructured":"Kumar, V.K.P., and Tsai, Y.-C. (1988, January 25\u201327). Synthesizing optimal family of linear systolic arrays for matrix computations. Proceedings of the International Conference on Systolic Arrays, San Diego, CA, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1109\/TVLSI.2005.859562","article-title":"Energy- and time-efficient matrix multiplication on FPGAs","volume":"13","author":"Jang","year":"2005","journal-title":"IEEE Trans. Very Large Scale Integr. VLSI Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Shen, J., Qiao, Y., Huang, Y., Wen, M., and Zhang, C. (2018, January 27\u201330). Towards a Multi-array Architecture for Accelerating Large-scale Matrix Multiplication on FPGAs. Proceedings of the 2018 International Symposium on Circuits and Systems, Florence, Italy.","DOI":"10.1109\/ISCAS.2018.8351474"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wei, X., Yu, C.H., Zhang, P., Chen, Y., Wang, Y., Hu, H., Liang, Y., and Cong, J. (2017, January 18\u201322). Automated Systolic Array Architecture Synthesis for High Throughput CNN Inference on FPGAs. Proceedings of the 54th Annual Design Automation Conference, Austin, TX, USA.","DOI":"10.1145\/3061639.3062207"},{"key":"ref_23","unstructured":"Walter, T., Ludwig, F., Rehlich, K., and Schlarb, H. (2013, January 12\u201317). Novel Crate Standard MTCA.4 for Industry and Research. Proceedings of the 4th International Particle Accelerator Conference, Shanghai, China."},{"key":"ref_24","unstructured":"Kuntzsch, M., Steinbr\u00fcck, R., Schurig, R., Hierholzer, M., Killenberg, M., Schmidt, C., Hoffmann, M., Iatrou, C., Rahm, J., and Rutkowski, I. (2017, January 20\u201324). MicroTCA.4-Based LLRF for CW Operation at ELBE - Status and Outlook. Proceedings of the 6th International Beam Instrumentation Conference, Grand Rapids, MI, USA."},{"key":"ref_25","unstructured":"Butkowski, \u0141., Kozak, T., Pr\u0119dki, P., Rybaniec, R., and Yang, B.Y. (2015, January 17\u201323). FPGA Firmware Framework for MTCA.4 AMC Modules. Proceedings of the 15th International Conference on Accelerator and Large Experimental Physics Control Systems, Melbourne, Australia."},{"key":"ref_26","unstructured":"(2022, March 30). Data Processing AMC Module for MTCA & ATCA. Available online: https:\/\/www.nateurope.com\/products\/NAT-AMC-TCK7.html."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Killenberg, M., Petrosyan, L.M., Schmidt, C., Marsching, S., and Piotrowski, A. (2014, January 15\u201320). Drivers and Software for MTCA.4. Proceedings of the 5th International Particle Accelerator Conference, Dresden, Germany.","DOI":"10.1109\/RTC.2014.7097449"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Dimitrakopoulos, G., Psarras, A., and Seitanidis, I. (2015). Microarchitecture of Network-on-Chip Routers: A Designer\u2019s Perspective, Springer Science+Business Media.","DOI":"10.1007\/978-1-4614-4301-8"},{"key":"ref_29","unstructured":"Clements, A. (2006). Principles of Computer Hardware, Oxford University Press Inc.. [4th ed.]."},{"key":"ref_30","unstructured":"(2022, May 15). 7 Series FPGAs Data Sheet: Overview. Available online: https:\/\/docs.xilinx.com\/v\/u\/en-US\/ds180_7Series_Overview."},{"key":"ref_31","unstructured":"(2022, May 15). 7 Series DSP48E1 Slice: User Guide. Available online: https:\/\/docs.xilinx.com\/v\/u\/en-US\/ug479_7Series_DSP48E1."},{"key":"ref_32","unstructured":"(2019). IEEE Standard for Floating-Point Arithmetic. (Revision of IEEE 754-2008) (Standard No. IEEE Std 754-2019)."},{"key":"ref_33","unstructured":"(2022, May 15). Floating-Point Operator v7.1: LogiCORE IP Product Guide. Available online: https:\/\/docs.xilinx.com\/v\/u\/en-US\/pg060-floating-point."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6236\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:12:21Z","timestamp":1760141541000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/16\/6236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,19]]},"references-count":33,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["s22166236"],"URL":"https:\/\/doi.org\/10.3390\/s22166236","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,8,19]]}}}