Commissioning the Fast Orbit Feedback System at SSRF Bocheng Jiang，Chongxian Yin Dec. 12, 2017 GM2017 2018年9月13日星期四

Contents 1、 System layout 2、 Sub system performance 2018年9月13日星期四 Contents 1、  System layout 2、  Sub system performance 3、  Algorithm of the feedback systems & Commissioning 4、  Summary

Main paramaters: 1、System layout Storage Ring Energy：3.5 GeV； 20 DBA cells / 4 superperiods Circumference：432m； Current：5/300 mA (S/M bunch)； emittance：3.9 nm rad； Strait section：4*12m，16*6.5m； RF voltage：4-6 MV Max Power：~600kW Orbit Stability：<10% beam size

Lattice Functions for One Super-Period 1、System layout Lattice Functions for One Super-Period Orbit stability requirement 5μm in horizontal plane 1 μm in vertical plane

1、System layout There are 60 air coils for FOFB in H/V plane respectively. The steering strength 0.08mrad (H) and 0.06mrad (V). At the place of air coil the vacuum chamber thickness is 2mm （SS） instead of 3mm for else where to reduce the eddy current. There are totally 140BPM in the ring, however only 40~60 BPMs used for FOFB.

1、System layout SOFB steer FOFB steer 2018年9月13日星期四 1、System layout SOFB steer FOFB steer For SOFB there are 80 steers in H/V plane respectively，the correctoin strength is 1.2mrad and 1.0mrad for H/V. SOFB can include all 140 BPMs，At present only 60～80 BPMs are controlled by SOFB, Those BPM with large noises are excluded。 The locations of SOFB steers and FOFB steers are different. The BPM of FOFB is sub-collection of SOFB.

1、System layout All electronics are installed in 10 stations, electronics in one station each control 2 cells: 2 VME single board computers, 4 BPM electronics (Libera) 4 interfaces to BPM electronics, 12 interfaces to power supply controller 12 power supply controllers (by power supply group), 12 power supply (by power supply group) 1 reflective memory, 1 timing module

1、System layout R-1 is based on SVD decomposing method. PID is simplied, with k control gain factor, a control singularity.

2、Sub system performance BPM Libera fast acquisition channel work at 5KHz. Now 40 ID BPM (at the ends of straight section has been upgrade to Libera brilliance, will going to work at 10KHz).

2、Sub system performance Air coil band width 1KHz

2、Sub system performance The step response of correctors in horizontal plane in vertical plane * the measured step response curve for 20 pairs correctors

2、Sub system performance Vacuum chamber bandwidth（1KHz）

3、 Algorithm of the feedback systems & Commissioning SOFB BPM SOFB steering FOFB steering FOFB BPM Communicate FOFB SOFB

3、 Algorithm of the feedback systems & Commissioning SOFB based on inverse response matrix generated SVD method. Global feedback, with several ID BPM higher weighted for orbit sensitive beam lines. FOFB inverse response matrix generated SVD method & PID controller. SOFB strong the correction strength, low feedback frequency <0.2Hz. FOFB weak the correction strength, saturate in few hours; fast the feedback frequency 5KHz. FOFB needs to transfer correction to SOFB frequently to avoid power supply saturate. SOFB get present orbit and FOFB power supply. New Orbit= present orbit + R * FOFB Power supply FOFB set reference orbit with New Orbit, the power supply is automatically reset to Zero. FOFB needs to reset Power supply Inform SOFB Inform FOFB The orbit distortion by FOBF power supply reset is detected by SOFB and corrected by SOFB 快校正铁饱和解决方案：将快校正铁静态校正量传输给慢校正铁。 途经：轨道慢反馈系统实时更新轨道快反馈系统参考轨道。 缺点：长时间轨道稳定性依然由慢反馈系统决定。 优点：快反馈系统外BPM处的轨道控制的更好。 技术难点：1、两套系统的校正铁是分立的，因此校正量不能完全替代。2、设置参考轨道和慢反馈校正轨道到参考轨道上无法避免的有时间差，在这个时间间隔中快反馈得到的是一个错误的参考轨道，因此会做出错误的校正，并会累积。 优化途经：尽量增加慢反馈系统奇异子个数，覆盖更多的特征向量；尽量减小设置参考轨道和参考轨道实际变化的时间差；快反馈系统选择合适的奇异子个数和PID参数。

3、 Algorithm of the feedback systems & Commissioning SOFB communicate with FOFB every 17 seconds. Although FOFB can work along for hours, in order to minimize the orbit disturb when resetting the FOFB power supply, it is necessary to reset when power supply is small. In 17 seconds, the FOFB power supply is only at several mA. The time can be 20,25 …seconds, 17 is a prime number, it is easy to identify the problem caused by SOFB+FOBF The response matrix of SOFB and FOFB is totally different, because the steers are at different phase advance. For SOFB doing SVD, the singular values should be used as more as possible to keep the capability to correct the orbit distortion by FOFB resetting yet not all to increase the noise tolerance. New Orbit= present orbit + R * FOFB Power supply, where R is a matrix generated by SVD decompose and multiply again with drop off some of the singular value to reduce the noise. The time gap between FOFB resetting and SOFB correct the distortion should be as small as possible.

3、 Algorithm of the feedback systems & Commissioning Singular value used for SOFB, 58 in X plane,59 in Y plane(#41~#58 less weighted),

3、 Algorithm of the feedback systems & Commissioning Singular value for FOFB, 40 for X plane, 41 for Y plane. PID setting k=0.25，a=0.85。

3、 Algorithm of the feedback systems & Commissioning The system is commissioned in 2013 successfully and put for user operation

3、 Algorithm of the feedback systems & Commissioning The FOFB can suppress orbit distortion within 100Hz, which covers the maximum noise source at 50Hz.

3、 Algorithm of the feedback systems & Commissioning Cumulative PSD

3、 Algorithm of the feedback systems & Commissioning The power supply of FOFB, when ID changes gap, it still less than 1A SOFB working together with FOFB for more than 45 hours. The orbit jitter is from ID gap adjust.

3、 Algorithm of the feedback systems & Commissioning BPMs controlled by FOFB system, the orbit jitter is smaller than that in SOFB while not in FOBF. RMS in X plane 0.26μm， RMS in Y plane 0.25 μm 。

3、 Algorithm of the feedback systems & Commissioning Data of 1Hz DCCT SOFB SOFB+FOFB

3、 Algorithm of the feedback systems & Commissioning BPM SA 10Hz data 2013.11.23 10：30AM SOFB +FOFB SOFB SOFB+FOFB SOFB

3、 Algorithm of the feedback systems & Commissioning 2008-2-19 499.68250 2012-2-10 499.683582 2011-2-23 499.679647 2013-3-9 499.678649 2009-3-5 499.676483 2010-3-10 499.677758 MHZ 2012-10-6 499.668675 2011-9-16 499.664618 2010-9-22 499.661131 2009-9-7 499.65945 2008-9-25 499.65552 RF frequency feedback is integrated in SOFB, ~30KHz summer to winter in 2008, and ~10KHz in 2013, Day to night around 200~300Hz

4、Summary The FOFB system is successfully commissioned and works well with SOFB. The long term orbit stability is determined by SOFB, FOFB is a sub system of SOFB which controls high frequency distortions (>1Hz) Despite of worst ground vibration for SSRF, the orbit stability at SSRF far bellow the specification 0.1σ

Acknowledgement I’d like to thank Jeff Corbett for many discussion on feedback Algorithm Thanks also goes to SSRF colleagues to solve the hardware problems.

Thanks