PEP-II longitudinal feedback and the low groupdelay woofer Dmitry Teytelman 1
Outline I. PEP-II longitudinal feedback and the woofer channel II. Low group-delay woofer topology III. Why do we need a separate woofer processor? IV. Prototype LGDW: system description V. User interface features VI. Experimental measurements with the low group-delay woofer VII.Production LGDW: system description VIII.Summary 2
PEP-II LFB and the woofer channel: original configuration BPM Beam Kicker structure LNA Comb generator Timing and control Power amplifier Kicker oscillator locked to 9/4 f rf 171 MHz Low-pass filter Phase servo ADC, downsampler Master oscillator locked to 6 f rf 2856 MHz DSP Farm of digital signal processors Holdbuffer, DAC Low-pass filter QPSK modulator Woofer link To RF stations 3
Why do we need a separate woofer processor? Any feedback system is limited - concepts of minimum and maximum gain. Minimum gain is important in instability control - below that value the system is unstable Maximum gain is defined by the gain margin of the feedback loop. Above the maximum gain the system again becomes unstable. Initially, as the loop gain is increased from the minimum value, the system becomes more stable (better damped). Gain (db) Angle (deg) 1 1 2 3 3 4 5 6 7 8 9 1 2 3 4 5 6 Open loop gain.74548 Dominant pole damping.4618 ms 1 7 2 3 4 5 6 7 8 9 As the gain starts to approach the maximum value the damping decreases. There is an optimal point between the two values where best damping is achieved. 4
Why do we need a separate woofer processor? Any feedback system is limited - concepts of minimum and maximum gain. Minimum gain is important in instability control - below that value the system is unstable Maximum gain is defined by the gain margin of the feedback loop. Above the maximum gain the system again becomes unstable. Initially, as the loop gain is increased from the minimum value, the system becomes more stable (better damped). Gain (db) Angle (deg) 1 1 2 3 2 3 4 5 6 7 8 9 1 2 3 4 5 6 Open loop gain 1.6152 Dominant pole damping 1.3922 ms 1 7 2 3 4 5 6 7 8 9 As the gain starts to approach the maximum value the damping decreases. There is an optimal point between the two values where best damping is achieved. 5
Why do we need a separate woofer processor? Any feedback system is limited - concepts of minimum and maximum gain. Minimum gain is important in instability control - below that value the system is unstable Maximum gain is defined by the gain margin of the feedback loop. Above the maximum gain the system again becomes unstable. Initially, as the loop gain is increased from the minimum value, the system becomes more stable (better damped). Gain (db) Angle (deg) 1 1 2 3 2 3 4 5 6 7 8 9 1 2 3 4 5 6 Open loop gain 2.4849 Dominant pole damping 2.7372 ms 1 7 2 3 4 5 6 7 8 9 As the gain starts to approach the maximum value the damping decreases. There is an optimal point between the two values where best damping is achieved. 6
Why do we need a separate woofer processor? Any feedback system is limited - concepts of minimum and maximum gain. Minimum gain is important in instability control - below that value the system is unstable Maximum gain is defined by the gain margin of the feedback loop. Above the maximum gain the system again becomes unstable. Initially, as the loop gain is increased from the minimum value, the system becomes more stable (better damped). Gain (db) Angle (deg) 1 1 2 3 2 3 4 5 6 7 8 9 1 2 3 4 5 6 Open loop gain 3.3547 Dominant pole damping 2.2778 ms 1 7 2 3 4 5 6 7 8 9 As the gain starts to approach the maximum value the damping decreases. There is an optimal point between the two values where best damping is achieved. 7
Why do we need a separate woofer processor? Any feedback system is limited - concepts of minimum and maximum gain. Minimum gain is important in instability control - below that value the system is unstable Maximum gain is defined by the gain margin of the feedback loop. Above the maximum gain the system again becomes unstable. Initially, as the loop gain is increased from the minimum value, the system becomes more stable (better damped). Gain (db) Angle (deg) 1 1 2 3 2 3 4 5 6 7 8 9 1 2 3 4 5 6 Open loop gain 4.2244 Dominant pole damping 1.775 ms 1 7 2 3 4 5 6 7 8 9 As the gain starts to approach the maximum value the damping decreases. There is an optimal point between the two values where best damping is achieved. 8
Why do we need a separate woofer processor? Any feedback system is limited - concepts of minimum and maximum gain. Minimum gain is important in instability control - below that value the system is unstable Maximum gain is defined by the gain margin of the feedback loop. Above the maximum gain the system again becomes unstable. Initially, as the loop gain is increased from the minimum value, the system becomes more stable (better damped). Gain (db) Angle (deg) 1 1 2 3 2 3 4 5 6 7 8 9 1 2 3 4 5 6 Open loop gain 5.941 Dominant pole damping 1.3222 ms 1 7 2 3 4 5 6 7 8 9 As the gain starts to approach the maximum value the damping decreases. There is an optimal point between the two values where best damping is achieved. 9
Why do we need a separate woofer processor? Any feedback system is limited - concepts of minimum and maximum gain. Minimum gain is important in instability control - below that value the system is unstable Maximum gain is defined by the gain margin of the feedback loop. Above the maximum gain the system again becomes unstable. Initially, as the loop gain is increased from the minimum value, the system becomes more stable (better damped). Gain (db) Angle (deg) 1 1 2 3 2 3 4 5 6 7 8 9 1 2 3 4 5 6 Open loop gain 5.9638 Dominant pole damping.9379 ms 1 7 2 3 4 5 6 7 8 9 As the gain starts to approach the maximum value the damping decreases. There is an optimal point between the two values where best damping is achieved. 1
Filter response: downsampled LFB PEP-II LFB system processes bunch motion every 6 turns. A 6-tap FIR filter has 3 taps * 6 turns = 18 turns of delay. With cable and sampling delays we get 152 µs Relatively large phase slope around the synchrotron frequency leads to limited gain margins. How can the situation be improved? Clearly, if we process beam motion on every turn the delay will be reduced. However the LFB has limited processing power and cannot be pushed beyond 6 turns downsamping. We built a separate processing channel just for the woofer signal that computes corrections on every turn! Phase (deg) Coeff Gain (db) 5 5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Sample 25 2 15 1 5 5 2 2 4 6 1 2 3 4 5 6 7 8 9 1 11 Group delay 151.6 µs 1 2 3 4 5 6 7 8 9 1 11 11
LFB and the low group-delay woofer channel BPM Beam Kicker structure LNA Comb generator Timing and control Power amplifier Kicker oscillator locked to 9/4 f rf 171 MHz Low-pass filter Phase servo ADC, downsampler Master oscillator locked to 6 f rf 2856 MHz DSP Farm of digital signal processors Low group-delay channel DSP at 9.81 MHz Holdbuffer, DAC Low-pass filter QPSK modulator Woofer link To RF stations 12
Filter response: low group-delay woofer Group delay is reduced by a factor of 2 Note the wider filter bandwidth - directly related to a shorter time-domain response. Still a very straightforward sampled sinewave design - more advanced filters need further work. Coeff 3 2 1 1 2 3 2 4 6 8 1 12 14 Sample 25 2 Gain (db) 15 1 5 1 1 2 3 4 5 6 7 8 9 1 11 Group delay 77.4 µs Phase (deg) 1 2 3 1 2 3 4 5 6 7 8 9 1 11 13
Damping provided by LGDW With the lower group delay the new woofer can achieve much faster damping, than the LFB. While the gain margin is an issue for both systems, the LGDW runs into the margin at higher loop gains Due to lower group delay the closed-loop bandwidth is higher. Peaking in the response happens further from the synchrotron frequency. Gain (db) Angle (deg) 1 1 2 Open loop gain.7753 3 2 3 4 5 6 7 8 9 1 11 1 2 3 4 5 6 Dominant pole damping.37755 ms 1 7 2 3 4 5 6 7 8 9 1 11 14
Damping provided by LGDW With the lower group delay the new woofer can achieve much faster damping, than the LFB. While the gain margin is an issue for both systems, the LGDW runs into the margin at higher loop gains Due to lower group delay the closed-loop bandwidth is higher. Peaking in the response happens further from the synchrotron frequency. Gain (db) Angle (deg) 1 1 2 Open loop gain 2.3544 3 2 3 4 5 6 7 8 9 1 11 1 2 3 4 5 6 Dominant pole damping 2.9552 ms 1 7 2 3 4 5 6 7 8 9 1 11 15
Damping provided by LGDW With the lower group delay the new woofer can achieve much faster damping, than the LFB. While the gain margin is an issue for both systems, the LGDW runs into the margin at higher loop gains Due to lower group delay the closed-loop bandwidth is higher. Peaking in the response happens further from the synchrotron frequency. Gain (db) Angle (deg) 1 1 2 Open loop gain 3.9383 3 2 3 4 5 6 7 8 9 1 11 1 2 3 4 5 6 Dominant pole damping 8.569 ms 1 7 2 3 4 5 6 7 8 9 1 11 16
Damping provided by LGDW With the lower group delay the new woofer can achieve much faster damping, than the LFB. While the gain margin is an issue for both systems, the LGDW runs into the margin at higher loop gains Due to lower group delay the closed-loop bandwidth is higher. Peaking in the response happens further from the synchrotron frequency. Gain (db) Angle (deg) 1 1 2 Open loop gain 5.5222 3 2 3 4 5 6 7 8 9 1 11 1 2 3 4 5 6 Dominant pole damping 6.6782 ms 1 7 2 3 4 5 6 7 8 9 1 11 17
Damping provided by LGDW With the lower group delay the new woofer can achieve much faster damping, than the LFB. While the gain margin is an issue for both systems, the LGDW runs into the margin at higher loop gains Due to lower group delay the closed-loop bandwidth is higher. Peaking in the response happens further from the synchrotron frequency. Gain (db) Angle (deg) 1 1 2 Open loop gain 7.16 3 2 3 4 5 6 7 8 9 1 11 1 2 3 4 5 6 Dominant pole damping 5.1445 ms 1 7 2 3 4 5 6 7 8 9 1 11 18
Damping provided by LGDW With the lower group delay the new woofer can achieve much faster damping, than the LFB. While the gain margin is an issue for both systems, the LGDW runs into the margin at higher loop gains Due to lower group delay the closed-loop bandwidth is higher. Peaking in the response happens further from the synchrotron frequency. Gain (db) Angle (deg) 1 1 2 Open loop gain 8.6899 3 2 3 4 5 6 7 8 9 1 11 1 2 3 4 5 6 Dominant pole damping 3.817 ms 1 7 2 3 4 5 6 7 8 9 1 11 19
Damping provided by LGDW With the lower group delay the new woofer can achieve much faster damping, than the LFB. While the gain margin is an issue for both systems, the LGDW runs into the margin at higher loop gains Due to lower group delay the closed-loop bandwidth is higher. Peaking in the response happens further from the synchrotron frequency. Gain (db) Angle (deg) 1 1 2 Open loop gain 1.2738 3 2 3 4 5 6 7 8 9 1 11 1 2 3 4 5 6 Dominant pole damping 2.5328 ms 1 7 2 3 4 5 6 7 8 9 1 11 2
Low group-delay woofer: prototype system The prototype is based on a off-the-shelf FPGA DSP board. It uses the existing LFB front-end monitor signal and the woofer output is passed to the existing back-end LFB module which drives the RF systems via fiber optic links. The LGDW prototype implements a 14 tap FIR filter, with a 9.81 MS/s processing rate. Only one working channel due to signal coupling in the DSP board. HER system was commissioned on May 6, 24. From HER and LER LFB phase monitors Offset&filter board #1 (HER) Offset&filter board #2 (LER) To HER back end module The low group-delay woofer allowed us to push the HER current from 138 ma to 156 ma while significantly reducing the rate of longitudinal instability aborts. ADC SRAM 64Kx16 SRAM 64Kx16 ADC To LER back end module FPGA XC485XLA FPGA XC485XLA DAC GVA 2 FPGA board DAC Connector board Front panel status LEDs, trigger inputs Ethernet Linux PC EPICS IOC Parallel port driver 21
LGDW prototype 22
LGDW uses a soft IOC running on a Linux PC User interface via EPICS and EDM display manager Top level panel: on/off control for both rings and status summary. Status colors: Green Yellow Orange Red No alarm Channel saturation Register verify error LGDW: user interface Missing clock or interface fault 23
Main control panel Two sets of 16 filter coefficients. Prototype used only the first 14. Control register: Memory control mode Data acquisition state Coefficient set select External trigger enable Shift gain Output delay 24
Memory control mode: CPU for EPICS access and ADC for data acquisition Data acquisition state: Stop and Run. When Run is selected memory is filled with input data, then acquisition stops Coefficient set select: modifying a coefficient in the active set is undesirable. Normally we modify the second set, then switch. Main control panel - continued External trigger enable: allows one to control the coefficient set and trigger data acquisition Shift gain: number of bits the output of the filter is shifted left (gain of 2 N ) Output delay: delay buffer length to time the kick to the beam 25
User interface features: beam diagnostics Diagnostic waveform panel. IOC can be configured to periodically acquire beam data and present it in 4 plots: mean signal over a turn, RMS (filtered) over a turn, filtered time domain record of the channel with the highest RMS, averaged spectrum The overall mean and rms values are also computed and can be stripcharted 26
Save and restore functions with confirm Clicking on the file name brings up a file selection dialog. Restore function is invasive and will disrupt the feedback for a short while, even if the restored settings are the same as current values. User interface: save/restore 27
Two types of grow/damp measurements: all modes BPM Beam Kicker structure LNA Comb generator Timing and control Power amplifier Kicker oscillator locked to 9/4 f rf 171 MHz Low-pass filter Phase servo ADC, downsampler Master oscillator locked to 6 f rf 2856 MHz DSP Farm of digital signal processors Low group-delay channel DSP at 9.81 MHz Holdbuffer, DAC Low-pass filter QPSK modulator Woofer link To RF stations 28
Two types of grow/damp measurements: HOMs only BPM Beam Kicker structure LNA Comb generator Timing and control Power amplifier Kicker oscillator locked to 9/4 f rf 171 MHz Low-pass filter Phase servo ADC, downsampler Master oscillator locked to 6 f rf 2856 MHz DSP Farm of digital signal processors Low group-delay channel DSP at 9.81 MHz Holdbuffer, DAC Low-pass filter QPSK modulator Woofer link To RF stations 29
Grow/damp measurements for the low modes During these measurements we turn off both wideband (LFB) and narrowband (LGDW) channels. Measures open-loop growth and closed-loop damping for the fundamental driven modes Due to optimized gain partitioning the system can recapture beam motion at larger amplitudes. For the grow/damp measurements this allows longer growth intervals and better SNR. Larger dynamic range of the new woofer will allow it to handle significantly larger beam transients due to injection, RF, etc. deg@rf 1.5 a) Osc. Envelopes in Time Domain 15 1 5 Bunch No. 6.3 6.299 6.298 6.297 6.296 6.295 2 1 Time (ms) 6.294 1742 1742.5 1743 1743.5 1744 Mode No. 6.63 6.625 6.62 6.615 c) Oscillation freqs (pre brkpt) e) Oscillation freqs (post brkpt) 6.61 1742 1742.5 1743 1743.5 1744 Mode No. deg@rf Rate (1/ms) Rate (1/ms).4.2 1.2.8.6.4.2 1 Mode No. 1 b) Evolution of Modes 2 1 Time (ms) d) Growth Rates (pre brkpt) 1742 1742.5 1743 1743.5 1744 Mode No..5 1 1.5 2 2.5 f) Growth Rates (post brkpt) 1742 1742.5 1743 1743.5 1744 Mode No. PEP II HER:feb244/17438: Io= 13.12mA, Dsamp= 6, ShifGain= 6, Nbun= 174, Gain1= 1, Gain2=, Phase1= 15, Phase2= 15, Brkpt= 52, Calib= 1.6. 3
Growth and damping rate summary (mode -3) Growth rates are similar to what we have seen historically. At 13 ma the new low group-delay woofer provides 3 to 3.5 ms -1 of net.2 damping. 6 8 1 12 14 Beam current (ma) Oscillation frequency (Hz) Growth rate (ms 1 ) 1.2 1.8.6.4 64 635 63 625 Open loop 62 6 8 1 12 14 Beam current (ma) Damping rate (ms 1 ) Oscillation frequency (Hz) 1 1.5 2 2.5 3 Closed loop 3.5 6 8 1 12 14 Beam current (ma) 67 665 66 655 65 645 6 8 1 12 14 Beam current (ma) 31
Rates from 6/19/23 for comparison: standard woofer Net damping with the standard woofer configuration is around 2 ms -1. Even with the preliminary filter design the low group delay woofer improves low mode damping by 5%. Oscillation frequency (Hz) Growth rate (ms 1 ) 2 1.5 1 Open loop.5 14 16 18 11 Beam current (ma) 545 54 535 53 525 14 16 18 11 Beam current (ma) Growth rate (ms 1 ) Oscillation frequency (Hz).5 1 1.5 Closed loop 2 14 16 18 11 Beam current (ma) 55 545 54 535 53 525 14 16 18 11 Beam current (ma) 32
Production woofers: hardware description What are we adding to the LGDW? Wideband amplifier to boost the LFB ADC signal and split the output into LFB and LGDW channels A PLL to generate the processing clock locally From the PDL CLC 144 A slow multi-channel DAC for offset trimming Current topology To the LFB ADC To the LGDW LPF Migrate from IEEE-1284 parallel port to USB using FT245BM USB FIFO chip on an off-the-shelf daughterboard module Production LGDW is based on bigger and better FPGA board (3x the logic capacity, 2x the memory) than the prototype. Minimal changes to the software - faster data readout, larger coefficient sets, possibly a peak kick level detector. 33
New low group-delay woofer: block diagram Integrates existing analog processing functions and digital interconnect board with USB functionality, PLL module, and slow DACs. Wideband amplifiers and splitters are not shown on this diagram To HER back end module 476 MHz Analog processing (HER) Ethernet ADC FPGA XCV8 6 DAC 9.81 MHz Processing clock PLL Linux PC EPICS IOC SRAM 128Kx16 GVA 25 FPGA board SRAM 128Kx16 USB interface, slow DACs USB driver ADC FPGA XCV8 6 DAC Analog processing (LER) FE offset To LER back end module Front panel status LEDs, trigger inputs 34
Summary Performance of PEP-II longitudinal stabilization systems is limited by the group delay and bandwidth considerations. Low group-delay woofer channel helps achieve high damping of the low-order modes excited by the RF cavity fundamental. The prototype system operated reliably and performed as expected. Low groupdelay woofer allowed us to significantly raise HER beam current. Final long-term systems are in production. LGDW is equipped with a simple, yet functional EPICS interface. Diagnostic information from the soft IOC can be routed to stripcharts, warning panels, etc. With separated control of low modes and HOMs new types of instability measurements become feasible. In addition the separation aids in tuning and optimizing the overall system damping. 35