1. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Superconductive cavity driving with FPGA controller Tomasz Czarski Warsaw University of Technology Institute of Electronic Systems ELHEP-DESY Group

2. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Low Level RF control system introduction Superconducting cavity modeling Cavity features Recognition of real cavity system Cavity parameters identification Control system algorithm Experimental results Main topics

3. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Functional block diagram of Low Level Radio Frequency Cavity Control System DOWN- CONVERTER 250 kHz VECTOR MODULATOR CAVITYENVIRONS ANALOG SYSTEM FPGA CONTROLLER FPGA I/Q DETECTOR KLYSTRON PARAMETERS IDENTIFICATION SYSTEM MASTER OSCILATOR 1.3 GHz CONTROLBLOCK PARTICLE FIELD SENSOR COUPLER DAC ADC DIGITAL CONTROL SYSTEM CAVITY RESONATOR and ELECTRIC FIELD distribution

4. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Superconductive cavity modeling dv/dt = A·v + ω 1/2 ·R·i A = -ω 1/2 +i∆ω v n = E·v n-1 + T·ω 1/2 ·R·i n-1 E = (1-ω 1/2 ·T) + i∆ω·T State space – continuous and discrete model Input signal I(s)↔i(t) RF current I(s–iω g ) RF voltage Z(s)∙I(s–iω g ) Output signal Z(s+iω g )∙I(s)↔v(t) Low pass transformation Z(s+iω g ) ≈ ω 1/2 ·R/(s +ω 1/2 – i∆ω) half-bandwidth = ω 1/2 detuning = ∆ω CAVITY transfer function Z(s) = (1/R+ sC+1/sL) -1 Modulation exp(iω g t) Demodulation exp(-iω g t) Analytic signal: a(t)·exp[i(ω g t + φ(t))] Complex envelope: a(t)·exp[iφ(t)] = [I,Q]

5. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Cavity features Field sensor Coupler Particle Carrier frequency Pulse time Repetition time Field gradient Beam pulse repetition Average beam current 1.3 GHz1.3 ms100 ms25 MV/m1µs1µs8 mA Resonance frequency Characteristic resistance Quality factor Half- bandwidth Detuning ω 0 = (LC) -½ 2π·1.3 GHz ρ = (L/C) ½ 520 Ω Q = R/ρ 3 · 10 6 ω 1/2 = 1/2RC 2π·215 Hz ∆ω = ω 0 - ω g ~ 2π· 600 Hz Cavity parameters: resonance circuit parameters: R L C

6. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Algebraic model of cavity environment system Internal CAVITY model Output calibrator Input offset compensator Input calibrator + u v Input offset phasor u0u0 Input distortion factor D C C’ + u’ 0 D’ Input phasor Output phasor External CAVITY model v’ k = E k-1 ·v’ k-1 + C·C’·D·[D’·u’ k-1 + u’ 0 + u 0 )] – C·C’·(u b ) k-1 v’ u’ Output distortion factor FPGA controller area Internal CAVITY model CAVITY environs v k = E k-1 ·v k-1 + u k-1 - (u b ) k-1 E = (1-ω 1/2 ·T) + i∆ω·T

7. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Parameters identification of cavity system in noisy and no stationary condition External CAVITY model v k+1 = E k ·v k + F k ·u k E k = (1- ω 1/2 ·T) + i∆ω k ·T Linear decomposition of no stationary parameter Y: Y = W*x W – matrix of base functions: polynomial or cubic B-spline set x – unknown vector of series coefficients Over-determined matrix equation for measurement range: V = Z*z V – total output vector, Z – total structure matrix z – total vector of unknown values Least square (LS) solution: z = (Z T *Z) -1 *Z T *V

8. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Implementation of parameters estimation for adaptive control of pulsed operated cavity [F] n Static [E] n Dynamic [U]n[U]n [V]n[V]n [V0][V0] Inverse solution [v k+1 = E k ·v k + F k ·u k ] n [U] n+1 Parameters identification RANGE SIGNAL CONDITION ASSUMPTION ESTIMATED VALUE DECAYu = 0, u b = 0–ω 1/2 and [∆ω] FILLIGu b = 0arg(F) = 0, ω 1/2 = const.[|F|] and [∆ω] FLATTOPu b = 0[∆ω] – linear, ω 1/2 = const.[F][F]

9. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Functional black diagram of FPGA controller and control tables determination I/Q DETECTOR FEED-FORWARD TABLE + GAIN TABLE – + CALIBRATION & FILTERING F P G A C O N T R O L L E R SET-POINT TABLE C O N T R O L FEED-FORWARDSET-POINT Filling Cavity is driven in resonance condition i(t) = Io·exp(iφ(t)) dφ(t)/dt =  (t) v(t) = i(t)·R(1– exp(-ω 1/2 ·t)) Flattop Envelope of cavity voltage is stable i(t) = V 0 ·(1-iΔω(t)/ω 1/2 )/Rv(t) = V 0 = V 0 ·exp(iΦ 0 )

10. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Functional diagram of cavity testing system CAVITY SYSTEM CONTROLLER CONTROL DATA PARAMETERS IDENTIFICATION CAVITY MODEL ≈ MEMORY FPGA SYSTEM MATLAB SYSTEM v u

11. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Adaptive feed-forward cavity driving first step of iterative procedure – real process

12. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Adaptive feed-forward cavity driving second step of iterative procedure – MATLAB simulation

13. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Feed-forward cavity driving CHECHIA cavity and model comparison

14. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Feedback cavity driving CHECHIA cavity and model comparison

15. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Cavity model has been confirmed according to reality Cavity parameters identification has been verified for control purpose CONCLUSION

16. LLRF_05 - CERN, October 10-13, 2005Institute of Electronic Systems Vector sum control with beam Forward and reflected signal application for control purpose Normal-conductive cavity control for RF Gun Future plans