Control System Modeling for SC Cavity FLASH seminar, DESY, June 13, 2006 Institute of Electronic Systems

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1 Control System Modeling for SC Cavity Experimental results for for ACC1 module driven with the SMCON board Tomasz Czarski Warsaw University of Technology nstitute of Electronic Systems ELHEP-DESY Group FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

2 Main topics of the presentation Low Level Radio Frequency system introduction Algebraic model of the LLRF control system Calibration and correction procedure Cavity parameters identification Control system algorithm Experimental results Summary FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

3 Functional block diagram of Low Level Radio Frequency Cavity Control System COUPLER Waveguide KLYSTRON 1.3 GHz MODULATOR PARTCLE CAVTY RESONATOR and ELECTRC FELD distribution ANALOG SYSTEM of CAVTY ENVRONS FELD SENSOR DOWN - CONVERTER 2 khz ADC DAC _ F P G A SYSTEM C ONTROLL ER _ / DETECTOR CALBRATOR F_F Gain S_P CONTROL BLOCK & PARAMETERS DENTFCATON SYSTEM M A T L A B FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

4 Algebraic model of the LLRF control system nternal CAVTY model Output u k = D k x k u k v k+1 = E k v k + A u k E k = (1-Tω 1/2 ) + T ω k i v k B x k Controller External CAVTY model v k+1 = E k v k + F u k F = A B C LS solution Calibration: v k = v k arg(f) = ω 1/2 = const. ω k = Σα i f i (k) F = const. + feedback G k error + Cavity v k C FF k Corrector SP k Calibrator FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

5 Parameters identification of cavity system in noisy and no stationary condition v k+1 = E k v k + F u k External CAVTY model E k = (1- Tω 1/2 ) + T ω k i Parameters: F, ω 1/2, ω k = Σα i f i (k) Approximation of time-varying detuning by series of base functions: Linear decomposition: ω = W*α W matrix of base functions: polynomial or cubic B-spline set α unknown vector of series coefficients Over-determined matrix equation for measurement range: V = Z*z V total output vector, Z total structure matrix z = [F; (1-Tω 1/2 ); α] - total vector of unknown values Least square (LS) solution for minimum RMS error: z = (Z T *Z) -1 *Z T *V FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

6 Multi-Channel System modeling Multi-Channel model Vector Sum D k u k v i k+1 = E i k v i k + F i u k v E i k = (1-Tωi 1/2 ) + T ωi k i i k + v k = i vi k E k v k = i (E i k vi k ) F= i F i x k Controller ω 1/2 = const. Multi-Cavity model v k+1 = E k v k +F u k (= H k x k ) E k = (1-Tω 1/2 ) + T ω k i H k = F D k ω k = Σα i f i (k) LS F = const. D k = u k /x k Cavity v k + FF k feedback error G k + Corrector SP k FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

7 Control Algorithm Determination of Control Tables : F_F S_P GAN Loop gain L v k = L (SP k v k ) CAVTY model v k+1 = E k v k + H k x k Cavity GAN v k+1 = E k v k -H k G k-1 v k-1 + H k (FF k-1 + G k-1 SP k-1 ) G k = L T(ω 1/2 - ω k i)/h k Stability condition L < 1/(T ω 1/2 - ω k i ) Controller x k+1 = FF k + G k (SP k v k ) CONTROLLER model MODE RANGE Filling Flattop FEED-FORWARD FF k = Tω 1/2 v exp(iφ k )/H k φ k = φ k-1 + T ω k FF k = V T(ω 1/2 - ω k i)/h k SET-PONT SP k = v [1 exp(-k Tω 1/2 )] exp(iφ k ) (SP end = V) u, φ 1 SP k = V = V exp(iφ) FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

8 Adaptive control for cavity driven with FPGA controller supported by MATLAB system CAVTY SYSTEM FPGA SYSTEM CONTROLLER CONTROL TABLES DA MEMORY DATA MATRX CONTROL DATA determination PARAMETERS identification MATLAB SYSTEM FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

9 Adaptive Feed Forward 1_st step C a vity o utp ut e nve lo p e [MV] C o ntro lle r o utp ut [m A] tim e [1-6 s] tim e [1-6 s]. C o ntro lle r Cavity C a vity d e tuning [Hz] half-bandwidth = 228 Hz order approx tim e [1-6 s] tim e [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

10 Adaptive Feed Forward 1 steps Cavity output envelope [MV] 1 1 C o n tro lle r [m A] tim e [1-6 s] tim e [1-6 s]. C o n tro lle r C a vity 4 Cavity detuning [Hz] half-bandwidth = 228 Hz order approx tim e [1-6 s] tim e [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

11 Adaptive Feed Forward 1_th step 2 2 C avity output e nve lope [MV] 1 1 C o ntro lle r a nd klys tro n (--) o utp ut [m A] time [1-6 s] time [1-6 s].4.2 Controller C a vity C a vity d e tuning [Hz] half-bandwidth = 228 Hz order approx time [1-6 s] time [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

12 Adaptive Feed Forward 1_th step zoomed flattop Cavity output envelope [MV] 1 1 Controller and klystron (--) output [ma] time [1-6 s] time [1-6 s].1.1 Controller C a vity Cavity detuning [Hz] ha lf-b a nd wid th = Hz time [1-6 s] 1 2-order approx time [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

13 Feed Forward driving 1 repetition readout 2 2 Cavity output envelope [MV] 1 1 C o ntro lle r o utp ut [m A] tim e [1-6 s] tim e [1-6 s] tim e [1-6 s] Controller C a vity order approx. C a vity d e tuning [Hz] half-bandwidth = 228 Hz tim e [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

14 Single cavity driving: Feed Forward and Feedback mode (gain=1) 2 2 Cavity output envelope [MV] 2 1 C o ntro lle r o utp ut [m A] tim e [1-6 s] tim e [1-6 s] 3 Cavity detuning [Hz] half-bandwidth = 228 Hz Controller C a vity 2-order approx tim e [1-6 s] tim e [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

15 Feed Forward and Feedback mode( gain=1) zoomed flattop area C a vity o utp ut e nve lo p e [MV] 2 1 C o ntro lle r o utp ut [m A] tim e [1-6 s] tim e [1-6 s] x C o n tro lle r C a vity C a vity d e tuning [Hz] half-bandwidth = 228 Hz tim e [1-6 s] 2-order approx tim e [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

16 Feed Forward and Feedback mode ( gain=2) 2 2 Cavity output envelope [MV] Controller output [ma] time [1-6 s] time [1-6 s] 3 Cavity detuning [Hz] half-bandwidth = 228 Hz Controller Cavity -1 2-order approx time [1-6 s] time [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

17 Feed Forward and Feedback mode ( gain=2) zoomed flattop area Cavity output envelope [MV] tim e [1-6 s] Controller output [ma] tim e [1-6 s].2 3 Cavity detuning [Hz].1.1 Controller C a vity half-bandwidth = 228 Hz o rd e r a p p ro x tim e [1-6 s] tim e [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

18 8 cavities driving: Feed Forward mode Multi-Cavity output envelope [MV] Controller output [ma] time [1-6 s] time [1-6 s] Cavity detuning estimation [Hz] half-bandwidth = 237 Hz CTRL KLY CAV time [1-6 s] time [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

19 8 cavities driving: Feed Forward and Feedback mode (gain=1) Multi-Cavity output envelope [MV] Controller output [ma] tim e [1-6 s] tim e [1-6 s] 3 C a vity d e tuning e s tim a tio n [Hz] half-bandwidth = 237 Hz CTRL KLY CAV tim e [1-6 s] tim e [1-6 s] FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

20 Summary of Procedures for Control Purpose mplemented in MATLAB System Estimation of complex envelope for: klystron, each one cavity, multi-cavity module Auto compensation of the input offset (DAC, VM) Parameters identification for: each one cavity, multi-cavity module Auto calibration of the cavities channels Auto correction of the klystron channel (linearization) Control tables determination: Set-Point, Feed-Forward, Complex Gain FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems

21 CONCLUSON Electrical model of the SC cavity has been verified for control purpose Algebraic model of the cavity environment has been effectively used for correction and calibration of signal path Feed Forward and Feedback control has been performed successfully FLASH seminar, DESY, June 13, 26 nstitute of Electronic Systems