1. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group TESLA Cavity driving with FPGA controller Tomasz Czarski WUT - Institute of Electronic Systems PERG-ELHEP-DESY Group

2. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group Low Level RF system introduction Superconducting cavity modeling Cavity features Recognition of real cavity system Cavity parameters identification Control system algorithm Experimental results Main topics

3. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group 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. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group 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. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group 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. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group 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·[u 0 + D’·(u’ k-1 + 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. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group 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 )

8. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group Cavity parameters identification idea External CAVITY model v k = E k ·v k-1 + F·u k-1 E k = (1-ω 1/2 ·T) + i∆ω k ·T Time varying parameters estimation by series of base functions: polynomial or cubic B-spline functions Linear decomposition of time varying parameter x:x = w * y w – matrix of base functions, y – vector of unknown coefficients Over-determined matrix equation for measurement range: V = W*z V – total output vector, W – total structure matrix of the model z – total vector of unknown values Least square (LS) solution:z = (W T *W) -1 *W T *V

9. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group Functional diagram of cavity testing system CAVITY SYSTEM CONTROLLER CONTROL DATA PARAMETERS IDENTIFICATION CAVITY MODEL ≈ MEMORY FPGA SYSTEM MATLAB SYSTEM v u

10. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group Feed-forward cavity driving CHECHIA cavity and model comparison

11. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group Feedback cavity driving CHECHIA cavity and model comparison

12. SPIE - WARSAW, August 30, 2005Institute of Electronics Systems, ELHEP Group Cavity model has been confirmed according to reality Cavity parameters identification has been verified for control purpose CONCLUSION