Feedback control of ECRH for MHD mode stabilization on TEXTOR
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1 -Institute for Plasma Physics Rijnhuizen Association Euratom- Feedback control of ECRH for MHD mode stabilization on TEXTOR Bart Hennen Tuesday, 25 November, 28 With contributions from: E. Westerhof, M. de Baar, J.W. Oosterbeek, G.W. Spakman, D. De Lazzari, A. Bürger, E.M.M. Demarteau, P.W.J.M. Nuij, M. Steinbuch, and the TEXTOR-Team
2 MHD stabilization Objective: Control of MHD modes - Magnetic islands (& sawteeth) - Preserve confinement & avoid disruptions Efficient & adequate ECRH / ECCD: - Fast & accurate mode detection - Alignment of ECRH power dep. w.r.t. mode ( tracking ) - Synchronize power modulation w.r.t. mode rotation - Power-efficient ECRH application Feedback control: guarantees fast response, accuracy, robustness and stability 2
3 TEXTOR ECRH installation Major components: - DED generation of magnetic islands - Fast & flexible launcher - Gyrotron 14 GHz, 8 kw, 1 s - Line-of-sight ECE diagnostic - Real-time control & DAQ electronic hardware Mirror suspension { Servo actuators Mirror Vacuum window 3
4 TEXTOR ECRH installation 4
5 Intermezzo: Launcher Analysis of dynamics using Frequency Response Function measurements Design of feedback + feedforward control structure (PID + Lead/Lag + Low-pass filter) Analysis of stability robustness & performance in simulation Real-time control implementation & performance assessment on mock-up of the actual launcher { Mirror suspension Servo actuators Mirror Vacuum window 5
6 Intermezzo: Launcher a) Mirror b) suspension Servo actuators Mirror Vacuum break Toroidal inj. angle [deg.] Reference trajectory Feedback response Servo error Time [s] Feedback + feedforward control: Speed of response: ~ 56 rotation sweep in 1 [ms] Positioning accuracy:.6 Bandwidth ± 1 Hz c) 6
7 Intermezzo: Line-of-sight ECE diagnostic Line-of-sight ECE diagnostic: - Dedicated feedback control sensor Measure ECE spectrum in the transmission path of ECRH beam: - Frequency selective decoupling - Power separation Advantages: - Actuator & sensor operate in same metric frame (refractive properties identical) - No need for plasma eq. reconstruction / absolute coordinate mapping 7
8 TEXTOR ECRH installation 25 a) Unperturbed Temperature profile Perturbed Temperature profile near X point Perturbed Temperature profile near O point.4 b) q=4 TEXTOR Vessel 2.3 q=3 T e / ev 15 1 z/m q=2 q=1 Launcher mirror R / m GHz chord R/m 8
9 Island recognition without ECRH Island recognition in ECE spectrum - DED induced m/n = 2/1 island - launcher 9 - island recognized between GHz & GHz Electron Temperature Te [ev] Electron Temperature Te [ev] Textor shot Time [s] channel 1, f = GHz channel 2, f = GHz channel 3, f = GHz channel 4, f = GHz channel 5, f = GHz channel 1, f = GHz channel 2, f = GHz channel 3, f = GHz channel 4, f = GHz channel 5, f = GHz Time [s] 9
10 Island recognition with ECRH (2 kw CW) Island recognition in ECE spectrum - DED induced m/n = 2/1 island - launcher 2 Electron Temperature Te [ev] Textor shot 1826 channel 1, GHz channel 2, GHz channel 3, GHz channel 4, GHz channel 5, GHz 2 ECRH Time [s] 1
11 Derivation of island control parameters Island control parameters: Radial location & rotation frequency / phase Generate reference trajectories for launcher and gyrotron in real-time Available hard- & software NI PXI DAQ & RTC (FPGA based, Labview) MATLAB / Simulink 11
12 12 Derivation of island control parameters Fast mode detection from ECE fluctuations: 1. Subtract running averages 2. Normalize 3. Correlate 4. Localized between channels for which correlator is below threshold N X X X n N n i c i c n c n + = 1,,, ~ ~ / ~ ~,,,, c n c n c n c n X X X X + = n N n i b i a i n b a X X C 1,,,
13 Derivation of island control parameters Fast mode detection from ECE fluctuations: ECE DC offset ECE channel 1: GHz ECE channel 3: GHz Summed correlation over N Time [s] Threshold Real-time implementation: discrete FIR filter (running sum low-pass filter) 13
14 Derivation of island control parameters Instantaneous frequency detection from ECE fluctuations: 1. Hilbert transform of real-valued function: Fourier Transform 9 phase shift Inverse FFT X r ( t) Xˆ ( t) 2. Analytical signal: X ( t) = X ( t) i Xˆ r + ( t) Xi(t) Im 3. Instantaneous phase: ˆ 1 X ( t) φ( t) = tan X r ( t) 4. Instantaneous frequency: φ Xr(t) Re f ( t) = 1 dφ 2π dt 14
15 Derivation of island control parameters Instantaneous frequency detection from ECE fluctuations: X O X O X ECE DC offset Inst. Phase ECE ch modulated ECRH ECE channel 1: GHz ECE channel 3: GHz Inst. Phase ECE ch. 3 Inst. freqs. ch. 1 & ch Time [s] 15
16 Derivation of island control parameters Instantaneous frequency detection from ECE fluctuations: 5 Textor shot : Spectrum inline ECE channel 4 15 Textor shot : Inst. freq. for inline ECE channel 1 5 derived from Hilbert transform 45 6 Frequency [Hz] DED on Instantaneous Frequency [Hz] Time [s] Time [s] Synchronization of ECRH power modulation w.r.t. island rotation frequency Repetitive Control 16
17 MATLAB / Simulink modeling Simplified plasma equilibrium (circular) Perturbed Electron Temperature profiles Synthetic line-of-sight ECE data Modified Rutherford equation: Including efficiency terms for Heating & Current Drive Including radial misalignment, deposition profiles, duty cycle modulation Trajectory generators (based on mode/freq. detection) Actuator models (launcher & gyrotron) Feedback loops 17
18 MATLAB / Simulink modeling 18
19 MATLAB / Simulink modeling Electron Temperature [A.U.] Launcher elev.: ~ -9 Island width: ~ 8 cm Bt = 2.25 T, Ip = 3 ka Time [s] Launcher elev. scan: ~ -15 to 15 Island width: ~ 8 cm Bt = 2.25 T, Ip = 3 ka Channel reference signal derived with mode detection algorithm Electron Temperature [A.U.] Inline ECE channel reference [GHz] Time [s] Time [s] 19
20 Summary & outlook TEXTOR well equiped for MHD feedback control experiments (DED, optimally controlled launcher, line-ofsight ECE) Capabilities of line-of-sight ECE diagnostic for integrated mode detection, phase tracking and ECRH launcher steering demonstrated Fast island detection algorithmes based on correlation techniques applied Instantaneous frequency & phase detection for synchronized gyrotron modulation applied Simulink model development for model-based controller design 2
21 Summary & outlook What comes next: Integrated feedback control simulation Installation / implementation control hardware Experimental validation of the control algorithms 21
22 Thanks for your attention! QUESTIONS? 22
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