Modelling control

1. Modelling control P. Piovesan, A. Soppelsa in collaboration with L. Grando, G. Marchiori, L. Marrelli, L. Piron, D. Terranova, P. Zanca Consorzio RFX, Euratom-ENEA Association, Padova, Italy

2. The goal … • The main goal is to realize an IDEAL SHELL through magnetic feedback Br=0 at r=a (plasma radius) + helical boundary conditions? (L. Marrelli and A. Boozer talks)

3. The goal … and real life • Our main goal is to realize an IDEAL SHELL through magnetic feedback • But in real life we have to face some facts: • Discrete active and sensor coils  ALIASING OF SIDEBAND HARMONICS • Gaps, portholes, …  MODE COUPLING, ERROR FIELDS • Active coils and sensors are coupled • Finite penetration time of Br through the shell • Finite bandwidth and current limits of power supplies + active coils • Shell proximity • … Br=0 at r=a (plasma radius) + helical boundary conditions? (L. Marrelli and A. Boozer talks)

4. PID gains chosen to induce mode rotation and phase unlocking, based onsimulations with the torque-balance code RFXlocking (by P. Zanca) • State-space Simulink e.m. model of the wall + feedback system (by G. Marchiori, A. Soppelsa) Inductance matrix among active coils and sensors from vacuum measurements Power supply + coil controller PID mode controller Irefm,n br,refm,n Irefi,j Ii,j Poloidal index: i=1,…,4 Toroidal index: j=1,2,…,48 bri,j C FFT-1 A M + bfi,j - m = -1,0,1,2 n = 0,1,…,24 br,clm,n br,cli,j Sideband cleaning + extrapolation to r=a FFT CLEAN Where we are … • Clean Mode Control br cleaned from the SIDEBAND HARMONICaliasing due to the discreteness of the active coils and sensors Mode unlocking  current up to 1.6MA  helical states with improved confinement

5. power supply saturation (1, -7) (1, -8) current on m=1,n mode (A) (1, -9) IP (MA) Where we are going … • When increasing the current above 1.6MA, we may encounter the current limit of the active coil power supplies • Related with self-organization to the helical state (1,-7) • Some coil power may be saved by reducing the CMC gains • RFXlocking code predicts that extrapolation to r=a needs more current without improving control (P. Zanca, PPCF 2009) • Alternative strategies should be tested at 1.5MA first

6. n = -1,…,-23 n = -7 Simulation Experiment Max. m=1 displacement of LCFS (mm) • RFXlocking (with 3 shells) may provide an estimate of the ultimate CMC limit, within some assumptions (e.g. uniform wall) • Quantitative comparisons with the experiment are ongoing (L. Piron, P. Zanca) Max. m=1 displacement of LCFS (mm) KP, proportional gain on (1,-7) IP (MA) Ultimate limit of CMC? • How far is CMC from IDEAL SHELL performance? • The secondary mode scaling is favourable, while the (1,-7) mode may fix the ultimate limit • Error fields may also play a role

7. br(a) / br(res) for (1,-7) mode we are here CMC optimization • Recent modelling with RFXlocking suggests that several optimizations of the CMC controller are possible: • Tuning of derivative gains 20% reduction of br for the (1,-7) mode and other modes • Remove complex gains? • Extend CMC to all modes? • Higher gains on m=0 modes at deep F • Alternative approaches? • Could stopping the mode rotation allow a further reduction of br? • Chose gains to induce an ordered rotation of locked mode? (more details in D. Terranova and G. Marchiori talk)

8. Locked mode angle • First correction tests with the dynamic pseudo-decoupler are promising and suggest some possible optimizations: • Less derivative action to reduce noise on output • Toroidal symmetry assumption may be too strong • All mutual inductances should be measured radial magnetic field (T) brefi,j Ii,j bri,j  brefi,j ~ M-1 M toroidal index Error fields at toroidal gaps • Major EFs identified  Should we avoid or correct them or both? • Main EF due to vertical field penetration through the two toroidal gaps: • Locked mode prefers gaps, especially during the start-up phase, but also during flattop • Effects on secondary modes and/or QSH?

9. Feedforward correction of error fields Ishell F IEF,refi,j bri,j Irefm,n br,refm,n Irefi,j Ii,j C FFT-1 A M + + - bfi,j br,clm,n br,cli,j FFT CLEAN Feedforward EF correction • More sophisticated feedforward EF correction schemes, to be applied also during plasma, may be designed and tested: • The m=0,n=1 current in the shell is measured and should be proportional to the EF • A pseudo-decoupler may be designed, starting from the inductance matrix among currents in the Field Shaping windings and radial field sensors • ANSYS simulations of the two gaps to determine the fine structure of the EF

10. EFs at the equatorial gap • The radial magnetic field penetrates faster through the equatorial gap, which may cause significant poloidal mode coupling • Is this comparable to the coupling introduced by toroidal geometry? Phase difference among bf1,n(a) and br1,n(a) bf1,n(a) (mT) br1,n(a) (mT) time (s) m=1, n=-7 + m=1, n=0 m=0, n=7 m=1, n=+7 m=2, n=7 I1,n (A) time (s)

11. erm,n Irefm,n br,reqm,n C M-1 ~ Reduced modal decoupler • To correct the EFs at the equatorial gap, a dynamic (or static) modal decoupler is being designed: • Start with reduced dimensions, e.g. m=1, n=-7 only  effects on QSH? • Then try to extend it to the main secondary modes

12. bri,j br,refi,j Irefi,j Ii,j CVS A M + - Advanced virtual shell • The virtual shell scheme on the other hand may have some advantages: • Does it make sense to Fourier decompose EFs and act on them as if they were modes?

13. bri,j br,refi,j Irefi,j Ii,j CVS A M + - br,cli,j CLEAN Advanced virtual shell • The virtual shell has some advantages: • Does it make sense to Fourier decompose EFs and act on them as if they were modes? • A Clean-VS scheme may be designed: • With sideband cleaning (presently without extrapolation to r=a)

14. Advanced virtual shell • The virtual shell has some advantages: • Does it make sense to Fourier decompose EFs and act on them as if they were modes? • A Clean-VS scheme may be designed: • With sideband cleaning (presently without extrapolation to r=a) • With different gains in different positions, to compensate for gaps and other features bri,j br,refi,j Irefi,j Ii,j CVS A M + - br,cli,j CLEAN

15. Advanced virtual shell • The virtual shell has some advantages: • Does it make sense to Fourier decompose EFs and act on them as if they were modes? • A Clean-VS scheme may be designed: • With sideband cleaning • With different gains in different positions, to compensate for gaps and other features • OR with a dynamic pseudo-decoupler (to be re-designed on cleaned measurements) bri,j br,refi,j Irefi,j Ii,j C A M D + - br,cli,j CLEAN

16. Advanced virtual shell • The virtual shell has some advantages: • Does it make sense to Fourier decompose EFs and act on them as if they were modes? • A Clean-VS scheme may be designed: • With sideband cleaning • With different gains in different positions, to compensate for gaps and other features • OR with a dynamic pseudo-decoupler (to be re-designed on cleaned measurements) • Is it worth developing all of this at plasma radius? • Mutual inductances among active coils and “virtual sensors” at r=a are needed: • Can they be measured from mutual inductances among active coils and bf sensors? • Very detailed and good measurements of mutual inductances would be needed • Can they be estimated from FEM e.m. codes, such as CARIDDI?

17. Hybrid scheme • More physics-driven control schemes may be designed, based on proper combinations of the VS, MC, and FF schemes introduced above (once these have been all investigated separately):

18. Ishelli,j FEEDFORWARD ERROR FIELD CORRECTION F MC + PSEUDO-DECOUPLER IEF,refi,j Irefm,n Filter n>n0 C FFT-1 D br,refm,n + + + - Iref1,-7 Filter n<n0 CD FFT-1 MODE DECOUPLER ON m=1, n=-7 or most important m=1 modes br,clm,n br,cli,j CLEAN FFT SIDEBAND CLEANING + EXTRAPOLATION TO r=a Hybrid scheme • More physics-driven control schemes may be designed, based on proper combinations of the VS, MC, and FF schemes introduced above (once these have been all investigated separately): Ii,j Irefi,j bri,j A M bfi,j