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Active Control of RWM Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK

Active Control of RWM Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK. Outline. Basic control theory Analytic theory for RWM control Cylindrical theory of RWM feedback Fitzpatrick-Aydemir model Numerical modelling Experimental results. Basic control theory (for RWM).

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Active Control of RWM Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK

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  1. Active Control of RWM Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK

  2. Outline • Basic control theory • Analytic theory for RWM control • Cylindrical theory of RWM feedback • Fitzpatrick-Aydemir model • Numerical modelling • Experimental results

  3. Basic control theory (for RWM) • Control diagram • Frequency-response approach • Nyquist diagram • State-space approach

  4. Control diagram

  5. MIMO control

  6. Basic control logic • Two essential components in feedback • Plasma dynamics (P) • Controller (K) • Mode dynamics normally described by plasma response models • Can be constructed from experimental data, like in vertical control. So far lack for n>0 RWM control • From analytical theory: works well for RFP plasmas • From toroidal calculations • Various ways for constructing plasma response model [Liu PPCF 48 969(2006), Liu CPC 176 161(2007)] • Pade approximation • Pole-residue expansion • Full-model frequency response, etc.

  7. Plasma dynamics: frequency approach • Find transfer function P(s) from control signal u to sensor signal y • Principle I: Closed loop stability all roots of 1+K(s)P(s)=0 have negative real part • Principle II: If P(s) has only one unstable pole, then closed loop stability Nyquist curve of open loop K(s)P(s) encircles -1 once counter-clock-wise • Nyquist curve of P(s) = complex plot of P(jw) as w goes from –∞ to +∞. • Principle II follows from Cauchy’s principle of phase variation (famous Argument Principle): n=N-P

  8. Plasma dynamics: state-space approach • Describe control problem by system of ODEs • Control design normally ends up with solving matrices equations • Most suitable for MIMO and nonlinear control for RWM • Time-domain and frequency domain (almost) tranformable via Laplace transform • We will focus on frequency approach ...

  9. Controller design: general idea

  10. Controller design: example

  11. Controller design: example

  12. Outline • Basic control theory • Analytic theory for RWM control • Cylindrical theory of RWM feedback • Fitzpatrick-Aydemir model • Numerical modelling • Experimental results

  13. Single mode analysis

  14. PRM for single mode

  15. Multi-mode analysis

  16. Outline • Basic control theory • Analytic theory for RWM control • Cylindrical theory of RWM feedback • Fitzpatrick-Aydemir model • Numerical modelling • Experimental results

  17. Fitzpatrick-Aydemir model

  18. Fitzpatrick-Aydemir model [Liu PPCF 48 969(2006)]

  19. Fitzpatrick-Aydemir model

  20. Fitzpatrick-Aydemir model

  21. Fitzpatrick-Aydemir model

  22. Outline • Basic control theory • Analytic theory for RWM control • Cylindrical theory of RWM feedback • Fitzpatrick-Aydemir model • Numerical modelling • Experimental results

  23. Numerical modelling • MARS-F code • Plasma response model (PRM) • Example of DIII-D modelling • ITER study • Sensor optimisation for RWM control

  24. MARS-F feedback formulation

  25. MARS-F numerics

  26. MARS-F benchmark

  27. RWM stability with 2D walls well benchmarked

  28. Control and PRM

  29. PRM from toroidal calculations

  30. PRM from toroidal calculations

  31. PRM from toroidal calculations

  32. Robust control Liu PPCF 44 L21(2002)

  33. Example of DIII-D modelling

  34. Example of DIII-D modelling

  35. Example of DIII-D modelling

  36. ITER equilibria from Scenario-4

  37. RWM control in ITER

  38. ITER modelling with external coils Liu NF 44 232(2004)

  39. Choice of active coils • Major debate: internal vs. external coils • Recent proposal: using 3x9 in-vessel copper coils (designed mainly for ELM control) … under investigation

  40. Sensor coil optimisation: idea

  41. Sensor signal optimisation: results • Sensor signal crucial factor in the feedback loop • E.g. it is now well established, by theory [Liu PoP 7 3681(2000)]and experiments, that internal poloidal sensors better than radial sensors • A new scheme for sensor optimisation is proposed, and shown very efficient in improving performance of radial sensors [Liu NF 47 648 (2007)]

  42. Outline • Basic control theory • Analytic theory for RWM control • Cylindrical theory of RWM feedback • Fitzpatrick-Aydemir model • Numerical modelling • Experimental results

  43. Expermental results • Results on reversed field pinches (RFP) • EXTRAP-T2R (Sweden) • RFX (Italy) • Results on DIII-D • Pressure-driven RWM feedback • Current-driven RWM feedback • RWM feedback planned on other tokamaks • KSTAR • ASDEX-U • ITER • ...

  44. Feedback experiments on RFP B B • Feedback has been proven successful for RWM control in DIII-D, both in experiments [Strait PoP 11 2505(2004)] and in simulations [Liu PoP 13 056120(2006)] • So far the most successful feedback experiments achieved in RFP machines • RFP, unlike tokamak, does not have strong vacuum magnetic field. • Due to plasma relaxation processes, toroidal field reverses sign close to plasma edge • Normally multiple unstable modes (different n) occur simultaneously, including • Internal/external resonant modes (tearing modes) • internal/external non-resonant modes (RWM) • RWM are not influenced by plasma flow, thus RFP provides an ideal platform for simultaneous control of multiple unstable RWM

  45. Feedback experiments on RFP [Brunsel PPCF 47 B25(2005)] • Experimental results on T2R • red: Reference shot w/o fb black: With intelligent shell feedback control • Refined intelligent shell mode of operation. • All unstable RWMs are suppressed (16 modes) • The field error amplification (n=+2) is suppressed. • Feedback results in a three-fold increase of the discharge duration • Stabilization is achieved for 10 wall times

  46. Feedback experiments on DIII-D • DIII-D uses C-coils (outside vacuum vessel) to perfrom dynamic error field correction • ... and I-coils (inside vacuum vessel) to perform direct feedback stabilisation of RWM • Experimental results do show direct feedback stabilisation of the mode

  47. Summary • Theory of active control of RWM well developed during last 10 years • Several feedback simulation codes developed and benchmarked. Toroidal simulations can give reasonable predictions of the experimental feedback results • Full model prediction for ITER will require consideration of 3D conducting structures (resistive walls) • Successful feedback experiments carried out on tokamaks. • Particularly impressive results obtained on RFP machines

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