1. YQ Liu, Peking University, Feb 16-20, 2009 Active Control of RWM Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK

2. YQ Liu, Peking University, Feb 16-20, 2009 Outline 1.Basic control theory 2.Analytic theory for RWM control 1)Cylindrical theory of RWM feedback 2)Fitzpatrick-Aydemir model 3.Numerical modelling 4.Experimental results

3. YQ Liu, Peking University, Feb 16-20, 2009 Basic control theory (for RWM)  Control diagram  Frequency-response approach  Nyquist diagram  State-space approach

4. YQ Liu, Peking University, Feb 16-20, 2009 Control diagram

5. YQ Liu, Peking University, Feb 16-20, 2009 MIMO control

6. YQ Liu, Peking University, Feb 16-20, 2009  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. Basic control logic

7. YQ Liu, Peking University, Feb 16-20, 2009  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(j  ) as  goes from –∞ to +∞.  Principle II follows from Cauchy’s principle of phase variation (famous Argument Principle): n=N-P Plasma dynamics: frequency approach

8. YQ Liu, Peking University, Feb 16-20, 2009 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. YQ Liu, Peking University, Feb 16-20, 2009 Controller design: general idea

10. YQ Liu, Peking University, Feb 16-20, 2009 Controller design: example

11. YQ Liu, Peking University, Feb 16-20, 2009 Controller design: example

12. YQ Liu, Peking University, Feb 16-20, 2009 Outline 1.Basic control theory 2.Analytic theory for RWM control 1)Cylindrical theory of RWM feedback 2)Fitzpatrick-Aydemir model 3.Numerical modelling 4.Experimental results

13. YQ Liu, Peking University, Feb 16-20, 2009 Single mode analysis

14. YQ Liu, Peking University, Feb 16-20, 2009 PRM for single mode

15. YQ Liu, Peking University, Feb 16-20, 2009 Multi-mode analysis

16. YQ Liu, Peking University, Feb 16-20, 2009 Outline 1.Basic control theory 2.Analytic theory for RWM control 1)Cylindrical theory of RWM feedback 2)Fitzpatrick-Aydemir model 3.Numerical modelling 4.Experimental results

17. YQ Liu, Peking University, Feb 16-20, 2009 Fitzpatrick-Aydemir model

18. YQ Liu, Peking University, Feb 16-20, 2009 Fitzpatrick-Aydemir model [Liu PPCF 48 969(2006)]

19. YQ Liu, Peking University, Feb 16-20, 2009 Fitzpatrick-Aydemir model

20. YQ Liu, Peking University, Feb 16-20, 2009 Fitzpatrick-Aydemir model

21. YQ Liu, Peking University, Feb 16-20, 2009 Fitzpatrick-Aydemir model

22. YQ Liu, Peking University, Feb 16-20, 2009 Outline 1.Basic control theory 2.Analytic theory for RWM control 1)Cylindrical theory of RWM feedback 2)Fitzpatrick-Aydemir model 3.Numerical modelling 4.Experimental results

23. YQ Liu, Peking University, Feb 16-20, 2009 Numerical modelling  MARS-F code  Plasma response model (PRM)  Example of DIII-D modelling  ITER study  Sensor optimisation for RWM control

24. YQ Liu, Peking University, Feb 16-20, 2009 MARS-F feedback formulation

25. YQ Liu, Peking University, Feb 16-20, 2009 MARS-F numerics

26. YQ Liu, Peking University, Feb 16-20, 2009 MARS-F benchmark

27. YQ Liu, Peking University, Feb 16-20, 2009 RWM stability with 2D walls well benchmarked

28. YQ Liu, Peking University, Feb 16-20, 2009 Control and PRM

29. YQ Liu, Peking University, Feb 16-20, 2009 PRM from toroidal calculations

30. YQ Liu, Peking University, Feb 16-20, 2009 PRM from toroidal calculations

31. YQ Liu, Peking University, Feb 16-20, 2009 PRM from toroidal calculations

32. YQ Liu, Peking University, Feb 16-20, 2009 Robust control Liu PPCF 44 L21(2002)

33. YQ Liu, Peking University, Feb 16-20, 2009 Example of DIII-D modelling

34. YQ Liu, Peking University, Feb 16-20, 2009 Example of DIII-D modelling

35. YQ Liu, Peking University, Feb 16-20, 2009 Example of DIII-D modelling

36. YQ Liu, Peking University, Feb 16-20, 2009 ITER equilibria from Scenario-4

37. YQ Liu, Peking University, Feb 16-20, 2009 RWM control in ITER

38. YQ Liu, Peking University, Feb 16-20, 2009 ITER modelling with external coils Liu NF 44 232(2004)

39. YQ Liu, Peking University, Feb 16-20, 2009 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. YQ Liu, Peking University, Feb 16-20, 2009 Sensor coil optimisation: idea

41. YQ Liu, Peking University, Feb 16-20, 2009 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. YQ Liu, Peking University, Feb 16-20, 2009 Outline 1.Basic control theory 2.Analytic theory for RWM control 1)Cylindrical theory of RWM feedback 2)Fitzpatrick-Aydemir model 3.Numerical modelling 4.Experimental results

43. YQ Liu, Peking University, Feb 16-20, 2009 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. YQ Liu, Peking University, Feb 16-20, 2009  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 BB BB  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 Feedback experiments on RFP

45. YQ Liu, Peking University, Feb 16-20, 2009 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 [Brunsel PPCF 47 B25(2005)] Feedback experiments on RFP

46. YQ Liu, Peking University, Feb 16-20, 2009 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. YQ Liu, Peking University, Feb 16-20, 2009 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