Tokamak plasma position control

1. Tokamak plasma position control Shayok Mukhopadhyay CSOIS, Utah state University AFC/FOC literature reading group meeting

2. Definition • A tokamak is one of several types of magnetic confinement devices, and it is one of the most-researched candidates for producing controlled thermonuclear fusion power. • The term Tokamak is a transliteration of the Russian word Токамак which itself is an acronym made from the Russian words: "тороидальная камера смагнитными катушками" (toroidal'naya kamera s magnitnymi katushkami) — toroidal chamber with magnetic coils (possibly Tochamac). It was invented in the 1950s by Soviet physicists Igor Yevgenyevich Tamm and Andrei Sakharov (who had been inspired by an original idea of "Oleg Lavrentyev"). • The tokamak is characterized by azimuthal (rotational) symmetry and the use of the plasma-borne electric current to generate the helical component of themagnetic field necessary for stable equilibrium.  *http://en.wikipedia.org/wiki/Tokamak AFC/FOC literature reading group meeting

3. Some History • 1987 USSR stamp, commemorating thermonuclear fusion research on Tokamak. *http://en.wikipedia.org/wiki/Tokamak AFC/FOC literature reading group meeting

4. A tour of a few tokamaks… *The Alcator tokamak – A.Hochstim & B.J. West, “Introduction to physical processes in nuclear fusion”, Energy, Vol.III AFC/FOC literature reading group meeting

5. A tour of a few tokamaks… *The Princeton tokamak – A.Hochstim & B.J. West, “Introduction to physical processes in nuclear fusion”, Energy, Vol.III AFC/FOC literature reading group meeting

6. The STOR-1M or the UTOR (USU) *Modeling and control of the STOR-M tokamak, Emaami, 1990 AFC/FOC literature reading group meeting

7. AFC/FOC literature reading group meeting

8. What you need to get plasma… AFC/FOC literature reading group meeting

9. With all that.. You get this… AFC/FOC literature reading group meeting

10. The actual scheme AFC/FOC literature reading group meeting

11. Original vertical field configuration AFC/FOC literature reading group meeting

12. Modified configuration AFC/FOC literature reading group meeting

13. Actual circuit AFC/FOC literature reading group meeting

14. Control objective • The pickup in the position coils is proportional to the displacement of the plasma. • The difference of the signals in-out, up-down should be zero if the plasma is centered. • http://w3.pppl.gov/~dstotler/Drift.html AFC/FOC literature reading group meeting

15. Gathering data AFC/FOC literature reading group meeting

16. Ic, Vc, and Current in dummy load (SCR2 not fired) AFC/FOC literature reading group meeting

17. Pick up of one of the actual position coils AFC/FOC literature reading group meeting

18. Ic, Vc, and Current in dummy load (SCR2 fired at 4.3ms) AFC/FOC literature reading group meeting

19. Plots of difference in position coil pick-up AFC/FOC literature reading group meeting

20. Task • Find system transfer function between each pickup coil output and Ic. • Or, find system transfer function between Ic / Vc and the difference of position coil outputs. • The following command is currently used for modeling • [B,A] = stmcb(meanup,icmean,num_ord,den_ord,iterations); AFC/FOC literature reading group meeting

21. Data analysis • Vc = 123 V, nominal case, SCR2 is always off • Minimum norm for up =0.11542 • Minimum orders are for up • Numerator order =5 • Denominator order =5 • Up transfer function = • Transfer function: • 0.9815*(9.578e-005 s^5 - 0.0003058 s^4 + 0.000365 s^3 - 0.0002165 s^2 + 8.246e-005 s - 2.091e-005) • ----------------------------------------------------------------------------------------- • s^5 - 3.185 s^4 + 3.793 s^3 - 2.25 s^2 + 0.862 s - 0.22 • Minimum norm for down =0.31316 • Minimum orders are for down • Numerator order =1 • Denominator order =1 • Down transfer function = • Transfer function: • 1.1762*(7.835e-005 s - 7.728e-005) • ------------------------- • s - 0.9877 AFC/FOC literature reading group meeting

22. Data analysis continued… • Minimum norm for in =0.45728 • Minimum orders are for in • Numerator order =4 • Denominator order =4 • In transfer function = • Transfer function: • 1.201*(0.0001001 s^4 - 0.0004002 s^3 + 0.0006023 s^2 - 0.0004045 s + 0.0001022) • ----------------------------------------------------------------------- • s^4 - 3.998 s^3 + 6.015 s^2 - 4.038 s + 1.02 • Minimum norm for out =0.26296 • Minimum orders are for out • Numerator order =5 • Denominator order =5 • Out transfer function = • Transfer function: • 0.9116*(0.000117 s^5 - 0.0005047 s^4 + 0.0008824 s^3 - 0.0007875 s^2 + 0.000362 s - 6.917e-005) • -------------------------------------------------------------------------------------- • s^5 - 4.302 s^4 + 7.499 s^3 - 6.671 s^2 + 3.057 s - 0.5822 AFC/FOC literature reading group meeting

23. How well does the model perform..? AFC/FOC literature reading group meeting Red = estimate, blue = actual (data from position coils)

24. Up Coil – PZ map AFC/FOC literature reading group meeting

25. Down Coil – PZ map AFC/FOC literature reading group meeting

26. In Coil – PZ map AFC/FOC literature reading group meeting

27. Out Coil – PZ map AFC/FOC literature reading group meeting

28. Model ‘vs’ actual data (relative position) Dotted = estimate, solid = actual (vertical position does not need to be worried about since there is no external force on the plasma in that direction) AFC/FOC literature reading group meeting

29. Conclusions • The data analysis has provided a certain initial transfer function. • From the pole – zero map of this transfer function it is seen that most all poles lie on the right half plane, thus making the system unstable (which is a practically experienced phenomenon as the plasma dies quickly due to moving and hitting the walls) • However the current transfer function does not capture the entire detail of the position data, and provides only a mean estimate. • Better modeling methods need to be used to get a more accurate model. AFC/FOC literature reading group meeting

30. To do list.. • Understanding system configuration. • Initial absolute position computation algorithm. • Trigger circuit to perturb system steady state at different times. • Nominal transfer function. • Correct absolute position algorithm. • Purely analog control board design and test. • Control system design. • Control system simulation tests • Plasma position calculator (hardware design & building). • Actuator design & building ‘or’ reconfigure/reuse existing actuator if possible. Done Ongoing Future work Being Redone AFC/FOC literature reading group meeting

31. Questions…? AFC/FOC literature reading group meeting