Egemen “Ege” Kolemen, S. Gerhardt, D. Gates

1. NSTX Supported by Development of Fiducial Shots with LLD: Strike Point Control Improvement and Incorporation in Regular Operation College W&M Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics New York U Old Dominion U ORNL PPPL PSI Princeton U Purdue U SNL Think Tank, Inc. UC Davis UC Irvine UCLA UCSD U Colorado U Maryland U Rochester U Washington U Wisconsin Culham Sci Ctr U St. Andrews York U Chubu U Fukui U Hiroshima U Hyogo U Kyoto U Kyushu U Kyushu Tokai U NIFS Niigata U U Tokyo JAEA Hebrew U Ioffe Inst RRC Kurchatov Inst TRINITI KBSI KAIST POSTECH ASIPP ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching ASCR, Czech Rep U Quebec Egemen “Ege” Kolemen, S. Gerhardt, D. Gates 2009 NSTX XP Review, ASC Room B-318 January 5th, 2009

2. This year NSTX will need a new fiducial shot development due to the new restrictions and requirements due to LLD installation. • We can’t let the strike point hit the LLD (at least not routinely) • Medium δ shots may be part of regular XPs. • Strike point controllers are operational but they are still not part of the regular run. • We need to improve and prove that the controller works robustly Need for Developing a New Fiducial with LLD

3. Long term aim: • Use all the PF coils to control the plasma shape together. • Very hard to implement at once. • Incrementally increase the control capability to reach aim Full Multiple-Input-Multiple-Output Control -Inner Gap -Lower Inner Strike Point -Vertical Position -Squareness Upper X-point Height …

4. Current System ID • System Id: Identify the effect of these coils on the boundary shape. • Last year: Reaction Curve Method • Results from last year: • Problem: • Many shots needed • Not precise P

5. Inner Strike Point Control on the Vertical Divertor via a PI controller with PF2L • PI tuned to [5000, 5000] for inner strike point. • RMS ~ 1cm (Has offset need higher I) Current Capability: Inner Strike Point Control PF1AL PF2L PF2L controls outer SP in red segments. PF1AL controls inner SP in the blue segment.

6. Outer Strike Point Control on the Inner Divertor via a PI controller with PF2L • PI controller gains are tuned using Ziegler and Nichols to [400, 800]. • RMS ~ 1.5 cm (Kappa ~2.2-2.3) Current Capability: Outer Strike Point on the Inner Divertor PF1AL PF2L PF2L controls outer SP in red segments.

7. Outer Strike Point Control on the Outer Divertor via a PI controller with PF2L • PI controller gains are tuned using Ziegler and Nichols to [400, 800]. • RMS ~ 2 cm (Has offset need higher I) Current Capability: Outer Strike Point on the Outer Divertor PF1AL PF2L PF2L controls outer SP in red segments. PF1AL controls inner SP in the blue segment.

8. Is bull-nose tile addition a problem for OSP? • Not a big problem. PCS uses a linear segment to find the SP, we can’t make it a curved surface. Maybe the line segment can be modified but not really that important. SP control tries to match flux on two points, if the reference is moved down. • Present status of OSP control on the inner divertor. Do we have a shot? Do we need more work? • We have a shot, need to add D gain to stabilize. • Transient control compared to control during the Ip flat top. • This is the main problem. Strike point moves all around. Plasma touches the bottom of the vessel. With sprayed lithium on the inner divertor, this may be a problem. • Implement X-point height control. • Adding D to SP controller. • Upper strike point controllers Problems That Needs to be Addressed before LLD Commissioning

9. This Year: Offline System ID (Subspace Numerical Method) • This year Offline System ID (via Subspace Numerical Method): • Find minimal-state realization by converting to a form where error matrix (wk and vk) is minized • We parameterize the matrices by A(θ) and B(θ), then solve NLP: • Best known method: L. Ljung: ARMAX input-output models used in Maximum Likelihood. • IMPORTANT: System Delays are not included in this formalism. • Include that as additional parameters in the optimization.

10. Offline System ID (via Subspace Numerical Method) • Requirements: • Need an equilibrium • Need variation of the control input (PF1/2…). • Thus a working controller (can be a very poor one) is needed. • Then clean up the response • Find the portion of the response that depends mostly on the control • Take out trend lines, biases… • Use Subspace Algorithm with delays to find system. • Pros: • Don’t need XP run time! • Great for improving a already existing controller. • Cons: • Precision may not be perfect. • Need a running controller

11. This Year: Offline System ID • This year Offline System ID (via Subspace Numerical Method): • Example: System Id for PF2L to OSP compared to XP data. • Enables better initial guess within a factor of 2 • Need a working controller for best results. • Guesses Obtained: • I for PF3 • D for SP (PF1/PF2) • Off-diagonal terms for PF1/PF2 to ISP/OSP controller. • Initial guess for X-point controller harder (no working controller) • When we reach this closed-loop plant response pattern the oscillation period (Pu) and the amplitude (A) of the plant response can be measured and used for PID controller tuning. where • Only a single experiment is needed. • Closed loop: More stable • K= 2.4e-6, T = 9.9 and L = 6.0 • K =3.5e-6, T=10, and L =7 • tauD_method2 = • 0.010 • Relay Feedback is almost implemented on PCS. Note that shot used for system ID is not in this list

12. We propose a 1 day XP: • Load shot 134986 and see if the shot is still the same and SP controllers are working (2 shots) • Improve control: We will be adding derivative gain and tuning the controllers for better performance (XMP): • Add D to PF2 for strike point control – Reduce RMS < 1 cm (3 shots) • Relay Feedback System ID • Multi-Input Multi-Output: PF1A/PF2 to ISP/OSP (3 shots) [May not work] • Add I to PF3 – Need to get rid of Bias Error (~1 cm) (3 shots) • Test Integral Fix (1 shot) • Add upper strike point controllers: Currently, the strike point controllers work only for the lower side, we will implement the upper strike point controller in PCS. (4 shots) • Scan the strike-point from 35-40-45-50-55-63 cm. (5 shots) • Improve transient phase: Study and tune the start phase to avoid the plasma touching the lower plasma boundary. (6 shots) Experimental Plan for the New Fiducial

13. Study and tune the start phase to avoid the plasma touching the lower plasma boundary. • Implement the X-point height controller • After the Integrator start fix, try to start the controller later (i.e during flat top). Set the PF1/PF2 to constant values for the ramp up. • Tweak the squareness and Drsep. • Change upper strike point locations • Other ideas? Other Ways to Improve Transient Phase?

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15. NSTX Supported by Combined X-point Height and Strike Point Control College W&M Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics New York U Old Dominion U ORNL PPPL PSI Princeton U Purdue U SNL Think Tank, Inc. UC Davis UC Irvine UCLA UCSD U Colorado U Maryland U Rochester U Washington U Wisconsin Culham Sci Ctr U St. Andrews York U Chubu U Fukui U Hiroshima U Hyogo U Kyoto U Kyushu U Kyushu Tokai U NIFS Niigata U U Tokyo JAEA Hebrew U Ioffe Inst RRC Kurchatov Inst TRINITI KBSI KAIST POSTECH ASIPP ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching ASCR, Czech Rep U Quebec Egemen “Ege” Kolemen, S. Gerhardt, D. Gates 2009 NSTX XP Review, ASC Room B-318 January 5th, 2009

16. The OSP controller kept the controller at requested position but problems during the transition During the transient phase of the discharge, equilibrium bifurcated to a nearby solution with a low X-point. Algorithm was jumping from one solution to the other one. To make more stable plasma: Added inner strike point controller. Previous Year: Inner Strike Point Control X-points bifurcation Flux error between real and requested strike point, 134986 (<1mW) Flux Error (webers/rad) Segment to control inner strike point

17. Improvement Needed for Transient Phase: X-point Height Control Problems with the transient phase of the shots with the outer strike point controller on. The X-point was touching the vessel wall. Last year, inner-strike point control instead of X-point control insufficient run time to implement X-point controller Use PF1AL to control X-point height System Id: Relay Feedback If necessary, include MIMO controller including PF2L Tune PID Time Requested: 1 day X-points bifurcation Flux error for shot 134986 Plasma touching the vessel During transient (<1mW) Flux Error (webers/rad)

18. Current System ID • System Id: Identify the effect of these coils on the boundary shape. • Last year: Reaction Curve Method • Results from last year: • Problem: • Many shots needed • Not precise P

19. This Year: Experimental Closed Loop System ID • This year: Auto-tuning with Relay Feedback Method • When we reach this closed-loop plant response pattern the oscillation period (Pu) and the amplitude (A) of the plant response can be measured and used for PID controller tuning. where • Only a single experiment is needed. • Closed loop: More stable • Relay Feedback is almost implemented on PCS. Control Output Process Output

20. Tuning Method Explained • Consider a stable linear system. If the input signal to the system is a sinusoid, then the output signal will also be a sinusoid after a transient. Only the phase and the amplitude are different. • Nyquist Plot shows the system response for all ω. • Ziegler-Nichols method uses the Kcu and Pu to tune the PID to give fastest response with M~2. Kcu, Pu Nyquist Plot Stability Margin (M) Choose PID: Stability Margin or ~2 gives

21. Experimental Plan for X-point Height/SP controller We propose: Load shot 134986 and see if the shot is still the same and SP controllers are working (2 shot) System Id from PF1AL to X-point height: Relay Feedback (3 shots) Tune PID (4 shots) Add off-diagonal terms (MIMO) to the controller including PF2L (5 shots). (Maybe after 5th) Scan X-point height with various strike point locations (6 shots). Time Requested: 1 day

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23. This Year: Offline System ID • This year: • When we reach this closed-loop plant response pattern the oscillation period (Pu) and the amplitude (A) of the plant response can be measured and used for PID controller tuning. where • Only a single experiment is needed. • Closed loop: More stable • Relay Feedback is almost implemented on PCS. Control Output

24. List of things to do: • Add info about Subspace Algorithm • Problem with error high • Problem with equilibrium – Put how flux at x point changes in time • But great for already working PID controlled system i.e. Tuning • XMP: • Find the D gain for OSP • Find the I gain for squareness • Find the matrix for I/OSP combined off-diagonal terms • Find the matrix for X-point height and SP combined • Write the XP proposals • Find the desired Ip and other parameters from the previous year to fill out the P form. • Kp Ki=Kp/Ti Kd=Kp*Td Ti=4*Td Given Kp and Ki find Kd • Kd = Kp*Ti/4 = Kp* Kp/Ki/4 = Kp^2/Ki/4 = 400^2/800/4 = 50 • For inner 5000,5000 Kd = 5000/4 = 12500 • For PF3L squareness Kp/Ti Ti~L/R I~Kp*R/L • For inner effected by pf2lKp_volt/200 %4.46e3 • (R*Kp/Ti)/200 %9.26e3 tau=0.008, tauD=0.002 • yss = 1.12e-6; • Half of Outer strike effect • For X-point effected by PF2L • yss = 2.5e-7; tau = 0.0082 tauD = 0.0086, Kp Ki 933.6293, 1.8591e+003 • 1/10th of outer strike • Find the magnitude of change in st_in versus st_out due to PF1A motion use that for the off diagonal term • This should be for your proposals: 
XP:  "Combined X-point height and OSP control" 
XMP: "Development of Fiducial Shots with LLD: Strike Point Control Improvement and Incorporation in Regular Operation"You should tell us 
 i) why we need these things, 
ii) how you are gonna do it.What are the problems with control in the present system? 
What are the individual components of the proposed upgrades? 
What modifications to PCS are required? 
How much run time? 
What will the shot list look like? • 
What new capabilities will we have when you are done?Also, I listed in the first email of this chain some additional things you should discuss, related to Control+LLD early in the run.I hope this helps. 
> > 
> >    As we discussed, it may be good if some of these things are done 
> > before the LLD XPs; others can maybe wait. That sequencing will be 
> > an important part of the early run planning. 
> > 
> >    So, in addition to whatever else you were going to present, can 
> > you make sure that the presentation discusses/summarizes summarize 
> > the following: 
> > 
> >    i) Present status of OSP radius control when the OSP is on the 
> > bull-nose tile. Do we have a reliable shot to reload? I think the 
> > answer is yes. 
> > 
> >    ii) Present status of OSP control when the OSP is on the 
> > horizontal inner divertor. We will want this early in the run, 
> > during the commissioning phase. Do we have a shot? Do we need more 
> > work? (Any PF-2L polarity issues?) 
> > 
> >    iii) Transient control (i.e. during the Ip ramp) compared to 
> > control during the Ip flat top. 
> > 
> >    iv) Your opinion on priorities for before/after LLD  
> commissioning. 
> > 
> > 
> >    Note that the present run-plan from Eric now has a day of control 
> > development before the LLD XPs. Ignoring issues of how long it will 
> > take to actually start-up & condition the machine, we should be 
> > prepared to do any important control work then. Indeed, any needed 
> > conditioning shots may provide additional time for control 
> > development. 
> >

25. 0. System ID with relay 1. Strike point for high elongation • Add upper strike control • Coordinate with squareness 2. X-point with strike MIMO (add off diagonal) • XMP • Add I to PF3 • Add D to PF2 • To strike point • Integral Fix • Plasma models • CREATE-L France • DINA Moscow • CORSICA LLML • TSC PPPL

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