TNO , Technical Sciences, Department of OptoMechatronics , NL-2600 AD, Delft, The Netherlands.

1. TNO, Technical Sciences, Department of OptoMechatronics, NL-2600 AD, Delft, The Netherlands. InstitutfürPlasmaforschung, Universität Stuttgart, D-70569 Stuttgart, Germany. Max-Planck-InstitutfürPlasmaphysik, EURATOM Association, D-17491 Greifswald, Germany. Differ, EURATOM Association, Nieuwegein, The Netherlands. Max-Planck-InstitutfürPlasmaphysik, EURATOM Association, D-85748 Garching, Germany. Controlled Mirror Motion Controlled Mirror Motion Systemfor Resonant Diplexersin ECRH Applications Niek Doelman1, R. van den Braber1, W. Kasparek2, V. Erckmann3, W. Bongers4, B. Krijger4, J. Stober5, E. Fritz1, B. Dekker1, W. Klop1, F. Hollmann3, G. Michel3, F. Noke3, F. Purps3, M. de Baar4, M. Maraschek5,F. Monaco5, S. Müller5, H. Schütz5, D. Wagner5, the ASDEX Upgrade Team5 and other teams at the contributing institutes.

2. FADIS diplexer functionality * Controlled Mirror Motion Operational point at output power curves where A) At resonance ( • In-line ECE, Gyrotron power combination, mode filter B) Off-resonance ( • Fast switching, power divider • possibly time-variant * see Kasparek, Bongers this conference

3. Controlled Mirror Motion FADIS system requirement • For proper operation the FADIS resonant diplexer needs to have the correct round-trip length L, despite all disturbances • Disturbances • Gyrotron frequency variations • Expansion of diplexer cavity due to temperature gradients • Structural vibrations

4. Controlled Mirror Motion Disturbances / Gyrotron frequency variations Note resonance width (FWHM) is in the order of 10-20 MHz

5. Controlled Mirror Motion • Diplexer resonator length expansion • Aluminium casing under DT • DL ~ 5e-5 DT Disturbances / Thermal effects Disturbances / Structural vibrations Uncontrolled system; mirror motion depends on mount stiffness

6. Controlled Mirror Motion Actively controlled mirror motion system Main requirements • Active control of single mirror • Positioning resolution : 1 - 10 µm (few % transmission) • Positioning stroke > 1.5 mm (1 period) • Mirror rotation (3 DOF) < 1 mrad • Lateral motion < 1 mm • Bandwidth > 10 – 100 Hz (in closed-loop) • Linear response characteristics

7. Fact Sensor Controlled Mirror Motion Mirror Cavity Frame flange elastic guiding mechanism mirror Mechanics of mirror motion Main principles • Linear motion: voice-coil actuator • Leaf springs as elastic guiding mechanism; free of friction • Internal optical encoder as position sensor voice coil actuator flange

8. Controlled Mirror Motion Movable Mirror mechanism implemented

9. Controlled Mirror Motion Mirror motion in action • Scanning motion Test IPF Stuttgart January 2012

10. Controlled Mirror Motion Increasing the system’s bandwidth • Position sensor feedback • Low order feedback controller gives higher effective stiffness • Higher bandwidth -> faster response -> higher performance • Functions as inner control-loop for main power control approach

11. Controlled Mirror Motion Controlling the mirror motion • Output powers are the controlled variables • Feedback of power signals is most direct approach

12. Controlled Mirror Motion The issue of power feedback • Effective gain in feedback loop is the derivative of the error curve • For power equalization • Sign is equal around optimum for 50% of the range • For power minimisation; • Gain and sign vary significantly around the optimum • Direct power feedback not feasible • 1. Adaptive approach/ 2. Alternative sensor lay-out

13. Controlled Mirror Motion Gradient-type optimisation • Given a cost function J(x), to be minimised • Recursive minimisation by gradient search • In case of FADIS, cost function J(x) could be the output power OUT 1 • However, the gradient of the power curves is unknown.

14. Controlled Mirror Motion Dither-based gradient optimisation • Add a small perturbation signal to the mirror position • Evaluate using a Taylor expansion + … O() • If is sinusoidal; + … O() • Take the product of and perturbation + O() • Averaging over time, yields an estimate of the gradient:

15. Controlled Mirror Motion Dither-based gradient optimization (2) • Add sinusoidal perturbation to current mirror position • Use small amplitude, typically 1 mm • Step-size of gradient algorithm is limited to have proper estimation => possibly slow convergence • The higher the dither frequency, the faster the convergence • Very robust approach; performs irrespective of shape of cost function • Also referred to as ExtremumSeeking Control

16. Controlled Mirror Motion Use of measured frequency signal Condition for resonance: • Resonator round-trip phase: • Adjust L to frequency variations • Requires very accurate knowledge of true resonator length L • L is in the order of 1-2 m • Accuracy of better than 10 mm is needed • Feedforward type of control; not robust • To be used in combination with power feedback

17. Controlled Mirror Motion Experiment (0) The effect of a stationary mirror position Test IPP Greifswald June 2010

18. Controlled Mirror Motion Experiments (1) Power equalisation • Minimisation of power balance: ()/() • Mirror motion mainly corrects for frequency variations Test IPP Greifswald June 2010

19. Controlled Mirror Motion Experiments (1) • Mirror motion follows the frequency variations Test IPP Greifswald June 2010

20. Controlled Mirror Motion Experiments (2) Fast (25 kHz) gyrotronfrequency modulation • Minimisation of power balance: ()/() • Mirror motion only corrects for low frequency effects aliasing Test AUG Garching April 2012

21. Controlled Mirror Motion Experiments (3) Power switching by mirror motion • Power trajectory is a 32 Hz sinusoid Test AUG Garching April 2012

22. Controlled Mirror Motion Experiments (4) Power minimisation • Minimisation of output power: /( • Dither-based power feedback; 120 Hz perturbation Test IPP Greifswald June 2010

23. Controlled Mirror Motion Experiments (5) Resonance control for in-line ECE • Minimisation of P1 power • Combined frequency feedforward • and power feedback Test AUG Garching April 2012

24. Controlled Mirror Motion Experiments (5) Combined frequency feedforward and power feedback • Fast initialisation by feedforward • Fine adjustment by power feedback Test AUG Garching April 2012

25. Controlled Mirror Motion W. Kasparek, EC-17 Experiments (6) Low power test using Magic-T based interferometric set-up Test IPF Stuttgart January 2012

26. Controlled Mirror Motion Conclusions • Mirror motion system to keep diplexer at required resonator length • Linear, friction-free actuation and guidance • Weight of mirror limits motion speed • Non-linear power curves complicate control • Several approaches possible: • Control at 1 slope of the curves (50% coverage) • Small perturbation based adaptive control (100% coverage) • Frequency signal feedforward • Interferometric Magic-T set-up • Combinations of the above • Generic controlled motion concept for active manipulation of mm-waves..(?)

27. Controlled Mirror Motion End of presentation

28. Controlled Mirror Motion Controlling the mirror motion • Response of mirror position sensor to actuator voltage is ‘slow’ but highly linear • The response of both output powers to mirror position is ‘fast’ but not linear