Poloidal Current Anti-Saturation Control Routine with DPCS Multi-processor Architecture

Transcription

1 Poloidal Current Anti-Saturation Control Routine with DPCS Multi-processor Architecture M. Ferrara, I.H. Hutchinson, S.M. Wolfe, J.A. Stillerman, T.W. Fredian Abstract: Ohmic and equilibrium field currents can reach their rails during high performance discharges or in the presence of a strong off-normal event, possibly resulting in loss of control and plasma disruptions. On C-Mod we designed and tested an anti-saturation routine which detects the impending saturation of OH and EF currents and interpolates to a neighboring safe equilibrium in real-time. The routine was implemented with a multi-processors, multi-time-scale control scheme, which is based on a master process and many asynchronous slave processes. The scheme is general and can be used for any computationally intensive algorithm. USDoE award DE-FC02-99ER

2 Motivation Poloidal field and ohmic currents may saturate during high-performance discharges or large off-normal events, if the design margin of the power supplies is not sufficient. The saturation of control currents causes a deviation from the desired (pre-programmed) magnetic configuration, with the consequence of: Shape degradation; Possible vertical instability and plasma disruptions. Adaptive routines have to be in place to handle these special events. 11/19/2008 APS DPP

3 Possible Strategies to Deal with Current Saturation 1. Dynamic adaptation in control [1]: Maintains the original high-performance target; Makes use of system redundancy to supplement saturating coils or switch between equivalent sets of control currents; Needs redundant resources (coils, power supplies, etc.), additional capital cost. 2. Adaptive pulse rescheduling [2], [3]: Simpler concept: if one or more currents are saturating, the control settings of the original target are interpolated to a less demanding compatible target or to an early ramp-down scenario; The original target is abandoned; The only solution with low system redundancy (e.g. C-Mod, ITER). [1] On-Line Calculation of Feedforward Trajectories for Tokamak Plasma Shape Control, M.L. Wlaker, R.D. Johnson, J.A. Leuer, B.G. Penaflor. In the Proceedings of the 44th IEEE Conference on Decision and Control, Seville, December [2] A Control Scheme to Deal With Coil Current Saturation in a Tokamak, G. Ambrosino, M. Ariola, A. Pironti, A. Portone, M. Walker. IEEE Transactions on Control Systems Technology 9, 831 (2001). [3] Some Nonlinear Controls for Nonlinear Processes in the DIII-D Tokamak, M.L. Walker, D.A. Humphreys, E. Schuster. In the Proceedings of the 42nd IEEE Conference on Decision and Control, Maui HI, December /19/2008 APS DPP

4 C-Mod Control Coils 11/19/2008 APS DPP

5 C-Mod Control Coils (Cont d) Different control currents are more effective for changing different shape and position parameters: OH2U and OH2L in anti-phase for the vertical position of the plasma; EF1U and EF1L for the vertical position of the upper and lower X-point (i.e. the elongation); EF2U and EF2L for the radial position of the upper and lower X-point (i.e. the top and bottom triangularity); EF3U and EF3L, connected in series, for the radial position of the plasma. However it is really a combination of all the currents that produces the magnetic moment necessary to obtain the desired shape. Therefore the control of the plasma shape and position is a Multiple-Input Multiple- Output (MIMO) problem. 11/19/2008 APS DPP

6 C-Mod Control Power Supplies 11/19/2008 APS DPP

7 C-Mod Feedback Control 11/19/2008 APS DPP

8 Adaptive Anti-saturation Routine in C-Mod C-Mod has very limited control redundancy, with only the EF4 coils potentially doubling symmetric EF2 and EF3 currents, however with a much longer penetration time. Therefore the natural solution is pulse rescheduling: Average Currents With Window Filter Read Values of Currents Average Time Derivatives With Window Filter 1. The poloidal equilibrium and ohmic currents are inputs of the Digital Plasma Control System (DPCS); 2. A window filter is used to reject noise; 3. The average time derivatives of the control currents are also calculated; 4. The ratio of the distance of the currents from their rails and the time derivatives are the time horizons to saturation; 5. When one of these exceeds a given time horizon, the routine starts to interpolate the target and feed-forward waveforms linearly to those of a safe equilibrium. Time Horizons Time Horizon < Threshold N Saturation Event = 1 Start Linear Interpolation of Targets and Feed-forwards 11/19/2008 APS DPP

9 Routine Parameters Threshold time horizon to saturation (Time Horizon): Small enough to avoid false positives; Large enough to avoid current saturation during interpolation. Speed of interpolation (Interpolation Time): Short enough to save the discharge by quickly moving to the safe equilibrium; Long enough to allow smooth transition, i.e. to avoid transients in the control currents and the plasma. The safe equilibrium to which the original target and feed-forward waveforms are interpolated: Can be completely different from the original target, but it should be possible to move to this equilibrium from the original target without large transients; The simplest safe equilibrium is designed by relaxing the original highperformance target. 11/19/2008 APS DPP

10 Experimental Tests (Setup) Target Plasma: High-triangularity equilibrium developed for use in similarity studies with JFT2-M [4] (red contour in figure); The EF2L current may reach its upper rail (0 Amps) and cause a plasma disruption. Safe Equilibrium: Designed by reducing the triangularity of the original target. Time Horizon and Interpolation Time: Chosen heuristically and optimized with Alcasim simulations [5]. [4] Comparisons of Small ELM H-Mode Regimes on the Alcator C-Mod and JFT-2M Tokamaks, A.E. Hubbard, K. Kamiya, N. Oyama, N. Basse, T. Biewer, E. Edlund, J.W. Hughes, L. Lin, M. Porkolab, W. Rowan, J. Snipes, J. Terry and S.M. Wolfe. Plasma Phys. Control. Fusion 48, A121 (2006). [5] Alcasim Axisymmetric Simulation Code for Alcator C-Mod, M. Ferrara, I.H. Hutchinson, S.M. Wolfe, J.A. Stillerman, T.W. Fredian. In the Proceedings of the 45th IEEE Conference on Decision and Control, San Diego CA, December /19/2008 APS DPP

11 Experimental Test ( , 016) 11/19/2008 APS DPP

12 Experimental Test ( , 016) The black traces show the EF2L current, the RXL target and the EFIT reconstruction of the original target plasma triangularity. The blue traces show results from shot : A saturation event is detected at 0.66s; Target and feed-forward waveforms (and in particular RXL) are interpolated to those of the safe equilibrium (RXL is 33% smaller than in the original plasma); The EF2L current moves away from its upper rail. The red traces show results from shot : A saturation event is detected at 0.66s; Target and feed-forward waveforms are interpolated to those of the safe equilibrium (RXL is 67% smaller than in the original plasma); The EF2L current moves away from its upper rail. Time Horizon = 20ms and Interpolation Time = 100ms are chosen with the help of Alcasim simulations. 11/19/2008 APS DPP

13 Experimental Test ( ) Time Horizon = 20ms and Interpolation Time = 20ms in this case; The short interpolation time causes a large perturbation of the vertical position and the plasma disrupts; The same experiment with Interpolation Time = 100ms succeeds in shot (blue traces). 11/19/2008 APS DPP

14 Multi-processor Multi-timescale Architecture The anti-saturation routine requires significant computation resources and its calculation in the main real-time process is marginal at the nominal speed 100µs/cycle; A more general multi-processor multi-timescale architecture was developed for which the routine is a convenient test-bed: Hardware: Dual-core quad-processor machine; Two DTACQ Acq196 digitizers with 96 inputs and 16 analog outputs each; INCAA DI02 decoder/timing module; cpci connection between host and digitizers via SBS bus extender module. Software: One master process, synchronous at 100µs/cycle, for the main real-time computations; One slave process, asynchronous, for the anti-saturation routine; Master and slave communicate through blocks of shared memory; memory access is managed with semaphores; Master creates and kills the slave process and initializes and frees shared resources. 11/19/2008 APS DPP

15 Process 1, 100µs/cycle Process 2, Asynchronous Targets Observers DPCS Inputs New Data in Shared Memory I? Observer Procedure N Shared Memory I Available? Shared Memory I Available? N Write To Shared Memory I Read From Shared Memory I N Saturation Event? Saturation Event? N Shared Memory II Available? Time Horizons N Read From Shared Memory II Time Horizon < Threshold Saturation Event = 1 Overwrite Targets With Values at Previous Iteration Overwrite Targets With Safe Ones Safe Targets Feedforward PID Errors Safe Feedforward Saturation Event? New Data From Shared Memory II? Controller Procedure Shared Memory II Available? Write To Shared Memory II N N Overwrite Feedforward With Values at Previous Iteration Overwrite Feedforward With Safe Ones Controllers 19/11/2008 APS DPP

16 Multi-processor Multi-timescale Architecture (Cont d) Master (Process 1): Reads the DPCS inputs and calculates the observers and the nominal target waveforms; Checks if write shared memory is available (orange blocks); Writes data to shared memory; Checks if there is a saturation event; Checks if read shared memory is available (yellow blocks); In case of a saturation event and no conflicts in memory access, the nominal target waveforms are overwritten with the results from the slave; in case of conflicts in memory access, the old targets at the previous timestep are used; A similar scheme is in place for the feed-forward waveforms. Slave (Process 2): Waits for new data from the master (orange blocks); s the time horizon to saturation for all the currents; Raises a saturation flag in case; Computes interpolated waveforms and writes them to shared memory if it is accessible (yellow blocks). 11/19/2008 APS DPP

17 Conclusions & Future Work An application of pulse rescheduling was demonstrated on C-Mod in the specific case of the impending saturation of the EF2L current during a high-triangularity discharge; A high-performance multi-processor multi-timescale architecture was specifically developed and successfully tested; The application is quite general, at least in an operation scenario where the targets are progressively more ambitious (elongation, triangularity, plasma current, etc.) and the safe equilibrium is set to be a previously run, less demanding discharge; However, a simple pair of scalar parameters Time Horizon and Interpolation Time might not be sufficient in a more general application, for example the time horizon might need to be different for different coils and maybe for different saturation scenarios. 11/19/2008 APS DPP

18 Conclusions & Future Work (Cont d) Future work should aim at making the routine more general. Ideally, the routine should be able to: Handle cases where an arbitrary number of currents are saturating; Decide in real-time how to interpolate and to which alternative scenario; Preserve loop stability, if pulse-rescheduling requires the interpolation of control gains. 11/19/2008 APS DPP