Nonlinear Simulation of DIII-D Plasma and Poloidal Systems Using DINA and SIMULINK. M.L.Walker, J.A.Leuer, R.D.Deranian, D.A.Humphreys General Atomics

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1 Nonlinear Simulation of DIII-D Plama and Poloidal Sytem Uing DINA and SIMULINK M.L.Walker, J.A.Leuer, R.D.Deranian, D.A.Humphrey General Atomic R.R.Khayrutdinov, V.Dokouka Triniti Laboratory A hardware-in-the-loop imulation capability [L] previouly developed for poloidal hape controller teting uing Matlab SIMULINK ha been upgraded by replacing the linearized plama model with the DINA nonlinear plama evolution code [K]. Thi upgrade expand the capabilitie of the imulation beyond hape and poition control to allow development and tudy of current profile control. Real time current profile information will oon be available in DIII-D uing the Plama Control Sytem (PCS) real time EFIT [F] calculation, enabled by an ongoing upgrade of PCS hardware. The DINA code incorporate a model of electron cyclotron current drive (ECCD). Study of open loop (e.g.,[lu]) and, more recently, cloed loop [H] interaction of ECCD with DIII-D plama ha been a major reearch thrut at DIII-D in the pat few year. The enhanced SIMULINK model allow complete imulation of the interaction of control for poloidal plama hape and current drive with a realitic, validated DIII-D ytem model. We decribe the incorporation of DINA into the SIMULINK DIII-D tokamak ytem model and reult of validating thi combined model againt DIII-D data. [L] J.A.Leuer, et.al., 18th IEEE/NPSS SOFE, Oct.25-29,1999, p [K] R.R.Khayrutdinov,V.E.Lukah, J. Comput. Phy 109 (1993) 193 [F] J.R.Ferron,et.al., Nucl.Fuion vol.38, no.7, July 1988, [Lu] T.C.Luce, et.al., General Atomic report GA-A23259 [H] D.A.Humphrey,et.al., Bull. Am. Phy. Soc. 46, 299 (2001)

2 OVERVIEW Simulator of the DIII-D poloidal field ytem ha been ued for everal year to aid development of plama control algorithm. Simple linear plama repone model ued to imulate global plama motion. Simulator contain detailed coil, power upply and paive conductor model of the component of DIII-D plant. Recent addition i ue of nonlinear plama evolution code DINA * in place of the linear plama repone model. Validation of imulation with DINA nonlinear model i preented. A general architecture which facilitate collaborative model development i outlined. * Developed by R.R.Khayrutdinov, et.al. at Triniti Lab.

3 DIII-D Simulator Simulation model running in the MATLAB/SIMULINK environment in ue for everal year. ACTUATOR INPUTS POWER SUPPLIES Field Shaping PS TOKAMAK MODEL DIAGNOSTIC PROCESSING DIAGNOSTIC OUTPUT Chopper Command Coil Voltage F filter F volt A D/A Actuator Command from PCS - DC PS Command Coil Current Com. PS Voltage Volt pf1a - B-coil vloop Vb filter F p B coil vloop pf1a F current B Command Ohmic PS V V vec. pi Unit A/D Diagnotic Output to PCS 1 Coil Voltage Input from Data Acquiition (Optional) Volt F-coil Volt VOLTAGE TESTING E-coil Volt F Switch E Switch Tokamak & Plama Model model diag. pi diag ep com. mater diag. 2 Output to Data Storage (Phyic Unit) Thi model (with linearized plama repone) ha been extenively teted & validated: acquired hot data injected (A) modeled output (B) and actual diagnotic output compared Tokamak & Plama Model block now can ue DINA nonlinear plama evolution code.

4 DIII-D Tokamak Poloidal Coil Sytem OHMIC HEATING COIL 8A POLOIDAL FIELD COILS 4A 3A 5A 9A 7A 2A 1A 1B 2B 6A 6B 3B 4B 5B 8B 9B 7B TOROIDAL FIELD COIL

5 Complex, Reconfigureable Poloidal Coil Circuit i Modeled in Simulator DIII-D ue a "patch panel" to change poloidal coil connection for different plama configuration. For example: E BUS VFI BUS HVS HV S HV S HV S FROM EPS CIRCUIT EA EB 7A 6A 7B 6B 1A 2A 3A 4A 5A 8A 9A 1B 2B 3B 4B 5B 8B 9B i 1 i 2 i 10 i 11 i 19 i20 i 3 i 4 i 5 i 6 i 7 i 8 i 9 i 12 i 13 i 14 i 15 i 16 i 17 i Ω (RV2 ) Ω (RV1) E - BUS HVS = High Voltage Supplie, = Low Voltage Supplie, EPS = Ohmic Coil (E-coil) Power Supply, VFI = Return current bu Model i dynamically configured to emulate DIII-D circuit for a particular hot. Include: linearized or nonlinear (DINA) plama highly nonlinear power upplie large, complex et of circuit equation for haping coil and paive element

6 "Block-Feedback" Simulation Architecture Provided by SIMULINK TM Simulation Superviory Code non-ohmic Heating Model DINA Energy Tranport Model Current Profile Repone Model Shape & Equilibrium Repone Model Actuator Command Device Specific Sytem Model Diagnotic Output Block Centric Model Development: Each model block define it' own input, output, and time evolution behavior. Model block developer provide input pecification: What' needed for block execution? Other (collaborator) block developer provide output pecification: What' needed from that block a input to other block?

7 Example of "Block-Feedback" Architecture in Ue Example 1: Rigid repone model (ubcript: =tabilizing conductor, p=plama): M di z di R di RI M di ψ c ψ m p p = V dt zc I dt Rm I dt dt L di p ψ p dr di ψ dz di RI M di m p c p p p p = 0 dt Rm I dt zc I dt dt (Diturbance term have been neglected.) Rewrite in feedback form to get Device Specific Block dynamic: di dt = M R I M V M V and Plama Block dynamic: di dt p loop ψ p dr ψ 1 1 m p dzc = Lp RpIp Lp M R I z I V M di p ψ zc ψ loop = p dt z I R c m m R I m c di dt p di dt Example 2: DINA implementation in DIII-D imulation: Device Specific Sytem Model coil current loop voltage at conductor Plama Repone Model coil power upplie veel bu connection diagnotic acquiition circuit equilibrium profile evolution

8 Model Repone Validation Execute in SIMULINK TM environment Operation in Open Loop Meaured data drive imulation either power upply voltage or power upply command Simulated data i compared with data acquired from hot DIII-D DATA STORAGE SYSTEM COMMAND DATA FROM PREVIOUS SHOT A DIII-D SIMULATOR SIMULINK MODE B SIMULATOR DIAGNOSTIC SIGNALS DIAGNOSTIC SIGNALS FROM PREVIOUS SHOT OPEN LOOP SIGNAL COMPARE

9 Control Analyi and Simulation Stand-alone imulation executable module i generated from validated SIMULINK TM model uing MATLAB Real Time Workhop. Thi module i called a SIMSERVER (SIMulation SERVER). Simerver imulation operate in Cloed Loop with the PCS jut like normal DIII-D experiment. Allow teting of control algorithm without need for experimental time. PLASMA CONTROL COMPUTER COMMANDS TO ACTUATORS TEST MODE SWITCH DIII-D TOKAMAK DIAGNOSTIC SIGNALS INPUT TO PCS A DIII-D SIMULATOR B TEST MODULE

10 Linearized Plama Replaced by DINA in Feedback with Device Model 1 p_volt19 current48 Vp19 diag Vpl48 curout48 m C CtrlPt R,Z dina DINA S-Function C zero 28 1 diag_out external ytem DINA code remain in original FORTRAN. SIMULINK TM S-function wrapper of DINA (written in C) provide I/O interface to imulation. SIMULINK Simulation FORTRAN S-Function Wrapper SIMULINK TM S-function provide eay method for incorporating legacy model code.

11 Simulator Accurately Reproduce Experimental Diagnotic Data Data hown (hot 99339) ha control driven intability at DINA_ red=ptdata; blue=d3d_im pcv1a x ecoila f1a f7b vloop pf1a pi7b mpi11m322 mpi7fb time ()

12 Not All Shape Parameter are Accurately Simulated Yet Data hown (hot 99339) ha control driven intability at 2. DINA/EFIT Compare Ip [MA] EFIT DINA 0.16 Beta p q_axi time, [] 1.8 Rmag [m] EFIT DINA

13 Not All Shape Parameter are Accurately Simulated Yet Data hown (hot 99339) ha control driven intability at DINA/EFIT Compare Zmag [m] EFIT DINA a [m] Elongation Xpt Triangularity Xpt EFIT DINA time, []

14 DINA Shape Evolution DINA ha approximately contant radial and vertical hift relative to EFIT recontruction EFIT DINA EFIT DINA

15 SUMMARY

16 Simulator Reduce Experimental Time Needed for Controller Development and Teting PCS normally connect to the DIII-D tokamak for real time control of the plant For teting, PCS can connect directly to oftware imulation. Simulation currently model all ytem important for axiymmetric control: - DC power upplie - fat witched power upplie - configurational witche - field haping & ohmic heating coil - paive conductor - plama dynamic - magnetic diagnotic - data filter - A/D & D/A ignal converion Allow teting of controller a implemented in PCS without uing experimental time. Simulation i expanding to include other control loop.

17 Validated Simulation Can Provide Bai for Sytem Code for Future Device Block-feedback architecture propoed for collaborative development of general ytem code. Baed on our experience with DINA integration. Individual block "plug-in" tructure facilitate collaborative development of ytem model Block input/output requirement define interface between block. SIMULINK TM wa pecifically deigned for thi approach. Creating block diagram produce executable imulation Uer built (e.g. legacy code) or SIMULINK TM provided model block Automatic variable time-tep and multiple time-cale integration (both continuou- and dicrete-time) Work begun on individual component: non-axiymmetric imulation model: RWM (ee Franon QP1.079) NTM (ee Welander QP1.078) Simple parametric phyic model (ee Deranian RP1.039)