Implementation of Fast Model Predictive Control at EXTRAP T2R Reversed-Field Pinch

A. C. Setiadi, P. R. Brunsell, L. FrassinettiDept. Fusion Plasma Physics, KTH Royal Institute of Technology, SE 100-44 Stockholm,

Sweden, Association EURATOM-VR

Introduction Control Scheme

MPC Formulation

EXTRAP T2R

Summary References

Active feedback control has been a crucial tool in suppress-ing MHD instabilities in fusion plasma. In EXTRAP T2R, the performance of the active feedback control had been shown to be able to supressed the undesired modes such as RWMs[1]. This poster present an alternative control method which o�ers better performance and reliability in handling complex multiple-input multiple-output (MIMO) system.

A model predictive control (MPC) is an optimal controller that generate its actuation based on prediction of the system. Furthermore MPC is known to be able to handle MIMO system directly and explicit contraints on the sys-tems. However, a major practical issues for the MPC is the computational cost especially when dealing with system with a fast time scale.

EXTRAP T2R

- Plasma current : ~80 kA- Major Radius : 1.24 m- Minor Radius : 0.183 m- Shell time constant : 6.3 ms- Electron temperature : ~200 eV

Without feedback, the plasma terminate around 15 ms

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power ampli�er

T2R shell & plasmacontroller

Σ Σ

ΣΣ

: reference signals

: dither signals

: actuator coil current

: sensor coil voltage

recent upgrade on control hardware :16 bit data acquisition; 3 GHz multi-core processor

sensor coils & actuator coils aredistributed evenly at 4 poloidal and 32 toroidal positions

both sets of coils are connected pairwise

Utilize Pseudo-random Binary Sig-nals as dithering signals to excite the dynamics of the system

Model selection & parameter estima-

tion

Test protocol

Model validation

Accept?

Start

End

System is assumed to be linear around equilibrium.Discrete time State Space model :

Subspace Identification Method SSARX [2][3] used to estimate system matrices

Perform bootstrap simulation:1. Synthesize an artificial set of data batches2. Estimate model3. Solve bivariate function :

Visualize function and compare with theoritical model.

System Identification

Spatial validation Time domain validationUse (unused) real experimental input-output data. Compare the real output with model output

*picture taken from [3]

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toroidal mode number(n)

MHD spectra : plasma

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toroidal mode number(n)

MHD spectra : vacuum

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current

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radial �eld

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Model Predictive Control

futurepast

k k+1 k+2 k+3 k+Np

reference

predicted output

planned input

prediction horizon

MC-MPC :- Allow for arbitrary mode suppresion without online FFT- Inteligent Shell -like can be achieved by setting L=I - L can be optimized by incorporating theoritical growth rates

MC-PID MC-MPC

Radi

al F

ield

Curr

ent

MPC is an optimal controllerReference

P. R. Brunsell, et al., “Resistive wall mode feedback control in EXTRAP T2R with improved steady-state error and transient response,” Physics of Plasmas,14, 102505, 2007.

K. E. J. Olofsson, et al.,“Cascade and multibatch subspace system identification for multivariate vacuum-plasma response characterization,” IEEE Conference on Decision and Control, 2614–2619, 2011.

K. E. J. Olofsson, “Nonaxisymmetric experimental modal analysis and control of resistive wall MHD in RFPs”, Doctoral Thesis, KTH, Stockholm, Sweden, 2012

S. Richter, et al., “High-speed online MPC based on a fast gradient method applied to power converter control,” American Control Conference, 4737–4743, 2010.

K. E. J. Olofsson,et al.,”Controlled Magnetohydrodynamic mode sustainment in the reversed-field pinch: Theory, design and experiments”, Fusion Engineering and Design, 84(7-11), 1455-1459, 2009.

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Comparison with Mode Control - Proportional Integral Derivative controller, similar to that of Revised Intelligent Shell [5] , excluding the axisymmetric part:

The MPC in this work used the Fast Gradient Method [4]. Fast gradient has better conver-gence rate than the conventional gradient method. The underlying idea of the fast gradi-ent method is to drop the strict condition of forming the relaxation sequence as in the con-ventional gradient method.

MPC able to handle con-straints on states and inputs

optimally

At every sampling instance :1. Collect measurement data2. Make prediction and plan ahead3. Apply only the first input4. Repeat

Current implementation of MPC at EXTRAP use a state space model of order 150 and 3 step predic-tion ahead. The average latency of MPC at EXTRAP is ~17%

For the implementation of MPC there is a trade off between model order & prediction length with computational cost

To implement MPC at fast cycle time (at EXTRAP the cycle time is 0.1 ms), the following steps are necessary:

Reduction of model order, this would mean that we allow to lose some of model accuracy to reduce latency

Utilize fast numerical library code for real time implementation.

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Practical Issue with the implementation of MPC:

Receeding Horizon Control : prediction + feedback

DFT matrix

Mode weighting matrix

Illustration: