Active Control of RWM Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK

transcript

YQ Liu, Peking University, Feb 16-20, 2009

Active Control of RWM

Yueqiang Liu

UKAEA Culham Science Centre

Abingdon, Oxon OX14 3DB, UK

Outline

1. Basic control theory

2. Analytic theory for RWM control1)Cylindrical theory of RWM feedback2)Fitzpatrick-Aydemir model

3. Numerical modelling

4. Experimental results

Basic control theory (for RWM)

Control diagram

Frequency-response approach Nyquist diagram

State-space approach

Control diagram

MIMO control

Two essential components in feedback Plasma dynamics (P) Controller (K)

Mode dynamics normally described by plasma response models Can be constructed from experimental data, like in vertical control. So far

lack for n>0 RWM control From analytical theory: works well for RFP plasmas From toroidal calculations

Various ways for constructing plasma response model [Liu PPCF 48 969(2006), Liu CPC 176 161(2007)]

Pade approximation Pole-residue expansion Full-model frequency response, etc.

Basic control logic

Find transfer function P(s) from control signal u to sensor signal y

Principle I: Closed loop stability all roots of 1+K(s)P(s)=0 have negative real part

Principle II: If P(s) has only one unstable pole, then closed loop stability Nyquist curve of open loop K(s)P(s) encircles -1 once counter-clock-wise

Nyquist curve of P(s) = complex plot of P(j) as goes

from –∞ to +∞.

Principle II follows from Cauchy’s principle of phase variation (famous Argument Principle): n=N-P

Plasma dynamics: frequency approach

Plasma dynamics: state-space approach

Describe control problem by system of ODEs

Control design normally ends up with solving matrices equations

Most suitable for MIMO and nonlinear control for RWM

Time-domain and frequency domain (almost) tranformable via Laplace transform

We will focus on frequency approach ...

Controller design: general idea

Controller design: example

Outline

Single mode analysis

PRM for single mode

Multi-mode analysis

Outline

Fitzpatrick-Aydemir model

[Liu PPCF 48 969(2006)]

Outline

Numerical modelling

MARS-F code

Plasma response model (PRM)

Example of DIII-D modelling

ITER study Sensor optimisation for RWM control

MARS-F feedback formulation

MARS-F numerics

MARS-F benchmark

RWM stability with 2D walls well benchmarked

Control and PRM

PRM from toroidal calculations

Robust control

Liu PPCF 44 L21(2002)

ITER equilibria from Scenario-4

RWM control in ITER

ITER modelling with external coils

Liu NF 44 232(2004)

Choice of active coils Major debate: internal vs. external coils

Recent proposal: using 3x9 in-vessel copper coils (designed mainly for ELM control) … under investigation

Sensor coil optimisation: idea

Sensor signal optimisation: results Sensor signal crucial factor in

the feedback loop E.g. it is now well established, by

theory [Liu PoP 7 3681(2000)] and experiments, that internal poloidal sensors better than radial sensors

A new scheme for sensor optimisation is proposed, and shown very efficient in improving performance of radial sensors [Liu NF 47 648 (2007)]

Outline

Expermental results Results on reversed field pinches (RFP)

EXTRAP-T2R (Sweden) RFX (Italy)

Results on DIII-D Pressure-driven RWM feedback Current-driven RWM feedback

RWM feedback planned on other tokamaks KSTAR ASDEX-U ITER ...

Feedback has been proven successful for RWM control in DIII-D, both in experiments [Strait PoP 11 2505(2004)] and in simulations [Liu PoP 13 056120(2006)]

So far the most successful feedback experiments achieved in RFP machines

RFP, unlike tokamak, does not have strong vacuum magnetic field. Due to plasma relaxation processes, toroidal field reverses sign close to plasma edge

Normally multiple unstable modes (different n) occur simultaneously, including

Internal/external resonant modes (tearing modes)internal/external non-resonant modes (RWM)

RWM are not influenced by plasma flow, thus RFP provides an ideal platform for simultaneous control of multiple unstable RWM

Feedback experiments on RFP

Experimental results on T2RExperimental results on T2R

red: Reference shot w/o fb black: With intelligent shell feedback control

Refined intelligent shell mode of operation.

All unstable RWMs are suppressed (16 modes)

The field error amplification (n=+2) is suppressed.

Feedback results in a three-fold increase of the discharge duration

Stabilization is achieved for 10 wall times

[Brunsel PPCF 47 B25(2005)]

Feedback experiments on RFP

Feedback experiments on DIII-D

DIII-D uses C-coils (outside vacuum vessel) to perfrom dynamic error field correction

... and I-coils (inside vacuum vessel) to perform direct feedback stabilisation of RWM

Experimental results do show direct feedback stabilisation of the mode

Summary Theory of active control of RWM well developed during last

10 years

Several feedback simulation codes developed and benchmarked. Toroidal simulations can give reasonable predictions of the experimental feedback results

Full model prediction for ITER will require consideration of 3D conducting structures (resistive walls)

Successful feedback experiments carried out on tokamaks.

Particularly impressive results obtained on RFP machines

Active Control of RWM Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK

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