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YQ Liu, Peking University, Feb 16-20, 2009 Active Control of RWM Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK
YQ Liu, Peking University, Feb 16-20, 2009
Active Control of RWM
Yueqiang Liu
UKAEA Culham Science Centre
Abingdon, Oxon OX14 3DB, UK
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
Basic control theory (for RWM)
Control diagram
Frequency-response approach Nyquist diagram
State-space approach
YQ Liu, Peking University, Feb 16-20, 2009
Control diagram
YQ Liu, Peking University, Feb 16-20, 2009
MIMO control
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
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 ...
YQ Liu, Peking University, Feb 16-20, 2009
Controller design: general idea
YQ Liu, Peking University, Feb 16-20, 2009
Controller design: example
YQ Liu, Peking University, Feb 16-20, 2009
Controller design: example
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
Single mode analysis
YQ Liu, Peking University, Feb 16-20, 2009
PRM for single mode
YQ Liu, Peking University, Feb 16-20, 2009
Multi-mode analysis
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
Fitzpatrick-Aydemir model
YQ Liu, Peking University, Feb 16-20, 2009
Fitzpatrick-Aydemir model
[Liu PPCF 48 969(2006)]
YQ Liu, Peking University, Feb 16-20, 2009
Fitzpatrick-Aydemir model
YQ Liu, Peking University, Feb 16-20, 2009
Fitzpatrick-Aydemir model
YQ Liu, Peking University, Feb 16-20, 2009
Fitzpatrick-Aydemir model
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
Numerical modelling
MARS-F code
Plasma response model (PRM)
Example of DIII-D modelling
ITER study Sensor optimisation for RWM control
YQ Liu, Peking University, Feb 16-20, 2009
MARS-F feedback formulation
YQ Liu, Peking University, Feb 16-20, 2009
MARS-F numerics
YQ Liu, Peking University, Feb 16-20, 2009
MARS-F benchmark
YQ Liu, Peking University, Feb 16-20, 2009
RWM stability with 2D walls well benchmarked
YQ Liu, Peking University, Feb 16-20, 2009
Control and PRM
YQ Liu, Peking University, Feb 16-20, 2009
PRM from toroidal calculations
YQ Liu, Peking University, Feb 16-20, 2009
PRM from toroidal calculations
YQ Liu, Peking University, Feb 16-20, 2009
PRM from toroidal calculations
YQ Liu, Peking University, Feb 16-20, 2009
Robust control
Liu PPCF 44 L21(2002)
YQ Liu, Peking University, Feb 16-20, 2009
Example of DIII-D modelling
YQ Liu, Peking University, Feb 16-20, 2009
Example of DIII-D modelling
YQ Liu, Peking University, Feb 16-20, 2009
Example of DIII-D modelling
YQ Liu, Peking University, Feb 16-20, 2009
ITER equilibria from Scenario-4
YQ Liu, Peking University, Feb 16-20, 2009
RWM control in ITER
YQ Liu, Peking University, Feb 16-20, 2009
ITER modelling with external coils
Liu NF 44 232(2004)
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
Sensor coil optimisation: idea
YQ Liu, Peking University, Feb 16-20, 2009
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)]
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
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 ...
YQ Liu, Peking University, Feb 16-20, 2009
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
BB
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
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
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
YQ Liu, Peking University, Feb 16-20, 2009
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
