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Plasma magnetic diagnostic and control at ITER & DEMO...
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Plasma magnetic diagnostic and controlat ITER & DEMO (& EAST)
Gianmaria De Tommasi1
with contributions of the CREATE team
Dipartimento di Ingegneria Elettrica e delle Tecnologie dell’Informazione (DIETI)Università degli Studi di Napoli Federico II, Napoli, Italy
International School of Fusion Reactors TechnologyEttore Majorana Foundation and Centre for Scientific Culture
28 April- 4 May - Erice-Sicily, Italy
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Outline
1 IntroductionMagnetic (control-oriented) modellingControl engineering jargon & toolsThe plasma magnetic control problem
2 The proposed architecture for ITER (as a reference)ITER magnetic diagnosticVertical stabilization controllerCurrent decoupling controllerPlasma current controllerPlasma shape controllerNonlinear validation
3 The DEMO caseVertical stabilization at DEMO
4 Experiments at EASTITER-like vertical stabilization at EAST
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Introduction
Nuclear Fusion for Dummies
Main AimProduction of energy by means ofa fusion reaction
D + T → 4He + n
PlasmaHigh temperature and pressure are neededFully ionised gas 7→ PlasmaMagnetic field is needed to confine the plasma
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Introduction
Plasma magnetic control
In tokamaks, magnetic control of the plasma is obtained by means ofmagnetic fields produced by the external active coils
In order to obtain good performance, it is necessary to have a plasma withvertically elongated cross section⇒ vertically unstable plasmasIt is important to maintain adequate plasma-wall clearance during operation
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Introduction
Plasma magnetic control
In tokamaks, magnetic control of the plasma is obtained by means ofmagnetic fields produced by the external active coilsIn order to obtain good performance, it is necessary to have a plasma withvertically elongated cross section⇒ vertically unstable plasmas
It is important to maintain adequate plasma-wall clearance during operation
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Introduction
Plasma magnetic control
In tokamaks, magnetic control of the plasma is obtained by means ofmagnetic fields produced by the external active coilsIn order to obtain good performance, it is necessary to have a plasma withvertically elongated cross section⇒ vertically unstable plasmasIt is important to maintain adequate plasma-wall clearance during operation
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Introduction Magnetic modelling
Main (basic) assumptions
1 The plasma/circuits system is axisymmetric
2 The inertial effects can be neglected at the time scale of interest,since plasma mass density is low
3 The magnetic permeability µ is homogeneous, and equal to µ0everywhere
Mass vs Massless plasma
It has been proven that neglecting plasma mass may lead to erroneous conclusion onclosed-loop stability.
M. L. Walker, D. A. HumphreysOn feedback stabilization of the tokamak plasma vertical instabilityAutomatica, vol. 45, pp. 665–674, 2009.
J. W. Helton, K. J. McGown, M. L. Walker,Conditions for stabilization of the tokamak plasma vertical instability using only a masslessplasma analysisAutomatica, vol. 46, pp. 1762.-1772, 2010.
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Introduction Magnetic modelling
Main (basic) assumptions
1 The plasma/circuits system is axisymmetric2 The inertial effects can be neglected at the time scale of interest,
since plasma mass density is low
3 The magnetic permeability µ is homogeneous, and equal to µ0everywhere
Mass vs Massless plasma
It has been proven that neglecting plasma mass may lead to erroneous conclusion onclosed-loop stability.
M. L. Walker, D. A. HumphreysOn feedback stabilization of the tokamak plasma vertical instabilityAutomatica, vol. 45, pp. 665–674, 2009.
J. W. Helton, K. J. McGown, M. L. Walker,Conditions for stabilization of the tokamak plasma vertical instability using only a masslessplasma analysisAutomatica, vol. 46, pp. 1762.-1772, 2010.
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Introduction Magnetic modelling
Main (basic) assumptions
1 The plasma/circuits system is axisymmetric2 The inertial effects can be neglected at the time scale of interest,
since plasma mass density is low3 The magnetic permeability µ is homogeneous, and equal to µ0
everywhere
Mass vs Massless plasma
It has been proven that neglecting plasma mass may lead to erroneous conclusion onclosed-loop stability.
M. L. Walker, D. A. HumphreysOn feedback stabilization of the tokamak plasma vertical instabilityAutomatica, vol. 45, pp. 665–674, 2009.
J. W. Helton, K. J. McGown, M. L. Walker,Conditions for stabilization of the tokamak plasma vertical instability using only a masslessplasma analysisAutomatica, vol. 46, pp. 1762.-1772, 2010.
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Introduction Magnetic modelling
Main (basic) assumptions
1 The plasma/circuits system is axisymmetric2 The inertial effects can be neglected at the time scale of interest,
since plasma mass density is low3 The magnetic permeability µ is homogeneous, and equal to µ0
everywhere
Mass vs Massless plasma
It has been proven that neglecting plasma mass may lead to erroneous conclusion onclosed-loop stability.
M. L. Walker, D. A. HumphreysOn feedback stabilization of the tokamak plasma vertical instabilityAutomatica, vol. 45, pp. 665–674, 2009.
J. W. Helton, K. J. McGown, M. L. Walker,Conditions for stabilization of the tokamak plasma vertical instability using only a masslessplasma analysisAutomatica, vol. 46, pp. 1762.-1772, 2010.
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Introduction Magnetic modelling
Plasma model
The input variables are:The voltage applied to the active coils vThe plasma current IpThe poloidal beta βp
The internal inductance li
Ip , βp and liIp , βp and li are used to specify the current density distribution insidethe plasma region.
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Introduction Magnetic modelling
Model outputs
Different model outputs can be chosen:
fluxes and fields where the magneticsensors are located
currents in the active and passivecircuits
plasma radial and vertical position(1st and 2nd moment of the plasmacurrent density)
geometrical descriptors describingthe plasma shape (gaps, x-point andstrike points positions)
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Introduction Magnetic modelling
Lumped parameters approximation
By using finite-elements methods, nonlinear lumped parameters approximation of the PDEsmodel is obtained
ddt
[M(y(t), βp(t), li (t)
)I(t)]
+ RI(t) = U(t) ,
y(t) = Y(I(t), βp(t), li (t)
).
where:
y(t) are the output to be controlled
I(t) =[ITPF (t) ITe (t) Ip(t)
]T is the currents vector, which includes the currents in the activecoils IPF (t), the eddy currents in the passive structures Ie(t), and the plasma current Ip(t)
U(t) =[UT
PF (t) 0T 0]T is the input voltages vector
M(·) is the mutual inductance nonlinear function
R is the resistance matrix
Y(·) is the output nonlinear function
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Introduction Magnetic modelling
Plasma linearized model
Starting from the nonlinear lumped parameters model, the following plasma linearized statespace model can be easily obtained:
δx(t) = Aδx(t) + Bδu(t) + Eδw(t), (1)
δy(t) = C δIPF (t) + Fδw(t), (2)
where:
A, B, E, C and F are the model matrices
δx(t) =[δITPF (t) δITe (t) δIp(t)
]T is the state space vector
δu(t) =[δUT
PF (t) 0T 0]T are the input voltages variations
δw(t) =[δβp(t) δli (t)
]T are the βp and li variations
δy(t) are the output variations
The model (1)–(2) relates the variations of the PF currents to the variations of the outputs around
a given equilibrium
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Introduction Control engineering jargon & tools
Linear time-invariant systems
A linear time-invariant (LTI) continuous-time system is described by
x(t) = Ax(t) + Bu(t) , x(0) = x0 (3a)y(t) = Cx(t) + Du(t) (3b)
where A ∈ Rn×n, B ∈ Rn×m, C ∈ Rp×n and D ∈ Rp×m.
A dynamical system with single-input (m = 1) and single-output(p = 1) is called SISO, otherwise it is called MIMO.
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Introduction Control engineering jargon & tools
Asymptotic stability of LTI systems
Asymptotic stability
This property roughly asserts that every solution of x(t) = Ax(t) tends to zero as t →∞.
For LTI systems the stability property is related to the system and not to a specificequilibrium
Theorem - System (3) is asymptotically stable iff A is Hurwitz, that is if every eigenvalue λi ofA has strictly negative real part
<(λi)< 0 , ∀ λi .
Theorem - System (3) is unstable if A has at least one eigenvalue λ with strictly positive realpart, that is
∃ λ s.t. <(λ)> 0 .
Theorem - Suppose that A has all eigenvalues λi such that <(λi)≤ 0, then system (3) is
unstable if there is at least one eigenvalue λ such that <(λ)
= 0 which corresponds to a Jordan
block with size > 1.
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Introduction Control engineering jargon & tools
Asymptotic stability of LTI systems
Asymptotic stability
This property roughly asserts that every solution of x(t) = Ax(t) tends to zero as t →∞.
For LTI systems the stability property is related to the system and not to a specificequilibrium
Theorem - System (3) is asymptotically stable iff A is Hurwitz, that is if every eigenvalue λi ofA has strictly negative real part
<(λi)< 0 , ∀ λi .
Theorem - System (3) is unstable if A has at least one eigenvalue λ with strictly positive realpart, that is
∃ λ s.t. <(λ)> 0 .
Theorem - Suppose that A has all eigenvalues λi such that <(λi)≤ 0, then system (3) is
unstable if there is at least one eigenvalue λ such that <(λ)
= 0 which corresponds to a Jordan
block with size > 1.
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Introduction Control engineering jargon & tools
Asymptotic stability of LTI systems
Asymptotic stability
This property roughly asserts that every solution of x(t) = Ax(t) tends to zero as t →∞.
For LTI systems the stability property is related to the system and not to a specificequilibrium
Theorem - System (3) is asymptotically stable iff A is Hurwitz, that is if every eigenvalue λi ofA has strictly negative real part
<(λi)< 0 , ∀ λi .
Theorem - System (3) is unstable if A has at least one eigenvalue λ with strictly positive realpart, that is
∃ λ s.t. <(λ)> 0 .
Theorem - Suppose that A has all eigenvalues λi such that <(λi)≤ 0, then system (3) is
unstable if there is at least one eigenvalue λ such that <(λ)
= 0 which corresponds to a Jordan
block with size > 1.
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Introduction Control engineering jargon & tools
Equilibrium stability for nonlinear systems
For nonlinear system the stability property is related to thespecific equilibrium
Theorem - The equilibrium state xe corresponding to the constantinput u a nonlinear system is asymptotically stable if all theeigenvalues of the correspondent linearized system have strictlynegative real part
Theorem - The equilibrium state xe corresponding to the constantinput u a nonlinear system is unstable if there exists at least oneeigenvalue of the correspondent linearized system which has strictlypositive real part
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Introduction Control engineering jargon & tools
Equilibrium stability for nonlinear systems
For nonlinear system the stability property is related to thespecific equilibrium
Theorem - The equilibrium state xe corresponding to the constantinput u a nonlinear system is asymptotically stable if all theeigenvalues of the correspondent linearized system have strictlynegative real part
Theorem - The equilibrium state xe corresponding to the constantinput u a nonlinear system is unstable if there exists at least oneeigenvalue of the correspondent linearized system which has strictlypositive real part
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Introduction Control engineering jargon & tools
Transfer function of LTI systems
Given a LTI system (3) the corresponding transfer matrix from u to y isdefined as
Y (s) = G(s)U(s) ,
with s ∈ C. U(s) and Y (s) are the Laplace transforms of u(t) and y(t)with zero initial condition (x(0) = 0), and
G(s) = C(sI − A
)−1B + D . (4)
For SISO system (4) is called transfer function and it is equal to theLaplace transform of the impulsive response of system (3) with zeroinitial condition.
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Introduction Control engineering jargon & tools
Transfer function
Given the transfer function G(s) and the Laplace transform of the inputU(s) the time response of the system can be computed as the inversetransform of G(s)U(s), without solving differential equations
As an example, the step response of a system can be computed as:
y(t) = L−1[G(s)
1s
].
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Introduction Control engineering jargon & tools
Poles and zeros of SISO systems
Given a SISO LTI system , its transfer function is a rational function of s
G(s) =N(s)
D(s)= ρ
Πi(s − zi)
Πj(s − pj),
where N(s) and D(s) are polynomial in s, withdeg
(N(s)
)≤ deg
(D(s)
).
We callpj poles of G(s)
zi zeros of G(s)
Every pole of G(s) is an eigenvalue of the system matrix A.However, not every eigenvalue of A is a pole of G(s)
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Introduction Control engineering jargon & tools
Poles and zeros of SISO systems
Given a SISO LTI system , its transfer function is a rational function of s
G(s) =N(s)
D(s)= ρ
Πi(s − zi)
Πj(s − pj),
where N(s) and D(s) are polynomial in s, withdeg
(N(s)
)≤ deg
(D(s)
).
We callpj poles of G(s)
zi zeros of G(s)
Every pole of G(s) is an eigenvalue of the system matrix A.However, not every eigenvalue of A is a pole of G(s)
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Introduction Control engineering jargon & tools
Block diagrams
When dealing with transfer functions, it is usual to resort to Blockdiagrams which permit to graphically represent the interconnectionsbetween system in a convenient way.
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Introduction Control engineering jargon & tools
Series connection
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Introduction Control engineering jargon & tools
Parallel connection
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Introduction Control engineering jargon & tools
Feedback connection
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Introduction Control engineering jargon & tools
Stability of interconnected systems
Given two asymptotically stable LTI systems G1(s) and G2(s)
the series connection G2(s)G1(s) is asymptotically stablethe parallel connection G1(s) + G2(s) is asymptotically stable
the feedback connection G1(s)1±G1(s)G2(s) is not necessarily stable
THE CURSE OF FEEDBACK!
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Introduction Control engineering jargon & tools
Stability of interconnected systems
Given two asymptotically stable LTI systems G1(s) and G2(s)
the series connection G2(s)G1(s) is asymptotically stablethe parallel connection G1(s) + G2(s) is asymptotically stable
the feedback connection G1(s)1±G1(s)G2(s) is not necessarily stable
THE CURSE OF FEEDBACK!
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Introduction Control engineering jargon & tools
Stability of interconnected systems
Given two asymptotically stable LTI systems G1(s) and G2(s)
the series connection G2(s)G1(s) is asymptotically stablethe parallel connection G1(s) + G2(s) is asymptotically stable
the feedback connection G1(s)1±G1(s)G2(s) is not necessarily stable
THE CURSE OF FEEDBACK!
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Introduction Plasma magnetic control problem
The magnetic control problems
The plasma (axisymmetric) magnetic control in tokamaks includes thefollowing three control problems
the vertical stabilization problemthe shape and position control problemthe plasma current control problem
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Introduction Plasma magnetic control problem
Vertical stabilization problem
ObjectivesVertically stabilize elongated plasmas in order to avoid disruptions
Counteract the effect of disturbances (ELMs, fast disturbancesmodelled as VDEs,. . .)It does not necessarily control vertical position but it simplystabilizes the plasmaThe VS is the essential magnetic control system!
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Introduction Plasma magnetic control problem
Vertical stabilization problem
ObjectivesVertically stabilize elongated plasmas in order to avoid disruptionsCounteract the effect of disturbances (ELMs, fast disturbancesmodelled as VDEs,. . .)
It does not necessarily control vertical position but it simplystabilizes the plasmaThe VS is the essential magnetic control system!
G. De Tommasi (Federico II) ISFRT16 30 April 2017 22 / 73
![Page 35: Plasma magnetic diagnostic and control at ITER & DEMO ...irfm.cea.fr/ISFRT16/Lectures/DeTommasi_Erice_Control.pdfIt has been proven that neglecting plasma mass may lead to erroneous](https://reader036.fdocuments.in/reader036/viewer/2022071409/6101a66dc3e49570a167bf93/html5/thumbnails/35.jpg)
Introduction Plasma magnetic control problem
Vertical stabilization problem
ObjectivesVertically stabilize elongated plasmas in order to avoid disruptionsCounteract the effect of disturbances (ELMs, fast disturbancesmodelled as VDEs,. . .)It does not necessarily control vertical position but it simplystabilizes the plasma
The VS is the essential magnetic control system!
G. De Tommasi (Federico II) ISFRT16 30 April 2017 22 / 73
![Page 36: Plasma magnetic diagnostic and control at ITER & DEMO ...irfm.cea.fr/ISFRT16/Lectures/DeTommasi_Erice_Control.pdfIt has been proven that neglecting plasma mass may lead to erroneous](https://reader036.fdocuments.in/reader036/viewer/2022071409/6101a66dc3e49570a167bf93/html5/thumbnails/36.jpg)
Introduction Plasma magnetic control problem
Vertical stabilization problem
ObjectivesVertically stabilize elongated plasmas in order to avoid disruptionsCounteract the effect of disturbances (ELMs, fast disturbancesmodelled as VDEs,. . .)It does not necessarily control vertical position but it simplystabilizes the plasmaThe VS is the essential magnetic control system!
G. De Tommasi (Federico II) ISFRT16 30 April 2017 22 / 73
![Page 37: Plasma magnetic diagnostic and control at ITER & DEMO ...irfm.cea.fr/ISFRT16/Lectures/DeTommasi_Erice_Control.pdfIt has been proven that neglecting plasma mass may lead to erroneous](https://reader036.fdocuments.in/reader036/viewer/2022071409/6101a66dc3e49570a167bf93/html5/thumbnails/37.jpg)
Introduction Plasma magnetic control problem
The plasma vertical instability
Simplified filamentary modelConsider the simplified electromechanical model with three conductiverings, two rings are kept fixed and in symmetric position with respect tothe r axis, while the third can freely move vertically.
If the currents in the two fixed ringsare equal, the vertical positionz = 0 is an equilibrium point for thesystem.
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Introduction Plasma magnetic control problem
Stable equilibrium - 1/2
If sgn(Ip) 6= sgn(I)
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Introduction Plasma magnetic control problem
Stable equilibrium - 2/2
If sgn(Ip) 6= sgn(I)
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Introduction Plasma magnetic control problem
Unstable equilibrium - 1/2
If sgn(Ip) = sgn(I)
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Introduction Plasma magnetic control problem
Unstable equilibrium - 2/2
If sgn(Ip) = sgn(I)
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Introduction Plasma magnetic control problem
Plasma vertical instability
The plasma vertical instability reveals itself in the linearizedmodel, by the presence of an unstable eigenvalue in the dynamicsystem matrixThe vertical instability growth time is slowed down by thepresence of the conducting structure surrounding the plasmaThis allows to use a feedback control system to stabilize theplasma equilibrium, using for example a pair of dedicated coilsThis feedback loop usually acts on a faster time-scale than theplasma shape control loop
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Introduction Plasma magnetic control problem
Shape and position control problem
The problem of controlling the plasma shape is probably the most understoodand mature of all the control problems in a tokamak
The actuators are the Poloidal Field coils, that produce the magnetic field actingon the plasma
The controlled variables are a finite number of geometrical descriptors chosen todescribe the plasma shape
Objectives
Precise control of plasma boundary
Counteract the effect of disturbances (βp and li variations)
Manage saturation of the actuators (currents in the PF coils)
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Introduction Plasma magnetic control problem
Shape and position control problem
The problem of controlling the plasma shape is probably the most understoodand mature of all the control problems in a tokamak
The actuators are the Poloidal Field coils, that produce the magnetic field actingon the plasma
The controlled variables are a finite number of geometrical descriptors chosen todescribe the plasma shape
Objectives
Precise control of plasma boundary
Counteract the effect of disturbances (βp and li variations)
Manage saturation of the actuators (currents in the PF coils)
G. De Tommasi (Federico II) ISFRT16 30 April 2017 29 / 73
![Page 45: Plasma magnetic diagnostic and control at ITER & DEMO ...irfm.cea.fr/ISFRT16/Lectures/DeTommasi_Erice_Control.pdfIt has been proven that neglecting plasma mass may lead to erroneous](https://reader036.fdocuments.in/reader036/viewer/2022071409/6101a66dc3e49570a167bf93/html5/thumbnails/45.jpg)
Introduction Plasma magnetic control problem
Shape and position control problem
The problem of controlling the plasma shape is probably the most understoodand mature of all the control problems in a tokamak
The actuators are the Poloidal Field coils, that produce the magnetic field actingon the plasma
The controlled variables are a finite number of geometrical descriptors chosen todescribe the plasma shape
Objectives
Precise control of plasma boundary
Counteract the effect of disturbances (βp and li variations)
Manage saturation of the actuators (currents in the PF coils)
G. De Tommasi (Federico II) ISFRT16 30 April 2017 29 / 73
![Page 46: Plasma magnetic diagnostic and control at ITER & DEMO ...irfm.cea.fr/ISFRT16/Lectures/DeTommasi_Erice_Control.pdfIt has been proven that neglecting plasma mass may lead to erroneous](https://reader036.fdocuments.in/reader036/viewer/2022071409/6101a66dc3e49570a167bf93/html5/thumbnails/46.jpg)
Introduction Plasma magnetic control problem
Plasma current control problem
Plasma current can be controlled by using the current in the PFcoils
Since there is a sharing of the actuators, the problem of trackingthe plasma current can be considered simultaneously with theshape control problemShape control and plasma current control are compatible, since itis possible to show that generating flux that is spatially uniformacross the plasma (but with a desired temporal behavior) can beused to drive the current without affecting the plasma shape.
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Introduction Plasma magnetic control problem
Plasma current control problem
Plasma current can be controlled by using the current in the PFcoilsSince there is a sharing of the actuators, the problem of trackingthe plasma current can be considered simultaneously with theshape control problem
Shape control and plasma current control are compatible, since itis possible to show that generating flux that is spatially uniformacross the plasma (but with a desired temporal behavior) can beused to drive the current without affecting the plasma shape.
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Introduction Plasma magnetic control problem
Plasma current control problem
Plasma current can be controlled by using the current in the PFcoilsSince there is a sharing of the actuators, the problem of trackingthe plasma current can be considered simultaneously with theshape control problemShape control and plasma current control are compatible, since itis possible to show that generating flux that is spatially uniformacross the plasma (but with a desired temporal behavior) can beused to drive the current without affecting the plasma shape.
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Introduction Plasma magnetic control problem
I need a break. What about you?
QUESTIONS?
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Magnetic control architecture
Plasma magnetic system
MotivationPlasma magnetic control is one of the the crucial issue to beaddressed
is needed from day 1is needed to robustly control elongated plasmas in high performancescenarios
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Magnetic control architecture
Plasma magnetic system
MotivationPlasma magnetic control is one of the the crucial issue to beaddressed
is needed from day 1
is needed to robustly control elongated plasmas in high performancescenarios
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Magnetic control architecture
Plasma magnetic system
MotivationPlasma magnetic control is one of the the crucial issue to beaddressed
is needed from day 1is needed to robustly control elongated plasmas in high performancescenarios
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Magnetic control architecture
A tokamak discharge
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Magnetic control architecture
A proposal for magnetic control in ITER & DEMO (and more)
A magnetic control system able to operate the plasma for an entire duration ofthe discharge, from the initiation to plasma ramp-down
Machine-agnostic architecture (aka machine independent solution)
Model-based control algorithms→ the design procedures relies on (validated) control-orientedmodels for the response of the plasma and of the surroundingconductive structures
The proposal is based on the JET experienceThe architecture has been proposed for ITER & DEMO (& JT-60SA) and partiallydeployed at EAST
R. Ambrosino et al.
Design and nonlinear validation of the ITER magnetic control systemProc. 2015 IEEE Multi-Conf. Sys. Contr., 2015
N. Cruz et al.,
Control-oriented tools for the design and validation of the JT-60SA magnetic control systemContr. Eng. Prac., 2017
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Magnetic control architecture
A proposal for magnetic control in ITER & DEMO (and more)
A magnetic control system able to operate the plasma for an entire duration ofthe discharge, from the initiation to plasma ramp-downMachine-agnostic architecture (aka machine independent solution)
Model-based control algorithms→ the design procedures relies on (validated) control-orientedmodels for the response of the plasma and of the surroundingconductive structures
The proposal is based on the JET experienceThe architecture has been proposed for ITER & DEMO (& JT-60SA) and partiallydeployed at EAST
R. Ambrosino et al.
Design and nonlinear validation of the ITER magnetic control systemProc. 2015 IEEE Multi-Conf. Sys. Contr., 2015
N. Cruz et al.,
Control-oriented tools for the design and validation of the JT-60SA magnetic control systemContr. Eng. Prac., 2017
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Magnetic control architecture
A proposal for magnetic control in ITER & DEMO (and more)
A magnetic control system able to operate the plasma for an entire duration ofthe discharge, from the initiation to plasma ramp-downMachine-agnostic architecture (aka machine independent solution)
Model-based control algorithms→ the design procedures relies on (validated) control-orientedmodels for the response of the plasma and of the surroundingconductive structures
The proposal is based on the JET experienceThe architecture has been proposed for ITER & DEMO (& JT-60SA) and partiallydeployed at EAST
R. Ambrosino et al.
Design and nonlinear validation of the ITER magnetic control systemProc. 2015 IEEE Multi-Conf. Sys. Contr., 2015
N. Cruz et al.,
Control-oriented tools for the design and validation of the JT-60SA magnetic control systemContr. Eng. Prac., 2017
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Magnetic control architecture
A proposal for magnetic control in ITER & DEMO (and more)
A magnetic control system able to operate the plasma for an entire duration ofthe discharge, from the initiation to plasma ramp-downMachine-agnostic architecture (aka machine independent solution)
Model-based control algorithms→ the design procedures relies on (validated) control-orientedmodels for the response of the plasma and of the surroundingconductive structures
The proposal is based on the JET experience
The architecture has been proposed for ITER & DEMO (& JT-60SA) and partiallydeployed at EAST
R. Ambrosino et al.
Design and nonlinear validation of the ITER magnetic control systemProc. 2015 IEEE Multi-Conf. Sys. Contr., 2015
N. Cruz et al.,
Control-oriented tools for the design and validation of the JT-60SA magnetic control systemContr. Eng. Prac., 2017
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Magnetic control architecture
A proposal for magnetic control in ITER & DEMO (and more)
A magnetic control system able to operate the plasma for an entire duration ofthe discharge, from the initiation to plasma ramp-downMachine-agnostic architecture (aka machine independent solution)
Model-based control algorithms→ the design procedures relies on (validated) control-orientedmodels for the response of the plasma and of the surroundingconductive structures
The proposal is based on the JET experienceThe architecture has been proposed for ITER & DEMO (& JT-60SA) and partiallydeployed at EAST
R. Ambrosino et al.
Design and nonlinear validation of the ITER magnetic control systemProc. 2015 IEEE Multi-Conf. Sys. Contr., 2015
N. Cruz et al.,
Control-oriented tools for the design and validation of the JT-60SA magnetic control systemContr. Eng. Prac., 2017
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Magnetic control architecture
A proposal for the ITER magnetic control system
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Magnetic control architecture
The proposed architecture
Four independent controllersCurrent decoupling controllerVertical stabilization controllerPlasma current controllerPlasma shape controller
The parameters of each controller can change on the base ofevents generated by an external supervisor
Clock events→ time-variant parameters
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Magnetic control architecture ITER magnetic diagnostic
ITER magnetic diagnostic system
In the current design of the ITER tokamak, more than one thousand of magneticprobes are spread around the reactor
These probes are used to reconstruct a large variety of physical quantities,among which there are the ones required by the plasma magnetic control systemUnder the ideal assumptions of axisymmetry and of absence of noise, themeasurements from only one sector should be sufficient to reconstruct theneeded plasma parameters with the required accuracy
Redundancy allows toreduce the noisesuppress the toroidal modesincrease the reliability/availability of the magnetic diagnostic
At ITERthe probes required for control are replicated on 6 different sectorsaveraging on 3 sectors is sufficient to reduce the noise to acceptable levelsThe current studies for DEMO suggest to averaging measurementson at least 6 different sectors
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Magnetic control architecture ITER magnetic diagnostic
ITER magnetic diagnostic system
In the current design of the ITER tokamak, more than one thousand of magneticprobes are spread around the reactorThese probes are used to reconstruct a large variety of physical quantities,among which there are the ones required by the plasma magnetic control system
Under the ideal assumptions of axisymmetry and of absence of noise, themeasurements from only one sector should be sufficient to reconstruct theneeded plasma parameters with the required accuracy
Redundancy allows toreduce the noisesuppress the toroidal modesincrease the reliability/availability of the magnetic diagnostic
At ITERthe probes required for control are replicated on 6 different sectorsaveraging on 3 sectors is sufficient to reduce the noise to acceptable levelsThe current studies for DEMO suggest to averaging measurementson at least 6 different sectors
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Magnetic control architecture ITER magnetic diagnostic
ITER magnetic diagnostic system
In the current design of the ITER tokamak, more than one thousand of magneticprobes are spread around the reactorThese probes are used to reconstruct a large variety of physical quantities,among which there are the ones required by the plasma magnetic control systemUnder the ideal assumptions of axisymmetry and of absence of noise, themeasurements from only one sector should be sufficient to reconstruct theneeded plasma parameters with the required accuracy
Redundancy allows toreduce the noise
suppress the toroidal modesincrease the reliability/availability of the magnetic diagnostic
At ITERthe probes required for control are replicated on 6 different sectorsaveraging on 3 sectors is sufficient to reduce the noise to acceptable levelsThe current studies for DEMO suggest to averaging measurementson at least 6 different sectors
G. De Tommasi (Federico II) ISFRT16 30 April 2017 37 / 73
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Magnetic control architecture ITER magnetic diagnostic
ITER magnetic diagnostic system
In the current design of the ITER tokamak, more than one thousand of magneticprobes are spread around the reactorThese probes are used to reconstruct a large variety of physical quantities,among which there are the ones required by the plasma magnetic control systemUnder the ideal assumptions of axisymmetry and of absence of noise, themeasurements from only one sector should be sufficient to reconstruct theneeded plasma parameters with the required accuracy
Redundancy allows toreduce the noisesuppress the toroidal modes
increase the reliability/availability of the magnetic diagnosticAt ITER
the probes required for control are replicated on 6 different sectorsaveraging on 3 sectors is sufficient to reduce the noise to acceptable levelsThe current studies for DEMO suggest to averaging measurementson at least 6 different sectors
G. De Tommasi (Federico II) ISFRT16 30 April 2017 37 / 73
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Magnetic control architecture ITER magnetic diagnostic
ITER magnetic diagnostic system
In the current design of the ITER tokamak, more than one thousand of magneticprobes are spread around the reactorThese probes are used to reconstruct a large variety of physical quantities,among which there are the ones required by the plasma magnetic control systemUnder the ideal assumptions of axisymmetry and of absence of noise, themeasurements from only one sector should be sufficient to reconstruct theneeded plasma parameters with the required accuracy
Redundancy allows toreduce the noisesuppress the toroidal modesincrease the reliability/availability of the magnetic diagnostic
At ITERthe probes required for control are replicated on 6 different sectorsaveraging on 3 sectors is sufficient to reduce the noise to acceptable levelsThe current studies for DEMO suggest to averaging measurementson at least 6 different sectors
G. De Tommasi (Federico II) ISFRT16 30 April 2017 37 / 73
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Magnetic control architecture ITER magnetic diagnostic
ITER magnetic diagnostic system
In the current design of the ITER tokamak, more than one thousand of magneticprobes are spread around the reactorThese probes are used to reconstruct a large variety of physical quantities,among which there are the ones required by the plasma magnetic control systemUnder the ideal assumptions of axisymmetry and of absence of noise, themeasurements from only one sector should be sufficient to reconstruct theneeded plasma parameters with the required accuracy
Redundancy allows toreduce the noisesuppress the toroidal modesincrease the reliability/availability of the magnetic diagnostic
At ITERthe probes required for control are replicated on 6 different sectors
averaging on 3 sectors is sufficient to reduce the noise to acceptable levelsThe current studies for DEMO suggest to averaging measurementson at least 6 different sectors
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Magnetic control architecture ITER magnetic diagnostic
ITER magnetic diagnostic system
In the current design of the ITER tokamak, more than one thousand of magneticprobes are spread around the reactorThese probes are used to reconstruct a large variety of physical quantities,among which there are the ones required by the plasma magnetic control systemUnder the ideal assumptions of axisymmetry and of absence of noise, themeasurements from only one sector should be sufficient to reconstruct theneeded plasma parameters with the required accuracy
Redundancy allows toreduce the noisesuppress the toroidal modesincrease the reliability/availability of the magnetic diagnostic
At ITERthe probes required for control are replicated on 6 different sectorsaveraging on 3 sectors is sufficient to reduce the noise to acceptable levels
The current studies for DEMO suggest to averaging measurementson at least 6 different sectors
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Magnetic control architecture ITER magnetic diagnostic
ITER magnetic diagnostic system
In the current design of the ITER tokamak, more than one thousand of magneticprobes are spread around the reactorThese probes are used to reconstruct a large variety of physical quantities,among which there are the ones required by the plasma magnetic control systemUnder the ideal assumptions of axisymmetry and of absence of noise, themeasurements from only one sector should be sufficient to reconstruct theneeded plasma parameters with the required accuracy
Redundancy allows toreduce the noisesuppress the toroidal modesincrease the reliability/availability of the magnetic diagnostic
At ITERthe probes required for control are replicated on 6 different sectorsaveraging on 3 sectors is sufficient to reduce the noise to acceptable levelsThe current studies for DEMO suggest to averaging measurementson at least 6 different sectors
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Magnetic control architecture ITER magnetic diagnostic
Example - ITER in-vessel AA probes
Figure: Positions of the AA probes in the ITER tokamak, according to the current design. The AA probes measure themagnetic field in six different sectors. On the right side the arrangement of the probes on one sector is shown.
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Magnetic control architecture ITER magnetic diagnostic
In-vessel & out-vessel probes
Both in-vessel and out-vessel probes (for magnetic control) will beinstalled at ITER
In-vessel probes are used as default to reconstruct the plasmaparameters that need to be controlled in real-timeThe use of out-vessel probes is currently envisaged only asbackup, as a complete or partial replacement of the in-vesselcoils
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Magnetic control architecture ITER magnetic diagnostic
In-vessel & out-vessel probes
Both in-vessel and out-vessel probes (for magnetic control) will beinstalled at ITERIn-vessel probes are used as default to reconstruct the plasmaparameters that need to be controlled in real-time
The use of out-vessel probes is currently envisaged only asbackup, as a complete or partial replacement of the in-vesselcoils
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Magnetic control architecture ITER magnetic diagnostic
In-vessel & out-vessel probes
Both in-vessel and out-vessel probes (for magnetic control) will beinstalled at ITERIn-vessel probes are used as default to reconstruct the plasmaparameters that need to be controlled in real-timeThe use of out-vessel probes is currently envisaged only asbackup, as a complete or partial replacement of the in-vesselcoils
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Magnetic control architecture Vertical stabilization
Architecture
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Magnetic control architecture Vertical stabilization
The vertical stabilization controller
The vertical stabilization controller has as input the centroid vertical velocity, and the current flowing in the VS3 circuit (anin-vessel coil set)
It generates as output the voltage references for the VS3 and VS1 power supplies (which are the PF outboard coils)
VVS3 = L−1 [Fvs(s)] ∗ (K1 z + K2IVS3)
VVS1 = K3IVS3
The vertical stabilization is achieved by the voltage applied to the VS3 circuit
The voltage applied to the VS1 circuit is used to reduce the current and the RMS ohmic power in the inner vessel coils
K1 should be scaled according to the value of Ip
G. Ambrosino et al.Plasma vertical stabilization in the ITER tokamak via constrained static output feedbackIEEE Trans. Contr. System Tech., 2011
G. De Tommasi et al.On plasma vertical stabilization at EAST tokamaksubmitted to 2017 IEEE Conf. Contr. Tech. Appl., 2017
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Magnetic control architecture Vertical stabilization
The vertical stabilization controller
The vertical stabilization controller has as input the centroid vertical velocity, and the current flowing in the VS3 circuit (anin-vessel coil set)
It generates as output the voltage references for the VS3 and VS1 power supplies (which are the PF outboard coils)
VVS3 = L−1 [Fvs(s)] ∗ (K1 z + K2IVS3)
VVS1 = K3IVS3
The vertical stabilization is achieved by the voltage applied to the VS3 circuit
The voltage applied to the VS1 circuit is used to reduce the current and the RMS ohmic power in the inner vessel coils
K1 should be scaled according to the value of Ip
G. Ambrosino et al.Plasma vertical stabilization in the ITER tokamak via constrained static output feedbackIEEE Trans. Contr. System Tech., 2011
G. De Tommasi et al.On plasma vertical stabilization at EAST tokamaksubmitted to 2017 IEEE Conf. Contr. Tech. Appl., 2017
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Magnetic control architecture Vertical stabilization
The vertical stabilization controller
The vertical stabilization controller has as input the centroid vertical velocity, and the current flowing in the VS3 circuit (anin-vessel coil set)
It generates as output the voltage references for the VS3 and VS1 power supplies (which are the PF outboard coils)
VVS3 = L−1 [Fvs(s)] ∗ (K1 z + K2IVS3)
VVS1 = K3IVS3
The vertical stabilization is achieved by the voltage applied to the VS3 circuit
The voltage applied to the VS1 circuit is used to reduce the current and the RMS ohmic power in the inner vessel coils
K1 should be scaled according to the value of Ip
G. Ambrosino et al.Plasma vertical stabilization in the ITER tokamak via constrained static output feedbackIEEE Trans. Contr. System Tech., 2011
G. De Tommasi et al.On plasma vertical stabilization at EAST tokamaksubmitted to 2017 IEEE Conf. Contr. Tech. Appl., 2017
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Magnetic control architecture Vertical stabilization
The vertical stabilization controller
The vertical stabilization controller has as input the centroid vertical velocity, and the current flowing in the VS3 circuit (anin-vessel coil set)
It generates as output the voltage references for the VS3 and VS1 power supplies (which are the PF outboard coils)
VVS3 = L−1 [Fvs(s)] ∗ (K1 z + K2IVS3)
VVS1 = K3IVS3
The vertical stabilization is achieved by the voltage applied to the VS3 circuit
The voltage applied to the VS1 circuit is used to reduce the current and the RMS ohmic power in the inner vessel coils
K1 should be scaled according to the value of Ip
G. Ambrosino et al.Plasma vertical stabilization in the ITER tokamak via constrained static output feedbackIEEE Trans. Contr. System Tech., 2011
G. De Tommasi et al.On plasma vertical stabilization at EAST tokamaksubmitted to 2017 IEEE Conf. Contr. Tech. Appl., 2017
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Magnetic control architecture Current decoupling controller
Architecture
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Magnetic control architecture Current decoupling controller
Current decoupling controller
The current decoupling controller receives as input the CS & PF coil currentsand their references, and generate in output the voltage references for the powersupplies
The CS & PF coil current references are generated as a sum of three termscoming from
the scenario supervisor, which provides the feedforwardsneeded to track the desired scenariothe plasma current controller, which generates the currentdeviations (with respect to the nominal ones) needed tocompensate errors in the tracking of the plasma currentthe plasma shape controller, which generates the currentdeviations (with respect to the nominal ones) needed tocompensate errors in the tracking of the plasma shape
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Magnetic control architecture Current decoupling controller
Current decoupling controller - Control law 1/2
1 Let LPF ∈ RnPF × RnPF be a modified version of the inductance matrix obtainedfrom a plasma-less model by neglecting the effect of the passive structures. Ineach row of the LPF matrix all the mutual inductance terms which are less than agiven percentage of the circuit self-inductance have been neglected (main aim:to reduce the control effort)
2 The time constants τPFi for the response of the i-th circuit are chosen and usedto construct a matrix Λ ∈ RnPF × RnPF , defined as:
Λ =
1/τPF1 0 ... 0
0 1/τPF2 ... 0... ... ... ...0 0 ... 1/τPFn
.
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Magnetic control architecture Current decoupling controller
Current decoupling controller - Control law 1/2
1 Let LPF ∈ RnPF × RnPF be a modified version of the inductance matrix obtainedfrom a plasma-less model by neglecting the effect of the passive structures. Ineach row of the LPF matrix all the mutual inductance terms which are less than agiven percentage of the circuit self-inductance have been neglected (main aim:to reduce the control effort)
2 The time constants τPFi for the response of the i-th circuit are chosen and usedto construct a matrix Λ ∈ RnPF × RnPF , defined as:
Λ =
1/τPF1 0 ... 0
0 1/τPF2 ... 0... ... ... ...0 0 ... 1/τPFn
.
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Magnetic control architecture Current decoupling controller
Current decoupling controller - Control law 2/2
3 The voltages to be applied to the PF circuits are then calculated as:
UPF (t) = KPF ·(IPFref (t)− IPF (t)
)+ RPF IPF (t) ,
where
KPF = LPF · Λ,RPF is the estimated resistance matrix for the PF circuits - to takeinto account the ohmic drop
F. Maviglia et al.
Improving the performance of the JET Shape ControllerFus. Eng. Des., vol. 96–96, pp. 668–671, 2015.
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Magnetic control architecture Current decoupling controller
Current decoupling controller - Closed-loop transfer functions
Figure: Bode diagrams of the diagonaltransfer functions.
Figure: Bode diagrams of the off-diagonaltransfer functions.
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Magnetic control architecture Ip controller
Architecture
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Magnetic control architecture Ip controller
The plasma current controller
The plasma current controller has as input the plasma current andits time-varying reference, and has as output a set of coil currentdeviations (with respect to the nominal values)The output current deviations are proportional to a set ofcurrent Kpcurr providing (in the absence of eddy currents) atransformer field inside the vacuum vessel, so as to reducethe coupling with the plasma shape controller
δIPF (s) = Kpcurr FIp (s)Ipe (s)
For ITER it is important, for the plasma current, to track thereference signal during the ramp-up and ramp-down phases, thedynamic part of the controller FIp (s) has been designed with adouble integral action
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Magnetic control architecture Ip controller
The plasma current controller
The plasma current controller has as input the plasma current andits time-varying reference, and has as output a set of coil currentdeviations (with respect to the nominal values)The output current deviations are proportional to a set ofcurrent Kpcurr providing (in the absence of eddy currents) atransformer field inside the vacuum vessel, so as to reducethe coupling with the plasma shape controller
δIPF (s) = Kpcurr FIp (s)Ipe (s)
For ITER it is important, for the plasma current, to track thereference signal during the ramp-up and ramp-down phases, thedynamic part of the controller FIp (s) has been designed with adouble integral action
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Magnetic control architecture Shape controller
The plasma shape controller
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Magnetic control architecture Shape controller
Plasma shape descriptors
Figure: Control segments.
Let gi be the abscissa along i-th control segment (gi = 0 at the first wall)
Plasma shape control is achieved by imposing
giref− gi = 0
on a sufficiently large number of control segments (gap control)
Moreover, if the plasma shape intersect the i-th control segment at gi , thefollowing equation is satisfied
ψ(gi ) = ψB
where ψB is the flux at the plasma boundary
Shape control can be achieved also by controlling to 0 the (isoflux control)
ψ(giref)− ψB = 0
ψB = ψX for limited-to-diverted transitionψB = ψL for diverted-to-limited transition
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Magnetic control architecture Shape controller
Controlled plasma shape descriptors
During the limiter phase, the controlled shape parameters are theposition of the limiter point, and a set of flux differences (isofluxcontrol)During the limiter/diverted transition the controlled shapeparameters are the position of the X-point, and a set of fluxdifferences (isoflux control)During the diverted phase the controlled variables are theplasma-wall gap errors (gap control)
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Magnetic control architecture Shape controller
Plasma shape control algorithm
The plasma shape controller is based on the eXtreme Shape Controller (XSC)approachThe main advantage of the XSC approach is the possibility of tracking a numberof shape parameters larger than the number of active coils, minimizing aweighted steady state quadratic tracking error, when the references are constantsignals
M. Ariola and A. PirontiPlasma shape control for the JET tokamak - An optimal output regulation approachIEEE Contr. Sys. Magazine, 2005
G. Ambrosino et al.Design and implementation of an output regulation controller for the JET tokamakIEEE Trans. Contr. System Tech., 2008
R. Albanese et al.A MIMO architecture for integrated control of plasma shape and flux expansion for the EAST tokamakProc. 2016 IEEE Multi-Conf. Sys. Contr., 2016
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Magnetic control architecture Shape controller
The XSC-like philosophy - 1/3
The XSC-like plasma shape controller can be applied both adopting a isoflux ora gap approach
It relies on the current PF current controller which achieves a good decouplingof the PF circuits
Each PF circuits can be treated as an independent SISO channel
IPFi (s) =IPFref ,i (s)
1 + sτPF
If δY (s) are the variations of the nG shape descriptors (e.g. fluxes differences,position of the x-point, gaps) – with nG ≥ nPF – then dynamically
δY (s) = CIPFref (s)
1 + sτPF
and staticallyδY (s) = CIPFref (s)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 1/3
The XSC-like plasma shape controller can be applied both adopting a isoflux ora gap approach
It relies on the current PF current controller which achieves a good decouplingof the PF circuits
Each PF circuits can be treated as an independent SISO channel
IPFi (s) =IPFref ,i (s)
1 + sτPF
If δY (s) are the variations of the nG shape descriptors (e.g. fluxes differences,position of the x-point, gaps) – with nG ≥ nPF – then dynamically
δY (s) = CIPFref (s)
1 + sτPF
and staticallyδY (s) = CIPFref (s)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 1/3
The XSC-like plasma shape controller can be applied both adopting a isoflux ora gap approach
It relies on the current PF current controller which achieves a good decouplingof the PF circuits
Each PF circuits can be treated as an independent SISO channel
IPFi (s) =IPFref ,i (s)
1 + sτPF
If δY (s) are the variations of the nG shape descriptors (e.g. fluxes differences,position of the x-point, gaps) – with nG ≥ nPF – then dynamically
δY (s) = CIPFref (s)
1 + sτPF
and staticallyδY (s) = CIPFref (s)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 1/3
The XSC-like plasma shape controller can be applied both adopting a isoflux ora gap approach
It relies on the current PF current controller which achieves a good decouplingof the PF circuits
Each PF circuits can be treated as an independent SISO channel
IPFi (s) =IPFref ,i (s)
1 + sτPF
If δY (s) are the variations of the nG shape descriptors (e.g. fluxes differences,position of the x-point, gaps) – with nG ≥ nPF – then dynamically
δY (s) = CIPFref (s)
1 + sτPF
and staticallyδY (s) = CIPFref (s)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 1/3
The XSC-like plasma shape controller can be applied both adopting a isoflux ora gap approach
It relies on the current PF current controller which achieves a good decouplingof the PF circuits
Each PF circuits can be treated as an independent SISO channel
IPFi (s) =IPFref ,i (s)
1 + sτPF
If δY (s) are the variations of the nG shape descriptors (e.g. fluxes differences,position of the x-point, gaps) – with nG ≥ nPF – then dynamically
δY (s) = CIPFref (s)
1 + sτPF
and staticallyδY (s) = CIPFref (s)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 1/3
The XSC-like plasma shape controller can be applied both adopting a isoflux ora gap approach
It relies on the current PF current controller which achieves a good decouplingof the PF circuits
Each PF circuits can be treated as an independent SISO channel
IPFi (s) =IPFref ,i (s)
1 + sτPF
If δY (s) are the variations of the nG shape descriptors (e.g. fluxes differences,position of the x-point, gaps) – with nG ≥ nPF – then dynamically
δY (s) = CIPFref (s)
1 + sτPF
and staticallyδY (s) = CIPFref (s)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 2/3
The currents needed to track the desired shape (in a least-mean-square sense)
δIPFref= C†δY
It is possible to use weights both for the shape descriptors and for the currents in the PFcircuitsThe controller gains can be computed using the SVD of the weighted output matrix:
C = QCR = USV T
The XSC minimizes the cost function
J1 = limt→+∞
(δYref − δY (t))T QT Q(δYref − δY (t)) ,
using ndof < nPF degrees of freedom, while the remaining nPF − ndof degrees of freedomare exploited to minimize
J2 = limt→+∞
δIPFN (t)T RT RδIPFN (t) .
(it contributes to avoid PF current saturations)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 2/3
The currents needed to track the desired shape (in a least-mean-square sense)
δIPFref= C†δY
It is possible to use weights both for the shape descriptors and for the currents in the PFcircuits
The controller gains can be computed using the SVD of the weighted output matrix:
C = QCR = USV T
The XSC minimizes the cost function
J1 = limt→+∞
(δYref − δY (t))T QT Q(δYref − δY (t)) ,
using ndof < nPF degrees of freedom, while the remaining nPF − ndof degrees of freedomare exploited to minimize
J2 = limt→+∞
δIPFN (t)T RT RδIPFN (t) .
(it contributes to avoid PF current saturations)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 2/3
The currents needed to track the desired shape (in a least-mean-square sense)
δIPFref= C†δY
It is possible to use weights both for the shape descriptors and for the currents in the PFcircuitsThe controller gains can be computed using the SVD of the weighted output matrix:
C = QCR = USV T
The XSC minimizes the cost function
J1 = limt→+∞
(δYref − δY (t))T QT Q(δYref − δY (t)) ,
using ndof < nPF degrees of freedom, while the remaining nPF − ndof degrees of freedomare exploited to minimize
J2 = limt→+∞
δIPFN (t)T RT RδIPFN (t) .
(it contributes to avoid PF current saturations)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 2/3
The currents needed to track the desired shape (in a least-mean-square sense)
δIPFref= C†δY
It is possible to use weights both for the shape descriptors and for the currents in the PFcircuitsThe controller gains can be computed using the SVD of the weighted output matrix:
C = QCR = USV T
The XSC minimizes the cost function
J1 = limt→+∞
(δYref − δY (t))T QT Q(δYref − δY (t)) ,
using ndof < nPF degrees of freedom, while the remaining nPF − ndof degrees of freedomare exploited to minimize
J2 = limt→+∞
δIPFN (t)T RT RδIPFN (t) .
(it contributes to avoid PF current saturations)
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Magnetic control architecture Shape controller
The XSC-like philosophy - 3/3
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Magnetic control architecture Shape controller
Plasma shape controller - Switching algorithm
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Magnetic control architecture Nonlinear validation
Limited-to-diverted transition
Results of nonlinear simulation of the limited-to-divertedconfiguration during the plasma current ramp-upSimulation starts at t = 9.9 s when Ip = 3.6 MA, and ends att = 30.9 s when Ip = 7.3 MAThe transition from limited to diverted plasma occurs at aboutt = 11.39 s, and the switching between the isoflux and the gapscontroller occurs at t = 11.9 s
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Magnetic control architecture Nonlinear validation
Plasma boundary snapshots
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The DEMO case
Assumptions
The design of plasma magnetic control requires information aboutpower supplies limitations, control performance requirements,envisaged disturbances,. . .
Most of the required data are lacking for DEMO (at the presentstage)Several assumptions have been made on the basis of what hasbeen designed for ITER
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The DEMO case
Assumptions
The design of plasma magnetic control requires information aboutpower supplies limitations, control performance requirements,envisaged disturbances,. . .Most of the required data are lacking for DEMO (at the presentstage)
Several assumptions have been made on the basis of what hasbeen designed for ITER
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The DEMO case
Assumptions
The design of plasma magnetic control requires information aboutpower supplies limitations, control performance requirements,envisaged disturbances,. . .Most of the required data are lacking for DEMO (at the presentstage)Several assumptions have been made on the basis of what hasbeen designed for ITER
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The DEMO case Vertical stabilization at DEMO
The vertical stabilization circuit at DEMO
At DEMO it is not possible to have in-vessel control coils
A similar solution adopted for the VS1 at ITERThe vertical velocity is controlled by the imbalance circuit that makes use of thePF2− 5 coils
Iimb = IPF2 + IPF3 − IPF4 − IPF5
The nominal (scenario) imbalance current should be as close as possible to zeroto minimize the control power
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The DEMO case Vertical stabilization at DEMO
The vertical stabilization circuit at DEMO
At DEMO it is not possible to have in-vessel control coilsA similar solution adopted for the VS1 at ITER
The vertical velocity is controlled by the imbalance circuit that makes use of thePF2− 5 coils
Iimb = IPF2 + IPF3 − IPF4 − IPF5
The nominal (scenario) imbalance current should be as close as possible to zeroto minimize the control power
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The DEMO case Vertical stabilization at DEMO
The vertical stabilization circuit at DEMO
At DEMO it is not possible to have in-vessel control coilsA similar solution adopted for the VS1 at ITERThe vertical velocity is controlled by the imbalance circuit that makes use of thePF2− 5 coils
Iimb = IPF2 + IPF3 − IPF4 − IPF5
The nominal (scenario) imbalance current should be as close as possible to zeroto minimize the control power
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The DEMO case Vertical stabilization at DEMO
The vertical stabilization circuit at DEMO
At DEMO it is not possible to have in-vessel control coilsA similar solution adopted for the VS1 at ITERThe vertical velocity is controlled by the imbalance circuit that makes use of thePF2− 5 coils
Iimb = IPF2 + IPF3 − IPF4 − IPF5
The nominal (scenario) imbalance current should be as close as possible to zeroto minimize the control power
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The DEMO case Vertical stabilization at DEMO
Additional assumption for the VS
For the power supply and the diagnostic dynamic behaviour, the ITERassumptions have been taken
The power supply of the imbalance circuit has been modeled as a firstorder filter and a delay
WPS =e−0.0025s
0.0075s + 1The diagnostics on the vertical position zc have been modeled as a firstorder filter
Wdiag =1
0.007s + 1Two different SISO controllers (PID) have been designed to assess the bestachievable performance of the VS system
a fast one, to be used only if in-vessel probes are available (it does notstabilize the plasma if out-vessel coils are used to reconstruct thevertical position)a slow one, can be be used also if out-vessel probes are used toreconstruct the plasma vertical position
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The DEMO case Vertical stabilization at DEMO
Additional assumption for the VS
For the power supply and the diagnostic dynamic behaviour, the ITERassumptions have been taken
The power supply of the imbalance circuit has been modeled as a firstorder filter and a delay
WPS =e−0.0025s
0.0075s + 1The diagnostics on the vertical position zc have been modeled as a firstorder filter
Wdiag =1
0.007s + 1
Two different SISO controllers (PID) have been designed to assess the bestachievable performance of the VS system
a fast one, to be used only if in-vessel probes are available (it does notstabilize the plasma if out-vessel coils are used to reconstruct thevertical position)a slow one, can be be used also if out-vessel probes are used toreconstruct the plasma vertical position
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The DEMO case Vertical stabilization at DEMO
Additional assumption for the VS
For the power supply and the diagnostic dynamic behaviour, the ITERassumptions have been taken
The power supply of the imbalance circuit has been modeled as a firstorder filter and a delay
WPS =e−0.0025s
0.0075s + 1The diagnostics on the vertical position zc have been modeled as a firstorder filter
Wdiag =1
0.007s + 1Two different SISO controllers (PID) have been designed to assess the bestachievable performance of the VS system
a fast one, to be used only if in-vessel probes are available (it does notstabilize the plasma if out-vessel coils are used to reconstruct thevertical position)
a slow one, can be be used also if out-vessel probes are used toreconstruct the plasma vertical position
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The DEMO case Vertical stabilization at DEMO
Additional assumption for the VS
For the power supply and the diagnostic dynamic behaviour, the ITERassumptions have been taken
The power supply of the imbalance circuit has been modeled as a firstorder filter and a delay
WPS =e−0.0025s
0.0075s + 1The diagnostics on the vertical position zc have been modeled as a firstorder filter
Wdiag =1
0.007s + 1Two different SISO controllers (PID) have been designed to assess the bestachievable performance of the VS system
a fast one, to be used only if in-vessel probes are available (it does notstabilize the plasma if out-vessel coils are used to reconstruct thevertical position)a slow one, can be be used also if out-vessel probes are used toreconstruct the plasma vertical position
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The DEMO case Vertical stabilization at DEMO
Performance assessment - 1/3
The performance of the DEMO VS have been evaluated in thepresence of a VDE of 5 cmThe vertical position reconstructed by using 60 measurementscoming from in-vessel probes
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The DEMO case Vertical stabilization at DEMO
Performance assessment - 1/3
The performance of the DEMO VS have been evaluated in thepresence of a VDE of 5 cmThe vertical position reconstructed by using 60 measurementscoming from in-vessel probes
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The DEMO case Vertical stabilization at DEMO
Performance assessment - 2/3
Figure: Effect of the blanket on the performance of the fast VS for DEMO.
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The DEMO case Vertical stabilization at DEMO
Performance assessment - 3/3
Figure: Effect of the blanket on the performance of the slow VS for DEMO.
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The DEMO case Vertical stabilization at DEMO
Probe irradiation in DEMO
Out-vessel probescannot be used tostabilize the plasma
In-vessel probes areessential for magneticcontrolIn-vessel probes areonly partially shielded bythe blanket
Figure: Irradiation map in DEMO in Gy/hr (T. Eade -CCFE).
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The DEMO case Vertical stabilization at DEMO
Probe irradiation in DEMO
Out-vessel probescannot be used tostabilize the plasmaIn-vessel probes areessential for magneticcontrol
In-vessel probes areonly partially shielded bythe blanket
Figure: Irradiation map in DEMO in Gy/hr (T. Eade -CCFE).
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The DEMO case Vertical stabilization at DEMO
Probe irradiation in DEMO
Out-vessel probescannot be used tostabilize the plasmaIn-vessel probes areessential for magneticcontrolIn-vessel probes areonly partially shielded bythe blanket
Figure: Irradiation map in DEMO in Gy/hr (T. Eade -CCFE).
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The DEMO case Vertical stabilization at DEMO
Possible location of the DEMO in-vessel probes
Figure: Tangential and normal pick-up coils used for the estimation of the basicplasma quantities (three different configurations: 118, 60, and 30 probes).
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Experiments at EAST
A MIMO controller for plasma shape and heat flux integratedcontrol at EAST
Figure: Option #1 - integratedcontrol of plasma shape and fluxexpansion. Figure: Option #2 - integrated
control of plasma shape anddistance between null points.
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Experiments at EAST
EAST architecture
The EAST architecture is compliant to the one proposed for ITER & DEMO
The control algorithms deployed within the EAST PCS do not satisfy therequirements needed to easily replace the shape controller
vertical stabilization is strongly coupled with plasma shapecontrolThe PF Coils current controller can be improved (better decoupling)
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Experiments at EAST
EAST architecture
The EAST architecture is compliant to the one proposed for ITER & DEMO
The control algorithms deployed within the EAST PCS do not satisfy therequirements needed to easily replace the shape controller
vertical stabilization is strongly coupled with plasma shapecontrolThe PF Coils current controller can be improved (better decoupling)
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Experiments at EAST
EAST architecture
The EAST architecture is compliant to the one proposed for ITER & DEMO
The control algorithms deployed within the EAST PCS do not satisfy therequirements needed to easily replace the shape controller
vertical stabilization is strongly coupled with plasma shapecontrol
The PF Coils current controller can be improved (better decoupling)
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Experiments at EAST
EAST architecture
The EAST architecture is compliant to the one proposed for ITER & DEMO
The control algorithms deployed within the EAST PCS do not satisfy therequirements needed to easily replace the shape controller
vertical stabilization is strongly coupled with plasma shapecontrolThe PF Coils current controller can be improved (better decoupling)
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Experiments at EAST ITER-like VS
ITER-like VS at EAST
UICref(s) =
1 + sτ1
1 + sτ2·(
Kv · Ipref ·s
1 + sτz· Zc(s) + KIC · IIC(s)
)
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Experiments at EAST ITER-like VS
Experimental results - 1/2
Figure: EAST pulse #70799. During this pulse the ITER-like VS was enabled from t = 2.1 s for 1.2 s. During this timewindow only Ip and rc were controlled, while zc was left uncontrolled. This first test confirmed that the ITER-like VS achieves bycontrolling zc and IIC , without the need to feed back the vertical position zc .
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Experiments at EAST ITER-like VS
Experimental results - 2/2
Figure: EAST pulses #70799 & #71423. Tuning of the controller parameters to reduce oscillations on zc .
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Experiments at EAST ITER-like VS
Current decoupling controller
Figure: Comparison of different current control algorithms for a 1kA request on the EAST circuit PFC1. The proposedcurrent decoupling controller improves the decoupling compared with the EAST SISO PIDs currently adopted (first tests plannedin June-July 2017.
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Conclusions
Conclusions
For a control engineer the most important part of a tokamak is the controlalgorithm (not even the control system)
For a plasma magnetic control expert the most important parts of atokamak are the plasma magnetic control algorithms (and sometimes themagnetic control system)
A control engineer is not a system engineer (complete different job)
Control system design is model-basedit requires rather simple (but highly reliable) mathematical models of theprocess/plant
Control system need deterministic diagnostic data (aka in real-time) with anaccuracy and time resolution that is usually different from the one needed forspecific post processing analysis
MORE QUESTIONS?
Thank you!
G. De Tommasi (Federico II) ISFRT16 30 April 2017 73 / 73
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Conclusions
Conclusions
For a control engineer the most important part of a tokamak is the controlalgorithm (not even the control system)
For a plasma magnetic control expert the most important parts of atokamak are the plasma magnetic control algorithms (and sometimes themagnetic control system)
A control engineer is not a system engineer (complete different job)
Control system design is model-basedit requires rather simple (but highly reliable) mathematical models of theprocess/plant
Control system need deterministic diagnostic data (aka in real-time) with anaccuracy and time resolution that is usually different from the one needed forspecific post processing analysis
MORE QUESTIONS?
Thank you!
G. De Tommasi (Federico II) ISFRT16 30 April 2017 73 / 73
![Page 135: Plasma magnetic diagnostic and control at ITER & DEMO ...irfm.cea.fr/ISFRT16/Lectures/DeTommasi_Erice_Control.pdfIt has been proven that neglecting plasma mass may lead to erroneous](https://reader036.fdocuments.in/reader036/viewer/2022071409/6101a66dc3e49570a167bf93/html5/thumbnails/135.jpg)
Conclusions
Conclusions
For a control engineer the most important part of a tokamak is the controlalgorithm (not even the control system)
For a plasma magnetic control expert the most important parts of atokamak are the plasma magnetic control algorithms (and sometimes themagnetic control system)
A control engineer is not a system engineer (complete different job)
Control system design is model-basedit requires rather simple (but highly reliable) mathematical models of theprocess/plant
Control system need deterministic diagnostic data (aka in real-time) with anaccuracy and time resolution that is usually different from the one needed forspecific post processing analysis
MORE QUESTIONS?
Thank you!
G. De Tommasi (Federico II) ISFRT16 30 April 2017 73 / 73
![Page 136: Plasma magnetic diagnostic and control at ITER & DEMO ...irfm.cea.fr/ISFRT16/Lectures/DeTommasi_Erice_Control.pdfIt has been proven that neglecting plasma mass may lead to erroneous](https://reader036.fdocuments.in/reader036/viewer/2022071409/6101a66dc3e49570a167bf93/html5/thumbnails/136.jpg)
Conclusions
Conclusions
For a control engineer the most important part of a tokamak is the controlalgorithm (not even the control system)
For a plasma magnetic control expert the most important parts of atokamak are the plasma magnetic control algorithms (and sometimes themagnetic control system)
A control engineer is not a system engineer (complete different job)
Control system design is model-basedit requires rather simple (but highly reliable) mathematical models of theprocess/plant
Control system need deterministic diagnostic data (aka in real-time) with anaccuracy and time resolution that is usually different from the one needed forspecific post processing analysis
MORE QUESTIONS?
Thank you!
G. De Tommasi (Federico II) ISFRT16 30 April 2017 73 / 73
![Page 137: Plasma magnetic diagnostic and control at ITER & DEMO ...irfm.cea.fr/ISFRT16/Lectures/DeTommasi_Erice_Control.pdfIt has been proven that neglecting plasma mass may lead to erroneous](https://reader036.fdocuments.in/reader036/viewer/2022071409/6101a66dc3e49570a167bf93/html5/thumbnails/137.jpg)
Conclusions
Conclusions
For a control engineer the most important part of a tokamak is the controlalgorithm (not even the control system)
For a plasma magnetic control expert the most important parts of atokamak are the plasma magnetic control algorithms (and sometimes themagnetic control system)
A control engineer is not a system engineer (complete different job)
Control system design is model-basedit requires rather simple (but highly reliable) mathematical models of theprocess/plant
Control system need deterministic diagnostic data (aka in real-time) with anaccuracy and time resolution that is usually different from the one needed forspecific post processing analysis
MORE QUESTIONS?
Thank you!
G. De Tommasi (Federico II) ISFRT16 30 April 2017 73 / 73
![Page 138: Plasma magnetic diagnostic and control at ITER & DEMO ...irfm.cea.fr/ISFRT16/Lectures/DeTommasi_Erice_Control.pdfIt has been proven that neglecting plasma mass may lead to erroneous](https://reader036.fdocuments.in/reader036/viewer/2022071409/6101a66dc3e49570a167bf93/html5/thumbnails/138.jpg)
Conclusions
Conclusions
For a control engineer the most important part of a tokamak is the controlalgorithm (not even the control system)
For a plasma magnetic control expert the most important parts of atokamak are the plasma magnetic control algorithms (and sometimes themagnetic control system)
A control engineer is not a system engineer (complete different job)
Control system design is model-basedit requires rather simple (but highly reliable) mathematical models of theprocess/plant
Control system need deterministic diagnostic data (aka in real-time) with anaccuracy and time resolution that is usually different from the one needed forspecific post processing analysis
MORE QUESTIONS?
Thank you!G. De Tommasi (Federico II) ISFRT16 30 April 2017 73 / 73