Nonlinear PDE-Based control of the electron temperature in H-mode tokamak plasmas

Mameche, H.; Witrant, Emmanuel; Prieur, Christophe

doi:10.1109/cdc40024.2019.9029527

Cited by 2 publications

(3 citation statements)

References 15 publications

(22 reference statements)

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“…Time-delay partial-differential-equation (PDE) systems have received increasingly more attention from researchers over the past several years since they are ubiquitous in many applications, for example, influenza prediction, 1 the model of population structure with spatial non-locality, 2 the impacts of maturation time delay and some other factors on single species dynamics, 3 oil industry, 4 Tomakak device, [5][6][7] multi-agent systems with input delay, 8 memristive neural networks, 9 a pollutant decontamination process, 10 traffic flow model. 11 Recently, systems with delays have merited deeper study.…”

Section: Introductionmentioning

confidence: 99%

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Guan

2022

Intl J Robust & Nonlinear

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In this article, a distributed control design is developed via partial differential equation (PDE) backstepping for a class of reaction-diffusion PDEs on n-ball under revolution symmetry conditions in the presence of radial spatially varying actuator delay. The actuator delay is modeled by a two-dimensional (2D) first-order hyperbolic PDE with spatially varying boundary, resulting in a cascaded transport-diffusion PDE system. Two-step backstepping transformation is introduced for the control design. First, a new Volterra transformation for the n-ball under revolution symmetry is proposed that allows the kernel function to be solvable. Different from the kernel in the 1D domain, which is expressed by the classical Fourier series, the kernel of the n-ball under revolution symmetry conditions is based on the Fourier-Bessel series. The resulting Volterra transformation is an implicit one that contains the state of the target system on both sides of the definition. Based on the implicit transformation, we employ the successive approximations approach to derive the second-step transformation, namely, an explicit transformation, and arrive at a stable target system. The inverse transformation is also derived, to prove L 2 exponential stability of the closed-loop system.The stability analysis requires more technical skills that are not needed in solving the spatially varying delay compensation problem when the domain is 1D.Numerical simulation examples of 3D and 4D revolution-symmetrical systems illustrate the effectiveness of the controller.

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Section: Introductionmentioning

confidence: 99%

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Guan

2022

Intl J Robust & Nonlinear

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“…Normally these feedback control algorithms are assessed numerically and/or experimentally, at least, in a specific plasma scenario of interest on one tokamak device. The proposed control techniques comprise simple proportional-integral-derivative (PID) control [11,12], linearquadratic-integral (LQI) control [13,14], H ∞ robust control [15,16], model predictive control [17][18][19], passivity-based control [20], Lyapunov-based control [21][22][23] and adaptive control [24]. More precisely, in [11], a simple PID controller is designed to control the central safety factor using the lower hybrid waves on the Joint Eurepean Torus (JET) tokamak.…”

Section: Introductionmentioning

confidence: 99%

“…In [22], a Lyapunov-based infinite dimensional controller for the safety factor profile combined with simple internal model control with proportional-integral structure (SIMC PI) for β is validated both numerically and experimentally in a TCV L-mode plasma. An infinite dimensional controller was also obtained for the nonlinear control of temperature profiles in H-mode scenarios in [23].…”

Section: Introductionmentioning

confidence: 99%

Robust real-time feedback algorithms for plasma kinetic control in advanced tokamak scenarios

Wang¹,

Moreau²,

Witrant³

et al. 2021

Plasma Phys. Control. Fusion

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Robust real-time control algorithms for tracking plasma kinetic parameters in advanced tokamak scenarios are developed based on linear state-space (LSS) dynamic models. The real-time control algorithms under study comprise the H ∞ robust control, the linear quadratic integral control and the internal model control. The plasma models used in this work are restricted to LSS models identified from dedicated simulation/experimental data, though the proposed control algorithms can conveniently be extrapolated to broadly incorporate linear models obtained from first-principles plasma theory. The control objective is to track plasma kinetic parameters of interest to desired operating points in advanced tokamak scenarios by actuating additional heating & current drive systems in real-time. Plasma kinetic parameters involve the poloidal pressure parameter β p , the internal inductance li, the average toroidal rotation angular speed Ω ϕ and the electron temperature on axis T e,0 while the actuators are the ion cyclotron resonance heating and lower hybrid current drive systems. In order to achieve enhanced control performance, two control layers are designed. The outer layer, i.e. an internal model-based proportional-integral actuator controller, operating on a fast timescale (≪ the energy confinement time τ E ) aiming at tracking the commands requested by the inner kinetic controllers, while the inner layer, i.e. a kinetic controller chosen from various alternatives, running on a slow timescale (∼τ E ) is dedicated to tailoring plasma kinetic parameters. Simulation results for the experimental advanced superconducting tokamak (EAST) tokamak are provided and compared to show the capabilities of each control approach. Dedicated kinetic control experiments conducted in an H-mode scenario on EAST are reported as well. The advantages and limits of these control algorithms are discussed and summarised.

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Nonlinear PDE-Based control of the electron temperature in H-mode tokamak plasmas

Cited by 2 publications

References 15 publications

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Robust real-time feedback algorithms for plasma kinetic control in advanced tokamak scenarios

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