Lyapunov-based distributed control of the safety-factor profile in a tokamak plasma

Argomedo, Federico Bribiesca; Witrant, Emmanuel; Prieur, Christophe; Brémond, S.; Nouailletas, R.; Artaud, Jean-François

doi:10.1088/0029-5515/53/3/033005

Cited by 41 publications

(25 citation statements)

References 34 publications

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“…mhd lim (35) As the MHD stability constraint (33) depends directly on the to-be-optimized parameters θ, it is included in the formulation of the actuator constraints (30).…”

Section: Formulation Of Actuator Trajectory Optimization Problemmentioning

confidence: 99%

“…Advances in developing models/ profile control strategies following a data-driven approach are discussed in [18][19][20][21][22][23][24][25]. Advances in developing profile control strategies following FPD techniques are discussed in [26][27][28][29][30][31][32][33][34][35]. In this work, we follow an FPD approach to design feedback algorithms, as FPD models provide the freedom to handle the trade-off between the physics accuracy and the tractability for control design of the models.…”

Section: Physics-model-based Nonlinear Actuator Trajectory Optimizati...mentioning

confidence: 99%

“…method. The nonlinear, constrained, actuator trajectory optimization problem is now to determine the to-be-optimized parameters θ that minimize cost functional (18) subject to the plasma dynamics (22), the control actuator trajectory parameterization (25), the actuator constraints (30), and the plasma state and MHD stability constraints (35). This optimization problem is written mathematically as…”

Section: Optimization Problem Statement and Solutionmentioning

confidence: 99%

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Physics-model-based nonlinear actuator trajectory optimization and safety factor profile feedback control for advanced scenario development in DIII-D

et al. 2015

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DIII-D experimental results are reported to demonstrate the potential of physics-model-based safety factor profile control for robust and reproducible sustainment of advanced scenarios. In the absence of feedback control, variability in wall conditions and plasma impurities, as well as drifts due to external disturbances, can limit the reproducibility of discharges with simple preprogrammed scenario trajectories. The control architecture utilized is a feedforward + feedback scheme where the feedforward commands are computed off-line and the feedback commands are computed on-line. In this work, a first-principles-driven (FPD), physics-based model of the q profile and normalized beta (β N) dynamics is first embedded into a numerical optimization algorithm to design feedforward actuator trajectories that steer the plasma through the tokamak operating space to reach a desired stationary target state that is characterized by the achieved q profile and β N. Good agreement between experimental results and simulations demonstrates the accuracy of the models employed for physics-model-based control design. Second, a feedback algorithm for q profile control is designed following an FPD approach, and the ability of the controller to achieve and maintain a target q profile evolution is tested in DIII-D high confinement (H-mode) experiments. The controller is shown to be able to effectively control the q profile when β N is relatively close to the target, indicating the need for integrated q profile and β N control to further enhance the ability to achieve robust scenario execution. The ability of an integrated q profile + β N feedback controller to track a desired target is demonstrated through simulation.

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“…mhd lim (35) As the MHD stability constraint (33) depends directly on the to-be-optimized parameters θ, it is included in the formulation of the actuator constraints (30).…”

Section: Formulation Of Actuator Trajectory Optimization Problemmentioning

confidence: 99%

Section: Physics-model-based Nonlinear Actuator Trajectory Optimizati...mentioning

confidence: 99%

Section: Optimization Problem Statement and Solutionmentioning

confidence: 99%

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Physics-model-based nonlinear actuator trajectory optimization and safety factor profile feedback control for advanced scenario development in DIII-D

et al. 2015

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“…However, control of internal profiles is still in its infancy [2]. Tokamaks are high order, distributed parameter, nonlinear systems with a large number of instabilities [4], so there are many extremely challenging mathematical modeling and control problems, which must be solved before a fusion power system becomes a viable entity [5][6][7][8][9]. The main focus of this paper is to study the current profile tracking of tokamak plasma which can be modeled by a parabolic PDE.…”

Section: Introductionmentioning

confidence: 99%

Optimal Tracking for a Divergent-Type Parabolic PDE System in Current Profile Control

Jiang

Ren

et al. 2014

Abstract and Applied Analysis

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We consider the optimal tracking problem for a divergent-type parabolic PDE system, which can be used to model the spatial-temporal evolution of the magnetic diffusion process in a tokamak plasma. With the feedforward trajectories generated by numerical optimization, we derive a linear system to describe the error evolution. The weak variation approach is then extended to cylindrical coordinates to obtain a Riccati-type PDE for feedback kernel synthesis. Then, a finite difference method is used to give numerical solutions for the Riccati-type PDE. The obtained feedback kernel is finally used to simulate the closed-loop system. The simulation results demonstrate that the proposed tracking method can attenuate the tracking error effectively.

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“…The robust control design problem of linear partial differential systems operating under uncertainty conditions has been particularly widely studied and published see [12], [13], [14], [15], [16], [17], [32], [28], [29] and references therein. Thus it is of interest to develop methods that are capable of using nonlinear partial differential models and of providing the desired system performance.…”

Section: Introductionmentioning

confidence: 99%

Robust control design of semilinear parabolic partial differential systems: A fuzzy approach

Gaye

Pagès

2014

2014 IEEE Conference on Control Applications (CCA)

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This communication deals with the robust H∞ stabilization of the semilinear partial differential system using Lyapunov theory. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of controls. In general, it is difficult to control partial differential systems. In order to simplify the design procedure of control law, a fuzzy partial differential system based on fuzzy interpolation approach is proposed. Based on this distributed model, the distributed robust control design is proposed to attenuate disturbances via solving linear matrix inequalities (LMIs). Finally, numerical results are presented and discussed to illustrate the effectiveness of the proposed approach.

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Lyapunov-based distributed control of the safety-factor profile in a tokamak plasma

Cited by 41 publications

References 34 publications

Physics-model-based nonlinear actuator trajectory optimization and safety factor profile feedback control for advanced scenario development in DIII-D

Physics-model-based nonlinear actuator trajectory optimization and safety factor profile feedback control for advanced scenario development in DIII-D

Optimal Tracking for a Divergent-Type Parabolic PDE System in Current Profile Control

Robust control design of semilinear parabolic partial differential systems: A fuzzy approach

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