Nonlinear Burn Control in Tokamak Fusion Reactors via Output Feedback

Boyer, Mark D.; Schuster, Eugenio

doi:10.3182/20140824-6-za-1003.01714

Cited by 4 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, the burn control schemes presented in this work may be assessed in 1D simulations of ITER before experimental testing (it is anticipated that the burn condition could be 'emulated' to some extent in present non-burning-plasma devices by using dedicated auxiliary sources). To overcome the issue of limited, noisy plasma diagnostics expected in ITER and future power reactors, the design of state estimators for burn control [34] will need to be further investigated. By employing the certainty equivalence principle [35] (assume θh = θ h ), the four control laws ( 19)-( 22) in section 5 can be formulated from (62).…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

Graber¹,

Schuster²

2022

Nucl. Fusion

View full text Add to dashboard Cite

ITER will be the first tokamak to sustain a fusion-producing, or burning, plasma. If the plasma temperature were to inadvertently rise in this burning regime, the positive correlation between temperature and the fusion reaction rate would establish a destabilizing positive feedback loop. Careful regulation of the plasma’s temperature and density, or burn control, is required to prevent these potentially reactor-damaging thermal excursions, neutralize disturbances and improve performance. In this work, a Lyapunov-based burn controller is designed using a full zero-dimensional nonlinear model. An adaptive estimator manages destabilizing uncertainties in the plasma confinement properties and the particle recycling conditions (caused by plasma-wall interactions). The controller regulates the plasma density with requests for deuterium and tritium particle injections. In ITER-like plasmas, the fusion-born alpha particles will primarily heat the plasma electrons, resulting in different electron and ion temperatures in the core. By considering separate response models for the electron and ion energies, the proposed controller can independently regulate the electron and ion temperatures by requesting that different amounts of auxiliary power be delivered to the electrons and ions. These two commands for a specific control effort (electron and ion heating) are sent to an actuator allocation module that optimally maps them to the heating actuators available to ITER: an electron cyclotron heating system (20 MW), an ion cyclotron heating system (20 MW), and two neutral beam injectors (16.5 MW each). Two different actuator allocators are presented in this work. The first actuator allocator finds the optimal mapping by solving a convex quadratic program that includes actuator saturation and rate limits. It is nonadaptive and assumes that the mapping between the commanded control efforts and the allocated actuators (i.e., the effector model) contains no uncertainties. The second actuator allocation module has an adaptive estimator to handle uncertainties in the effector model. This uncertainty includes actuator efficiencies, the fractions of neutral beam heating that are deposited into the plasma electrons and ions, and the tritium concentration of the fueling pellets. Furthermore, the adaptive allocator considers actuator dynamics (actuation lag) that contain uncertainty. This adaptive allocation algorithm is more computationally efficient than the aforementioned nonadaptive allocator because it is computed using dynamic update laws so that finding the solution to a static optimization problem is not required at every time step. A simulation study assesses the performance of the proposed adaptive burn controller augmented with each of the actuator allocation modules.

show abstract

Section: Discussionmentioning

confidence: 99%

“…Recall that the upper and lower saturation limits are given by ū and u = 0, respectively. By introducing a Lagrangian function with Lagrangian parameter vector λ, the constrained optimization problem (34) can be written as an unconstrained optimization problem, i.e.…”

Section: Adaptive Dynamic Actuator Allocatormentioning

confidence: 99%

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

Graber¹,

Schuster²

2022

Nucl. Fusion

View full text Add to dashboard Cite

show abstract

“…Zero-dimensional simulations illustrate the performance of the closed loop system when moving between operating points, responding to disturbances, and dealing with constraints. Ongoing work includes studying the effect of different recycling model parameters on the performance of the control strategy, and the design of nonlinear observers to estimate states that may not be measurable in the harsh environment of a reactor [41]. In future work, a Monte Carlo simulation study will be used to systematically select the free design parameters based on assessment of performance and robustness of the proposed scheme within a range of expected conditions and model parameters.…”

Section: Discussionmentioning

confidence: 99%

“…Step 3. Having selected P aux and γ * in the previous steps, we must next choose S inj D and S inj T to ensure that Ẽ, γ , and ñ, which are governed by (51), (52), and (41), are driven to zero. We consider the Lyapunov function…”

Section: Nominal Control Designmentioning

confidence: 99%

Nonlinear control and online optimization of the burn condition in ITER via heating, isotopic fueling and impurity injection

Boyer¹,

Schuster²

2014

Plasma Phys. Control. Fusion

View full text Add to dashboard Cite

The ITER tokamak, the next experimental step toward the development of nuclear fusion reactors, will explore the burning plasma regime in which the plasma temperature is sustained mostly by fusion heating. Regulation of the fusion power through modulation of fueling and external heating sources, referred to as burn control, is one of the fundamental problems in burning plasma research. Active control will be essential for achieving and maintaining desired operating points, responding to changing power demands, and ensuring stable operation. Most existing burn control efforts use either non-model-based control techniques or designs based on linearized models. These approaches must be designed for particular operating points and break down for large perturbations. In this work, we utilize a spatially averaged (zero-dimensional) nonlinear model to synthesize a multi-variable nonlinear burn control strategy that can reject large perturbations and move between operating points. The controller uses all of the available actuation techniques in tandem to ensure good performance, even if one or more of the actuators saturate. Adaptive parameter estimation is used to improve the model parameter estimates used by the feedback controller in real-time and ensure asymptotic tracking of the desired operating point. In addition, we propose the use of a model-based online optimization algorithm to drive the system to a state that minimizes a given cost function, while respecting input and state constraints. A zero-dimensional simulation study is presented to show the performance of the adaptive control scheme and the optimization scheme with a cost function weighting the fusion power and temperature tracking errors.

show abstract

“…Moreover, a study of the complete TMHD model, including mass and entropy balance equations is necessary to consider the burn control problem (i.e. control of the plasma with the fusion reaction) which comes next after plasma confinement problems (see for instance preliminary works of [43,44,42,8,9]).…”

Section: Introductionmentioning

confidence: 99%

A structured control model for the thermo-magneto-hydrodynamics of plasmas in tokamaks

Lefèvre

Maschke

2016

Mathematical and Computer Modelling of Dynamical Systems

View full text Add to dashboard Cite

International audienceA thermo-magneto-hydrodynamics port-Hamiltonian model is derived for the plasmas in tokamaks. Electromagnetic field and material domain balance equations are expressed in covariant forms, together with the magneto-hydrodynamics interconnection structure connecting them together. The balance equations for the entropy, mass and momentum, as well as closure equations in the material domain, are derived from the Boltzmann equation (kinetic theory). The Gibbs-Duhem equation is used to compute the irreversible entropy source term and to define the interdomain R-field of the model. All derived interdomain couplings in the material domain are represented using Dirac and Stokes-Dirac structures and the resistivity R-field structure. The complete model is summarized in a Bond Graph

show abstract

Nonlinear Burn Control in Tokamak Fusion Reactors via Output Feedback

Cited by 4 publications

References 14 publications

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

Nonlinear control and online optimization of the burn condition in ITER via heating, isotopic fueling and impurity injection

A structured control model for the thermo-magneto-hydrodynamics of plasmas in tokamaks

Contact Info

Product

Resources

About