On Self-Tuning Control of Tokamak Thermokinetics

Miley, George H.; Varadarajan, V.

doi:10.13182/fst92-a30078

Cited by 13 publications

(7 citation statements)

References 16 publications

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“…Prior work combining actuation concepts include [13][14][15][16][17][18] for zero-dimensional (volume-averaged) models. Studies of kinetic control and thermal stability for 1D (radial profile) models can be found in [19][20][21]. In [22], a diagonal multiinput, multi-output linear control scheme for burning plasma kinetics was developed by observing actuator influences during numerical simulations of plasma physics codes.…”

Section: Prior Workmentioning

confidence: 99%

Nonlinear burn condition control in tokamaks using isotopic fuel tailoring

Boyer¹,

Schuster²

2015

Nucl. Fusion

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One of the fundamental problems in tokamak fusion reactors is how to control the plasma density and temperature in order to regulate the amount of fusion power produced by the device. Control of these parameters will be critical to the success of burning plasma experiments like ITER. The most previous burn condition control efforts use either non-model based control designs or techniques based on models linearized around particular operating points. Such strategies limit the potential operational space and must be carefully retuned or redesigned to accommodate changes in operating points or plasma parameters. In this work, a nonlinear dynamic model of the spatial averages of energy and ion species densities is used to synthesize a nonlinear feedback controller for stabilizing the burn condition. The nonlinear model-based control strategy guarantees a much larger operational space than previous linear controllers. Because it is not designed around a particular operating point, the controller can be used to move from one burn condition to another. The proposed scheme first attempts to use regulation of the auxiliary heating power to reject temperature perturbations, then, if necessary, uses isotopic fuel tailoring as a way to reduce fusion heating during positive temperature perturbations. A global model of hydrogen recycling is incorporated into the model used for design and simulation, and the proposed control scheme is tested for a range of recycling model parameters. As we find the possibility of changing the isotopic mix can be limited for certain unfavorable recycling conditions, we also consider impurity injection as a backup method for controlling the system. A simple supervisory control strategy is proposed to switch between the primary and backup control schemes based on stability and performance criteria. A zero-dimensional simulation study is used to study the performance of the control scheme for several scenarios and model parameters. Finally, a one-dimensional simulation is done to test the robustness of the control scheme to spatially varying parameters.

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Section: Prior Workmentioning

confidence: 99%

Nonlinear burn condition control in tokamaks using isotopic fuel tailoring

Boyer¹,

Schuster²

2015

Nucl. Fusion

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“…Given the desired shapes (∂ /∂ r) and spatially averaged values (<>) for the effective atomic number and electron density (indicated by the star notation in the figure), equilibrium profiles are computed satisfying these specifications. These equilibrium profiles are then converted to corresponding hydrogen and impurity ion density equilibrium profiles (n H ,n I ) using the inverse transformations (3) and (4). The set of equilibrium profiles are then utilized by the backstepping controller to actuate the ion densities at the plasma edge in order to achieve the desired shapes and spatially averaged values for the electron density and effective atomic.…”

Section: Backstepping Techniquementioning

confidence: 99%

“…Precise profile control in experimental devices could also be useful in providing insight into the transport process and allow for conclusions to be made about the validity of proposed transport models. The importance of kinetic profile control in tokamak reactors is recognized by previous work in the field [3], [4], [5], [6], [7]. In these pieces of work, the 1-D model is represented by a set of partial differential equations (PDEs) and different methods are used to reduce the distributed parameter description of the system to a lumped parameter description.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous control of effective atomic number and electron density in non-burning tokamak plasmas

Boyer

Schuster

2010

Proceedings of the 2010 American Control Conference

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The control of plasma density profiles is one of the most fundamental problems in fusion reactors. During reactor operation, the density profiles of hydrogen ions and heavier impurity ions must be precisely regulated, and while the uncontrolled open-loop behavior of these profiles is stable in non-burning plasmas, the system response time may be very slow. In this work, a controller is sought to improve the response of ion density profiles in a non-burning plasma and to track reference profiles for the electron density and effective atomic number, a set of coupled variables that are directly dependent on the hydrogen and impurity ion density profiles. A one-dimensional approximation of the transport equation for ion densities is represented in cylindrical coordinates by a partial differential equation (PDE). To control the density profiles, the PDE is discretized in space using a finite difference method and a backstepping design is applied to obtain a discrete transformation from the original system into an asymptotically stable target system. Numerical simulations of the resulting control law show that density profiles can be successfully controlled with just one step of backstepping. Tracking of electron density and effective atomic number profiles is then simulated by first transforming the profiles into corresponding ion density profiles for use by the backstepping controller. Simulations show the successful tracking of reference profiles.

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“…The importance of controlling kinetic profiles in burning plasmas has been recognized in previous work, including, [4], [5], [6], [7], and [8]. In these pieces of work, a 1-D plasma model is represented by a set of partial differential equations (PDEs) and various methods are utilized to reduce the distributed parameter model to a lumped-parameter one.…”

Section: Introductionmentioning

confidence: 99%

Burn control in fusion reactors using simultaneous boundary and distributed actuation

Boyer

Schuster

2013

52nd IEEE Conference on Decision and Control

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The control of the plasma density and temperature profiles is one of the fundamental problems in nuclear fusion reactors. During reactor operation, the spatial profiles of deuterium-tritium fuel, alpha particles generated by fusion reactions, and energy must be precisely regulated. In this work we combine distributed actuation with a backstepping boundary control law to stabilize an unstable equilibrium in a burning plasma. Disturbance estimation update laws are included to improve disturbance rejection and tracking. A one-dimensional approximation of the transport equation for energy, as well as for the densities of deuterium-tritium fuel ions and alpha particles, is represented in cylindrical coordinates by a system of partial differential equations (PDEs). The PDE system is discretized in space using a finite difference method and a backstepping design is applied to obtain a discrete transformation from the original system into a particular target system chosen to facilitate the use of additional actuators distributed throughout the plasma. Numerical simulations show that a controller designed on a very coarse grid can stabilize the system and that distributed actuation improves the system response.

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On Self-Tuning Control of Tokamak Thermokinetics

Cited by 13 publications

References 16 publications

Nonlinear burn condition control in tokamaks using isotopic fuel tailoring

Nonlinear burn condition control in tokamaks using isotopic fuel tailoring

Simultaneous control of effective atomic number and electron density in non-burning tokamak plasmas

Burn control in fusion reactors using simultaneous boundary and distributed actuation

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