Actuator allocation for integrated control in tokamaks:Architectural design and a mixed-integer programming algorithm

\u3cp\u3ePlasma control systems (PCS) in tokamaks need to fulfill a number of control tasks to achieve the desired physics goals. In present-day devices, actuators are usually assigned to a single control task. However, in future tokamaks, only a limited set of actuators is available for multiple control tasks at the same time. The priority to perform specific control tasks may change in real-time due to unforeseen plasma events and actuator availability may change due to failure. This requires the real-time allocation of available actuators to realize the requests by the control tasks, also known as actuator management.In this paper, we analyze possible architectures to interface the control tasks with the allocation of actuators inside the PCS. Additionally, we present an efficient actuator allocation algorithm for Heating and Current Drive (H&CD) actuators. The actuator allocation problem is formulated as a Mixed-Integer Quadratic Programming optimization problem, allowing to quickly search for the best allocation option without the need to compute all allocation options. The algorithms performance is demonstrated in examples involving the full proposed ITER H&CD system, where the desired allocation behavior is successfully achieved. This work contributes to establishing integrated control routines with shared actuators on existing and future tokamaks.\u3c/p\u3

Subspace identification of MIMO LPV systems using a periodic scheduling sequence

A novel subspace identification method is presented which is able to reconstruct the deterministic part of a multivariable state-space LPV system with affine parameter dependence, in the presence of process and output noise. It is assumed that the identification data is generated with the scheduling variable varying periodically during the course of the identification experiment. This allows to use methods from LTI subspace identification to determine the column space of the time-varying observability matrices. It is shown that the crucial step in determining the original LPV system is to ensure the obtained observability matrices are defined with respect to the same state basis. Once the LPV model has been identified, it is valid for other nonperiodic scheduling sequences as well. © 2007 Elsevier Ltd. All rights reserved

Sawtooth pacing by real-time auxiliary power control in a tokamak plasma

In the standard scenario of tokamak plasma operation, sawtooth crashes are the main perturbations that can trigger performance-degrading, and potentially disruption-generating, neoclassical tearing modes. This Letter demonstrates sawtooth pacing by real-time control of the auxiliary power. It is shown that the sawtooth crash takes place in a reproducible manner shortly after the removal of that power, and this can be used to precisely prescribe, i.e., pace, the individual sawteeth. In combination with preemptive stabilization of the neoclassical tearing modes, sawtooth pacing provides a new sawtooth control paradigm for improved performance in burning plasmas. © 2011 American Physical Society. SP - 24500

Design and simulation of a Kalman filter for a rigid plasma electromagnetic model on TCV

This report describes the procedure of the design and simulation of a Kalman observer for control of the vertical plasma position in TCV. The design of the observer is based on knowledge of a linearised system representation of the tokamak with its surrounding active poloidal eld coil systems and vessel wall. One of the pillars for this linearised system are the circuit equations for the plasma with its surroundings. Other important components of the model are the vertical and radial force balance equations. Together these equations lead to a state space representation with 19 active coil voltages as inputs and 95 measurements as outputs. The measurements consist of the 19 active coil currents obtained from current transducers inside the coils, 38 poloidal eld loops which measure the local magnetic ux and 38 magnetic eld probes that measure the magnetic eld at the probe location. Due to the elongated plasma form the vertical plasma position is an unstable variable that needs to be controlled. With the obtained state space model a Proportional Derivative controller is designed that stabilizes the vertical plasma position. The input for the PD controller is the vertical plasma position. The plasma position cannot be measured directly and has to be reconstructed using an observer. Currently this plasma position is being reconstructed using a static least-squares observer that uses a priori system equilibrium knowledge. This observer however is very sensitive for measurement noise. For high noise levels the estimated vertical position from the observer has a noisy character where the absolute value of the time derivative is very high. Since this is an input for the controller the reconstruction has to be improved. Here the dynamic observer comes into play. These observers reconstruct states using the measurement outputs, the system inputs and system knowledge. A dynamical observer system is constructed which has the state estimates as its own states. When designed appropriately the state estimates asymptotically converge to the true state values. However, when the system contains noise, the design of the dynamical observer system becomes more dicult. The Kalman observer is an dynamical observer designed using a method that accounts for the noise characteristics and the resulting observer optimally reconstructs the system states. Simulation of this Kalman observer indeed shows a good state reconstruction and appropriate control of the vertical plasma position

Parameter estimation for a nonlinear control-oriented tokamak profile evolution model

\u3cp\u3eA control-oriented tokamak profile evolution model is crucial for the development and testing of control schemes for a fusion plasma. The RAPTOR (RApid Plasma Transport simulatOR) code was developed with this aim in mind (Felici 2011 Nucl. Fusion 51 083052). The performance of the control system strongly depends on the quality of the control-oriented model predictions. In RAPTOR a semi-empirical transport model is used, instead of a first-principles physics model, to describe the electron heat diffusivity in view of computational speed. The structure of the empirical model is given by the physics knowledge, and only some unknown physics of , which is more complicated and less well understood, is captured in its model parameters. Additionally, time-averaged sawtooth behavior is modeled by an ad hoc addition to the neoclassical conductivity and electron heat diffusivity. As a result, RAPTOR contains parameters that need to be estimated for a tokamak plasma to make reliable predictions. In this paper a generic parameter estimation method, based on the nonlinear least-squares theory, was developed to estimate these model parameters. For the TCV tokamak, interpretative transport simulations that used measured profiles were performed and it was shown that the developed method is capable of finding the model parameters such that RAPTOR's predictions agree within ten percent with the simulated q profile and twenty percent with the measured profile. The newly developed model-parameter estimation procedure now results in a better description of a fusion plasma and allows for a less ad hoc and more automated method to implement RAPTOR on a variety of tokamaks.\u3c/p\u3

A dynamic state observer for real-time reconstruction of the tokamak plasma profile state and disturbances

A dynamic observer is presented which can reconstruct the internal state of a tokamak fusion plasma, consisting of the spatial distribution of current and temperature, from measurements. Today, the internal plasma state is usually reconstructed by solving an ill-conditioned inversion problem using a large number of measurements at one point in time. Such an approach does not take into account the time evolution of the underlying dynamical system (the plasma) and strongly relies on (technically challenging) internal measurements. The observer-based approach presented here includes the dynamics of the plasma current and temperature, modeled by a set of coupled nonlinear 1-D PDEs which are discretized in space and time to yield a finite-dimensional nonlinear model. The observer, which is based on an Extended Kalman Filter, estimates the state of an augmented model which includes additive state disturbances modeled as a random walk. Simulation results demonstrate the effectiveness of this observer in the case of perturbed models and input disturbances

Simultaneous closed-loop control of the current profile and the electron temperature profile in the TCV tokamak

\u3cp\u3eTwo key properties that are often used to define a plasma operating scenario in nuclear fusion tokamak devices are the current and electron temperature (T\u3csub\u3ee\u3c/sub\u3e) profiles due to their intimate relationship to plasma performance and stability. In the tokamak community, the current profile is typically specified in terms of the safety factor (q) profile or its inverse, the rotational transform (ι = 1/q) profile. The plasma poloidal magnetic flux (Ψ) and T\u3csub\u3ee\u3c/sub\u3e dynamics are governed by an infinite-dimensional, nonlinear, coupled, physics-based model that is described by the magnetic diffusion equation and the electron heat transport equation. In this work, an integrated feedback controller is designed to track target ι (proportional to the spatial gradient of Ψ) and T\u3csub\u3ee\u3c/sub\u3e profiles by embedding these partial differential equation models into the control design process. The electron thermal conductivity profile is modeled as an uncertainty, and the controller is designed to be robust to an expected uncertainty range. The performance of the integrated ι + T\u3csub\u3ee\u3c/sub\u3e profile controller in the TCV tokamak is demonstrated through simulations with the simulation code RAPTOR by first tracking a nominal target, and then modulating the T\u3csub\u3ee\u3c/sub\u3e profile between equilibrium points while maintaining the ι profile in a stationary condition.\u3c/p\u3

Self-consistent simulation of tearing modes during ECCD experiments on TCV

No abstract

A mimetic spectral element solver for the Grad-Shafranov equation

\u3cp\u3eIn this work we present a robust and accurate arbitrary order solver for the fixed-boundary plasma equilibria in toroidally axisymmetric geometries. To achieve this we apply the mimetic spectral element formulation presented in [56] to the solution of the Grad-Shafranov equation. This approach combines a finite volume discretization with the mixed finite element method. In this way the discrete differential operators (∇, ∇×, ∇.) can be represented exactly and metric and all approximation errors are present in the constitutive relations. The result of this formulation is an arbitrary order method even on highly curved meshes. Additionally, the integral of the toroidal current J\u3csub\u3eφ\u3c/sub\u3e is exactly equal to the boundary integral of the poloidal field over the plasma boundary. This property can play an important role in the coupling between equilibrium and transport solvers. The proposed solver is tested on a varied set of plasma cross sections (smooth and with an X-point) and also for a wide range of pressure and toroidal magnetic flux profiles. Equilibria accurate up to machine precision are obtained. Optimal algebraic convergence rates of order p+1 and geometric convergence rates are shown for Soloviev solutions (including high Shafranov shifts), field-reversed configuration (FRC) solutions and spheromak analytical solutions. The robustness of the method is demonstrated for non-linear test cases, in particular on an equilibrium solution with a pressure pedestal.\u3c/p\u3

Plasma internal profile control using IDA-PBC:application to TCV

\u3cp\u3eIn this paper, new results of plasma ι-profile and β control on TCV, using total plasma current I \u3csub\u3e p \u3c/sub\u3e, and ECCD (Electron Cyclotron heating and Current Drive) heating source have been discussed. The control model is governed by the resistive diffusion equation coupled with the thermal transport equation, written in PCH (Port-Controlled Hamiltonian) formulation. The IDA-PBC (Interconnection and Damping Assignment - Passivity based Control) controller is developed and tested on simulation as well as on TCV real plant. Two test scenarios are considered: ι control only, and ι and β control. The spatial distributions of ECCD profiles are pre-defined and only input powers are used for control design. Thus, a stationary control is defined in order to consider all non-linearity and actuator constraint, and a linear feedback IDA-PBC will ensure the convergence speed and the robustness of the closed-loop system. The obtained results are encouraging towards using routinely such plasma advanced control algorithm in a near future.\u3c/p\u3