M Menno Lauret

SYNCHRONIZATION AND GRAPH TOPOLOGY

This paper clarifies the relation between synchronization and graph topology. Applying the Connection Graph Stability method developed by Belykh et al. [2004a] to the study of synchronization in networks of coupled oscillators, we show which graph properties matter for synchronization. In particular, while we explicitly link the stability of synchronization with the average path length for a wide class of coupling graphs, we prove by a simple argument that the average path length is not always the crucial quantity for synchronization. We also show that synchronization in scale-free networks can be described by means of regular networks with a star-like coupling structure. Finally, by considering an example of coupled Hindmarsh–Rose neuron models, we demonstrate how global stability of synchronization depends on the parameters of the individual oscillator.

Demonstration of sawtooth period locking with power modulation in TCV plasmas

Corroborating evidence is presented that the sawtooth period can follow the modulation frequency of an externally applied high power electron cyclotron wave source. Precise, fast and robust open loop control of the sawtooth period with a continuously changing reference period has been achieved. This period locking is not associated with the crash, but with the phase evolution of the inter-crash dynamics. This opens new possibilities of open loop control for physics studies and maybe for reactor performance control.

Numerical demonstration of injection locking of the sawtooth period by means of modulated EC current drive

In this paper the sawtooth period behaviour under periodic forcing by electron cyclotron waves is investigated. The deposition location is kept constant while the gyrotron power is modulated with a certain period and duty cycle. Extensive simulations on a representative dynamic sawtooth model show that when this modulation is properly chosen, the sawtooth period quickly synchronizes to the same period and remains locked at this value. It is shown that the range of modulation periods and duty cycles over which sawtooth period locking occurs, depends on the deposition location, but is particularly large for depositions near the q = 1 surface. The simulation results reveal a novel approach to control the sawtooth period in open loop, based on injection locking, which is a well-known technique to control limit cycles of non-linear dynamic oscillators. The locking and convergence results are therefore used in a simple open-loop locking controller design, with which accurate sawtooth period tracking to any desired value is indeed demonstrated. Injection locking appears to let the sawtooth period converge to the modulation period quickly, partly because it does not suffer from slow EC mirror launcher dynamics. Moreover, simulations show that the method has a relatively large robustness against general uncertainties and disturbances. Hence, injection locking is expected to outperform conventional sawtooth control methods using a variable deposition location and constant gyrotron power. Finally, the recent result with sawtooth pacing is shown to be a special case of the general locking effect.

Nonlinear control for stabilization of small neoclassical tearing modes in ITER

In this paper, the feasibility of feedback stabilization of neoclassical tearing modes at small island sizes, corresponding to otherwise unstable island sizes in ITER scenario 2, is demonstrated. The islands are stabilized by application of electron cyclotron resonance heating and current drive in a regime where the application of current drive in open loop normally results in a complete suppression of the island. By applying current drive in closed loop with feedback of real-time measurements of the island width, complete suppression is avoided and the island is stabilized at a specific reduced size. In contrast to complete suppression, control of islands at a specific size will allow the manipulation of a plasmas current density profile in hybrid scenarios. Three conceptual (non-)linear feedback controllers with varying complexity, performance, robustness and required model knowledge are introduced. Simulations show the theoretical feasibility of small island stabilization at a specific reduced width. The controllers are applied to the generalized Rutherford equation, which governs the island evolution subject to electron cyclotron current drive. A strategy for the gradual implementation of the controllers is suggested. Stabilization of small islands by feedback control will allow the use of system identification to extend the model knowledge on the evolution of small islands, and in addition will extend the operational regime.

Predictive control of the tokamak q profile to facilitate reproducibility of high-q min steady-state scenarios at DIII-D

We consider control of the q profile while simultaneously regulating the plasma stored energy for the DIII-D tokamak. The main objective is to improve the shot-to-shot reproducibility and facilitate the accessibility of operating conditions that have steady-state potential, i.e. plasmas with large non-inductive current drive fractions. At DIII-D, non-inductive current sources including electron cyclotron current drive (ECCD) and neutral beam injection (NBI) allow the possibility of shaping the plasma current density distribution, and therefore enabling control of the q profile. A feedback controller is designed in a model predictive control framework to regulate the q profile while simultaneously regulating the plasma stored energy. The effectiveness of the control approach is demonstrated with experiments.

A switched system approach to optimize mixing of fluids

Abstract In this paper, we discuss the problem of efficient fluid mixing which is tackled by means of (approximate) dynamic programming from a switched systems perspective. In current practice, typically pre-determined periodic mixing protocols are used. As we will show in this paper, feedback control can be used to improve mixing significantly. To make this control problem tractable, temporal and spatial discretization is used by means of the cell-mapping method on the original infinite-dimensional fluid models. This translates the original control problem into the design of a (sub)optimal switching law that determines discrete mixing actions for a discrete-time switched linear system. Exploiting this switched systems perspective, a novel feedback law for mixing fluids is proposed inspired by suboptimal rollout policies in dynamic programming contexts. By design, this feedback law for mixing guarantees a performance improvement over any given (open-loop) periodic mixing protocol. This new design methodology is validated by means of simulations for the benchmark journal bearing flow showing improved performance with respect to periodic mixing strategies.

Current profile and energy control in DIII-D plasmas using discrete-time variable-structure control

One of the most promising candidates to produce clean nuclear fusion energy is the tokamak, a device magnetically confining an extremely hot plasma (i.e. an ionized gas) where the fusion reactions take place. To produce nuclear fusion energy using tokamak devices, it is crucial that the poloidal magnetic flux (characterized by the so-called q profile) and the plasma internal energy are tightly controlled to avoid magnetohydrodynamic instabilities and to reach the high pressures and temperatures that are needed for high fusion-power density. Simultaneous control of the q profile and the internal energy is challenging for a number of reasons: the system is nonlinear, there are significant parameter uncertainties and large disturbances, the available number of actuators is small, and the actuation authority is limited from a control perspective. Therefore, a variable-structure controller is proposed in this work to tackle this plasma control problem since this type of controllers can typically diminish the impact of serious disturbances and nonlinearities while still leading to good performance. Simulations and recent experiments on the DIII-D tokamak in a challenging high-confinement (H-mode) plasma regime show that this control approach does indeed lead to good and repeatable control of the q profile and the internal energy.