Fractional Order Modeling and Control: Development of Analog Strategies for Plasma Position Control of the Stor-1M Tokamak

This work revolves around the use of fractional order calculus in control science. Techniques such as fractional order universal adaptive stabilization (FO-UAS), and the fascinating results of their application to real-world systems, are presented initially. A major portion of this work deals with fractional order modeling and control of real-life systems like heat flow, fan and plate, and coupled tank systems. The fractional order models and controllers are not only simulated, they are also emulated using analog hardware. The main aim of all the above experimentation is to develop a fractional order controller for plasma position control of the Saskatchewan torus-1, modified (STOR-1M) tokamak at the Utah State University (USU) campus. A new method for plasma position estimation has been formulated. The results of hardware emulation of plasma position and its control are also presented. This work performs a small scale test measuring controller performance, so that it serves as a platform for future research efforts leading to real-life implementation of a plasma position controller for the tokamak

Integrated Control in Tokamaks using Nonlinear Robust Techniques and Actuator Sharing Strategies

Tokamaks are devices whose final purpose is obtaining energy by means of nuclear fusion reactions. To achieve such purpose, a gas is injected into the tokamak\u27s torus-shaped chamber and heated up to extremely high temperatures, giving birth to a plasma. When the necessary conditions of temperature, density, and confinement time are achieved, virtually inexhaustible energy can be produced in a tokamak. The main contribution of this dissertation is the development of integrated control strategies for tokamak plasmas. The development of integrated control architectures is necessary for tokamaks to become efficient and commercially competitive power plants. Because a tokamak plasma is a highly nonlinear, coupled dynamical system, the great diversity of complex control problems that coexist in a tokamak are indeed closely interrelated. However, this variety of control problems must be tackled by means of a limited number of actuators. A functional design for integrated tokamak-control architectures should employ multi-input multi-output controllers to simultaneously regulate as many plasma variables as possible with the available actuators. Supervisory and exception handling systems that monitor the plasma state arise as a necessity to ensure a safe tokamak-operation. Finally, actuator sharing and management capabilities should also exist in order to utilize the available actuators in an optimal way. Various control problems are tackled in this dissertation, including kinetic, magnetic, and instability control problems. Control-oriented, physics-based models that characterize some specific aspects of the plasma dynamics have been employed to develop new control-oriented simulation codes and integrated-control solutions that employ nonlinear, robust control techniques and optimization-based actuator-management strategies. Some of those control solutions have been experimentally tested in the DIII-D tokamak

Free-Boundary Simulations of ITER Advanced Scenarios

The successful operation of ITER advanced scenarios is likely to be a major step forward in the development of controlled fusion as a power production source. ITER advanced scenarios raise specific challenges that are not encountered in presently-operated tokamaks. In this thesis, it is argued that ITER advanced operation may benefit from optimal control techniques. Optimal control ensures high performance operation while guaranteeing tokamak integrity. The application of optimal control techniques for ITER operation is assessed and it is concluded that robust optimisation is appropriate for ITER operation of advanced sce- narios. Real-time optimisation schemes are discussed and it is concluded that the necessary conditions of optimality tracking approach may potentially be appropriate for ITER operation, thus offering a viable closed-loop optimal control approach. Simulations of ITER advanced operation are necessary in order to assess the present ITER design and uncover the main difficulties that may be encountered during advanced operation. The DINA-CH&CRONOS full tokamak simulator is used to simulate the operation of the ITER hybrid and steady-state scenarios. It is concluded that the present ITER design is appropriate for performing a hybrid scenario pulse lasting more than 1000s, with a flat-top plasma current of 12MA, and a fusion gain of Q ∼= 8. Similarly, a steady-state scenario without internal transport barrier, with a flat-top plasma current of 10MA, and with a fusion gain of Q ∼= 5 can be realised using the present ITER design. The sensitivity of the advanced scenarios with respect to transport models and physical assumption is assessed using CRONOS. It is concluded that the hybrid scenario and the steady- state scenario are highly sensitive to the L-H transition timing, to the value of the confinement enhancement factor, to the heating and current drive scenario during ramp-up, and, to a lesser extent, to the density peaking and pedestal pressure

A flexible architecture for plasma magnetic control in tokamak reactors

Plasma magnetic control is one of the core engineering issues to be tackled in a fusion device. Over the last years, model based approaches have been proposed to face this issue, proving their effectiveness and allowing to reduce the time span needed for control testing and validation. The first part of this work is intended to give an overview of the subject, from the historical milestones to the underlying physics; the most common techniques for tokamak plasmas electromagnetic modeling and control are also introduced and discussed. After this introduction, a general architecture for plasma magnetic control in tokamaks is proposed. Finally, the proposed solution is applied to the Experimental Advanced Superconducting Tokamak (EAST) tokamak, where a new plasma magnetic control architecture was developed and implemented during the 2016-2018 experimental campaigns, and to the Japan Torus-60 Super Advanced (JT-60SA) device, which is currently under construction in Japan

A flexible architecture for plasma magnetic control in tokamak reactors

Plasma magnetic control is one of the core engineering issues to be tackled in a fusion device. Over the last years, model based approaches have been proposed to face this issue, proving their effectiveness and allowing to reduce the time span needed for control testing and validation. The first part of this work is intended to give an overview of the subject, from the historical milestones to the underlying physics; the most common techniques for tokamak plasmas electromagnetic modeling and control are also introduced and discussed. After this introduction, a general architecture for plasma magnetic control in tokamaks is proposed. Finally, the proposed solution is applied to the Experimental Advanced Superconducting Tokamak (EAST) tokamak, where a new plasma magnetic control architecture was developed and implemented during the 2016-2018 experimental campaigns, and to the Japan Torus-60 Super Advanced (JT-60SA) device, which is currently under construction in Japan

Enhancing the control of tokamaks via a continuous nonlinear control law

The control of the current, position and shape of an elongated cross-section tokamak plasma is complicated by the instability of the plasma vertical position. In this case the control becomes a significant problem when saturation of the power supplies is considered. Current saturation is relatively benign due to the integrating nature of the tokamak, resulting in a reasonable time horizon for strategically handling this problem. On the other hand, voltage saturation is produced by the feedback controller itself, with no intrinsic delay. In practice, during large plasma disturbances, such as sawteeth, ELMs and minor disruptions, voltage saturation of the power supply can occur and as a consequence the vertical position control can be lost. If such a loss of control happens the plasma displaces vertically and hits the wall of the vessel, which can cause damage to the tokamak. The consideration and study of voltage saturation is especially important for ITER. Due to the size and therefore the cost of ITER, there will naturally be smaller margins in the Poloidal Field coil power supplies implying that the feedback will experience actuator saturation during large transients due to a variety of plasma disturbances. The next generation of tokamaks under construction will require vertical position and active shape control and will be fully superconducting. When the magnetic transverse field in superconducting magnets changes, the magnet generates two types of heat loss, the so-called coupling loss and the so-called hysteresis loss, grouped together as AC losses. Superconducting coils possess superconducting properties only below a critical temperature around a few K. AC losses are detrimental since they heat up the superconducting material. Thus, if AC losses are too large, the cryogenic plant can no longer hold the required temperature to maintain the superconductivity properties. Once the superconductivity is lost, the electric currents in the coils produce an enormous heat loss due to the ohmic resistivity, which can lead to a possible damage to the coils. In general, the coils are designed with enough margin to absorb all likely losses. A possible loss reduction could allow us to downsize the superconducting cross section in the cables, reducing the overall cost, or simply increase the operational cooling margin for given coils. In this thesis we have tried to take into consideration these two major problems. The thesis is therefore focused on the following main objectives: i) the stability analysis of the tokamak considering voltage saturation of the power supplies and ii) the proposition of a new controller which enhances the stability properties of the tokamak under voltage saturation and iii) the proposition of a controller which takes into consideration the problem of reducing the AC losses. The subject of the thesis is therefore situated in an interdisciplinary framework and as a result the thesis is subdivided into two principal parts. The first part is devoted to tokamak physics and engineering, while the second part focuses on control theory. In the tokamak physics and engineering part we present the linear tokamak models and the nonlinear tokamak code used for the controller design and the validation of the new proposed controller. The discussion is especially focused on the presence of a single unstable pole when the vertical plasma position is unstable since this characteristic is essential for the work presented in the control theory part. In order to determine the enhancement of the stability properties we have to bring the new proposed controller to its stability limits by means of large disturbances. Validation by means of simulations with either linear or nonlinear tokamak models are imperatively required before considering the implementation of the new controller on a tokamak in operation. A linear tokamak model will probably be inadequate since large disturbances can move its state outside its validity regions. A full nonlinear tokamak evolution code like DINA is indispensable for this purpose. We give a detailed description of the principal plasma physics implemented in the DINA code. Additionally, validation of DINA is provided by comparing TCV experimental VDE responses with DINA code simulations. To allow a study of the AC losses reduction, the nature of the AC losses has to be reduced to a simplified form. We analyse to what extent the accumulated AC losses in ITER could be reduced by taking into account the losses themselves when designing the feedback control loops. In order to be able to carry out this investigation a simple and fast AC loss model, referred to as "AC-CRPP" model, is proposed. In the control theory part we study the stability region in state space, referred to as the region of attraction, for linear tokamak-like systems with input saturation (voltage saturation) and a linear state feedback. Only linear systems with a single unstable pole (mode) and a single saturated input are considered. We demonstrate that the characterisation of the region of attraction is possible for a second order linear system with one unstable and one stable pole. For such systems the region of attraction possesses a topological bifurcation and we provide an analytical condition under which this bifurcation occurs. Since the analysis relies on methodologies like Poincaré and Bendixson's theorems which are unfortunately only valid for second order systems it is evident that there is no way to apply the results for second order systems to higher order systems. It turned out that the search for characterising the region of attraction for higher order systems was illusory and thus this research direction had to be abandoned. We therefore focused on controllers for which the region of attraction is the maximal region of attraction that can be achieved under input saturation. This region is referred to as the null controllable region and its characterisation is simple for any arbitrary high order system possessing a single unstable pole. We present a new globally stabilising controller for which its region of attraction is equal to the null controllable region. This result is obtained by incorporating a simple continuous nonlinear function into a linear state feedback controller. There are several advantages linked to this new controller: i) the stability properties are enhanced, ii) the performance, AC loss reduction and fast disturbance rejection, can be taken into account, iii) the controller can be applied to any arbitrary high order system and iv) the controller possesses a simple structure which simplifies the design procedure. We close the control theory part by focusing on the application of the proposed new controller to tokamaks. Since this controller is a state feedback controller one of the major problems is linked to the state reconstruction. Other pertinent topics are: i) the study of the effect of the disturbances on the closed-loop system stability, ii) the problem inherent to the nature of a state feedback controller when we want an output of the system to track a reference signal and iii) the discussion of the detrimental effects on stability if a pure time delay or a limited bandwidth are added to the closed-loop system, as is the case in reality. The validation of the proposed controller is carried out by means of simulations. We present results for ITER-FEAT and JET using the linear tokamak model CREATE-L. Finally, we present a validation for the case of TCV using the nonlinear DINA-CH code