Experimental validation of a Lyapunov-based controller for the plasma safety factor and plasma pressure in the TCV tokamak

Mavkov, Bojan; Witrant, Emmanuel; Prieur, Christophe; Maljaars, E.; Felici, F.; Sauter, O.

doi:10.1088/1741-4326/aab16a

Cited by 23 publications

(17 citation statements)

References 59 publications

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“…Take the derivative of v(r, s, t) with respect to s and t, respectively. Then, combining the characters of target system ( 19)-( 23) with the initial condition (6), it obtains that the kernel function 𝜉(r, s, 𝜌) satisfies that…”

Section: Inverse Transformationmentioning

confidence: 99%

“…Time-delay partial-differential-equation (PDE) systems have received increasingly more attention from researchers over the past several years since they are ubiquitous in many applications, for example, influenza prediction, 1 the model of population structure with spatial non-locality, 2 the impacts of maturation time delay and some other factors on single species dynamics, 3 oil industry, 4 Tomakak device, [5][6][7] multi-agent systems with input delay, 8 memristive neural networks, 9 a pollutant decontamination process, 10 traffic flow model. 11 Recently, systems with delays have merited deeper study.…”

Section: Introductionmentioning

confidence: 99%

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Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Guan

2022

Intl J Robust & Nonlinear

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In this article, a distributed control design is developed via partial differential equation (PDE) backstepping for a class of reaction-diffusion PDEs on n-ball under revolution symmetry conditions in the presence of radial spatially varying actuator delay. The actuator delay is modeled by a two-dimensional (2D) first-order hyperbolic PDE with spatially varying boundary, resulting in a cascaded transport-diffusion PDE system. Two-step backstepping transformation is introduced for the control design. First, a new Volterra transformation for the n-ball under revolution symmetry is proposed that allows the kernel function to be solvable. Different from the kernel in the 1D domain, which is expressed by the classical Fourier series, the kernel of the n-ball under revolution symmetry conditions is based on the Fourier-Bessel series. The resulting Volterra transformation is an implicit one that contains the state of the target system on both sides of the definition. Based on the implicit transformation, we employ the successive approximations approach to derive the second-step transformation, namely, an explicit transformation, and arrive at a stable target system. The inverse transformation is also derived, to prove L 2 exponential stability of the closed-loop system.The stability analysis requires more technical skills that are not needed in solving the spatially varying delay compensation problem when the domain is 1D.Numerical simulation examples of 3D and 4D revolution-symmetrical systems illustrate the effectiveness of the controller.

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Section: Inverse Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Guan

2022

Intl J Robust & Nonlinear

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“…The advent of transport simulations that can operate faster than real time [14] will be important for discharge monitoring and control. Simultaneous control of plasma pressure and safety factor using model-based control has been demonstrated in TCV [15]. In DIII-D, as shown in Fig.…”

Section: Plasma Configuration Controlmentioning

confidence: 99%

Progress in disruption prevention for ITER

Strait¹,

Barr²,

Baruzzo³

et al. 2019

Nucl. Fusion

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Key plasma physics and real-time control elements needed for robustly stable operation of high fusion power discharges in ITER have been demonstrated in US fusion research. Optimization of the current density profile has enabled passively stable operation without n " 1 tearing modes in discharges simulating ITER's baseline scenario with zero external torque. Stable rampdown of the discharge has been achieved with ITER-like scaled current ramp rates, while maintaining an X-point configuration. Significant advances have been made toward real-time prediction of disruptions: machine learning techniques for prediction of disruptions have achieved 90% accuracy in offline analysis, and direct probing of ideal and resistive plasma stability using 3D magnetic perturbations has shown a rising plasma response before the onset of a tearing mode. Active stability control contributes to prevention of disruptions, including direct stabilization of resistive-wall kink modes in high-β discharges, forced rotation of magnetic islands to prevent wall locking, and localized heating/current drive to shrink the islands. These elements are being integrated into stable operating scenarios and a new event-handling system for off-normal events in order to develop the physics basis and techniques for robust control in ITER.

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“…See [21,22,23,24] for Lyapunov design control on the safety factor dynamics. See [139,141] with the coupling with electron temperature profile and finally [140] for real experiments on the tokamaks using Lyapunov based control and ISS properties.…”

Section: Applicationsmentioning

confidence: 99%

Input-to-state stability of infinite-dimensional systems: recent results and open questions

Mironchenko¹,

Prieur²

2019

Preprint

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In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems. This property allows to estimate the impact of inputs and initial conditions on both the intermediate values and the asymptotic bound on the solutions. ISS has unified the input-output and Lyapunov stability theories and is a crucial property in stability theory of control systems as well as for many applications whose dynamics depend on parameters, unknown perturbations, or other inputs. In this paper, starting from classic results for nonlinear ordinary differential equations, we motivate the study of ISS property for distributed parameter systems. Then fundamental properties are given, as an ISS superposition theorem and characterizations of (global and local) ISS in terms of Lyapunov functions. We explain in detail the functional-analytic approach to ISS theory of linear systems with unbounded input operators, with a special attention devoted to ISS theory of boundary control systems. Lyapunov method is shown to be very useful for both linear and nonlinear models, including parabolic and hyperbolic partial differential equations. Next, we show the efficiency of ISS framework to study stability of large-scale networks, coupled either via the boundary or via the interior of the spatial domain. ISS methodology allows reducing the stability analysis of complex networks, by considering the stability properties of its components and the interconnection structure between the subsystems. An extra section is devoted to ISS theory of time-delay systems with the emphasis on techniques, which are particularly suited for this class of systems. Finally, numerous applications are considered in this survey, where ISS properties play a crucial role in their study. This survey contains recent as well as classical results on systems theory and suggests many open problems throughout the paper.

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Experimental validation of a Lyapunov-based controller for the plasma safety factor and plasma pressure in the TCV tokamak

Cited by 23 publications

References 59 publications

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Radially varying delay‐compensated distributed control of reaction‐diffusion PDEs on n‐ball under revolution symmetry conditions

Progress in disruption prevention for ITER

Input-to-state stability of infinite-dimensional systems: recent results and open questions

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