| Description |
1 online resource |
| Series |
SpringerBriefs in electrical and computer engineering, Control, automation and robotics |
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SpringerBriefs in electrical and computer engineering. Control, automation and robotics.
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| Contents |
880-01 Mathematical model of the safety factor and control problem formulation -- A polytopic LPV approach for finite-dimensional control -- Infinite-dimensional Control -- Lyapunov Function -- Controller implementation |
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880-01/(S Machine generated contents note: 1. Introduction -- 1.1. Challenges in Plasma Physics for Tokamaks -- 1.2. Control Challenges for Distributed Parameter Systems -- 1.3. Problem Statement and Background -- 1.4. Main Contributions -- 1.5. Outline -- References -- 2. Mathematical Model of the Safety Factor and Control Problem Formulation -- 2.1. Inhomogeneous Transport of the Poloidal Magnetic Flux -- 2.2. Periferal Components Influencing the Poloidal Magnetic Flux -- 2.2.1. Resistivity and Temperature Influence -- 2.2.2. Inductive Current Sources -- 2.2.3. Non-inductive Current: Sources and Nonlinearity -- 2.3. Control Problem Formulation -- 2.3.1. Equilibrium and Regulated Variation -- 2.3.2. Interest of Choosing ψ as the Regulated Variable -- 2.3.3. Control Challenges -- References -- 3. Poly topic LPV Approach for Finite-Dimensional Control -- 3.1. LPV Model -- 3.2. Controller Synthesis -- 3.3. Results for a Tore Supra Plasma Shot -- 3.3.1. Implementation -- 3.3.2. Simulation Results -- 3.4. Summary and Conclusions on the Polytopic Approach -- References -- 4. Infinite-Dimensional Control-Lyapunov Function -- 4.1. Lyapunov Functions for Distributed Parameter Systems -- 4.2. Some Possible Lyapunov Functions -- 4.2.1. First Candidate Lyapunov Function -- 4.2.2. Second Candidate Lyapunov Function -- 4.3. Selected Candidate Lyapunov Function and Nominal Stability -- 4.3.1. Selected Lyapunov Function -- 4.4. Input-to-State Stability and Robustness -- 4.4.1. Disturbed Model -- 4.5. D1-Input-to-State Stability -- 4.5.1. Strict Lyapunov Function and Sufficient Conditions for D1-Input-to-State Stability -- 4.6. Control of the Poloidal Magnetic Flux Profile in a Tokamak Plasma -- 4.6.1. Stability and Numerical Computation of the Lyapunov Function -- 4.6.2. ISS Property and Robust Unconstrained Control of the Magnetic Flux Gradient -- 4.6.3. Using the Lyapunov Approach to Include Actuation Constraints -- References -- 5. Controller Implementation -- 5.1. Total Plasma Current Dynamic Model -- 5.1.1. Perfect Decoupling and Cascade Interconnection of ISS Systems -- 5.1.2. Interconnection Without Perfect Decoupling -- 5.2. Modified Lyapunov Function -- 5.3. Simulation Result: Closed-Loop Tracking Using METIS -- 5.3.1. General Description -- 5.3.2. Simulation Scenario: METIS, Independent Ip, Control, Large Variations of Pth, ICRH Heating Disturbance -- 5.3.3. Simulation Scenario: METIS, Independent Ip Control, Large Variations of Nll, ICRH Heating Disturbance -- 5.4. Some Preliminary Extensions -- 5.4.1. Profile Reconstruction Delays -- 5.4.2. Extension for TCV -- 5.5. Summary and Conclusions -- References -- 6. Conclusion -- References |
| Summary |
Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, time-dependent, partial differential equations (PDEs). This is because of the spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium. Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radio-frequency waves (distributed inputs). The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linear-parameter-varying formulation). The limitations of this finite-dimensional approach motivate new developments in the infinite-dimensional framework. The text then tackles the construction of an input-to-state-stabilityLyapunov function for the infinite-dimensional system that handles the medium anisotropy and provides a common basis for analytical robustness results. This function is used as a control-Lyapunov function and allows the amplitude and nonlinear shape constraints in the control action to be dealt with. Finally, the Brief addresses important application- and implementation-specific concerns. In particular, the coupling of the PDE and the finite-dimensional subsystem representing the evolution of the boundary condition (magnetic coils) and the introduction of profile-reconstruction delays in the control loop (induced by solving a 2-D inverse problem for computing the magnetic flux) is analyzed. Simulation results are presented for various operation scenarios on Tore Supra (simulated with METIS) and on TCV (simulated with RAPTOR). Control of the Safety Factor Profile in a Tokamak will be of interest to both academic and industrially-based researchers interested in nuclear energy and plasma-containment control systems, and graduate students in nuclear and control engineering |
| Analysis |
engineering |
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kernfysica |
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nuclear physics |
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controle |
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control |
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Engineering (General) |
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Techniek (algemeen) |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Tokamaks -- Safety measures
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Ingénierie.
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Tokamaks -- Safety measures
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| Form |
Electronic book
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| Author |
Witrant, Emmanuel, author
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Prieur, Christophe, author
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| ISBN |
9783319019581 |
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3319019589 |
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130619976X |
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9781306199766 |
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