Download Safety Factor Profile Control in a Tokamak by Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe PDF

By Federico Bribiesca Argomedo, Emmanuel Witrant, Christophe Prieur (auth.)

Control of the security issue Profile in a Tokamak makes use of Lyapunov concepts to handle a not easy challenge for which even the easiest bodily proper versions are represented via nonlinear, time-dependent, partial differential equations (PDEs). the reason for this is that of the spatiotemporal dynamics of shipping phenomena (magnetic flux, warmth, densities, etc.) within the anisotropic plasma medium.

Robustness concerns are ubiquitous within the research and regulate layout given that direct measurements at the magnetic flux are most unlikely (its estimation depends upon digital sensors) and massive uncertainties stay within the coupling among the plasma debris and the radio-frequency waves (distributed inputs).

The short starts with a presentation of the reference dynamical version and maintains via constructing a Lyapunov functionality for the discretized approach (in a polytopic linear-parameter-varying formulation). the constraints of this finite-dimensional strategy encourage new advancements within the infinite-dimensional framework. The textual content then tackles the development of an input-to-state-stability Lyapunov functionality for the infinite-dimensional method that handles the medium anisotropy and gives a standard foundation for analytical robustness effects. This functionality is used as a control-Lyapunov functionality and permits the amplitude and nonlinear form constraints within the keep watch over motion to be dealt with.

Finally, the short addresses very important program- and implementation-specific issues. particularly, the coupling of the PDE and the finite-dimensional subsystem representing the evolution of the boundary situation (magnetic coils) and the advent of profile-reconstruction delays within the regulate loop (induced by means of fixing a 2-D inverse challenge for computing the magnetic flux) is analyzed. Simulation effects are provided for varied operation eventualities on Tore Supra (simulated with METIS) and on TCV (simulated with RAPTOR).

Control of the security issue Profile in a Tokamak might be of curiosity to either educational and industrially-based researchers drawn to nuclear power and plasma-containment regulate structures, and graduate scholars in nuclear and keep an eye on engineering.

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Extra info for Safety Factor Profile Control in a Tokamak

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A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, volume 16 of Progress in nonlinear differential equations and their applications. 2). For control purposes, this model was spatially discretized (in N+2 ∂2 points) using the (finite-differences) midpoint rule to approximate the operators ∂r 2 ∂ and r1 ∂r . Details of the process used for the discretization and relevant implementation details can be found in [11]. The calculations are made to allow for a non-uniform spatial step distribution.

State z belongs to R Ne , where Ne = Nc + N . 2 Controller Synthesis In order to construct the polytopic control law, we must first define the vertices of the polytope. In the case considered in this chapter the polytope is, in fact, a scaled . hypercube constructed by defining the set of all partitions of N p = {1, 2, . . , n p } as 26 3 A Polytopic LPV Approach For Finite-Dimensional Control ⎦ . ⎤ Ω(N p ) = (C j , D j ) | C j ∩ D j = ≤, C j ∞ D j = N p . The cardinality of this set is car d Ω(N p ) = 2n p (each element can be, or not, in a given subset).

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