14 pagesInternational audience— In this paper, early lumping estimation of space-time varying diffusion coefficient and source term for a non-homogeneous linear parabolic partial differential equation (PDE) describing Tokamak plasma heat transport is considered. The analysis of this PDE is achieved in a finite dimensional framework using the cubic b-splines finite element method with the Galerkin formulation. This leads to a finite dimensional linear time-varying state-space model with unknown parameters and inputs. The Extended Kalman Filter with Unknown Inputs Without Direct Feed-through (EKF-UI-WDF) is applied to estimate simultaneously the unknown parameters and inputs and an adaptive fading memory coefficient is introduced in the EKF-UI-WDF, to deal with time varying parameters. Conditions under which the direct problem is well posed and the reduced order model converges to the initial one are established. Insilico and real data simulations are provided to evaluate the performances of the proposed technique
Abstract-In this paper, we investigate the problem of bilinear control of a solar collector plant using the available boundary and solar irradiance measurements. The solar collector is described by a first-order 1D hyperbolic partial differential equation where the pump volumetric flow rate acts as the plant control input. By combining a boundary state observer and an internal energy-based control law, a nonlinear observer based feedback controller is proposed. With a feed-forward control term, the effect of the solar radiation is cancelled. Using the Lyapunov approach we prove that the proposed control guarantees the global exponential stability of both the plant and the tracking error. Simulation results are provided to illustrate the performance of the proposed method.
: In this paper, the adaptive estimation of spatially varying diffusion and source term coefficients for a linear parabolic partial differential equation describing tokamak plasma heat transport is considered. An estimator is defined in the infinite-dimensional framework having the system state and the parameters' estimate as its states. Our scheme allows to estimate constant, spatially distributed and spatio-temporally distributed parameters as well as input with known upper bounds in time. While the parameters convergence depends on the plant signal richness assumption, the state convergence is established using the Lyapunov approach. Since the estimator is infinite-dimensional, the Galerkin finite-dimensional technique is used to implement it. In silico simulations are provided to illustrate the performance of the proposed approach.
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