stabilization of the current profile in tokamak plasmas via an LMI approach

Abstract

This paper deals with the H∞ stabilization of the spatial distribution of the current profile of tokamak plasmas using a Linear Matrix Inequalities (LMIs) approach. The control design is based on the one dimensional resistive diffusion equation of the magnetic flux that governs the plasma current profile evolution. The feedback control law is derived in the infinite dimensional setting without spatial discretisation. The proposed distributed control is based on a proportional-integral state feedback taking into account both interior and boundary engineering actuators. Supporting numerical simulations are presented and tuning of the controller parameters attenuating uncertain disturbances is discussed.

Robust control design of semilinear parabolic partial differential systems: A fuzzy approach

“…For solving the H ∞ problem we follow an idea, proposed in [28], and carry out conditions that guarantee the negative definiteness of the form…”

“…to ensures the negative definiteness of Φ γ in (28). This inequality can be used to compute robust gain k u , ∀γ > 0.…”

“…The robust control design problem of linear partial differential systems operating under uncertainty conditions has been particularly widely studied and published see [12], [13], [14], [15], [16], [17], [32], [28], [29] and references therein. Thus it is of interest to develop methods that are capable of using nonlinear partial differential models and of providing the desired system performance.…”

A New State-Space Representation for Coupled PDEs and Scalable Lyapunov Stability Analysis in the SOS Framework

“…Additional work on the use of computational methods and LMIs for computing Lyapunov functions for PDEs can be found in the work of [9], [10], [11]. Other examples of LMI methods for stability analysis of PDEs include [12]. This Recently, Sum-of-Squares (SOS) optimization methods have been applied to the problem of finding Lyapunov functions which prove stability of vector-valued PDEs.…”

Fixed‐Structure ℋ∞ Controller Design for Systems with Polytopic Uncertainty: An LMI Solution

“…The problems of disturbance rejection, evaluating the performance of the feedback system, and assessing the robustness with respect to unstructured uncertainties all can be cast as H ∞ problems. As present, there are widespread applications known for H ∞ control in engineering fields . In addition, the problem of robust H ∞ control that also considers the uncertainties in the dynamical model of the systems has attracted the interest of a large number of researchers over the past two decades .…”