Feedback Stabilization of Distributive Systems with Applications to Plasma Stabilization

Abstract

Theories for the feedback stabilization and control of dynamical systems with finite degrees of freedom have been extensively developed. The extension of some of these theories to systems with infinite degrees of freedom has been made only recently [1–2]. In the area of plasma stabilization, most studies have been associated with various thermonuclear plasma confinement schemes involving static magnetic field configurations or specified forms of high-frequency electromagnetic fields [3–6]. Recently, attempts have been made in using feedback to suppress certain forms of plasma oscillations [7–11] and to stabilize the unstable equilibria of hydromagnetic systems [12]. An important advantage of this approach is that the undesirable effects of system parameter variations may be reduced with the proper introduction of feedback and thereby relaxing the required tolerances in the system components such as the confining magnetic field structures. Further studies in this approach may lead to alternate practical means of plasma stabilization.