Abstract
In this paper we present a control study of the Lorenz system via feedback linearization using the Rayleigh number as a control variable. The effects of the state transformation on the dynamics of the system are studied first. Then, composite controls are derived for both stabilization and tracking problems. The transition through the manifold where the state transformation is singular and the system is insensitive to the control is achieved by inducing the natural chaotic response of the system within a boundary layer. Outside the boundary layer, the control designed via feedback linearization is applied. Tracking problems that involve single and cooperative objectives are studied by using differential flatness. A good understanding of the system dynamics proves to be invaluable in the design of better controls.
Get full access to this article
View all access options for this article.