Stability Proof of Gain-Scheduling Controller for Skid-to-Turn Missile Using Kharitonov Theorem

Abstract

Gain scheduling is one of the most popular nonlinear control design approaches which has been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide application of gain scheduling controllers, there is a notable lack of analysis on the stability of these controllers. The most common application of these kinds of controllers is in the field of flight control and autopilots. The main goal of this paper is to apply a methodology to prove stability of a gain scheduled controller used in directing Skid-to-Turn missiles. One of the most widespread applications of gain scheduling controller is the main problem of this paper. To design the controller we use pole placement in state feedback controllers and a kind of innovative interpolation to reduce jumping in gains related to changing the flight conditions. Finally we utilize root locus and Kharitonov’s Theorem to prove stability of the linearized plant. The presented approach for stability analysis is distinctive in the literature.