FULL-STATE FEEDBACK CONTROL DESIGN WITH “DELAY SCHEDULING” FOR CART-and-PENDULUM DYNAMICS

Abstract

A new approach is proposed to design fixed full-state feedback controllers for linear time invariant (LTI) systems with multiple time delays. This approach takes advantage of the recently introduced “delay scheduling” concept, which opens a new direction in synthesizing the control. “Delay scheduling” strategy suggests further prolonging the existing (and unavoidable) delays in order to recover stability or to improve the control performance features. To be able to do this, however, system should have multiple stable operating zones in the domain of the delays. The main contribution of this paper is to develop a procedure for designing a control law which facilitates such pockets. It starts with a selection of the feedback gains for non-delayed systems. We utilize a recent paradigm, Cluster Treatment of Characteristic Roots (CTCR), to examine the stability outlook when the delays are introduced in the dynamics. A scheme is also introduced to modify this gain structure so that the system exhibits a desirable set of stable pockets to facilitate the “delay scheduling”. The paper describes the methodology, without loss of generality, on a fully-actuated cart-pendulum system. Relevant experiments are carried out to show the viability of the proposed idea.