Full-state feedback controller design with “delay scheduling” for cart-and-pendulum dynamics

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 the feedback in order to recover stability or to improve the control performance features. To be able to do this, however, system should have large (and maybe multiple) stable operating zones in the domain of the delays. The main contribution of this paper is to develop a methodology for designing a control law to create this feature. The operation starts with a selection of the feedback gains for a stable non-delayed system. We then utilize a recent paradigm, Cluster Treatment of Characteristic Roots (CTCR), to examine the stability outlook when the delays are present in the dynamics. A scheme is also introduced to modify this gain structure so that the system exhibits a desirably large stable pocket(s) to enable 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.

Research highlights
► A methodology to synthesize a full state feedback control logic for LTI systems with delay.
► Delay scheduling concept, which facilitates to increase the existing delays to improve the stability and tracking performance features in the dynamics.