Robust control of cart-pendulum dynamics against uncertain multiple time delays

Abstract

We consider a fixed control law on a well- known underactuated dynamics, the cart-and-pendulum system. The contributory aspect of this research which is different from the traditional treatment is that, the feedback line is affected by multiple independent time delays. It is known that time-delayed LTI systems may exhibit multiple stable operating zones (pockets) in the space of delays. But finding these pockets analytically and demonstrating them experimentally are complex and challenging problems. The main aim of this effort is to accomplish a successful trajectory tracking on a practical, underactuated mechanical system under the presence of multiple time delays. First, we model the system as precisely as we can and over this model we use a powerful methodology for handling the delays. This method is called cluster treatment of cluster treatment of characteristic roots (CTCR) which reveals the stability pockets in the delay space. Then, we experimentally verify the analytical findings of CTCR. As a novel contribution to the controls area, this study shows that underactuated systems with multiple delays may exhibit better performance (such as faster disturbance rejection capability) for larger delay values when they are properly selected. This is a counter-intuitive outcome of the study, and it enables us to utilize 'delay scheduling' procedure. In delay scheduling, we declare the set of larger delays (than those that are present) for which the control routine performs better. This procedure offers to the control system designer a powerful tool.