Robust Stabilization Design via Delayed Feedback Control and Its Applications

点击翻译按钮获取中文摘要

The purpose of the present research is to disclose the ability of the delayed feedback control cited in the area of chaos control, and to establish the design method with a view to applying it to various engineering problems. The delayed feedback has some merit in robustness, but its applicability has been long unclear. We have shown that it can really stabilize if the associated unstable poles are of even number, and if it is allowed to use a compensator, first-order compensator with an unstable pole is sufficient for stabilizing a system with an odd number of unstable poles. In this project, we have shown under a mild condition that approximating a stabilizing derivative controller by a difference can yield a stabilizing delayed feedback controller. However, it has been also shown that such replacement does not work for a special class of multi-input multi-output systems. Further we have obtained criteria which determine if such a difference approximation is successful to preserve the closed-loop stability. It is also clarified that the difference approximation is superior in the closed-loop stability to other alternate means such as realization by a sampled-data system and the derivative feedback with a small delay.As an application, we have adopted a cart-pendulum system moving on a curving surface. A guide of design is to firstly design a stabilizing derivative feedback and secondly replace it by a difference counterpart and adjust the delay involved to obtain a good overall performance where an LMI approach is effective. While simulation is favorable, in the experiment we have faced with some oscillations of cart motion, and still the cause is undetermined.