Robust Stabilization Design via Delayed Feedback Control and Its Applications

延迟反馈控制的鲁棒稳定设计及其应用

• 批准号: 13650494
• 负责人: KOKAME Hideki
• 金额: $ 0.45万
• 依托单位: Osaka Prefecture University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650494/
• 关键词: Delayed feedback; Stabilization; Cart-Pendulum System; Derivative feedback; 台車-倒立振子系

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.

本研究的目的是揭示在混沌控制领域引用的延迟反馈控制的能力，并建立设计方法，以期将其应用于各种工程问题。延迟反馈在鲁棒性方面有一定的优点，但其适用性一直不清楚。我们已经证明，它可以真正稳定，如果相关的不稳定极点是偶数，如果允许使用补偿器，一阶补偿器的不稳定极点是足够的稳定系统的奇数个不稳定极点。在这个项目中，我们已经证明了在一个温和的条件下，用一个差来逼近一个稳定的微分控制器可以得到一个稳定的延迟反馈控制器。然而，它也已被证明，这种替代不适用于一类特殊的多输入多输出系统。此外，我们已经得到的标准，确定如果这样的差分近似是成功的，以保持闭环稳定。本文还阐明了差分逼近在闭环稳定性方面上级其他替代方法，如采样系统实现和小时滞微分反馈。作为应用，我们采用了一个在曲面上运动的小车-单摆系统。设计的指导思想是首先设计一个稳定的微分反馈，然后用一个差分反馈代替它，并调整所涉及的延迟，以获得良好的整体性能，其中LMI方法是有效的。虽然模拟是有利的，但在实验中，我们遇到了推车运动的一些振荡，原因仍然不确定。

项目成果

H.Kokame, T.Mori: "Stability Preserving Transition from Derivative Feedback to Its Difference Counterparts"Proc. 15th IFAC World Congress. (CD-ROM). (2002)

H.Kokame，T.Mori：“从导数反馈到差分反馈的稳定性保持过渡”Proc。

H.Kokame, T.Mori: "A Tutorial on Stability and Stabilization of Delay-Differential Systems"SICE Annual Conference 2003. (発表予定).

H.Kokame、T.Mori：“时滞微分系统的稳定性和稳定性教程”SICE 年会 2003。（待提交）。

H. Kokame and T. Mori: "Stability Preserving Transition from Derivative Feedback to Its Differnce Counterparts"Proc. 15th IFAC World Congress. CD-ROM. (2002)

H. Kokame 和 T. Mori：“从导数反馈到差分反馈的稳定性保持过渡”Proc。

H. Kokame and T. Mori: "A Tutorial on Stability and Stabilization of Delay-Differential Systems"SICE Annual Conference. to appear. (2003)

H. Kokame 和 T. Mori：“时滞微分系统稳定性和稳定性教程”SICE 年会。