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Synthesis of robust control systems based on the unification of modelling and design

基于建模与设计统一的鲁棒控制系统综合

基本信息

批准号：
60550297
负责人：
KIMURA Hidenori
金额：
$ 0.96万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1985
资助国家：
日本
起止时间：
1985 至 1986
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60550297/
关键词：
robustness stability deadbeat control interpolation problem モデリング

项目摘要

The uncertainty included in the nominal model given to the design engineer crucially depends on the method of modelling and the data reliability. Therefore, to handle the uncertainty properly, it is necessary to take into account the process of modelling. In this sense, modelling and design are inseparably connected in the design of robust control systems. This is the principal viewpoint of this project.Our primary concern has been on the robust stabilization which is the most fundamental issue of robust control. We derived a necessary and sufficient condition for the existence of robust stabilizer based on classical Nevanlinna-Pick interpolation theory. In this project, this result for SISO systems has been extended to MIMO cases in the two directions. One is based on the harmonic function theory of contraction operators and the other is based on the "directional interpolation theory". In both approaches, a complete parametrization of all robust stabilizers is obtained. However, the problem of quantification of the model uncertainty in this parametrization remains to be solved.We also derived a method of designing robust deadbeat control both for SISO cases and MIMO cases. In this method, a robustness index is introduced that is closely related to the sensitivity of the closed-loop system. Under the constraint of deadbeat response, this robustness index is optimized. The resulting system exhibits superior performance with respect to parameter variation.Finally, we derive an effective method of generating signals for identification. Actually, this result establishes the effectiveness of minimum phase systems.Though the problem now seems to be much more difficult than we assumed at the start of this project and the results obtained are not much, it can be said that the basis for future developement is obtained.

提供给设计工程师的标称模型中包含的不确定性主要取决于建模方法和数据可靠性。因此，为了正确处理不确定性，有必要考虑建模过程。从这个意义上说，在鲁棒控制系统的设计中，建模和设计是不可分割的。这是本项目的主要观点，我们主要关注的是鲁棒镇定这一鲁棒控制中最基本的问题。基于经典的Nevanlinna-Pick插值理论，给出了鲁棒镇定器存在的充分必要条件。在这个项目中，SISO系统的这一结果已被扩展到MIMO情况下的两个方向。一种是基于压缩算子的调和函数理论，另一种是基于“方向插值理论”。在这两种方法中，一个完整的参数化的所有鲁棒稳定器。然而，在这种参数化的模型的不确定性的量化问题有待解决。我们还推导了一种方法，设计鲁棒无差拍控制SISO情况下和MIMO情况。在该方法中，鲁棒性指标是密切相关的闭环系统的灵敏度。在无差拍响应约束下，对该鲁棒性指标进行了优化。最后，我们推导出一种产生辨识信号的有效方法。实际上，这一结果确立了最小相位系统的有效性。虽然现在看来，这个问题比我们开始这个项目时设想的要困难得多，而且所获得的结果也不多，但可以说，为今后的发展奠定了基础。