Development and Application of control theory based on organic combination of algebraic and analytic methods

代数与解析方法有机结合的控制理论的发展与应用

基本信息

批准号：
15560375
负责人：
HAGIWARA Tomomichi
金额：
$ 1.92万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

Regarding stability analysis, the frequency response operators of sampled-data systems defined in the frequency domain have been utilized, and an associated theory for positive-realness has been completed. For example, the relationship between positive-realness and some eigenvalue conditions has been clarified, and an algebraic method for checking positive-realness has been established based on a inertia law about the eigenvalues of operators. Furthermore, regarding the Nyquist stability criterion for periodically time-varying systems, the two-regularized determinant about the associated frequency response operator was employed to lead to a new result based on the principle of argument. These results about stability analysis can readily be applied to robust stability analysis and robust performance analysis of sampled-data systems ; it can be said that they have laid a path to advanced methods for robust stability/performance analysis by properly bridging the gap between algebraic methods and analytic methods.As a side remark, some novel ideas have been derived from such fundamental analysis, and their basic properties have been partially derived. Also, regarding methods for discretization and reduction of continuous-time controllers, theoretical studies as well as numerical studies have been carried out. Through such studies, our future research direction has been suggested. Furthermore, regarding the analysis of periodically time-varying systems, some approximate methods have been introduced which does not require the solution of infinite-dimensional equations, and their effectiveness was clarified by establishing some convergence property via error analysis. Finally, as an example for demonstrating the effectiveness of our research direction, a new method has been shown that enables one to deal with the positive-realness analysis and the bounded-realness analysis of linear time-invariant systems in a systematic and transparent way.

关于稳定性分析，已经利用了频域定义的采样数据系统的频率响应算子，并且已经完成了正面真实性的相关理论。例如，已经阐明了积极现实与某些特征值条件之间的关系，并且基于关于操作员特征值的惯性法，已经建立了用于检查正面真实性的代数方法。此外，关于定期时间变化系统的Nyquist稳定性标准，采用了有关相关频率响应操作员的两次调节决定因素，从而基于参数原理导致新的结果。这些有关稳定性分析的结果可以轻松地应用于采样数据系统的稳健稳定性分析和稳健的性能分析。可以说，他们通过正确弥合代数方法和分析方法之间的差距，为稳健稳定/性能分析提供了高级方法的途径。作为旁注，一些新颖的想法是从这种基本分析及其基本分析中得出的。属性已被部分得出。同样，关于离散和减少连续时间控制器的方法，已经进行了理论研究以及数值研究。通过这样的研究，我们提出了我们未来的研究方向。此外，关于定期时间变化系统的分析，已经引入了一些近似方法，这些方法不需要解决方案的解决方案解决方案，并通过通过误差分析来建立某些收敛性来阐明它们的有效性。最后，作为证明我们研究方向有效性的一个例子，已经证明了一种新方法，它使人们能够以系统透明的方式处理线性时间不变系统的正面真实性分析和有限的真实性分析。