Quantitative Characterization of Easily Controllable Systems Considering Physical Constraints

考虑物理约束的易控制系统的定量表征

• 批准号: 14550439
• 负责人: HARA Shinji
• 金额: $ 1.92万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14550439/
• 关键词: Feedback control system; Integrated design; Control performance limitation; Unstable poles; zeros; Finite frequency property; Linear matrix inequality; Sampled-data control; Nonlinear control system

The purpose of the research project is to characterize easily controllable dynamical systems under physical constraints and to propose a new integrated design method for plant and controller in feedback control systems. The following three issues have been investigated.1)Control performance limitation :We have examined the best achievable H_2 control performance under physical constraints for LTI systems including continuous-time systems, discrete-time systems, and sampled-data systems. A unified approach to derive analytical closed form expressions for the limitations has been proposed. The results clearly demonstrate the deteriorations caused by the plant gain characteristics as well as unstable poles/zeros of the plant, and some engineering applications have been provided.2)Finite frequency KYP lemma :We have first developed a necessary and sufficient condition for an S-procedure to be lossless, and used the result to generalize the Kalman-Yakubovic-Popov (KYP) lemma in two aspects ---the finite frequency range and the class of systems ---and to unify various existing versions by a single theorem. It has been shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain/phase properties in several frequency ranges. A soft wear tool for the analysis and synthesis has been also developed on MATLAB.3)Nonlinear control system :We have investigated the easiness and difficulties of controlling a class of non-holonomic systems. Especially, we have shown that the there exists no continuous control input which achieves complete tracking with set point of non-equilibrium point for both linear and nonlinear dynamical systems.

该研究项目的目的是表征物理约束下易于控制的动力系统，并提出一种新的反馈控制系统中的被控对象和控制器的集成设计方法。研究了以下三个问题。1)控制性能限制：我们研究了LTI系统在物理约束下可实现的最佳H_2控制性能，包括连续时间系统、离散时间系统和采样数据系统。已经提出了一种导出限制的解析闭合形式表达式的统一方法。结果清楚地证明了受控对象增益特性以及受控对象不稳定极点/零点引起的恶化，并提供了一些工程应用。2）有限频率KYP引理：我们首先提出了S过程无损的充要条件，并利用该结果从有限频率范围和系统类别两个方面推广了Kalman-Yakubovic-Popov（KYP）引理。 ---并通过一个定理统一各种现有版本。事实证明，我们的结果使我们能够解决某一类系统设计问题，并在多个频率范围内对增益/相位特性进行多种规范。在MATLAB上还开发了用于分析和综合的软磨损工具。3）非线性控制系统：我们研究了控制一类非完整系统的难易程度。特别是，我们已经证明，对于线性和非线性动力系统，不存在能够实现对非平衡点设定点的完全跟踪的连续控制输入。

项目成果

Time domain interpretations of frequency domain inequalities on (semi)finite ranges

• DOI: 10.1016/j.sysconle.2004.11.007
• 发表时间: 2005-07
• 期刊: Syst. Control. Lett.
• 作者: T. Iwasaki;S. Hara;Alexander L. Fradkov

Best tracking and regulation performance under control energy constraint

• DOI: 10.1109/tac.2003.815012
• 发表时间: 2003-08
• 期刊: IEEE Trans. Autom. Control.
• 作者: Jie Chen;S. Hara;Gang Chen