Multi-objective Robust Control System Design Based on Finite Frequency KYP Lemma and Its Applications

基于有限频率KYP引理的多目标鲁棒控制系统设计及其应用

• 批准号: 17360195
• 负责人: HARA Shinji
• 金额: $ 5.73万
• 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 (B)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17360195/
• 关键词: Control system design; Robust control; Multi-objective control; KYP lemma; Frequency characteristics; Linear matrix inequality

The purpose of this research project is to develop a unified theory of control synthesis based on the analytical results on generalized KYP lemma, which is a finite frequency version of the original KYP lemma Especially, our main focus are on a systematic design method considering the more practical situations and on the design algorithms.The results on the synthesis theory are as follows:(1) PID controller synthesis based on the generalized KYP lemma.(2) A time-domain interpretation of the generalized KYP lemma, which includes an equivalence of positive-realness in frequency-domain and passivity in time-domain as a special case. It is a first step of the investigation for nonlinear systems.(3) An SoS (Sum of Squares) decomposition characterization of the generalized KYP lemma The result is useful for plant design from the view point of control.(4) A dual characterization of the generalized KYP lemma and its computational complexity analysis.A analysis/synthesis tool box has been developed based on our theoretical results. We also implemented primal-dual algorithms for solving the generalized KYP based optimization problems and compared the computational costs. The comparison shows that the positive semi-definite optimization problems derived from the generalized KYP lemma are very hard to solve in general. This motivates us to develop a new algorithm considering the structure.

The purpose of this research project is to develop a unified theory of control synthesis based on the analytical results on generalized KYP lemma, which is a finite frequency version of the original KYP lemma Especially, our main focus are on a systematic design method considering the more practical situations and on the design algorithms.The results on the synthesis theory are as follows:(1) PID controller synthesis based on the generalized KYP lemma.(2) A广义KYP引理的时间域解释，其中包括频率域的正面真实性和时域的被动性等效。这是对非线性系统进行调查的第一步。（3）从控制角度来看，SOS（正方形之和）分解表征对植物设计的表征对植物设计很有用。（4）基于我们的合成工具盒，基于我们的计算复杂性分析了广义的KYP Lemma及其计算复杂性分析。我们还实施了原始二重算法，以解决基于广义的KYP优化问题并比较计算成本。比较表明，总体上很难解决从广义的KYP引​​理得出的阳性半明确优化问题。这激发了考虑到结构的新算法。

项目成果

Robust PID Using Generalized KYP Synthesis : Direct open-loop shaping in multiple frequency ranges

使用广义 KYP 综合的鲁棒 PID：在多个频率范围内直接开环整形

• 发表时间: 2006
• 期刊: Control System Magazine 26・1
• 作者: Shinji Hara;Tetsuya Iwasaki;Daisuke Shiokata
• 通讯作者: Daisuke Shiokata

Feedback control synthesis of multiple frequency domain specifications via generalized KYP lemma

• DOI: 10.1002/rnc.1123
• 发表时间: 2007-03
• 期刊: International Journal of Robust and Nonlinear Control
• 影响因子: 3.9
• 作者: T. Iwasaki;S. Hara

A Unification of Analytical Expressions for Control Performance Limitations via Reciprocal Transform

通过倒数变换统一控制性能限制的解析表达式

• 发表时间: 2007
• 作者: Shinji Hara;Tetsuya Iwasaki;Daisuke Shiokata;S. Hara
• 通讯作者: S. Hara