Optimal design of two-degree-freedom control systems with preview feedforward based on noncausal inversion

基于非因果反演的预前馈二自由度控制系统优化设计

• 批准号: 18560444
• 负责人: SOGO Takuya
• 金额: $ 1.79万
• 依托单位: Chubu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18560444/
• 关键词: preview feedforward control; noncausal inversion; sampled-data systems; unstable zero; inverse problem; integral equation

For this research project, it was investigated that the design problem of an infinite-time preview feedforward controller from the viewpoint of the model-matching problem based on the two-sided Laplace transform. It was shown that the so-mlled preview-based stable inversion for linear time-invariant systems is equivalent to the noncalisal solution to the model-matching problem. The preview feedforward controller can be easily discussed in the frequency domain where the design method for the optimal feedback controller has already been established. Moreover, with the same approach as stable inversion, we derived a transfer-function representation for the algorithm of adjoint-based iterative learning control. This indicates that the algorithm can be applied to infinite-dimensional systems such as flexible structures. This was demonstrated through an experiment on the tip control of a flexible arm.Next, preview feedforward control for sampled-data systems was investigated. Since the transfer function of sampled-data systems with a short sampling period frequently has zeros outside the unit circle, it is recognized that iterative learning control (ILC), which is an iterative approach to obtain an inversion of a system, cannot be applied to such systems. In order to overcome this difficulty, we introduced a non-causal bounded inversion to a sampled-data system and investigate the limiting property of the inversion. It was demonstrated that a simple relation between the n-th differential operator and n Euler operators that are included in the pulse transfer function of the n-th integral element. Based on this relation, it was proved that the inversion of the sampled-data system approximates its continuous-time counterpart in a non-causal framework. This result suggests that ILC can be applied to sampled-data systems in this framework.

本研究项目从基于双边拉普拉斯变换的模型匹配问题的角度研究了无限时间预览前馈控制器的设计问题。结果表明，线性时不变系统的基于预览的稳定反演等价于模型匹配问题的非校准解。预览前馈控制器可以在频域中轻松讨论，其中最优反馈控制器的设计方法已经建立。此外，采用与稳定反演相同的方法，我们推导了基于伴随的迭代学习控制算法的传递函数表示。这表明该算法可以应用于柔性结构等无限维系统。这通过柔性臂尖端控制的实验得到了证明。接下来，研究了采样数据系统的预览前馈控制。由于具有短采样周期的采样数据系统的传递函数经常在单位圆之外具有零点，因此人们认识到迭代学习控制（ILC）是一种获得系统反演的迭代方法，不能应用于这样的系统。为了克服这个困难，我们向采样数据系统引入了非因果有界反演，并研究了反演的限制性质。证明了第n个积分元件的脉冲传递函数中包含的第n个微分算子和n个欧拉算子之间的简单关系。基于这种关系，证明了采样数据系统的反演近似于非因果框架中的连续时间反演。这一结果表明 ILC 可以应用于该框架中的采样数据系统。

项目成果

サンプル値逆系による連続時間逆系の近似とその反復学習制御への応用〜両側z変換による逆問題への代数的アプローチ

使用采样逆系统逼近连续时间逆系统及其在迭代学习控制中的应用 - 使用两侧 z 变换的逆问题代数方法

• 发表时间: 2007
• 期刊: 計測自動制御学会論文集 43
• 作者: Eisuke Ikuta;Michio Miyano;Fumio Nagashima and Jun Ozaki;田中友博,川上哲太朗;川上哲太朗,青木由香利;田中 友博;川上 哲太朗;川上 哲太朗;川上 哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;田中 友博;川上哲太朗;川上哲太朗;Takuya Sogo;Takuya Sogo;十河 拓也
• 通讯作者: 十河 拓也

不安定零点を持つサンプル値フィードバック系の予見的フィードフォワード補償と反復学習制御

零点不稳定样本值反馈系统的预期前馈补偿与迭代学习控制

• 发表时间: 2007
• 作者: Eisuke Ikuta;Michio Miyano;Fumio Nagashima and Jun Ozaki;田中友博,川上哲太朗;川上哲太朗,青木由香利;田中 友博;川上 哲太朗;川上 哲太朗;川上 哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;田中 友博;川上哲太朗;川上哲太朗;Takuya Sogo;Takuya Sogo;十河 拓也;Takuya Sogo;十河 拓也;十河 拓也
• 通讯作者: 十河 拓也

Approximation of continuous-time inverse systems with the sampled-data counterparts and its application to iterative learning control : An appoarch to inverse problems with the two-sided z transform

具有采样数据对应项的连续时间逆系统的逼近及其在迭代学习控制中的应用：双边 z 变换逆问题的方法

• 发表时间: 2007
• 期刊: Transactions of the Society of Instrument and Control Engineers 43-1
• 作者: Eisuke Ikuta;Michio Miyano;Fumio Nagashima and Jun Ozaki;田中友博,川上哲太朗;川上哲太朗,青木由香利;田中 友博;川上 哲太朗;川上 哲太朗;川上 哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;田中 友博;川上哲太朗;川上哲太朗;Takuya Sogo;Takuya Sogo;十河 拓也;Takuya Sogo
• 通讯作者: Takuya Sogo

Inversion of sampled-data system approximates the continuous-time counterpart in a noncausal framework

采样数据系统的反演近似于非因果框架中的连续时间对应物

• 发表时间: 2008
• 期刊: Automatica 44
• 作者: Eisuke Ikuta;Michio Miyano;Fumio Nagashima and Jun Ozaki;田中友博,川上哲太朗;川上哲太朗,青木由香利;田中 友博;川上 哲太朗;川上 哲太朗;川上 哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;川上哲太朗;田中 友博;川上哲太朗;川上哲太朗;Takuya Sogo
• 通讯作者: Takuya Sogo

「研究成果報告書概要(和文)」より

摘自《研究结果报告摘要（日文）》

• 发表时间: 2005
• 作者: Kawauchi;et. al.;Nishimura et al.;Dezawa et al.;Yoshizawa et al.;星野 幹雄;星野 幹雄
• 通讯作者: 星野 幹雄