Optimization of sampled-data systems with finite-dimensional linear continuousperiodic process and delay

具有有限维线性连续周期过程和延迟的采样数据系统的优化

基本信息

批准号：
316189657
负责人：
Professor Dr.-Ing. Torsten Jeinsch, since 11/2016
金额：
--
依托单位：
Institut für Automatisierungstechnik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2021-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/316189657?language=en
关键词：
Optimization sampled data systems finite

项目摘要

The project concerns the development of methods for the solution of H2 and L2 optimization problems for linear sampled-data systems. The systems consist of a linear continuous periodic multi-input multi-output (MIMO) process with arbitrary pure delays, and a MIMO controller, which is realized as a program on a digital processor. The connection between the continuous and digital parts is accomplished by an ideal analogue-to-digital converter and a zero-order hold with free selectable shape of the pulses. The sampling period Ts is synchronized with the period of the continuous process T, such that both commensurate. Let N>1 be a natural number. Then the following cases should be investigated: Ts=T (equally clocked), Ts=T/N (interpolating), and Ts=NT (decimating).The procedures should yield exact solutions and they also have to consider the intersample behavior. Despite of the theoretical and practical importance of the named class of problems, there does not exist systematic literature about it. The reason for that could be the absence of an appropriate mathematical tool.The chosen approach for the investigations is based on the parametric transfer matrix (PTM) concept. In preceding research projects, the applicant has refined this concept in theoretical directions, and in cooperation with his partners he also successfully applied it to various sampled-data control problems. Alternative approaches are not known, which are able to provide exact solutions, when all three difficulties are present:continuous periodic process + delay + sampling.On the way to the solution of the above formulated H2 and L2 optimization problems, the following steps have to be taken:* Floquet-Lyapunov transformation for extracting the dynamics and hosting them in the time-invariant part* Establishing the PTM for the open chain, and then for the closed loop* Construction of the parametrized set of all stabilizing controllers* Construction of the H2 norm and of the cost functional* Extension and application of the Wiener-Hopf method for the analytical solution* Programming of software tools and their integration into the Matlab-Toolbox DirectSD

该项目涉及线性采样数据系统的 H2 和 L2 优化问题的解决方法的开发。该系统由具有任意纯延迟的线性连续周期性多输入多输出 (MIMO) 过程和 MIMO 控制器组成，该控制器以数字处理器上的程序形式实现。连续部分和数字部分之间的连接是通过理想的模数转换器和具有自由可选脉冲形状的零阶保持来完成的。采样周期Ts与连续过程T的周期同步，使得两者相称。设N>1为自然数。然后应研究以下情况：Ts=T（同等时钟）、Ts=T/N（插值）和 Ts=NT（抽取）。该过程应产生精确的解决方案，并且还必须考虑样本间行为。尽管指定的一类问题具有理论和实践重要性，但尚不存在关于它的系统文献。其原因可能是缺乏适当的数学工具。所选择的研究方法基于参数传递矩阵 (PTM) 概念。在之前的研究项目中，申请人在理论方向上完善了这一概念，并与合作伙伴合作，成功地将其应用于各种采样数据控制问题。当所有三个困难都存在时，尚不知道能够提供精确解决方案的替代方法：连续周期过程+延迟+采样。在解决上述公式化的H2和L2优化问题的过程中，必须执行以下步骤采取：* 用于提取动力学并将其托管在时不变部分的 Floquet-Lyapunov 变换* 为开链建立 PTM，然后为闭环建立 PTM* 构建所有稳定控制器的参数化集* H2 范数和成本函数的构建* 解析解的 Wiener-Hopf 方法的扩展和应用* 软件工具编程及其集成到 Matlab-Toolbox DirectSD 中