Inherent Design Limitations for Periodic and Sampled-Data Feedback Systems

本提案的目标是推进采样数据和周期控制系统的现状。将对理论、应用和教学法作出贡献。将发展采样数据和周期性反馈系统的固有设计限制理论，以描述由于模拟装置中的非最小相位零、不稳定极点和时间延迟而导致的鲁棒性和性能权衡。已经提出了各种方法，通过故意引入采样或其他形式的周期控制来规避线性时不变系统中存在的设计限制。待开发的理论将用于批判这些方法。设计限制理论考虑了样本间行为，并表明一些所谓的抽样克服设计限制的优势是虚幻的，因为它们只考虑采样时刻的行为。用于开发结果的技术是复变量理论中的波德积分和泊松积分，并结合1950年代早期开发的用于计算采样数据系统中模拟信号对正弦输入的响应的方法。特别强调的是，离散频率响应依赖于模拟响应的混叠高频分量。这种依赖关系是由于高频模型误差导致的灵敏度和鲁棒性困难的原因。拟议研究的理论部分将与澳大利亚纽卡斯尔大学的里克·米德尔顿合作进行。对申请的贡献将在两个领域进行。首先，将开发分析技术，以使用频率响应图而不是模拟来评估采样数据控制设计的质量。其次，构建固有混合模型，以评估其带宽限制和设计难度程度。这样的系统可以在汽车应用中找到，其中发动机点火事件本质上是离散的，以及在等离子处理中使用的CCD相机和光学多通道分析仪等传感设备中找到。这项工作支持了密歇根大学在汽车排放控制和半导体制造领域正在进行的应用项目。对教育学的贡献来自于使用标准教科书中教授的技术来分析固有局限性和样本间行为。待开发的理论填补了目前存在于模拟理论和采样数据反馈系统理论之间的教育学空白。＊＊＊

Fruedenberg 9414822 The objectives of this proposal are to advance the current state of sampled-data and periodic control systems. Contributions will be made to theory, applications, and pedagogy. A theory of inherent design limitations for sampled-data and periodic feedback systems will be developed to describe robustness and performance tradeoffs due to nonminimum phase zeros, unstable poles, and time delays in the analog plant. Various methodologies have been proposed for circumventing design limitations present in linear time invariant systems by purposely introducing sampling or other forms of periodic control. The theory to be developed will be used to critique these methodologies. The theory of design limitations takes intersample behavior into account, and shows that some of the purported advantages of sampling for overcoming design limitations are illusory because they only consider behavior at sampling instants. The techniques to be used in developing the results are the Bode and Poisson integrals from complex variable theory in conjunction with methods developed in the early 1950's for computing the response of an analog signal in a sampled-data system to a sinusoidal input. Particular emphasis is placed upon the fact that the discrete frequency response depends on aliased high frequency components of the analog response. This dependence is responsible for sensitivity and robustness difficulties due to high frequency model error. The theoretical portion of the proposed research will be carried out in collaboration with Rick Middleton of the University of Newcastle, Australia. Contributions to applications will be made in two areas. First, analysis techniques will be developed for assessing the quality of a sampled-data control design using frequency response plots instead of simulations. Second, models of inherently hybrid will be constructed for the purpose of assessing their bandwidth limitations and degree of design difficulty. Such systems are found in automotive applications, where the engine firing event is inherently discrete, and in sensing devices such as CCD cameras and Optical Multichannel Analyzers which are used in plasma processing. This work supports ongoing applications projects at the University of Michigan in the areas of automotive emission control and semiconductor manufacturing. Contributions to pedagogy arise from the used of techniques taught in standard textbooks to analyze inherent limitations and intersample behavior. The theory to be developed fills a gap in pedagogy that currently exists between the theory of analog and of sampled-data feedback systems. ***