A Generalized Absolute Stability Approach to Dealing with Saturation Nonlinearities: Analysis, Design and Applications to Magnetic Bearing Systems

饱和非线性在工程系统中普遍存在。在控制系统中，每个物理执行器都受到最大和最小饱和限制。在这些最大和最小限制之间，物理执行器的输入输出特性通常既不是精确线性的，也不是确切已知的。因此，在许多高性能控制系统的分析和设计中，用标准的饱和函数来建模执行器特性是不够的。考虑执行器特性中的非线性和不确定性的一种直接方法是将分析和控制设计问题表述为经典的绝对稳定性问题，其中执行器特性被假设在线性扇区内。这种处理执行器非线性的方法导致了严重的保守性，因为两条直线是线性扇区的边界，不能紧密地约束执行器特性。该研究将发展一种广义绝对稳定性方法来分析和设计存在执行器非线性的线性系统。与经典的绝对稳定性理论相比，该方法的主要创新之处在于它允许执行器的非线性位于两条非线性曲线之间，而不是两条直线之间。PI的初步研究表明，该方法极大地改进了经典绝对稳定性理论所能得到的结果。所提出的研究有望为分析和控制设计的各个方面提供一套强有力的工具，包括在给定反馈律下的闭环系统性能评估，以及用于镇定、干扰抑制和输出调节的反馈律的设计。该项目的一个完整部分是对我们实验室的几个磁悬浮轴承系统进行实验验证。这项拟议的研究将通过推进磁悬浮飞轮储能技术和为磁悬浮人工心脏泵提供高效的控制设计而产生强大的社会影响。这项研究的其他更广泛的影响包括在控制理论、磁轴承和医学科学研究社区之间发展更密切的互动，以及在研究生和本科生水平上加强课程。

Saturation nonlinearities are ubiquitous in engineering systems. In control systems, every physical actuator is subject to maximum and minimum saturation limits. In between these maximum and minimum limits, the input-output characteristic of a physical actuator is often neither precisely linear nor exactly known. Thus, in the analysis and design of many high performance control systems, it is inadequate to model the actuator characteristic by a standard saturation function. A straightforward approach to accounting for the nonlinearities and uncertainties in the actuator characteristic is to formulate the analysis and control design problem as the classical absolute stability problem, where the actuator characteristic is assumed to be within a linear sector. Such an approach to dealing with actuator nonlinearities leads to severe conservativeness as the two straight lines, the boundaries ofa linear sector, cannot tightly bound the actuator characteristic.The proposed research will develop a generalized absolute stability approach to the analysis and control design of linear systems in the presence of actuator nonlinearities. In comparison with the classical absolute stability theory, the main innovation of this proposed approach is that it allows the actuator nonlinearities to reside in between two nonlinear curves, rather than two straight lines. The initial investigation by the PIs has shown that the proposed approach drastically improves the results that can be obtained by the classical absolute stability theory. The proposed research is expected to lead to a set of powerful tools for various aspects of analysis and control design, including the assessment of closed-loop performance under a given feedback law and the design of feedback laws for stabilization, disturbance rejection and output regulation. An integrated part of the project is to experimentally verify the obtained theoretical results on some magnetic bearing/suspension systems in our laboratory. The proposed research will have a strong societal impact by advancing magnetically suspended flywheel energy storage technology and by providing efficient control design for magnetically suspended artificial heart pumps. Other broader impacts of this research include the development of closerinteraction among the control theory, the magnetic bearings, and the medicalscience research communities and curriculum enhancement at the graduate and undergraduate levels.