奇异摄动系统的高频动态分析和设计

Many physics systems have multi-time scale property, which usually be modelled as singularly perturbed model. Singular perturbation and time scale decomposition is an efficient technique to deal with such complex systems, coupled with fast and slow dynamics.However,when considering the optimization analysis and design, the exist technique considered it in the overall frequency,resulting of more conservatism for design and thus can not apply it to the industry control efficiently, since it did not realize the singularly perturbed systems have the different property in frequency scale.This project will combine the time-scale decomposition and its inherent frequency property, suggesting a new control strategy:composite、coordination control based on time-scale decomposition and frequency-scale decomposition. The project start from H∞ robust tracking of singularly perturbed systems, using generalized KYP lemma to study how the frequency values in high and low frequency affect the tracking performance of the original systems; Moreover,using the new optimization model to study the H∞ filtering in the finite frequency;Using the Generalized KYP lemma and Lambert-W function to study the composite controller in the finite frequency, moreover study the H∞ filtering for the delayed singularly perturbed systems in the finite frequency;Using the generalized internal model and UIO-based observer to study the fault diagnosis for the delayed singularly perturbed systems in the finite frequency, furthermore, design the fault tolerant controller. Apply the corresponding results to the fault diagnosis and detection of the power system.

大量实际系统都具有多尺度特性，通常被建模成奇异摄动模型。时标分解技术是处理这类快、慢动态耦合复杂系统的有效工具。但现有的时标分解技术不区分该类系统在低频段和高频段的不同特性，均作全频处理，这给系统优化设计带来很大的保守性且无法有效应用于工程实际。为此，本项目拟将快、慢分解的经典控制思想与奇异摄动系统自身的频率特性相结合，提出并研究一类分时标、分频标的复合协调控制策略。以奇异摄动系统有限频段 H∞控制为突破口，寻找快、慢尺度动态最佳分频点，进而研究奇异摄动系统有限频段H∞滤波器设计；采用广义KYP引理和Lambert-W函数，研究时滞奇异摄动系统在有限频段上的复合控制器设计，进而研究时滞奇异摄动系统H∞ 滤波；采用广义内模定理和基于未知输入观测器研究时滞奇异摄动系统在有限频段的故障诊断及检测技术，进而设计时滞奇异摄动系统的附加容错控制器。并将项目所提关键技术应用于电力系统故障诊断和检测中。

大量实际系统的设计都是在有限频段内进行的，为此本项目针对奇异摄动系统的快、慢动态特性提出分时标、分频标控制策略，并在此框架下展开了系列的工作：研究了奇异摄动系统在有限频段上的H∞控制技术，利用广义KYP引理和内膜定理，给出奇异摄动系统在有限频段上满足H∞鲁棒跟踪解存在的充分条件；研究了奇异摄动系统在有限频段上的正实引理，利用广义KYP引理和线性矩阵不等式方法，给出奇异摄动系统在有限频段内正实的充分必要条件；研究了时滞奇异摄动系统在有限频段内的H∞性能分析，利用Lyapunov方法给出该系统在有限频段内满足H∞性能的时滞依赖条件；研究了时滞奇异摄动系统在有限频段上的H∞滤波器设计，利用投影定理给出该系统在有限频段上滤波器设计的一般框架；研究了时滞奇异摄动系统在有限频段上的故障诊断和容错控制技术，利用W-lambert函数和广义Luenberger观测器方法给出时滞奇异摄动系统当执行器发生故障时的容错控制技术。并将上述技术应用到电力系统故障诊断和检测技术中。项目研究成果可以为时滞奇异摄动系统的研究提供新的思路和视角。