饱和控制系统稳定性及干扰抑制研究

【作者】 魏爱荣；

【导师】 赵克友；

【作者基本信息】 山东大学 ， 控制理论与控制工程， 2006， 博士

【摘要】 饱和特性广泛的存在于现实控制系统中，但传统的控制理论又常漠视之，直至发生多起灾难事故后才引起学者关注。饱和是强非线性，它的加入增加了系统分析与设计的复杂性，如执行器饱和导致驱动力锁定而失去调节作用，传感器饱和导致信号锁定而不能反映信息变化，致使原设计性能大打折扣，以至恶化到不可想象地步。被控对象的特征不是一组数学公式所能完全反映的，更毋庸说运行中参数漂移了，故模型具有不确定性；由于反应物反应、输运及测量等会造成时延，因此含时滞的模型是反映实际的。上述饱和、不确定性及时滞不仅影响控制系统动态性能，而且使系统分析和设计变得困难。近些年来人们对饱和控制系统、不确定系统和时滞系统的研究各取得不少进展，人们也重视(上述情况)混合的饱和控制系统的研究，但仍欠深入，并有许多未解问题，影响实际应用。 在回顾和综述饱和受限控制的发展历程、国内外研究现状后，本文主要研究了以下问题并给出相应研究结论： ●单输出、多输出传感器饱和连续／离散时间系统稳定域估计； ●单输入执行器饱和连续／离散时间系统稳定域估计及控制器设计； ●单输入、多输入执行器饱和不确定连续／离散时间系统稳定域估计、干扰抑制及控制器设计； ●执行器饱和连续／离散时间不确定时滞系统稳定域估计、干扰抑制及控制器设计。 分析基于Lyapunov稳定性理论，综合基于迭代解Ricatti方程和LMI约束优化。 首先对单输入执行器饱和连续时间系统提出了基于饱和度函数的描述，运用Lvapunov直接法得到状态反馈闭环系统稳定性—全局渐近稳定(GAS)与区域渐近稳定(RAS)的判据，对RAS情况计算出不变吸引椭球，并提供了寻找能得到尽量大不变吸引椭球的反馈增益迭代法。已有结果多是在某些限制条件或需要烦琐的求解过程，与之不同的是本文用不变吸引椭球去对饱和受限系统的吸引域做估计，通过仿真和与其它文献比较，这个分析和设计方法简单且保守性低，并且对系统矩阵不加任何限制。然后把这一方法推广到单更多还原

【Abstract】 Saturating nonlinear actuators is one of the common nonlinearities, and exists in many practical situations. If the control system is designed to be stable without considering the saturation, the stability of the closed-loop controlled system can’t be guaranteed. In addition, as we know, it is almost impossible to obtain accurate mathematics model for object systems due to the complex dynamical behaviors in the practical control process under which the controller is designed is usually different to the real plant owing to some kinds of model approximation or reduction methods, and the difference can be regarded as a certain uncertainty. Since robust control theory is a powerful methodology of control law design for uncertain systems. On the other hand, it is well know that time delays can be encountered in various process due to the effect of transportation, measurement, reaction process, etc. A large number of practical systems can be modeled as time-delay systems. It is recognized that time delay often is the main source of instability and poor performance. Stability and performance are always the key issue in the control theory and control engineering, so the study of delay systems is noticed in the control theory literature. However there are few researches on saturating actuator systems in the exiting results on robust control theory. To the above systems there are several key issues to study deeply.With the survey of birth and development and the research on constrained systems, to systems with actuator/sensor saturation, uncertain saturating nonlinear continuous /discrete time systems, uncertain saturating continuous /discrete time systems with time delay, some issues are studied in detail in this thesis. Based on Lyapunov stability theory, Controller design strategies based on LMI and iterative ARE are developed.With the deeper analysis of state feedback single input linear system subject to actuator saturation, the paper presents a sufficient condition which guarantees the systems are GAS or RAS, calculates an invariant attractive ellipsoid for the更多还原