离散时间系统采样零动态的稳定分布  

Stability Distribution of Sampling Zero Dynamics of Discrete-time System

作　　者：曾诚[1,2] 梁山[2] 

机构地区：[1]贵州理工学院理学院,贵州贵阳550003 [2]重庆大学自动化学院,重庆400044

出　　处：《信息与控制》2015年第3期328-333,345,共7页Information and Control

基　　金：国家自然科学基金资助项目(60574003;61403055);重庆市科委自然科学基金计划资助项目(cstc2012jj A40026);贵州省科学技术基金资助项目(黔科合LH字[2014]7364号;黔科合J字LKG[2013]46号)

摘　　要：为解决采样过程中离散系统零动态的稳定性通常不能保存,影响了镇定控制器设计的问题,针对相对阶为2的线性连续时间系统,分析了零阶保持器(zero-order hold,ZOH)条件下的离散时间系统描述,并且导出了相应离散化采样零动态的关于采样周期T的近似幂级数表达形式.给出的结果包括关于采样零动态渐近性质的线性近似公式,以及保证其稳定的条件,提升了采样零动态的精确程度.特别地,该稳定条件还可用于一类非线性控制系统采样零动态稳定性的判别.The stability of discrete system zero dynamics is not always presented in the sampling process, and it deeply limits the achievable control performance for controller design. To solve this problem, we analyze the representation for discrete-time models and derive the discretization dynamics properties of sampling zero dy- namics for a linear discrete-time system corresponding to a continuous-time system with relative degree two in the case of a zero-order hold. More importantly, we also provide approximate expressions of sampling zero dynamics in the form of a power series expansion up to the fourth order term for sampling periods. Meanwhile, the asymptotic behavior of sampling zero dynamics is discussed for small sampling periods and a new stability condition, which is an extension of the previous results, is derived. The condition for ensuring the stability of sampling zero dynamics of the desired linear model is also extended. It assures the stability of sampling zero dynamics in nonlinear control systems.

关 键 词：采样零动态 离散时间系统 稳定分布 线性控制系统 非线性控制系统 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]