基于模式运动的一类复杂生产过程的状态反馈渐近稳定性

State feedback asymptotic stability of a kind of complex production processes based on pattern moving

针对基于模式运动描述的一类复杂生产过程的稳定性,给出了系统稳定的定义,提出了分析与判断系统渐近稳定的方法和充分条件.首先,介绍了基于模式运动的控制系统动力学描述方法.针对描述方法中的强非线性的分类、度量映射难以采用可运算函数描述的问题,推导并建立了相应的控制系统非线性状态空间模型.然后,利用李雅普诺夫稳定性理论研究了在状态反馈控制下时间离散、状态离散的非线性系统渐近稳定的充分条件,建立了系统输出的类别划分、状态空间模型的线性部分系统矩阵与系统渐近稳定的关系.最后,采用烧结机实际生产数据与非线性数值算例对该方法进行了仿真实验,结果验证了所提条件的有效性.

Considering the stability of a kind of complex production processes based on pattern moving, system stability is defined, analysis methods and sufficient conditions of asymptotic stability are proposed. Firstly, the method of system dynamics description based on pattern moving is introduced, and the nonlinear state space model is put forward for the problem that it is hard to describe the nonlinear classification and measurement mappings by computable functions. And then sufficient conditions of discrete-time and discrete-state system asymptotic stability are given based on the Lyapunov stability theory, the relations between class partition of system output, the matrix of the linear part of the state space model and the asymptotic stability are established. Finally, simulation experiments using data of an actual sintering process and nonlinear numerical examples are carried out to demonstrate the validity of the proposed conditions.