离散系统的初始条件剖析  

Analysis the Initial Conditions to the Discrete System With Simulating Block Diagram

作　　者：于德泳[1] 钱培怡[1] 

机构地区：[1]抚顺石油学院信息工程分院,辽宁抚顺113001

出　　处：《抚顺石油学院学报》2002年第1期52-54,共3页Journal of Fushun Petroleum Institute

摘　　要：N阶离散系统的分析 ,就是求解给定一组初始条件的差分方程。求解的方法分为经典的求解法和零输入响应加零状态响应法。齐解和零输入响应的形式在给定同一差分方程的条件下是相同的 ,确定齐解和零输入响应待定系数的初始条件是不同的。前者是激励和系统储能共同引起的 ,而后者仅是系统储能引起的。因此 ,为严格区分这两种性质不同的条件 ,有的教科书和文献称前者为初始条件 (0 + ) ,后者称之为起始条件 (0 -)。当差分方程描述的是因果系统 ,一般有 y(n) |n <0 一定是零输入响应的初始条件。但是 ,存在一个k >0使得 y(n) |n <k,一定是零输入响应的初始条件 ,而 y(n) |n≥k,一定是确定全解的初始条件。k值与系统的阶数及系统的结构相关联 。In the N th discrete system analysis,it is to determine the solution for differential equation. The methods are divided into classical method,that is to solute the complete solution that consists of the sum of a particular and homogeneous solution,and to determine the complete solution that consists of the zero input response and zero states response.The homogeneous solution and zero input are all the same on the form for the same the condition of the equations,but do not for the conditions with which to determine the facts of the homogeneous solution and zero input response.The former,complete solution,is excited by the input and stored energy of the system,and the later,zero input response,is only by stored energy of the system.Hence,in order to different from the conditions that have the different property,some textbooks know former as the initial condition(0 +) and later stert conditions(0 -).In the causal system,the differential equation descirbed,the y(n)| n <0 is must be the initial conditions of the zero input response.But,it is a k <0,making the y(n)| n<k is the conditions to determine zero input response and y(n)| n≥k must be the conditions to determine the complete solution. The k is related the order and the structure of the discrete system.The paper demonstrated the problems with the simulate block diagram of the discrete system.

关 键 词：差分方程 离菜系统 零输入响应 初始条件 时域分析 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] TP273[自动化与计算机技术—控制科学与工程]