关于F(s)和F(z)对应性的研究

A study of the correspondence of F(s) and F(z)

在计算机测控系统上应用控制理论,首先要建立被控对象的时间离散的数学模型。把s传递函数近似转换成z传递函数的方法很多,用“L变换和Z变换表”得到的z传递函数对于脉冲输入的响应性能相当满意,然而对于阶跃输入的响应虽然形状相似而幅度相差太大以至于不能用。反之,用MATLAB的control-tools得到的z传递函数对于阶跃输入的响应性能相当满意,然而对于脉冲输入的响应虽然形状相似而幅度相差太大以至于不能用。这是每个应用计算机控制理论的工程师必须知道的知识。

The primary step for applying a control theory to any computer control system is to build up a math-model or the controlled object in discrete time. There are ninny methods to transform s-transfer functions into z-transfer functions. A z-transfer function taken from the tables of both Laplace transforms and Z-transforms will correspond well with the original s-transfer function responding to an impulse input, but not to a step input. However, a z-transfer function taken from the MATLAB control-tools will correpond well with the original s-transfer function responding to a step input, but not to an impulse input. It is a very important working knowleget, which is necessary for the engineers to apply the computer control theory.