Δ变换与数字控制器误差分析

Error Analysis of Digital Controller Using δ Operators

当采样周期T→ 0时 ,Δ变换描述的离散模型收敛于连续系统 .引入Δ变换离散方法 ,分析δ算子的浮点误差 .以二阶系统为算例 ,在离散域内设计极点配置控制器 ,跟踪理想输出 .仿真结果表明 ,与z算子相比 ,在计算机有限字长实现时 ,δ算子受舍入截尾扰动的影响较小 ,精度高 。

A discrete model described by Δ transform converges to its continuous counterpart as sample time T→0.Introducing Δ transform as a new digital control method.This paper analyses the floating error of the corresponding δ operator and designs a poleassignment controller to track ideal output directly in discrete field.The simulation results from a 2 order system show that δ operator has better performance for round off noise caused by finite word length,higher accuracy and stability than z operator.