一种非线性状态参数延时系统的离散化方法

A Discretization Method for Nonlinear State Delay Systems

为了得到非线性状态参数延时系统的离散模型,提出了一种非线性状态参数延时系统的离散方法。该方法基于泰勒级数和Scaling and Squaring技术,可以为非线性状态参数延时系统提供准确的离散模型。所得到的模型具有有限的维数,因此该模型可以用来设计相应的非线性控制器。当采样周期增大的时候,为了得到足够准确的离散模型,必须增加泰勒级数的阶数。但这样会大大增加计算的负担。通过利用Scaling and Squaring技术该离散方法可以解决大采样周期的问题。最后设计了一个非线性状态参数延时系统的仿真去验证该方法的有效性。

A method to obtain a sampled-data representation of the nonlinear state delay system is proposed based on the Taylor series and the scaling and squaring technique. This method can provide a precise sampled-data representation of the nonlinear state delay system. This sampled-data representation possesses the finite dimension to which the existing controller design techniques can be applied. When the sampling period is increased, the truncation order of the Taylor series must be enlarged to get the satisfied discretization results, whcich increases the computational burden greatly. By using the scaling and squaring technique, this discretization method can solve the problem of low sampling rates. The performance of the proposed discretization procedure was evaluated using a nonlinear state delay system：