基于有无重复极点加滞后模型的参数辨识方法  

Parameter Identification Method Based on Repetitive and Non-repetitive Pole Plus Delay Model

作　　者：李闯 王亚刚[1] LI Chuang;WANG Yanggang(College of Optoelectronic Information and Computer Engineering,Shanghai University of Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学光电信息与计算机工程学院,上海200093

出　　处：《信息与控制》2020年第3期315-322,共8页Information and Control

基　　金：国家自然科学基金资助项目(61074087,61703277);国家自然科学基金青年基金资助项目(11502145)。

摘　　要：系统辨识方法一般分为非参数辨识和参数辨识,本文介绍一种新的参数辨识方法.本文采用两种传递函数模型拟合被控对象,求取传递函数在频域的拉普拉斯形式,在此基础上仅需要进行两次微分处理,就可以获得参数求解的积分公式.通过Matlab中的Simulink仿真得到开环和闭控制系统下被控对象的阶跃响应输入输出数据,引入合适的阻尼因子带入拉普拉斯公式,然后编写Matlab程序利用梯形积分算法计算得到传递函数及其一次和二次微分公式的值.当传递函数模型采用重极点加滞后模型时,模型只有两个未知参数,可以根据传递函数及其一次和二次微分公式的关系直接计算出来;当传递函数采用二阶加滞后模型时,模型有三个未知参数,本文采用一种极小化误差方法-最小二乘法来计算参数.最后,给出了六种类型的仿真被控对象,分别用两种辨识模型对其中的三种对象进行辨识,并和近年来的辨识方法进行对比,通过Matlab仿真来观察给定模型和辨识模型Nyquist图以及输出误差值,结果表明本文辨识方法算法简单,计算量小,辨识的精度高且鲁棒性好.System identification methods are generally divided into non-parametric identification and parameter identification.This study introduces a new parameter identification method.Two transfer function models are used to fit the controlled object,and the Laplacian form of transfer function in frequency domain is obtained.On this basis,only two differential treatments are required to obtain the integral formula of parameters.Simulink in MATLAB is used to obtain the input and output data of the step response of the controlled object under open and closed control systems.The appropriate damping factor is introduced into the Laplace formula.Then,the transfer function and its primary and secondary differential formulas are calculated using the trapezoidal integral algorithm in MATLAB.When the transfer function model adopts the multiple poles plus timedelay model,the model has only two unknown parameters,which can be calculated directly based on the transfer function and its first and second differential formulas.When the transfer function adopts the secondorder plus time-delay model,the model has three unknown parameters.This study adopts a minimization error-least square method to calculate the parameters.Finally,six types of simulation controlled objects are provided.Three of them are identified by two identification models compared with the identification methods in recent years.The Nyquist diagram and the output error value of the model and identification model are obtained through MATLAB simulation.Results show that the identification method in this study is simple and effective,and it has the advantages of small calculation,high identification accuracy,and good robustness.

关 键 词：模型辨识 参数求解 滞后 最小二乘法 MATLAB仿真 开环与闭环 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]