线性延时系统的参数辨识及其在电路模型中的应用

Parameter Identification of Linear Delay System and Its Application in Circuit Model

摘要: 本文研究一类具有未知延时的线性系统的参数辨识问题。辨识问题包括延时估计和系统参数估计。首先，把延时和参数估计问题转化为具有遗忘因子的关于延时的非线性优化问题，借助Gauss-Newton法得到延时的估计，进而基于最小二乘方法得到系统参数估计。该辨识问题以实际电路系统为研究对象，充分考虑了延时和实际噪声的影响。最后，通过搭建实际电路系统，并以其输入和状态值作为实际测量数据，用本文所提辨识方法进行延时和系统参数辨识。验证结果表明了带有延时的线性微分方程模型的科学性和辨识方法的有效性。

Abstract: In this paper, the problem of parameter identification for a class of linear systems with unknown delay is studied. The identification problem includes the estimation of delay and system parame-ters. Firstly, the estimation of delay and parameters is transformed into a nonlinear optimization problem with forgetting factor, and the estimation of delay is obtained by Gauss-Newton method, then the parameters of the system are estimated based on the least square method. The problem of parameter identification takes the real circuit system as the research object and considers the effect of delay and real noise sufficiently. Finally, by building an actual circuit system and taking its input and state values as actual measurement data, the identification algorithm proposed in this paper is used to identify the delay and system parameters. The results show that the linear differential equation model with time delay is scientific and the method of identification is effective.