连续时间传递函数的赋值化指数积分变换逼近辨识

Continuous-time transfer function identification based on approximations of value-assigned exponential integral transformation

中文关键词  传递函数  系统辨识  参数估计  指数积分变换  连续时间  逼近

英文关键词  transfer function  system identification  parameter estimation  exponential integral transformation  continuous time  approximation

中文摘要

      通过将常规的复域Laplace变换直接化简为实域上的指数积分变换,提出了连续时间传递函数辨识的赋值化指数积分变换逼近(AVE)方法.其主要特征是以采样序列为基础先行沿时间轴构造不同赋值下系统变量的指数积分变换(EIT)逼近,继而沿指数变量方向实现模型参数估计的二维化在线递推计算.文中分析了有限EIT逼近的渐近收敛性和时间连续化逼近的代数精度,以及具有一定噪声抑制能力的指数因子赋值条件.在一致激励和有界响应前提下, 通过相对复杂而苛刻的仿真算例,充分验证了AVE方法对各种典型工况的有效性,清晰表明了它对于最小相位及非最小相位系统, 开环或闭环的系统运行方式,乃至刚性参数情形, 所具有的宽泛适应性.

英文摘要

      In this paper a parameter identification method of continuous-time transfer function is proposed by means of the approximations of value-assigned exponential-integral-transformation (AVE) in real-domain simplified from common complex-domain Laplace transformation. The main feature is the online and recursive way in two-dimension space, that is, the exponential integral transformation (EIT) of system variables with different assignments is approximated along the timeline only by using sampling data, and then the model parameters are estimated along exponential variable axis. In addition, the asymptotical convergence and its algebraic accuracy of EIT approximation in finite time are analyzed, as well as the condition to choose exponential variable values with a certain extent suppression to sampling noise is discussed. Under bounded response with consistent excitation, the effectiveness of AVE method for various typical operating conditions is sufficiently simulated and verified by a relatively complex and harsh example, which clearly shows the wide adaptability to minimum phase or non-minimum phase system, open-loop or closed-loop running, or even stiff cases.