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首页> 外文期刊>American journal of applied sciences >Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations
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Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations

机译：时滞微分方程特征根的时延估计

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摘要

Problem statement: For ordinary dynamic systems (i.e., non-delayed), various methods such as linear least-squares, gradient-weighted least-squares, Kalman filtering and other robust techniques have been widely used in signal processing, robotics, civil engineering. On the other hand, time-delay estimation of systems with unknown time-delay is still a challenging problem due to difficulty in formulation caused. Approach: The presented method makes use of the Lambert W function and analytical solutions of scalar first-order Delay Differential Equations (DDEs). The Lambert W function has been known to be useful in solving delay differential equations. From the solutions in terms of the Lambert W function, the dominant characteristic roots can be obtained and used to estimate time-delays. The function is already embedded in various software packages (e.g., MATLAB) and thus, the presented method can be readily used for time-delay systems. Results: The presented method and the provided examples show ease of formulation and accuracy of time-delay estimation. Conclusion: Estimation of time-delays can be conducted in an analytical way. The presented method will be extended to general systems of DDEs and application to physical systems.
机译：问题陈述：对于普通动态系统（即无延迟），各种方法，例如线性最小二乘，梯度加权最小二乘，卡尔曼滤波和其他鲁棒技术已广泛用于信号处理，机器人技术，土木工程中。另一方面，由于公式化的困难，具有未知时延的系统的时延估计仍然是一个具有挑战性的问题。方法：提出的方法利用了Lambert W函数和标量一阶时滞微分方程（DDE）的解析解。众所周知，Lambert W函数可用于求解延迟微分方程。从关于Lambert W函数的解中，可以得到主要特征根并将其用于估计时间延迟。该功能已经被嵌入各种软件包（例如，MATLAB）中，因此，所提出的方法可以容易地用于时延系统。结果：所提出的方法和所提供的实例显示了易于制定和时延估计的准确性。结论：可以通过分析的方式来估计时延。提出的方法将扩展到DDE的一般系统，并扩展到物理系统。

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