School of Engineering and Physics, The University of the South Pacific, Laucala Campus, Fiji.
School of Computing, Information and Mathematical Sciences, The University of the South Pacific, Laucala Campus, Fiji.
ISA Trans. 2018 Sep;80:371-380. doi: 10.1016/j.isatra.2018.07.019. Epub 2018 Jul 25.
In this paper, fractional-order time delay system modeling is presented using Haar wavelet operational matrix of integration. Therefore, it does not require any prior knowledge of transfer function structure or partial information about fractional differentiation order. It allows the estimation of the implicit time delay parameter together with other model parameters by utilizing new delay operational matrix of Haar wavelet based on Riemann-Liouville definition. The proposed technique reduces the complexity of identification by converting the complex fractional calculus equations into simple algebra. The efficacy of the approach is verified on various integer and non-integer (fractional) order systems in simulation. For realistic condition, proposed method is verified in the presence of noise in simulation and also demonstrated on the real-time process control temperature system.
本文提出了一种使用 Haar 小波积分运算元对分数阶时滞系统进行建模的方法。因此，它不需要任何关于传递函数结构或分数阶导数部分信息的先验知识。它通过利用基于黎曼-利奥维勒定义的新的 Haar 小波延迟运算元，可以估计隐式延迟参数以及其他模型参数。该方法通过将复杂的分数微积分方程转换为简单的代数，降低了识别的复杂性。该方法在各种整数和非整数（分数）阶系统的仿真中得到了验证。为了模拟实际情况，该方法在仿真中存在噪声的情况下进行了验证，并在实时过程控制温度系统上进行了演示。
