A novel approach of fractional-order time delay system modeling based on Haar wavelet. (September 2018) - Kothari, Kajal; Mehta, Utkal; Vanualailai, Jito
Abstract: 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. Highlights: System identification in fractional-order using Haar wavelet operational matrices. The technique reduces the complexity of identification by converting the complex fractional calculus equations into simple algebra. Proposed method facilitates simultaneous estimation of time delay, differentiation orders and other model parameters. The real-time temperature control system is estimated by fractional order models and compared with classical models.