Identification of fractional order systems using modulating functions method

摘要: The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize to on-line fractional order systems based on Riemann-Liouville derivatives. First, a new integration by parts formula involving derivative function is given. Then, apply system, which derivatives input output can be transferred into ones functions. By choosing set functions, system algebraic equations obtained. Hence, unknown parameters estimated solving system. Using method, do not need any initial values are usually equal zero. Also estimate noisy output. Moreover, it shown that proposed estimators robust against high frequency sinusoidal noises due class stochastic processes. Finally, efficiency stability confirmed some numerical simulations.