A bias correction method for fractional closed-loop system identification. (September 2015) - Yakoub, Z.; Chetoui, M.; Amairi, M.; Aoun, M.
Abstract : Highlights: A detailed study of the closed-loop system identification with fractional models in a noisy output context. Using the indirect approach, which supposes the prior knowledge of the controller, both coefficients and fractional orders of the process are estimated. A bias correction method is developed to deal with the bias problem in system identification without any restriction of the controller order. The performances of the proposed algorithm are assessed through a numerical example via Monte Carlo simulations. Abstract: In this paper, the fractional closed-loop system identification using the indirect approach is presented. A bias correction method is developed to deal with the bias problem in the continuous-time fractional closed-loop system identification. This method is based on the least squares estimator combined with the state variable filter approach. The basic idea is to eliminate the estimation bias by adding a correction term in the least squares estimates. The proposed algorithm is extended, using a nonlinear optimization algorithm, to estimate both coefficients and commensurate-order of the process. Numerical example shows the performances of the fractional order bias eliminated least squares method via Monte Carlo simulations.