A bias correction method for fractional closed-loop system identification

• 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.

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.