Indirect approach for closed-loop system identification with fractional models

A bias correction method for fractional closed-loop system identification

“…In the closed-loop, ϕ f and f are always correlated which justify the presence of the bias in the ols estimates ( ˆ ols / = 0) [15].…”

“…The simulation results presented in [15] have shown that for an important additive noise the estimated parameters are biased. To eliminate this bias, the optimal instrumental variable method combined with a nonlinear optimization algorithm is handled to identify both fractional transfer function coefficients and fractional orders [24].…”

“…Recently, some works present contributions in the fractional closed-loop system identification context [15,17,24]. The simulation results presented in [15] have shown that for an important additive noise the estimated parameters are biased.…”

“…Using the filtered input and output signals denoted, respectively, by y c f (t) and y f (t), equation (15) can be rewritten as…”

“…In [14], an unstable fractional first-order system with input time-delay has been identified using a graphical method based on the step response of the fractional closed-loop system. A more general indirect approach has been proposed in [15] where the least squares algorithm combined with the state variable filter is used. Simulation results have shown the presence of a bias on the estimates when the system is contaminated by a high level additive white noise.…”