On the Closed-Loop System Identification with Fractional Models

A bias correction method for fractional closed-loop system identification

“…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.…”

“…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]. An extension of the bias eliminated least squares (bels) method to fractional order case has been proposed in [17].…”

Robust stabilization and control using fractional order integrator

“…After an identification step of the parameters ( a k and b k ) by using one of the existing methods in the literature (Yakoub et al, 2015), a robust performance control can be obtained for uncertain systems. Therefore, when the controller gain is taken as the inverse of the system gain (i.e.…”

On the fractional closed-loop linear parameter varying system identification under noise corrupted scheduling and output signal measurements

“…This need cannot be avoided when the process is unstable and requires control or when the opening of the loop is difficult or even impossible owing to the reasons of production or safety. Furthermore, one of the main factors that make fractional identification from closed-loop experiments more important than the open-loop system identification is the correlation between the input and the output noise of the plant which may be amplified due to the long memory aspect of the fractional systems (Yakoub et al, 2015a). Therefore, during the last few years, the fractional closed-loop linear time invariant (LTI) system identification has been a well-studied research topic and significant efforts have been spent on developing efficient approaches.…”

“…In a brief historical review in 2014, Tavakoli-Kakhki and Tavazoei (2014) proposed a graphical method using a closed-loop step response data to identify the order and the coefficients of an unstable fractional order system with input time delay. Subsequently, in 2015, an iterative simplified refined instrumental variables (SRIV) method has been extended to the fractional closed-loop case by Yakoub et al (2015a). Then, the fractional order optimization closed-loop bias eliminated least squares method has been addressed to surmount the bias problem caused by the correlation between the input signal and the output noise signal (Yakoub et al, 2015b).…”