Algorithms for recursive/semi-recursive bias-compensating least squares system identification within the errors-in-variables framework

Abstract

Algorithms for the recursive/semi-recursive estimation of the system parameters as well as the measurement noise variances for linear single-input single-output errors-in-variables systems are considered. Approaches based on three offline techniques are presented: namely, the bias eliminating least squares, the Frisch scheme and the extended bias compensating the least squares method. Whilst the underlying equations used within these approaches are identical under certain design choices, the performances of the recursive/semi-recursive algorithms are investigated via simulation, in order to determine the most suitable technique for practical applications.

Identification–Oriented Control Designs with Application to a Wind Turbine Benchmark

“…Thus, a recursive Frisch scheme identification approach is extended to enhance its on-line applicability. It is shown that by incorporating adaptation via the introduction of exponential forgetting, the algorithm is able to compensate for the systematic errors, which arise in the original scheme [10]. Therefore, this adaptive recursive Frisch scheme is able to deal with linear time-varying systems, and it is used in connection with the design of an adaptive control scheme, shown in Section IV-A.…”

“…A modification of the Frisch scheme algorithm is proposed here to identify dynamical Errors-In-Variables (EIV) models [10,17]. For the update of the estimated model parameters, a recursive bias-compensating strategy is also www.ijacsa.thesai.org implemented.…”

“…Therefore, this paper suggests the implementation of controllers based on adaptive identification schemes, used for the on-line estimation of the controlled process, which can be affected by uncertainty and errors. The recursive Frisch extended to the adaptive case making use of exponential forgetting is considered here [10]. It also overcomes potential numerical difficulties with the existing recursive scheme.…”

“…This identification scheme exploited for the estimation of the TS model parameters has been integrated into the FMID toolbox for Matlab ® by one of the same authors. This approach developed by one of the same authors is usually preferred when the TS model should serve as predictor, as it computes the consequent parameters via the Frisch scheme, developed for the Errors-In-Variables (EIV) descriptions [10].…”

“…In this adaptive control application, it is essential to obtain on-line estimates of the model parameters θ(k) in (7), while the process generating the data is running. In fact, this application study is focusing on adaptive control, where the control action at time step k relies on a current estimate of the plant model, which is estimated using data up to the sample k. Therefore, the Frisch scheme relying on batch expressions has to be modified in a recursive algorithm, as described in [10]. The on-line identification method described here was implemented by the author in the Matlab ® and Simulink ® environments, and integrated in the Simulink ® toolbox [11].…”