Considerations about Parameters Estimation into a Minimum Variance Control System

Abstract

The starting point to design a minimum variance control law consists in identifying a linearized mathematical model (valid around an operating point) of a nonlinear process, respectively the on-line estimation of the parameters of this model. This paper presents a comparative study regarding the estimation of these parameters for the case when the process operates in open-loop, respectively the process is integrated into a closed-loop system specific to a minimum variance control. The comparison is made both analytically (for the general case) and through a validation study (by simulation) particularized for the case of an induction generator integrated into a wind energy conversion system. The main contribution of this paper consists in proving the fact that, in closed-loop (under the constraints imposed by the control law), the process parameters estimates differ from the real ones identified in open-loop (in free operating mode, without constraints). In addition, as a novelty, the paper demonstrates that, in steady-state, the process gain estimates are identical, both in closed-loop and open-loop, even though they are calculated based on different estimates of these linear model parameters. Thus, based on parameters estimates in closed-loop, the parameter estimator rather allows the estimation of the real process gain, although it does not accurately estimate the real values of the linearized model parameters (correctly estimated only in open-loop).