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).
Highlights
The on-line estimation of the parameters of a linearized model around an operating point is an essential step in many adaptive control strategies
Considering a minimum variance control system, the present paper demonstrates, both analytically and by simulation for a concrete case study that, in steady-state closed-loop, parameters estimates differs from the real ones in the open-loop, the process gain estimates are similar in both situations
The parameter estimator rather allows an accurate estimation of the process gain factor and not of the real parameters of the linearized model used to implement the control law
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. It will be proved analytically and validated through a numerical simulation (for a particular chosen case) that, in the closed-loop (due to the constraints imposed by the minimum variance control law), the linear model parameters estimates are not identical with the real ones estimated when the process operates in open-loop. In spite of this fact, in the steady-state (and based on different estimates for the open-loop, respectively the closed-loop regime), the process gain computation for both cases leads to similar values. All these findings are valid only for the identification and control of a nonlinear process (whose limited functionality around an operating point can obviously be described by a linearized model)
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