Basis Of Closed-loop Data Research Articles

Variance reduction in Covariance Based Realization Algorithm with application to closed-loop data

The Covariance Based Realization Algorithm (CoBRA), one branch of subspace methods, enables the estimation of multivariable models using a large number of data points due to the use of finite size covariance matrices. In addition, the covariance pre-processing allows CoBRA to ignore any (high-order) noise dynamics and focus on the estimation of the low-order deterministic model. However, subspace methods and CoBRA in particular are not maximum-likelihood methods. In this paper, an in-depth study on the statistical behavior of the noise effects is conducted. An approach is provided to reduce the variance of an estimate obtained by CoBRA via the choice of optimal row and column weighting matrices. For closed-loop implementation of CoBRA, a two stage procedure is proposed with the estimate on an intermediate instrument. At the first stage, a least-length perturbation of a scalar accuracy function is used to obtain an analytic solution for the optimal weighting matrices. The resulting instruments produced by the first stage are used for the identification at the second stage to extract the plant model. Simulation examples are given to illustrate the efficiency of the proposed two stage CoBRA method on the basis of closed-loop data and compared with other subspace methods.

On the frequency domain accuracy of closed-loop estimates

It has been argued that the frequency domain accuracy of high model-order estimates obtained on the basis of closed-loop data is largely invariant to whether direct or indirect approaches are used. The analysis underlying this conclusion has employed variance expressions that are asymptotic both in the data length and the model order, and hence are approximations when either of these are finite. However, recent work has provided variance expressions that are exact for finite (possibly low) model order, and hence can potentially deliver more accurate quantification of estimation accuracy. This paper, and a companion one, revisits the study of identification from closed-loop data in light of these new quantifications and establishes that, under certain assumptions, there can be significant differences in the accuracy of frequency response estimates. These discrepencies are established here and in the companion paper to be dependent on what type of direct, indirect or joint input–output identification strategy is pursued.

Coprime factor perturbation models for closed-loop model validation techniques

This paper addresses the problem of checking the consistency of experimental closed-loop frequency-domain data with uncertainty models that are structured using coprime factorizations. The uncertainty models presented in this paper use the knowledge of a stabilizing feedback controller to structure and formulate the uncertainty on a model. Subsequently, the controller dependent coprime factor uncertainty model can be used to formulate model (in)validation tests on the basis of closed-loop data. Closed-loop model validation results are developed for the cases of noise-free and noise perturbed closed-loop data. The model validation tests involve the computation of a structured singular value over a finite frequency grid. It is also shown that the computation of the structured singular value simplifies considerably when the feedback controller used for the closed-loop experiments is the same as the controller used for formulating the controller dependent coprime factor uncertainty model.

Asymptotic variance expressions for closed-loop identification

Asymptotic variance expressions are analyzed for models that are identified on the basis of closed-loop data. The considered methods comprise the classical 'direct' method. as well as the more recently developed indirect methods, employing coprime factorized models, dual Youla/Kucera parametrizations and the two-stage approach. The variance expressions are compared with the open-loop ituation, and evaluated in terms of their relevance for subsequent model-based control design. (C) 2001 Elsevier Science Ltd. All rights reserved.

Asymptotic variance expressions for closed-loop identification

Asymptotic variance expressions are analyzed for models that are identified on the basis of closed-loop data. The considered methods comprise the classical ‘direct’ method, as well as the more recently developed indirect methods, employing coprime factorized models, dual Youla/Kucera parametrizations and the two-stage approach. The variance expressions are compared with the open-loop situation, and evaluated in terms of their relevance for subsequent model-based control design.

Asymptotic Variance Expressions for Closed-Loop Identification and Their Relevance in Identification for Control

Abstract Asymptotic variance expressions are analysed for models that are identified on the basis of closed-loop data. The considered methods comprise the classical ’direct’ and ’indirect’ method, as well as the more recently developed indirect methods, employing coprime factorized models and model parametrizations based on the dual Youla/Kucera parametrization. The variance expressions are compared with the open-loop situation, and evaluated in terms of their relevance for subsequent model-based control design. Additionally it is specified what is the optimal experimental situation in identification (open-loop or closed-loop), in view of the variance of the resulting model-based controller.

Multivariable Control of a Continuous Crystallization Process Using Experimental Input-Output Models

Results from closed-loop control of a continuous evaporative crystallization process on the basis of identified input-output models are presented. Experimental results show that open-loop identification of a crystallization process may lead to poor models as the process has a tendency to oscillate. Improved experimental conditions are achieved under feedback control, using a simple single-loop PI controller. Identification of low-order models, on the basis of closed-loop data, is studied using linear multivariable input-output models. Controllability analysis reveals that only two output quantities can be controlled independently: the mass production rate and a quantity related to the density of small crystals (fines) in the system. A two input two output model predictive controller (MPC) is designed and tested on the pilot crystallizer. Experimental results show that an improvement of the performance of the closed-loop system is obtained.