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Closed-loop Identification: Methods, Theory, and Applications

Author: U. Forssell
Published: PhD. Thesis, 1999.
Research area: Identification
Keywords: Identification; Prediction error methods

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Abstract:
System identification deals with constructing mathematical models of dynamical systems from measured data. Such models have important applications in many technical and nontechnical areas, such as diagnosis, simulation, prediction, and control. The theme in this thesis is to study how the use of closed-loop data for identification of open-loop processes affects different identification methods. The focus is on prediction error methods for closed-loop identification and a main result is that we show that most common methods correspond to different parameterizations of the general prediction error method. This provides a unifying framework for analyzing the statistical properties of the different methods. Here we concentrate on asymptotic variance expressions for the resulting estimates and on explicit characterizations of the bias distribution for the different methods. Furthermore, we present and analyze a new method for closed-loop identification, called the projection method, which allows approximation of the open-loop dynamics in a fixed, user-specified frequency domain norm, even in the case of an unknown, nonlinear regulator.

In prediction error identification it is common to use some gradient-type search algorithm for the parameter estimation. A requirement is then that the predictor filters along with their derivatives are stable for all admissible values of the parameters. The standard output error and Box-Jenkins model structures cannot be used if the underlying system is unstable, since the predictor filters will generically be unstable under these circumstances. In the thesis, modified versions of these model structures are derived that are applicable also to unstable systems. Another way to handle the problems associated with output error identification of unstable systems is to implement the search algorithm using noncausal filtering. Several such approaches are also studied and compared.

Another topic covered in the thesis is the use of periodic excitation signals for time-domain identification of errors-in-variables systems. A number of compensation strategies for the least-squares and total least-squares methods are suggested. The main idea is to use a nonparametric noise model, estimated directly from data, to whiten the noise and to remove the bias in the estimates.

``Identification for Control' deals specifically with the problem of constructing models from data that are good for control. A main idea has been to try to match the identification and control criteria to obtain a control-relevant model fit. The use of closed-loop experiments has been an important tool for achieving this. We study a number of iterative methods for dealing with this problem and show how they can be implemented using the indirect method. Several problems with the iterative schemes are observed and it is argued that performing iterated identification experiments with the current controller in the loop is suboptimal. Related to this is the problem of designing the identification experiment so that the quality of the resulting model is maximized. Here we concentrate on minimizing the variance error and a main result is that we give explicit expressions for the optimal regulator and reference signal spectrum to use in the identification experiment in case both the input and the output variances are constrained.

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Bibentry:

@phdthesis{Forssell:99,
    author = "Forssell, Urban",
    title = "Closed-loop Identification: Methods, Theory, and Applications",
    year = "1999",
    month = Mar,
    type = "Linköping Studies in Science and Technology. Thesis No 566",
}