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Closed-loop Identification: Methods, Theory, and Applications
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1999 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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 identication of open-loop processes affects dierent identification methods. The focus is on prediction error methods for closed-loop identification and a main resultis that we show that most common methods correspond to diefferent 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 beused 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.

"Identication for Control" deals specically with the problem of constructing models from data that are good for control. A main idea has been to try to match the identication 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

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1999. , 247 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 566
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-98129ISBN: 91-7219-432-4 (print)OAI: oai:DiVA.org:liu-98129DiVA: diva2:652232
Public defence
1999-03-31, C3, Hus C, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Supervisors
Available from: 2013-10-09 Created: 2013-09-30 Last updated: 2013-10-09Bibliographically approved
List of papers
1. Closed-Loop Identification Revisited - Updated Version
Open this publication in new window or tab >>Closed-Loop Identification Revisited - Updated Version
1998 (English)Report (Other academic)
Abstract [en]

Identification of systems operating in closed loop has long been of prime interest in industrial applications. The problem offers many possibilities, and also some fallacies, and a wide variety of approaches have been suggested, many quite recently. The purpose of the current contribution is to place most of these approaches in a coherent framework, thereby showing their connections and display similarities and differences in the asymptotic properties of the resulting estimates. The common framework is created by the basic prediction error method, and it is shown that most of the common methods correspond to different parameterizations of the dynamics and noise models. The so-called indirect methods, e.g., are indeed “direct” methods employing noise models that contain the regulator. The asymptotic properties of the estimates then follow from the general theory and take different forms as they are translated to the particular parameterizations. We also study a new projection approach to closed-loop identification with the advantage of allowing approximation of the open-loop dynamics in a given, and user-chosen frequency domain norm, even in the case of an unknown, nonlinear regulator.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1998. 55 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2021
Keyword
System identification, Closed-loop identification, Prediction error methods, Modelling, Statistical analysis
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-55637 (URN)LiTH-ISY-R-2021 (ISRN)
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-08
2. A Projection Method for Closed-Loop Identification
Open this publication in new window or tab >>A Projection Method for Closed-Loop Identification
1997 (English)Report (Other academic)
Abstract [en]

A new method for closed-loop identification that allows fitting the model to the data with arbitrary frequency weighting is described and analyzed. Just as the direct method, this new method is applicable to systems with arbitrary feedback mechanisms. This is in contrast to other methods, such as the indirect method and the two-stage method, that assume linear feedback. The finite sample behavior of the proposed method is illustrated in a simulation study.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1997. 7 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 1984
Keyword
Arbitrary frequency weighting, Cybernetik Informationsteori, Maskinelement Servomekanismer Automation, Reglerteori, Reglerteori
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-55403 (URN)LITH-ISY-R-1984 (ISRN)
Available from: 2010-04-29 Created: 2010-04-29 Last updated: 2014-09-16Bibliographically approved
3. Efficiency of Prediction Error and Instrumental Variable Methods for Closed-Loop Identification
Open this publication in new window or tab >>Efficiency of Prediction Error and Instrumental Variable Methods for Closed-Loop Identification
1998 (English)In: Proceedings of the 37th IEEE Conference on Decision and Control, 1998, 1287-1288 vol.2 p.Conference paper, Published paper (Refereed)
Abstract [en]

We study the efficiency of a number of closed-loop identification methods. Results will be given for methods based on the prediction error approach as well as those based on the instrumental variable approach. Moreover, interesting insights in the properties of a recently suggested subspace method for closed-loop identification are obtained by exploring the links between this method and the instrumental variable method.

Keyword
Closed loop systems, Covariance matrices, Feedback, Linear systems, Parameter estimation
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-91591 (URN)10.1109/CDC.1998.758456 (DOI)0-7803-4394-8 (ISBN)
Conference
37th IEEE Conference on Decision and Control, Tampa, FL, USA, December, 1998
Available from: 2013-06-03 Created: 2013-04-28 Last updated: 2013-10-09
4. Identification of Unstable Systems using Output Error and Box-Jenkins Model Structures
Open this publication in new window or tab >>Identification of Unstable Systems using Output Error and Box-Jenkins Model Structures
1998 (English)In: Proceedings of the 37th IEEE Conference on Decision and Control, 1998, 3932-3927 vol.4 p.Conference paper, Published paper (Refereed)
Abstract [en]

It is well known that the output error and Box-Jenkins model structures cannot be used for prediction error identification of unstable systems. The reason for this is that the predictors in this case generically will be unstable. Typically this problem is handled by projecting the parameter vector into the region of stability which gives erroneous results when the underlying system is unstable. The main contribution of this work is that we derive modified, but asymptotically equivalent, versions of these model structures that can be applied also in the case of unstable systems.

Keyword
Errors, Identification, Stability, Box-Jenkin
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-91592 (URN)10.1109/CDC.1998.761844 (DOI)0-7803-4394-8 (ISBN)
Conference
37th IEEE Conference on Decision and Control, Tampa, FL, USA, December, 1998
Available from: 2013-06-03 Created: 2013-04-28 Last updated: 2013-10-09
5. Maximum Likelihood Estimation of Models with Unstable Dynamics and Non-minimum Phase Noise Zeros
Open this publication in new window or tab >>Maximum Likelihood Estimation of Models with Unstable Dynamics and Non-minimum Phase Noise Zeros
1998 (English)Report (Other academic)
Abstract [en]

Maximum likelihood estimation of single-input/single-output linear timeinvariant (LTI) dynamic models requires that the model innovations (the nonmeasurable white noise source that is assumed to be the source of the randomness of the system) can be computed from the observed data. For many model structures, the prediction errors and the model innovations coincide and the prediction errors can be used in maximum likelihood estimation. However, when the model dynamics and the noise model have unstable poles which are not shared or when the noise dynamics have unstable zeros this is not the case. One such example is an unstable output error model. In this contribution we show that in this situation the model innovations can be computed by anti-causal filtering. Different implementations of the model innovations filter are also studied.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1998. 14 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2043
Keyword
Prediction error methods, Output error methods, Cybernetik Informationsteori
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-55650 (URN)LiTH-ISY-R-2043 (ISRN)
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-12Bibliographically approved
6. Time-Domain Identification of Dynamic Errors-in-Variables Systems using Period Excitation Signals
Open this publication in new window or tab >>Time-Domain Identification of Dynamic Errors-in-Variables Systems using Period Excitation Signals
1999 (English)In: Proceedings of the 14th IFAC World Congress, 1999, 421-426 p.Conference paper, Published paper (Refereed)
Abstract [en]

The use of periodic excitation signals in identification experiments is advocated. With periodic excitation it is possible to separate the driving signals and the disturbances, which for instance implies that the noise properties can be independently estimated. In the paper a non-parametric noise model, estimated directly from the measured data, is used in a compensation strategy applicable to both least squares and total least squares estimation. The resulting least squares and total least squares methods are applicable in the errors-in-variables situation and give consistent estimates regardless of the noise. The feasibility of the idea is illustrated in a simulation study.

Keyword
Periodic input, Errors-in-variables
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-91197 (URN)978-0080432137 (ISBN)
Conference
14th IFAC World Congress, Beijing, China, July, 1999
Available from: 2013-04-22 Created: 2013-04-17 Last updated: 2013-10-09
7. Identification for Control: Some Results on Optimal Experiment Design
Open this publication in new window or tab >>Identification for Control: Some Results on Optimal Experiment Design
1998 (English)In: Proceedings of the 37th IEEE Conference on Decision and Control, 1998, 3384-3389 vol.3 p.Conference paper, Published paper (Refereed)
Abstract [en]

The problem of designing identification experiments to make them maximally informative with respect to the intended use of the model is studied. Focus is on model based control and we show how to choose the feedback regulator and the spectrum of the reference signal in case of closed-loop experiments. A main result is that when only the misfit in the dynamics model is penalized and when both the input and the output power are constrained then the optimal controller is given by the solution to a standard LQ problem. When only the input power is constrained, it is shown that open-loop experiments are optimal. Some examples are also given to exemplify the theoretical results

Keyword
Closed loop systems, Control system synthesis, Design of experiments, Feedback, Identification, Linear quadratic control
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-91593 (URN)10.1109/CDC.1998.758224 (DOI)0-7803-4394-8 (ISBN)
Conference
37th IEEE Conference on Decision and Control, Tampa, FL, USA, December, 1998
Available from: 2013-06-07 Created: 2013-04-28 Last updated: 2013-10-09
8. Asymptotic Variance Expressions for Identified Black-Box Models
Open this publication in new window or tab >>Asymptotic Variance Expressions for Identified Black-Box Models
1998 (English)Report (Other academic)
Abstract [en]

The asymptotic probability distribution of identified black-box transfer function models is studied. The main contribution is that we derive variance expressions for the real and imaginary parts of the identified models that are asymptotic in both the number of measurements and the model order. These expressions are considerably simpler than the corresponding ones that hold for fixed model orders, and yet they frequently approximate the true covariance well already with quite modest model orders. We illustrate the relevance of the asymptotic expressions by using them to compute uncertainty regions for the frequency response of an identified model.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1998. 20 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2089
Keyword
Identification, Prediction error methods, Covariance, Uncertainty, Cybernetik Informationsteori
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-55663 (URN)LiTH-ISY-R-2089 (ISRN)
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-12Bibliographically approved

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