| 1. |
- Forssell, Urban, et al.
(författare)
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An Alternative Motivation for the Indirect Approach to Closed-Loop Identification
- 1999
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 44:11, s. 2206-2209
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Tidskriftsartikel (refereegranskat)abstract
- Direct prediction error identification of systems operating in closed loop may lead to biased results due to the correlation between the input and the output noise. The authors study this error, what factors affect it, and how it may be avoided. In particular, the role of the noise model is discussed and the authors show how the noise model should be parameterized to avoid the bias. Apart from giving important insights into the properties of the direct method, this provides a nonstandard motivation for the indirect method.
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| 2. |
- Forssell, Urban
(författare)
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Closed-loop Identification : Methods, Theory, and Applications
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)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 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
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| 3. |
- Forssell, Urban, et al.
(författare)
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Comparison of Methods for Probabilistic Uncertainty Bounding
- 1999
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Ingår i: Proceedings of the 38th IEEE Conference on Decision and Control. - 0780352505 ; , s. 522-527 vol.1
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Konferensbidrag (refereegranskat)abstract
- The problem of computing probabilistic uncertainty regions for the frequency responses of identified models is studied. A novel method for uncertainty bounding that uses bootstrap is presented and compared to a classical method using estimated covariance information. It is shown that, with bootstrap, it is possible to compute realistic uncertainty regions that closely resemble those obtainable through Monte Carlo simulations.
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| 4. |
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| 5. |
- Forssell, Urban, et al.
(författare)
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Time-Domain Identification of Dynamic Errors-in-Variables Systems using Period Excitation Signals
- 1999
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Ingår i: Proceedings of the 14th IFAC World Congress. - 9780080432137 ; , s. 421-426
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 6. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Bias, Variance and Optimal Experiment Design: Some Comments on Closed Loop Identification
- 1999
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this contribution we shall describe a rather unified way of expressing bias and variance in prediction error estimates. Theemphasis is on systems operating in closed loop. We shall describe the identification criterion function in the frequencydomain. The crucial entity is the joint spectrum of input and noise source. Different factorizations of this spectrum give differentinsights into the bias mechanisms of closed loop identification. It will be shown that so called {em indirect identification} is theanswer to the question of how to obtain consistent estimates of the dynamics part, even with an erroneous noise model. Wealso consider optimal design of experiments that seek to minimize the weighted variance of the dynamics estimate. It is shownthat open loop experiments are optimal if the input power is constrained. However for any criteria that involve any kind ofconstraints on the output power, closed loop experiments will be optimal. The optimal regulator does not depend on theweighting function in the criterion to be minimized.
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| 7. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Closed-Loop Identification Revisited
- 1999
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 35:7, s. 1215-1241
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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