| 1. |
- Forssell, Urban, et al.
(författare)
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A Projection Method for Closed-Loop Identification
- 1998
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 2. |
- Forssell, Urban
(författare)
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Asymptotic Variance Expressions for Identified Black-Box Models
- 1998
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 3. |
- Forssell, Urban, et al.
(författare)
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Efficiency of Prediction Error and Instrumental Variable Methods for Closed-loop Identification
- 1998
-
Ingår i: Proceedings of the 37th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780343948 ; , s. 1287-1288 vol.2
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 4. |
- Forssell, Urban, et al.
(författare)
-
Time-Domain Identification of Dynamic Errors-in-Variables Systems Using Periodic Excitation Signals
- 1998
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Rapport (övrigt vetenskapligt/konstnärligt)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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| 5. |
- Hjalmarsson, Håkan, 1962-, et al.
(författare)
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Maximum Likelihood Estimation of Models with Unstable Dynamics and Non-minimum Phase Noise Zeros
- 1998
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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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
- 1998
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Ingår i: Proceedings of the 1998 Conference on Perspectives in Control - A tribute to Ioan Dore Landau. - 1852330422 ; , s. 205-216
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Konferensbidrag (refereegranskat)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 - Updated Version
- 1998
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Rapport (övrigt vetenskapligt/konstnärligt)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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| 8. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Identification for Control: Some Results on Optimal Experiment Design
- 1998
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Ingår i: Proceedings of the 37th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780343948 ; , s. 3384-3389 vol.3
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Konferensbidrag (refereegranskat)abstract
- 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
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| 9. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Identification of Unstable Systems using Output Error and Box-Jenkins Model Structures
- 1998
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Ingår i: Proceedings of the 37th IEEE Conference on Decision and Control. - 0780343948 ; , s. 3932-3927 vol.4
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Konferensbidrag (refereegranskat)abstract
- 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.
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