| 1. |
- Enqvist, Martin, 1976-
(författare)
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A Weighting Method for Approximate Nonlinear System Identification
- 2007
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Ingår i: Proceedings of the 46th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 9781424414987 - 9781424414970 ; , s. 5104-5109
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Konferensbidrag (refereegranskat)abstract
- Many approximation results in nonlinear system identification concern particular signal distributions. This seems to limit the applicability of these results to cases where the relevant signals have these distributions. However, by using a weighting method that modifies the cost function used in the identification method, the available approximation results can be used also for rather general classes of signal distributions. The purpose of this paper is to describe this weighting approach and to point at some interesting application areas within nonlinear system identification. In particular, it will be described how the impulse response of a Hammerstein system can be estimated consistently for an arbitrary input signal.
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| 2. |
- Enqvist, Martin, 1976-
(författare)
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Benefits of the Input Minimum Phase Property for Linearization of Nonlinear Systems
- 2005
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Ingår i: Proceedings of the 2005 International Symposium on Nonlinear Theory and Its Applications. - Linköping : Linköping University Electronic Press. ; , s. 618-
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Konferensbidrag (refereegranskat)abstract
- Linear approximations of nonlinear systems can be obtained by fitting a linear model to data from a nonlinear system, for example, using the prediction-error method. In many situations, the type of linear model and the model orders are selected after estimating several models and evaluating them using various validation techniques. Two commonly used validation methods for linear models are spectral and residual analysis. Unfortunately, these methods will not always work if the true system is nonlinear. However, if the input can be viewed as if it has been generated by filtering white noise through a minimum phase filter, spectral and residual analysis can be used for validation of linear models of nonlinear systems. Furthermore, it can be shown that the input minimum phase property guarantees that a certain optimality result will hold. Here, the benefits of using minimum phase instead of non-minimum phase filters for input design will be shown both theoretically and in numerical experiments.
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| 3. |
- Enqvist, Martin, 1976-, et al.
(författare)
-
Estimating Nonlinear Systems in a Neighborhood of LTI-approximants
- 2002
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Ingår i: Proceedings of the 41st IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780375165 ; , s. 1005-1010 vol.1
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Konferensbidrag (refereegranskat)abstract
- The estimation of Linear Time Invariant (LTI) models is a standard procedure in system identification. Any real-life system will however be nonlinear and time-varying, and the estimated model will converge to the LTI second order equivalent (LTI-SOE) of the true system. In this paper we consider some aspects of this convergence and the distance between the true system and its LTI-SOE. We show that there may be cases where even the slightest nonlinearity may cause big differences in the LTI-SOE. We also show a result that gives conditions that guarantee that the LTI-SOE is close to "the natural" LTI approximant. Finally, an upper bound on the distance between the LTI-SOE of a nonlinear FIR system with a white input signal and the linear part of the system is derived.
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| 4. |
- Enqvist, Martin, 1976-
(författare)
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Identification of Hammerstein Systems Using Separable Random Multisines
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The choice of input signal is very important in identification of nonlinear systems. In this paper, it is shown that random multisines with a flat amplitude spectrum are separable. The separability property means that certain conditional expectations are linear and it implies that random multisines easily can be used to obtain accurate estimates of the linear time-invariant part of a Hammerstein system. This is illustrated in a numerical example.
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| 5. |
- Enqvist, Martin, 1976-, et al.
(författare)
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Linear Approximations of Nonlinear FIR Systems for Separable Input Processes
- 2005
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Ingår i: Automatica. - Linköping : Elsevier. - 0005-1098 .- 1873-2836. ; 41:3, s. 459-473
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Tidskriftsartikel (refereegranskat)abstract
- Nonlinear systems can be approximated by linear time-invariant (LTI) models in-many ways. Here, LTI models that are optimal approximations in the mean-square error sense are analyzed. A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse response (FIR) model is presented. This condition says that the in ut should be separable of a certain order, i.e., that certain conditional expectations should be,P linear. For the special case of Gaussian input signals, this condition is closely related to a generalized version of Bussgang's classic theorem about static nonlinearities. It is shown that this generalized theorem can be used for structure identification and for the identification of generalized Wiener-Hammerstein systems.
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| 6. |
- Enqvist, Martin, 1976-
(författare)
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Linear Models of Nonlinear FIR Systems with Gaussian Inputs
- 2002
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Ingår i: Proceedings of the 4th Conference on Computer Science and Systems Engineering. - Linköping : Linköping University Electronic Press. ; , s. 147-151
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We show a result that can be viewed as a generalization of Bussgang's classic theorem about static non-linearities with Gaussian inputs. This new result is used to characterize the best linear approximation of a non-linear finite impulse response (NFIR) system with a Gaussian input. The best linear approximation is here defined as the causal LTI system that minimizes the expected squared prediction error. Furthermore, we discuss how this characterization can be used for structure identication and for identication of generalized Hammerstein and Wiener systems.
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| 7. |
- Enqvist, Martin, 1976-, et al.
(författare)
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LTI Approximations of Slightly Nonlinear Systems : Some Intriguing Examples
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Approximations of slightly nonlinear systems with linear time-invariant (LTI) models are often used in applications. Here, LTI models that are optimal approximations in the mean-square error sense are studied. It is shown that these models can be very sensitive to small nonlinearities. Furthermore, the significance of the distribution of the input process is discussed. From the examples studied here, it seems that LTI approximations for inputs with distributions that are Gaussian or almost Gaussian are less sensitive to small nonlinearities.
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| 8. |
- Enqvist, Martin, 1976-, et al.
(författare)
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The CDIO Initiative from an Automatic Control Project Course Perspective
- 2004
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The CDIO (Conceive Design Implement Operate) Initiative is explained, and some of the results at the Applied Physics and Electrical Engineering program at Linköping University, Sweden, are presented. A project course in Automatic Control is used as an example. The projects within the course are carried out using the LIPS (Linköping interactive project steering) model. An example of a project, the golf playing industrial robot, and the results from this project are also covered.
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| 9. |
- Enqvist, Martin, 1976-
(författare)
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Variance-Bias Tradeoff in Finite Impulse Response Estimates Obtained by Correlation Analysis
- 2002
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Correlation analysis can in some cases produce better identification results than an ordinary least squares approach. This is for example the case when a Finite Impulse Response system is estimated from ill-conditioned input-output measurements. In this report, the correlation analysis method is rewritten as a regularized least squares algorithm and the performance of the method is discussed in this context. It turns out that the fact that correlation analysis can be viewed as a kind of regularization explains why and in what sense this method sometimes produces more accurate estimates than the ordinary least squares approach.
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| 10. |
- Glad, Torkel, 1947-, et al.
(författare)
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Controllers for Amplitude Limited Model Error Models
- 2005
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Ingår i: Proceedings of the 16th IFAC World Congress. - Linköping : Linköping University Electronic Press. - 9783902661753 ; , s. 662-662
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Konferensbidrag (refereegranskat)abstract
- In this paper, systems where information about model accuracy is contained in a model error model are considered. The validity of such a model is typically restricted to input signals that are limited in amplitude. It is then natural to require the same amplitude restriction when designing controllers. The resulting implications for controller design are investigated in both the continuous and the discrete time case.
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