In this paper we study how to estimate autoregressive moving average (ARMA) processes via a high order autoregressive (AR) estimate and model reduction. The model reduction techniques considered are based on the L 2 -...
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In this paper we study how to estimate autoregressive moving average (ARMA) processes via a high order autoregressive (AR) estimate and model reduction. The model reduction techniques considered are based on the L 2 -norm. internally balanced realizations, or the Hankelnorm. We apply this estimation technique to the problem of finding narrow-band signals in white noise.
Models and model quality are prime concerns for most design issues in control and system analysis. The success of a simulation study hinges upon the reliability of the model used. In this contribution we discuss how t...
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Models and model quality are prime concerns for most design issues in control and system analysis. The success of a simulation study hinges upon the reliability of the model used. In this contribution we discuss how to build mathematical models that given certain constraints, are of optimum quality for a prespecified application. We then taken into account the influence of both bias errors and random errors on the model. It turns out that for a fairly broad class of identification methods in the prediction error family, the optimal choices of design variables can be given in an explicit form.
It is customary to use the w.p.l limit and the asymptotic distribution (or asymptotic covariance matrix) as an accuracy measure in system identification. Experiment Design and the choice of estimation techniques may b...
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It is customary to use the w.p.l limit and the asymptotic distribution (or asymptotic covariance matrix) as an accuracy measure in system identification. Experiment Design and the choice of estimation techniques may be decided upon, using this covariance expression. If we are going to make just one experiment, we may ask about the rationale for such decisions. How do the properties of my particular data set relate to the (then esoteric and imaginary) asymptotic distribution. In this contribution we discuss how the usual probabilistic environment of the identification problem relates to the single-realization behaviour of the resulting models.
The frequency domain properties of pole placement regulators are studied, and the influence of the regulator on the model quality is discussed. Some methods to affect the regulator properties are discussed.
The frequency domain properties of pole placement regulators are studied, and the influence of the regulator on the model quality is discussed. Some methods to affect the regulator properties are discussed.
This paper gives improved energy functions for power systems based on structure preserving models (SPM's). These models have considerable advantages over models based on impedance loads and a reduced network. The ...
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This paper gives improved energy functions for power systems based on structure preserving models (SPM's). These models have considerable advantages over models based on impedance loads and a reduced network. The emphasis is on clarifying the role of different types of damping and bus power transformations while giving clean derivations via first integral and Popov criterion methods.
The variance of recursive transfer function estimates for systems with finite impulse response structure is studied. Expressions for the variance are derived using asymptotic methods. The variance expressions explicit...
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The variance of recursive transfer function estimates for systems with finite impulse response structure is studied. Expressions for the variance are derived using asymptotic methods. The variance expressions explicitly show the influence of step length, input spectrum, noise variance, parameter variations and model order.
Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-type models. Expre...
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Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-type models. Expressions for the variances of the transfer function estimates are derived, that are asymptotic both in the number of observed data and in the model orders. The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise. The factor of proportionality is the ratio of model order to number of data. This result is independent of the particular model structure used. The result is applied to evaluate the performance degradation due to variance for a number of typical model uses. Some consequences for input design are also drawn.
This paper treats the close conceptual relationships between basic approaches to the estimation of transfer functions of linear systems. The classical methods of frequency and spectral analysis are shown to be related...
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This paper treats the close conceptual relationships between basic approaches to the estimation of transfer functions of linear systems. The classical methods of frequency and spectral analysis are shown to be related to the well-known time domain methods of prediction error type via a common “empirical transfer function estimate”. Asymptotic properties of the estimates obtained by the respective methods are also described and discussed. An important feature that is displayed by this treatment is a frequency domain weighting function that determines the distribution of bias in case the true system cannot be exactly described within the chosen model set. The choice of this weighting function is made in terms of noise models for time-domain methods. The noise model thus has a dual character from the system approximation point of view.
A common approach to regulator design is to define an objective function, which is minimized with respect to adjustable regulator parameters. Here we discuss how such objective functions can be minimized on-line, thus...
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A common approach to regulator design is to define an objective function, which is minimized with respect to adjustable regulator parameters. Here we discuss how such objective functions can be minimized on-line, thus providing adaptive control. Such an approach to adaptive control has its roots in early contributions to learning systems, and it is here further developed and discussed in the light of the recent development of the field. A general algorithm is given and special attention is paid to minimization of quadratic criteria. A key problem is to obtain information about the system dynamics in order to compute the derivatives of the criterion with respect to the regulator parameters. It is shown that the self-tuning regulator is obtained as a special case, corresponding to a particular quadratic criterion and a particular way of estimating the system dynamics. Explicit ways using instrumental variables techniques based on extra injected noise are also discussed. A specific feature of the algorithm is that it does not utilize specific knowledge about how to calculate the optimal regulator. The algorithm is the same for minimum phase as well as for non-minimum phase systems.
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