L1 Robust Identification of Fractional Transfer Functions

Identification of Transfer Function in a Feedback System and Autoregressive Analysis

Identification of transfer functions and statistical inverse problems

The paper presents a systematic approach for finding the optimal set of predictors for consistent identification of a single transfer function in an acyclic dynamic network. It is assumed that the topology of the network is known, the forcing inputs are not measured, and the observations have positive additive costs. For a class of networks where the target node is not involved in a feedback loop, sufficient and necessary conditions are derived to consistently identify a certain transfer function via a multi-input single-output prediction error method. This enables designing a systematic graphical approach based on the notion of d-separation to look for an optimal set of predictors that minimizes an appropriate additive cost function. It is shown that the required conditions for consistency and optimality are equivalent to the notion of separation in an undirected graph resulted from systematically manipulating the graphical representation of the network. Then, some well-known algorithms from computer science can be used to find the optimal set of predictors.

For the purpose of research, modelling and simulation of control plants, linear models are commonly used. There are many methods of creating linear models of plant dynamics. Artificial intelligence methods are used in many areas of science and technology. There are also several known applications of artificial intelligence in automatic controllers. The authors have developed a method of linear modelling by means of evolutionary algorithms, which enable searching for optimal values of the transfer function coefficients. For a method validation, an experiment with a real thermal plant was conducted. This paper presents identification of a linear transfer function of a thermal plant.

This paper studies the generation of stable transfer functions for which the real or imaginary part takes prescribed values at discrete uniformly spaced points on the unit circle. Formulas bounding the error between a particular interpolating function and any function consistent with the data are presented, which have the desirable property that the error goes to zero exponentially fast with the number of interpolating points. The paper also examines generation of stable minimum phase transfer functions for which the magnitude takes prescribed values at uniformly spaced points on the unit circle, and presents error bounds for this problem. Connection with the discrete Hilbert transform is made. The effect of uncertainty in the original data is also examined.

A unified theory of identification in a feedback system is presented from the viewpoint of inverse problem on reactor noise. A power reactor described by a 4 block feedback model is expressed in terms of equivalent correlation functions as a 5 block feedback model with an additional loop, if one of subsystems of the reactor becomes unstable, however, the total system is stable by negative feedback effects, and if noise sources are not independent. The addition of a loop in the feedback system leads errors in estimation of open loop transfer functions. In the case, modified open loop transfer functions are identified instead of original ones. From the viewpoint of reactor diagnosis, notes on system identification are discussed on an open loop transfer function in a low power reactor and on effects of diagonalization in covariance space of noise sources.

Identification of transfer function matrices in a feedback system is discussed by using the singular value decomposition of Hankel matrix from the viewpoint of inverse problems. A method of model reduction is considered, and selection criteria are proposed for identification of them. Transformation formula between open loop and closed loop transfer function matrices are determined from the feedback loop structure, and they are needed for identification of open loop transfer function matrices under such a condition where the feedback system is in a minimum phase. Though the identifiability of open loop transfer function matrices can be examined in the framework of innovation model equivalent to the feedback system, there are pole-zero cancellations in the identification of them. The method to reduce a model order of an open loop transfer function is discussed by using the singular value decomposition of a gramian given by the open loop transfer function with higher degree. To check reliability of the present algorithm, a simulation study is performed for an example.

From the viewpoint of stochastic inverse problem, identification of transfer functions in feedback systems has been examined by the previous papers[1][2]. In this paper it is applied for a new approach to electroencephalography (EEG). Some transfer functions between measurement regions of EEG are identified by our method of inverse problem in a stochastic feedback system. In our method for stochastic inverse problem an innovation model must be self-consistent: Since an innovation model equivalent to correlation functions has minimum phase and suitable properties from the theoretical considerations[3], innovation models with their properties are selected for dynamic analysis of EEG. Hence, a stochastic feedback model in the stationary process can be determined from EEG time series data of measurement regions, and we can obtain transfer functions between measurement regions.

From the viewpoint of stochastic inverse problem, identification of transfer functions in feedback systems has been examined by the previous papers[1][2], and applied to EEG analysis[3]. Some transfer functions between measurement regions are identified by our method of inverse problem in a stochastic feedback system. However, there are still open problems of our method for stochastic inverse problem: One problem is that there occurs a chaos-like behavior in matrix Riccati equation and it affects a property of identified innovation model. The other is a filtering effect on transfer functions for pre-processing of high pass filter. These problems are discussed from the viewpoint of statistical inverse problem.

This article proposes a modified adaptive control architecture for doubly fed induction generator DFIGs connected to the power grid that can be augmented with the existing conventional vector control of DFIG. The architecture uses online identification of the system transfer function using recursive least squares (RLS). An auto-regressive moving average system model is identified by the RLS algorithm. A minimum variance control architecture then defines an adaptive control law based on the identified model parameters for DFIG control by minimizing the difference of the system output from the model output. The control method nullifies the issues commonly experienced with conventional techniques (e.g., malfunctioning sensors, parameter variations) and ensures acceptable performance during variable grid operating conditions, where the conventional proportional-integral controller commonly fails. Several test cases are performed to analyze and validate the overall performance using real-time simulation for a 1.5 MW wind turbine system.

Asymptotic properties of set membership identification algorithms

A general methodology is presented for the state equation approximation of a multiple input/output linear system from transfer matrix data. A complex transformation matrix, obtained by eigenanalysis at a fixed frequency, is used for diagonalization of the transfer matrix over the whole frequency range. A scalar estimation procedure is applied for identification of the modal transfer functions. The state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall error of the approximation. The developed methodology is applied to the phase domain modeling of untransposed transmission lines. The approach makes it possible to perform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time. >

Identification of power system transfer functions using neural networks

Experimental analysis and numerical identification of flame transfer functions at high Reynolds numbers in a premixed swirl combustor

In the process of statistical analysis of signature/response pairs collected in the Tyrrhenian Sea during the Napoli 85 Trial, a novel deconvolution method has been developed for identifying the ocean transfer function (OTF) when its bandwidth is larger than the bandwidth of the emitted pulse. The analysis itself is described in the preceding paper [L. Ju. Fradkin, J. Acoust. Soc. Am. 87, XXXX (1990)]. Here, the underlying convolution formula relating the received signal to the signature as well as other important physical constraints are derived under the assumptions (reasonable in the analyzed case) that the emitted pulse contains no low frequencies, and that it travels along the paths none of which reverses the phase (i.e., no reflections or caustics are involved). The results of processing a representative signature/response pair with the proposed method are discussed briefly. It is shown that for the given source/receiver configuration at least two deep sea (and hence non-phase-reversing) paths exist. It is also shown that the ‘‘internal waves’’ model, rejected by other investigators in the course of their analysis of the environmental data, would not allow for existence of the second macropath. It is concluded that in certain circumstances, the proposed deconvolution method could be used to assess models of medium fluctuations.