Showing papers on "System identification published in 1991"

Paradigms and puzzles in the theory of dynamical systems

Abstract: A self-contained exposition is given of an approach to mathematical models, in particular, to the theory of dynamical systems. The basic ingredients form a triptych, with the behavior of a system in the center, and behavioral equations with latent variables as side panels. The author discusses a variety of representation and parametrization problems, in particular, questions related to input/output and state models. The proposed concept of a dynamical system leads to a new view of the notions of controllability and observability, and of the interconnection of systems, in particular, to what constitutes a feedback control law. The final issue addressed is that of system identification. It is argued that exact system identification leads to the question of computing the most powerful unfalsified model. >

System identification using Laguerre models

Abstract: The traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear-in-the-parameters predictor models leads to approximations of very high order in cases of rapid sampling and/or dispersion in time constants. By using prior information about the time constants of the system more appropriate expansions, related to Laguerre networks, are introduced and analyzed. It is shown that the model order can be reduced, compared to ARX (FIR, AR) modeling, by using Laguerre models. Furthermore, the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the Laguerre parameter. Consistency (error bounds), persistence of excitation conditions. and asymptotic statistical properties are investigated. This analysis is based on the result that the covariance matrix of the regression vector of a Laguerre model has a Toeplitz structure. >

Control oriented system identification: a worst-case/deterministic approach in H/sub infinity /

Abstract: The authors formulate and solve two related control-oriented system identification problems for stable linear shift-invariant distributed parameter plants In each of these problems the assumed a priori information is minimal, consisting only of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level The first of these problems involves identification of a point sample of the plant frequency response from a noisy, finite, output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest This problem leads naturally to the second problem, which involves identification of the plant transfer function in H/sub infinity / from a finite number of noisy point samples of the plant frequency response Concrete plans for identification algorithms are provided for each of these two problems >

Identification of continuous-time systems

Abstract: System identification is a well-established field. It is concerned with the determination of particular models for systems that are intended for a certain purpose such as control. Although dynamical systems encountered in the physical world are native to the continuous-time domain, system identification has been based largely on discrete-time models for a long time in the past, ignoring certain merits of the native continuous-time models. Continuous-time-model-based system identification techniques were initiated in the middle of the last century, but were overshadowed by the overwhelming developments in discrete-time methods for some time. This was due mainly to the 'go completely digital' trend that was spurred by parallel developments in digital computers. The field of identification has now matured and several of the methods are now incorporated in the continuous time system identification (CONTSID) toolbox for use with Matlab. The paper presents a perspective of these techniques in a unified framework.

Neural networks for nonlinear internal model control

Abstract: A novel technique, directly using artificial neural networks, is proposed for the adaptive control of nonlinear systems. The ability of neural networks to model arbitrary nonlinear functions and their inverses is exploited. The use of nonlinear function inverses raises questions of the existence of the inverse operators. These are investigated and results are given characterising the invertibility of a class of nonlinear dynamical systems. The control structure used is internal model control. It is used to directly incorporate networks modelling the plant and its inverse within the control strategy. The potential of the proposed method is demonstrated by an example.

System identification approach to detection of structural changes

Abstract: This paper explores the potential of a time-domain identification procedure to detect structural changes on the basis of noise-polluted measurements. The method of approach requires the use of excitation and acceleration response records, to develop an equivalent multi-degree-of-freedom (MDOF) mathematical model whose order is compatible with the number of sensors used. Application of the identification procedure under discussion yields the optimum value of the elements of equivalent linear system matrices. By performing the identification task before and after potential structural changes (damage) in the physical system have occurred, quantifiable changes in the identified mathematical model can be detected. The usefulness of the identification procedure under discussion for damage detection is demonstrated by means of an example of three-degree-of-freedom (DOF) linear system. This system is used to conduct synthetic experiments to generate noise-polluted “data” sets that are subsequently analyzed to determine the mean, variance, and probability density function corresponding to each element of the identified system matrices. Different versions of the model are investigated in which the location as well as the magnitude of the “damage” is varied. On the basis of this exploratory study, it appears that determining the probability density functions of the identified system matrices may furnish useful indices that can be conveniently extracted during an experimental test, to quantify changes in the characteristics of physical systems.

On the series expansion approach to the identification of Hammerstein systems

Abstract: A polynomial identification algorithm for recovering a nonlinearity in the Hammerstein system is proposed. The estimate employs the Legendre orthogonal system with adaptively selected number of terms. The global consistency along with rates of convergence are established. No assumptions concerning continuity of the nonlinearity or its functional form are made. A data-driven method using the cross-validation technique for selecting the number of terms in the estimate is presented. >

Orthogonal approaches to time-series analysis and system identification

Abstract: Some recent, efficient approaches to nonlinear system identification, ARMA modeling, and time-series analysis are described and illustrated. Sufficient detail and references are furnished to enable ready implementation, and examples are provided to demonstrate superiority over established classical techniques. The ARMA identification algorithm presented does not require a priori knowledge of, or assumptions about, the order of the system to be identified or signal to be modeled. A suboptimal, recursive, pairwise search of the orthogonal candidate data records is conducted, until a given least-squares criterion is satisfied. In the case of nonlinear systems modeling, discrete-time Volterra series is stressed, or rather a more efficient parallel-cascade approach. The model is constructed by adding parallel paths (each consisting of the cascade of dynamic linear and static nonlinear systems). In the case of time-series analysis, a non-Fourier sinusoidal series approach is stressed. The relevant frequencies are estimated by an orthogonal search procedure. A search of the candidate sinusoids is conducted until a given mean-square criterion is satisfied. >

Robust identification and interpolation in H

Abstract: We consider system identification in H∞ in the framework proposed by Helmicki, Jacobson and Nett. An algorithm using the Jackson polynomials is proposed that achieves an exponential convergence rate for exponentially stable systems. It is shown that this, and similar identification algorithms, can be successfully combined with a model reduction procedure to produce low-order models. Connections with the Nevanlinna-Pick interpolation problem are explored, and an algorithm is given in which the identified model interpolates the given noisy data. Some numerical results are provided for illustration. Finally, the case of unbounded random noise is discussed and it is shown that one can still obtain convergence with probability 1 under natural assumptions.

Implicit Linear Systems

Abstract: System models.- The Kronecker form.- Analysis of singularities.- Systems of minimal dimension.- Canonical representations.- Algebraic design applications.- Optimization with quadratic cost.- System identification.- Large-scale systems.- Extensions.

Linear and nonlinear algorithms for identification in H ∞ with error bounds

Abstract: In this paper, a linear and a nonlinear algorithm are presented for the problem of system "identification in H∞", posed by Helmicki, Jacobson and Nett. We derive some error bounds for the linear algorithm which indicate that if the model error is not too high, then this algorithm has good guaranteed error properties. The linear algorithm requires only FFT (fast Fourier transform) computations. A nonlinear algorithm, which requires an additional step of solving a Nehari best approximation problem, is also presented that has the robust convergence property.

Identification of Continuous-Time Systems: Methodology and Computer Implementation

Abstract: 1 Continuous-time models and approaches.- 2 Discrete-time modeling and identification of continuous-time systems: a general framework.- 3 The relationship between discrete time and continuous time linear estimation.- 4 Transformation of discrete-time models.- 5 Methods using Walsh functions.- 6 Use of the block-pulse operator.- 7 Recursive block pulse function method.- 8 Continuous model identification via orthogonal polynomials.- 9 Use of numerical integration methods.- 10 Application of digital filtering techniques.- 11 The Poisson moment functional technique - Some New Results.- 12 Identification, estimation and control of continuous-time systems described by delta operator models.- 13 Identification of multivariable continuous- time systems.- 14 Use of pseudo-observability indices in identification of continuous-time multivariable models.- 15 SVD-based subspace methods for multivariable continuous-time systems identification.- 16 Identification of continuous-time systems using multiharmonic test signals.- 17 Adaptive model approaches.- 18 Nonparametric approaches to identification.- 19 From fine asymptotics to model selection.- 20 Real time issues in continuous system identification.

Robust identification and Galois sequences

Abstract: Worst-case l1 identification is studied for BIBO stable linear shift-invariant systems. It is shown that the Chebyshev identification method when used with Galois input designs satisfies a certain robust convergence property and provides l1 model error bounds in worst-case identification of BIBO stable systems with a uniformly bounded noise set-up. The robust identification methodology developed is compatible with the modelling requirements of modern robust control design.

Parameters identification of an induction machine with regard to dependencies on saturation

Abstract: The author illustrates the basic dependencies of induction machine parameters on flux and current and describes them by simple equations. Differences of the magnetizing current at single-phase and three-phase excitation are considered. A novel identification technique determines accurately all parameters and their dependencies on saturation from a few easy-to-perform offline measurements. This technique has been designed for use at traction drives with direct self-control during system startup. The proposed method has been automated and is well suited for application in the field. Optimal operating points for quasi-stationary operation are derived from identified parameter dependencies and compared to practical measurements. >

Secant-method adjustment for structural models

Abstract: On-orbit testing will be required for final tuning and validation of any mathematical model of large space structures Identification methods using limited response data to produce optimally adjusted property matrices seem ideal for this purpose, but difficulties exist in the application of previously published methods to large space truss structures This article presents new stiffness matrix adjustment methods that generalize optimal-update secant methods found in quasi-Newton approaches for nonlinear optimization Many aspects of previously published methods of stiffness matrix adjustment may be better understood within this new framework of secant methods One of the new methods preserves realistic structural connectivity with minimal storage requirements and computational effort A method for systematic compensation for errors in measured data is introduced that also preserves structural connectivity Two demonstrations are presented to compare the new methods' results to those of previously published techniques

On the duality between fast QR methods and lattice methods in least squares adaptive filtering

Abstract: The authors show that fast QR methods and lattice methods in least squares adaptive filtering are duals and follow from identical geometric principles. Whereas the lattice methods compute the residuals of a projection operation via the forward and backward prediction errors, the QR methods compute instead the weights used in the projections. Within this framework, the parameter identification problem is solved using fast QR methods by showing that the reflection coefficients and tap parameters of a least squares lattice filter operating in the joint process mode are immediately available as internal variables in the fast QR algorithms. This parameter set can be readily exploited in system identification, signal analysis, and linear predictive coding, for example. The relations derived also lead to a fast least squares algorithm of minimal complexity that is a hybrid between a QR and a lattice algorithm. The algorithm combines the order recursive properties of the lattice approach with the robust numerical behavior of the QR approach. >

H/sub 2/ iterative model refinement and control robustness enhancement

Abstract: Many practical applications of control system design based on input-output measurements permit the repeated application of a system identification procedure operating on closed-loop data together with successive refinement of the designed controller. A paradigm is developed for such an iterative design. The key to the procedure is to account for evaluated modeling error in the control design and, equally, to allow for the requirements of the closed-loop controller in performing the identification. With an H/sub 2/ control problem, this is achieved by frequency weighting the linear quadratic control criterion and by filtering the identifier signals in a logical fashion. >

Issues in system identification

Abstract: A brief outline is given of mainstream system identifications, i.e. the typical approaches, algorithms, and properties in the world of data-based model construction. A number of important problems that are not sufficiently understood are pointed out. Particular attention is given to the problem of how to develop constructive and systematic ways to determine suitable model structures, i.e. to move from parameter estimation to system identification. >

Identification of Linear Structures Using Discrete‐Time Filters

Abstract: Most of the previous studies considered structural system identification in the continuous‐time domain. The discrete‐time approach to the problem is more natural since all the recordings are in the discrete‐time form. This study presents a discrete‐time method for system identification by using discrete‐time linear filters. The method itself is well known in electrical and systems engineering fields, and therefore is not new. The objective in the paper is to present the method by emphasising its relation to the more familiar continuous‐domain modal analysis approach that is widely used in structural engineering. In addition to the method, some practical but important problems are also discussed in the paper, such as the processing of data, the selection and validation of models in the identification, and the detection of soil‐structure interaction. As an example, a 12‐story building was identified by using recordings from the magnitude 6.4, San Fernando, California earthquake of February 9, 1971.

Structural element stiffness identification from static test data

Abstract: A finite element based method for static parameter identification of structures is presented for the systematic identification of plate-bending stiffness parameters for a one-third scale, reinforced-concrete pier-deck model. The plate- bending stiffnesses of the pier deck are identified at the element level by using static test data on a subset of the degrees of freedom used to define the finite element model. The finite element model of the reinforced-concrete pier deck is generated by using three-dimensional isoparametric elements to model the beams, and hourglass plate-bending elements to model the orthotropic slab. Several parameter identification examples are performed on the pier deck using simulated static force and displacement measurements. The level of acceptable er­ ror is investigated for the convergence of the algorithm. Probabilistic parameter identification is performed to simulate an actual test setup. It is believed that con­ tinued research of this approach of static parameter identification will lead to a practical procedure for damage assessment and load-carrying capacity determina­ tion of full-scale structures.

Interactive System Identification: Prospects and Pitfalls

Abstract: This book intends to provide users of identification software with the fundamental insight needed to carry out the interactive design of models of physical objects. The text begins with the fundamental conditions for setting up correct identification problems, continues by highlighting the roles of the validation and falsification of models, and concludes with concrete procedures for the interactive design of stochastic dynamic models. The book does not concentrate on the usual blackbox models. It emphasizes the purpose of the design and the importance of supplementing experimental data with the partial knowledge that is often available to the designer. The book also emphasizes the prospects and limitations of identification. It clarifies what can and cannot be inferred about the object under various circumstances, and, consequently, what kind of modelling errors the computer can and cannot diagnose.

On constructing nonlinear observers

Abstract: Two algorithmic approaches to constructing nonlinear observers currently exist. Here one of these is improved by finding an explicit solution to the partial differential equations describing the change of state coordinates, thereby avoiding expensive bracket computations. This simplifies the algorithm and has implications for system identification.

A fast, recursive MIMO state space model identification algorithm

Abstract: The authors present a fast recursive implementation for the ordinary MIMO (multiple input, multiple output output-error state-space model identification, MOESP) algorithm. The core of the implementation is a partial update of an LQ factorization followed by a rank-one update of a SVD (singular value decomposition) step. The computational complexity of a single measurement update is O(L/sup 2/), where L is related to the dimension of the matrices to be processed. When one would straightforwardly apply existing rank-one update schemes as presented by J.R. Bunch et al. (1978), the order of complexity would be O(L/sup 3/). The key point in obtaining this reduction in order of complexity is the rank-one update of a tridiagonal matrix instead of a diagonal matrix. The authors apply the proposed scheme to the identification of slowly time-variant systems and illustrate some of the potential of the MOESP scheme in estimating a nominal state-space model and error bounds when using error-affected measurements. >

Optimal asymptotic identification under bounded disturbances

Abstract: A general framework for analyzing asymptotically optimal algorithms and experiment designs for worst-case identification is described. The authors develop the framework and state the general results. These are then applied to analyze three specific identification problems of stable and unstable plants. >