Showing papers on "System identification published in 1974"

System Identification Parameter and State Estimation

Abstract: System identification: parameter and state estimation , System identification: parameter and state estimation , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Parametrizations of linear dynamical systems: Canonical forms and identifiability

Abstract: We consider the problem of what parametrizations of linear dynamical systems are appropriate for identification (i.e., so that the identification problem has a unique solution, and all systems of a particular class can be represented). Canonical forms for controllable linear systems under similarity transformation are considered and it is shown that their use in identification may cause numerical difficulties, and an alternate approach is proposed which avoids these difficulties. Then it is assumed that the system matrices are parametrized by some unknown parameters from a priori system knowledge. The identiability of such an arbitrary parametrization is then considered in several situations. Assuming that the system transfer function can be identified asymptotically, conditions are derived for local and global identifiability. Finally, conditions for identifiability from the output spectral density are given for a system driven by unobserved white noise.

Approximate linear realizations of given dimension via Ho's algorithm

Abstract: Ho's Algorithm generates exact realizations of finite-dimensional linear systems, given exact data. We discuss here a variant of the algorithm that generates approximate realizations of specified dimension from approximate data.

Optimal inputs for linear system identification

Abstract: This paper considers the design of optimal inputs for identifying parameters in linear dynamic systems. The criterion used for optimization is the sensitivity of the system output to the unknown parameters as expressed by the weighted trace of the Fisher information matrix. It is shown that the optimal energy constrained input is an eigenfunction of a positive self-adjoint operator corresponding to its largest eigenvalue. Several different representations of the optimal input and several methods for its numerical computation are considered. The results are extended to systems with process noise, and the relationship to other criteria for input design are brought out. Three analytical examples are solved in closed form which show that the optimal input is a sum of sine and cosine functions at appropriate frequencies. Optimal elevator deflections for identifying the short period parameters of C-8 aircraft are computed numerically and compared with the doublet input currently in use.

Stable Adaptive Schemes for System Identification and Control - Part II

Abstract: The extension of some of the results contained in Part I [1] to the case when only the plant outputs rather than all its state variables are accessible for measurement is discussed. A unified approach to the synthesis of an adaptive observer is presented whereby the plant state and parameters are simultaneously estimated. Uniform asymptotic stability of the scheme is proved using Lyapunov's direct method. The information provided by the adaptive observer is used to synthesize an adaptive controller for the plant. While all the principal results obtained here are for the case of a single-input single-output plant, extensions to special classes of multivariable systems is indicated.

The Analysis of Closed-Loop Dynamic-Stochastic Systems

Abstract: In the process industries data must often be obtained under conditions of closedloop operation; that is, under conditions where feedback control is being applied. In the analysis of such data care is needed to properly take account of the manner of its generation. In particular, if standard open-looped procedures of model identification, estimation and diagnostic checking are applied to closed-loop data incorrect models niay result and lack of fit not be detected. This paper discusses the identification, estimation and diagnostic checking of closedloop systems and illustrates the ideas on two real sets of data.

Canonical forms for the identification of multivariable linear systems

Abstract: The advantage of using a unique parameterization in a numerical procedure for the identification of a system from operating records has been well established. In this paper several sets of canonical forms are described for state space models of deterministic multivariable linear systems; the members of these sets having therefore the required uniqueness property within the equivalence classes of minimal realizations of the system. In the identification of a stochastic system, it is shown how the problem depends also upon determining a unique factorization of the spectral density matrix of the system, and the sets of canonical forms obtained for the deterministic system are extended to this case.

Identification of multiinput-multioutput transfer function and noise model of a blast furnace from closed-loop data

Abstract: A procedure is described for the identification of multiinput-multioutput transfer function and the disturbance model from closed-loop data. The basic step of the identification procedure is to obtain a multivariate time series model for the input and the output series. A new method-viz., the method of successive orthogonalization is given for the modeling of multiple time series. Real data on closed-loop operation of a blast furnace are analyzed.

Applications of principal component analysis and factor analysis in the identification of multivariable systems

Abstract: The identification of a multivariable stochastic system, usually, involves the estimation of a transfer function matrix, which is a general function of frequency. This estimation involves inversion of a large Hermitian matrix, which sometimes may become unwieldly. In this paper we describe how "principal component analysis" in the frequency domain may be used to replace the input/output variables by some function of smaller dimensions without much "loss of information." The analogy between the "factor analysis" of time series in frequency domain and the minimal realization of state space models is pointed out. The principal component approach described in this paper is applied in the case of a simulated system.

System identification: methods and applications

Abstract: Certain systematic approaches which rely on the use of experimental data for the construction of predictive models are given the name of system identification. These methods in principle, are capable of determining the cause-effect relationship in a physical system (in this case a mathematical model and/or its parameters) if the input excitation and the corresponding system response are known. The techniques of system identification are briefly outlined, followed by a more detailed discussion of the state of knowledge in parameter estimation and application of the methods to equipment design and qualification.

Coupled design of test signals, sampling intervals, and filters for system identification

Abstract: This paper discusses the problem of optimal design of experimental conditions for linear system identification. It is demonstrated that, in general, to achieve maximal return from an experiment, coupled design of all the experimental conditions, namely the test signal, sampling intervals and filters, should be carried out simultaneously. For the case of uniform sampling it is shown that joint design of the presampling filter, sampling rate and input can be carded out in the frequency domain. For the case of nonuniform sampling a sequential design procedure is developed which optimizes the information increment between samples.

Transfer function matrix identification

Abstract: A method is presented for identifying the transfer function matrix of a multi-input multi-output finite-dimensional continuous linear time invariant system from input-output observations in the presence of arbitrary initial conditions. A simple and efficient scheme is provided to handle these unknown initial conditions. The method avoids signal differentiation through the use of multiple integration. A set of equations, linear in the unknown parameters of the system transfer function matrix, are formed using the integrated values of inputs and outputs for different values of time. These equations are modified so as to yield an efficient method for computing the system parameters in the presence of additive measurement noise.

Maximum likelihood identification of power system dynamic equivalents

Abstract: This paper presents a technique for identifying unknown parameters for a dynamic equivalent of a portion of an electric power system from on-line measurements made in another portion of the system. The resulting model is suitable for use in a standard transient stability program such as those used by system analysts for evaluating the security of a proposed or existing system. The method is based on stochastic system identification using the maximum likelihood technique and relies on natural system fluctuation. This paper describes the mathematical development of a maximum likelihood identifier for a dynamic model of a power system. The resulting identification program was tested using a simulated power system tuned to match measurements made on a real system.

On hierarchical structure adaptation and systems identification

Abstract: This paper demonstrates that Magill's method of structure adaptation can be incorporated into the framework of hierarchical estimation and system identification. The associated reduction in computational requirements potentially allows efficient parallel processing of these algorithms for use with systems of high dimension.

III-posed and well-posed problems in systems identification

Abstract: Impulse response identification almost always leads to an ill-posed mathematical problem. This fact is the basis for the well-known numerical difficulties of identification by means of the impulse response. The theory of regularizable ill-posed problems furnishes a unifying point of view for several specific methods of impulse response identification. In this paper we introduce a class of input/output representations, which we call λ-representations, for linear, time-invariant systems. For many cases of practical interest the identification of one of these representations is mathematically well-posed. Its determination is thus relatively insensitive to certain experimental uncertainties, and rational error-in-identification bounds may be found, so that λ-identification is often an attractive alternative to impulse response identification in the nonparametric modeling of physical systems which must be identified from input/ output records. We investigate the effects of input and output uncertainties (noise) on λ-identification, and discuss the problem of finding minimal realizations from these representations. We illustrate the work with an example of electromagnetic pulse (EMP) threat prediction using experimental data. Hard error bounds are provided on the predicted threat. For this problem, the appropriate λ-representation turns out to be the ramp response.

Hierarchical system identification of states and parameters in interconnected power systems

Abstract: This paper presents an application of hierarchical identification procedures of the previous paper to the identification of interconnected power system states and parameters from input—output observed data. A three-area interconnected power system model is used to demonstrate the decomposition of the original system based on its particular characteristics and the implementation of hierarchical algorithms for system identification. The adaptivity of these procedures to structural changes are also illustrated. Numerical results are obtained by conducting a digital simulation of the three-area system and using the hierarchical identification and coordination algorithms to estimate the states and unknown system parameters. Computational aspects of the hierarchical system identification solutions are discussed.

Frequency-variation method for system identification

Abstract: A frequency-variation method is established for identifying a linear system transfer function from a single set of frequency response data. The method generally applies three different Cauer continued fraction forms. Based on the real and imaginary parts of the frequency response data, a corresponding transfer function can be identified. The identification processes can be carried out with a digital computer.

On the identification of continuous linear processes

Abstract: 1ON THE IDENTIfICATION Of CONTINUOUS LINEAR PROCESSES

Parametric solution to the joint system identification and optimization problem

Abstract: This study is concerned with the simultaneous identification and optimization of static systems. The necessity and the advantages of an integrated approach to the identification and optimization of the system model is established theoretically as well as computationally. A parametric approach to the integrated problem is proven to converge to the integrated problem solution. The general methodology of decomposition of large-scale systems is extended by implementingfeasible decomposition of the joint problem. A multilevel approach is then utilized to successfully solve example problems. Handling the system constraints via a penalty-function technique is shown to be an efficient approach when using the parametric formulation of the joint problem. Numerical results for two example problems are presented using the Univac 1108 digital computer, revealing the economic advantages and disadvantages of the integrated approach to the identification and optimization problems.

Subcritical flutter testing and system identification

Abstract: Treatment is given of system response evaluation, especially in application to subcritical flight and wind tunnel flutter testing of aircraft. An evaluation is made of various existing techniques, in conjuction with a companion survey which reports theoretical and analog experiments made to study the identification of system response characteristics. Various input excitations are considered, and new techniques for analyzing response are explored, particularly in reference to the prevalent practical case where unwanted input noise is present, such as caused by gusts or wind tunnel turbulence. Further developments are also made of system parameter identification techniques.

On simultaneous structure and parameter identification of linear dynamical systems

Abstract: In the identification of linear systems the model may be of lower or higher dimension than the system. The second case which is of particular interest requires a proper formulation of the model equations to guarantee a finite solution of the parameter estimate. Without noise the solution of the parameter vector is, in general, not unique. With noise at the system output its estimate, though biased, is shown to be unique. If a model of higher dimension is used in conjunction with an algorithm for unbiased estimation, the estimate, though finite, may be nonunique. Numerator and denominator factorization should be used to reveal the excess pairs of poles and zeros which cancel. Thus, the structure of the system can be identified along with its parameters.

Identification of Aircraft Stability and Control Parameters Using Hierarchical State Estimation

Abstract: Previous attempts to identify aircraft stability and control derivatives from flight test data, using three-degrees-of-freedom (3-DOF) longitudinal or lateral-directional perturbation equation-of-motion models, suffer from the disadvantage that the coupling between the longitudinal and lateral-directional dynamics has been ignored. In this paper, the identification of aircraft stability parameters is accomplished using a more accurate 6-DOF model which includes this coupling. Hierarchical system identification theory is used to reduce the computational effort involved. The 6-DOF system of equations is first decomposed into two 3-DOF subsystems, one for the longitudinal dynamics and the other for the lateral-directional dynamics. The two subsystem parameter identification processes are then coordinated in such a way that the overall system parameter identification problem is solved. Next, a six-subsystem decomposition is considered. Computational considerations and comparison with the unhierarchically structured problem are presented.

Synthesis of distributed systems by network matching

Abstract: A distributed parameter system described by the general linear telegraphers equations is considered. A new equivalent network for the distributed system is developed, such that the parameters of this network satisfy stable, initial valued Riccati equations. The identification of system parameters is translated into a network matching problem.

Time-domain synthesis of optimal inputs for system identification

Abstract: In this paper new results are derived for the computation of D-optimal randomized input designs to identify unknown parameters in linear systems with process noise and in non-linear and distributed parameter systems without process noise. The Kiefer-Wolfowitz experimental design approach that was extended earlier by the author to frequency-domain synthesis of optimal inputs is generalized here to the computation of optimal probability measures on the space of time-domain inputs. Both discrete-time and continuous-time systems are considered and algorithms converging to the global optima are given. Extensions to other criteria and bounds for suboptimal designs are also derived.

System identification in behavioural science

Abstract: An identification method is described which allows the approximation of experimental observations by means of a phenomenalistic model. The method is theoretically based on system theory and is adapted to the needs of behavioural science. Special emphasis will be laid on a system representation, which is transferable to a large group of dynamic systems as well as on an exact formulation of the assumptions connected with the proposed method. A short summary of results determined by a behaviour analysis in the field of social psychology will give a practical view of the possibilities and limits of the described identification method.