Showing papers on "Transfer function published in 1975"

Fast and accurate switching transient calculations on transmission lines with ground return using recursive convolutions

Abstract: The paper presents a new approach to the calculation of transients on transmission lines with frequency-dependent parameters. Its purpose is to obtain significant computer-time savings by avoiding convolutions. This is achieved by approximating all line and ground distortions and also time variable characteristic admittances by exponential functions, i.e. solutions of linear differential equations. The method produces a simple Norton-type line equivalent which permits its incorporation into an existing system representation like the B.P.A. program for the calculation of transients. The program has been tested on systems of different degrees of complexity and proved to be superior, in terms of speed and accuracy, to other advanced methods.

Digital signal analysis

Abstract: Review of least squares, orthogonality and the Fourier series review of continuous transforms transfer functions and convolution sampling and measurement of signals the discrete Fourier transform the fast Fourier transform the z-transform non-recursive digital systems digital and continuous systems simulation of continuous systems analogue and digital filter design review of random functions correlation and power spectra least-squares system design random sequences and spectral estimation.

Linear system reduction using Pade approximation to allow retention of dominant modes

Abstract: A new method of reduction in order of linear time-invariant systems is introduced. It combines the desirable features of the time-moments and the modal methods of reduction. The methods is based on the concept of Pade approximation about more than one point. The reduced model derived by this method, retains the dominant modes (or any desirable modes) and fits the initial time-moments of the system The method is extended to the problem of reducing a high-order multivariable system described by its matrix transfer function. Several illustrative examples are discussed throughout the paper.

Least-squares identification of closed-loop systems

Abstract: The problem of least-squares estimation of closed-loop systems is examined. The particular configuration considered is the single input-single output discrete linear system controlled by a linear, stationary feedback regulator. Results are obtained which determine the conditions for uniqueness and consistency of the least-squares estimates of the forward-path transfer function. In particular, it is shown that if two orthogonal unobservable noise sources are present, one in each path, the system is uniquely identifiable. When the feedback path is noise-free the uniqueness of the estimates is dependent upon the order of the regulator regression polynomials. The consistency of the estimates in the case of a white forward-path disturbance is assured provided that there is at least one delay term in the loop.

Scattering analysis of nonlinearly loaded antennas

Abstract: A novel technique-Volterra series analysis-is applied to the analysis of a nonlinearly loaded antenna. The electromagnetic field problem is first reduced to a network problem by application of the method of moments. The nonlinear network problem is then solved using the Volterra technique. A procedure with sinusoidal inputs for obtaining a time domain solution from the frequency domain solution without using fast Fourier transform techniques is demonstrated. The i-v characteristic of the nonlinear load is approximated from scattered power measurements. The derived i-v characteristic is then used to predict scattered power levels at different intermodulation responses of the loaded antenna.

Superiority of transfer function over state-variable methods in linear time-invariant feedback system design

Abstract: The objectives and achievements of state-variable methods in linear time-invariant feedback system synthesis are examined. It is argued that the philosophy and objectives associated with eigenvalue realization by state feedback, with or without observers, are highly naive and incomplete in the practical context of control systems. Furthermore, even the objectives undertaken have not really been attained by the state-variable techniques which have been developed. The extremely important factors of sensor noise and loop bandwidths are obscured by the state-variable formulation and have been ignored in the state-variable literature. The basic fundamental problem of sensitivity in the face of significant plant parameter uncertainty has hardly received any attention. Instead, the literature has concentrated primarily on differential sensitivity functions and even those results are so highly obscured in the state-variable formation as to lead to incorrect conclusions. In contrast, the important practical considerations and constraints have been clearly revealed and considered in the transfer function formulation. Differential sensitivity results are simple and transparent. For single input-output systems, there exists an exact design technique for achieving quantitative sensitivity specifications in the face of significant parameter uncertainty, which is optimum in an important practical sense. This problem is much more difficult and has not been completely solved for multivariable systems, but it has at least been realistically attacked by some transfer function methods. Finally, the concepts of controllability and observability so much emphasized in the state-variable literature are examined. It is argued that their importance in this problem class has been greatly exaggerated. On the one hand, transfer function methods can be used to check for their existence. On the other hand, nothing is lost when they are ignored, if the synthesis problem is treated as one with parameter uncertainty by transfer function methods.

A continuous model for the tapped-inductor boost converter

Abstract: A continuous, low-frequency, small-signal averaged model for the tapped-inductor boost converter with input filter is developed and experimentally verified, from which the dc transfer function and the small-signal line input and duty ratio input describing functions can easily be derived. A new effect due to storage-time modulation in the transistor switch is shown to explain observed excess filter damping resistance without associated loss in conversion efficiency. The presence of an input filter can cause a severe disturbance, even a null, in the control duty ratio describing function, with consequent potential performance difficulties in a converter regulator.

The feedback interconnection of lumped linear time-invariant systems☆

Abstract: This paper considers the feedback interconnection of two multi-input multi-output subsystems characterized by rational transfer functions Ĝ1 and Ĝ functions are not assumed to be proper nor exponentially stableThe effect of output disturbances on stability is taken into account. Ten examples are given to show that instabilities may appear anywhere around the loop. Next, under a sequence of successively more restrictive assumptions, we prove four sets of necessary and sufficient conditions for the exponential stability of the system. Using coprime factorizations, we obtain four equivalent expressions for the system characteristic polynomial. Two stability tests are derived, the first one is based exclusively on transfer functions, the second is based on the characteristic polynomial. The paper ends by providing translation rules for reformulating all definitions and theorems for the discrete-time case (i.e. instead of Laplace transforms use Z-transforms, etc.).

Dynamics of the head-neck system in response to small perturbations: analysis and modeling in the frequency domain.

Abstract: The response of the head-neck system to forces of small amplitude (up to 15 N) is described. Sinusoidal (0.6–20 Hz) and impulsive (duration: 100 msec) forces are applied in the sagittal plane to the head of the subject who is instructed to resist the disturbancy. In the case of sinusoidal forces of frequency less than about 2 Hz the active effort to resist the disturbancy results in a largely distorted sinusoidal displacement. Above this frequency the response becomes almost linear. The variations with frequency of the amplitude and the phase of the linear response relative to the applied force (transfer function) are used to characterize the dynamics of the system. The transfer functions evaluated from the impulse response are very similar in shape to those obtained with sinusoidal forces. In both cases the results suggest that the system behaves as a quasi-linear second order system with two degrees of freedom. The most prominent nonlinearities, beyond those present in the low frequency range, are related to the properties of the neck muscles. In particular, the transfer functions clearly show that the rigidity of the system increases as a function of the continuous value of the applied force. On the basis of previous work, both the passive properties of the muscles and those pertaining to the neuronal control system are pooled together in the form of viscoelastic parameters. A simple model of the system is introduced and applied to the experimental results. Its main features are 1) the presence of two centers of rotation. 2) the dependency of the viscoelastic parameters (stiffness and viscosity) on the frequency. It is suggested that both these features are necessary and sufficient to account for the observed behaviour above 2 Hz.

The finite Fourier transform definition of an edge on the solar disk.

Abstract: A new technique for locating the edge of the Sun is proposed. The technique uses a finite Fourier transform of the observed limb darkening function to achieve reduced sensitivity to atmospheric and instrumental effects and heightened sensitivity to the shape of the intrinsic limb darkening function. A theory is developed that predicts these sensitivities. In order to facilitate wider application, general relations are calculated. A testing program which complements the theory is also reported. The location of the edge is shown to be influenced only by solar phenomena down to the milli-arcsecond range. (AIP)

Singular perturbation analysis of the transfer function matrices of a class of multivariable linear systems

Abstract: Singular perturbation methods are used to demonstrate that the transfer function matrices of multivariable linear systems containing small ‘parasitic’ elements have a distinctive structure which can be exploited in the design of controllers fur systems of this class by the application of frequency-domain methods.

Complex Demodulation of Geomagnetic Data and the Estimation of Transfer Functions

Abstract: Summary Complex demodulation is a technique that allows the examination of the variation with time of the amplitude and phase of selected frequency components of a time series. Complex demodulates can form the basis for estimates of the power spectrum of the time series. They are computed most efficiently by the use of the Fast Fourier Transform. Two examples of the application of complex demodulation to the analysis of geomagnetic time series are given. In the first example, the technique is used to demonstrate the modulation of a periodic phenomenon, the daily variation, by mechanisms with apparent periods of 6 months and 27 days. The second example, discussed in greater detail, is an application to the calculation of Geomagnetic Deep Sounding transfer functions. The spectra of simultaneous records of variations in the three components (H, D and Z) of the magnetic field recorded at a single station are divided into bands, and each band demodulated in turn. The polarization azimuth of the horizontal field at each instant of time can be computed, and, for the example considered, the azimuth tends to be constrained to the north-south direction. The detailed response of the local conductive structure to different source field polarizations can be demonstrated. Everett & Hyndman's Unit Vector Method is used to investigate the effect of the observed bias in the azimuth of the source field on estimates of GDS transfer functions made by conventional methods. The demodulates can be used to devise criteria for selecting events according to their signal/noise ratio. The selection procedure is most useful when applied to records containing only sporadic activity in the frequency band of interest.

Design of decoupled control systems A frequency domain approach

Abstract: In this paper a frequency domain approach is used for the design of decoupled control systems. Necessary and sufficient conditions for the existence of proportional output feedback laws as well as a constructive procedure for finding these feedback laws are given. A simple relationship between the overall system transfer functions and the output feedback laws is derived.

Four-quadrant DC variable-speed drives—Design considerations

Abstract: An overview is given of the design criteria applicable to a variable-speed dc drive with dual-converter power supply. The control strategy, machine-converter and controller transfer functions, the problems associated with discontinuous conduction, and power flow reversal are considered. A representative bibliography of the voluminous literature on this topic is included.

A coherent optical feedback system for optical information processing

Abstract: A unique optical feedback system for coherent optical data processing is described. With the introduction of feedback, the well-known transfer function for feedback systems is obtained in two dimensions. Operational details of the optical feedback system are given. Experimental results of system applications in image restoration, contrast control and analog computation are presented.

Two design techniques for digital phase networks

Abstract: Two computer-aided algorithms for the design of all-pass digital filters are presented. The first technique is based on a linear programming approach to solving the approximation problem posed by the minimax design of an all-pass digital filter. A new iterative algorithm with stability constraints is offered for direct form design. The second technique implements a gradient search for those quadratic factors of an all-pass transfer function that lead to a locally optimal approximation (in the least-squares sense) of a desired phase function. New initial guess procedures and the parameterization of linear-phase offset enhance the least-squares design procedure. Examples illustrating the result of both procedures are included.

Transfer-function-parameter estimation from frequency response data: A FORTRAN program

Abstract: A FORTRAN computer program designed to fit a linear transfer function model to given frequency response magnitude and phase data is presented. A conjugate gradient search is used that minimizes the integral of the absolute value of the error squared between the model and the data. The search is constrained to insure model stability. A scaling of the model parameters by their own magnitude aids search convergence. Efficient computer algorithms result in a small and fast program suitable for a minicomputer. A sample problem with different model structures and parameter estimates is reported.

Analysis of Multiloop, Multirate Sampled=Data Systems

Abstract: Based upon new identities between z-transforms at a basis rate, z-transforms at faster rates, and modified z-transforms, the equivalence between the frequency decomposition method and the switch decomposition method is precisely presented so that results of one method are easily obtained from results of the other. Next, a method is developed for determining the closed loop transfer function of multiloop, multirate sampled-data systems with noninteger ratio sampling rates. Previously, this process involved solving a complex system of equations with rational polynomial coefficients. Herein, this is avoided by introducing a systematic decomposition of matrix operators which naturally arise from the switch decomposition method. The matrix operators are simplified by introducing the shifted transforms of signals sampled at one of the faster rates.

Finite band approximation for distributed and digital selective linear phase transfer functions

Abstract: Using the recently derived formula which interpolates to a linear phase response at equidistant frequency intervals in a distributed variable, transfer functions are constructed which exhibit flat amplitude and linear phase characteristics over a finite band. Reciprocal realizations for the implementation in distributed structures are derived, together with a non-reciprocal version ideally suited for recursive digital filter design. Their superiority over the corresponding maximally flat solutions is also illustrated.

Identification of Nonlinear Systems in Frequency Domain

Abstract: A frequency domain technique for identifying a class of nonlinear systems is presented. The class of nonlinear systems we consider in this paper consists of a power series nonlinearity sandwiched between two linear systems and the problem we address is one of identifying the transfer functions of the linear systems and the coefficients of the power series nonlinearity from the terminal behavior of the system. The identification procedure is based on a frequency domain model of the nonlinear system. The system is modeled by a set of nonlinear transfer functions in the frequency domain and the relationships between the transfer functions of the linear system, the power series coefficients of the nonlinearity, and the nonlinear transfer functions of the system are developed. The identification procedure is based on a simple algorithm for factoring the non-linear transfer functions of the system. The experimental data required for applying our identification procedure consists of the amplitude response of the system to multitone sinusoidal input. A minimum phase transfer function in a single variable is used to approximate the experimental data and the repeated application of the factoring algorithm leads to the identification of the system. Examples illustrating the use of the proposed procedure are also presented.

Noise burst source for transfer function testing

Abstract: A method and apparatus for accurately measuring the transfer function of a linear system or the linear part of a non-linear system. This is accomplished by using a spectrum estimation technique which utilizes a "transient random" stimulus consisting of a short burst of random signals applied to a system under test for a period of time that is shorter than the time used to measure a single spectrum. Thus the measurement period includes the time for the "transient random" burst and for the response of the system to substantially decya to zero. The spectrum measured over this period is used to form a first estimate of the transfer function. Other "transient random" stimuli, uncorrelated with the prior records, are then generated and the above procedure is repeated to achieve an average value for the transfer function estimate of the desired accuracy. Through the use of several "transient random" stimuli, leakage and distortion in the measurement are minimized, thus greatly improving the accuracy of the estimation technique in measuring the transfer function of the system under test.

A frequency domain approach to minimal-order observer design for several linear functions of the state

Abstract: A design procedure for minimal-order observers which is applicable to linear, observable, time-invariant systems is developed based on certain polynomial matrices associated with the transfer functions of the plant. The approach is to select the observer dynamics so that the feedback control law is satisfied with a minimal-order system. The method is a frequency domain technique but is significantly different from earlier results. Necessary and sufficient conditions for construction of a minimal-order observer to observe several linear functions of the state are given.

Transfer function synthesis

Abstract: The paper describes a method for assessing the admissibility of a desired transfer function, and synthesizing it, for a linear multivariable system using constant feedback and cascade matrices. The simplicity of the method is its main feature

Identification of linear time-invariant systems using exponential signals

Abstract: A new method of system identification for linear time invariant systems based on Prony's method of exponential interpolation has been suggested in this correspondence. This method of identification uses an exponential signal for system excitation and has the advantages of simplicity, independent determination of numerator and denominator of the system transfer function, and determination of initial conditions without any difficulty. The simplicity of the method has resulted because of the simple but particularly suitable formulation in the state variable form used.

Minimal realization of transfer function matrices A comparative study of different methods

Abstract: A comparative study is made of three basically different methods for obtaining minimal-order realizations of linear multivariable systems in the form of state equations for specified rational transfer function matrices. Computational efficiency and suitability for practical implementation are the main criteria used for the comparison. The possibilities of direct realization in canonical forms suitable for special applications are also examined.

Dyadic expansion, characteristic loci and multivariable-control-systems design

Abstract: Recent results in the dyadic representation of system interactions are used to derive a systematic approach to the manipulation and compensation of the characteristic loci of a system described by the NxN transfer function matrix (G)s, using rational transfer function approximations to the characteristic loci

Determination of matrix transfer function in the form of matrix fraction from input-output observations

Abstract: This short paper concerns the identification of a linear time-invariant discrete system represented by a matrix transfer function in the form of a matrix fraction. The relations between external and internal descriptions are discussed, and all matrix transfer functions satisfying given input-output observations are determined.

The synthesis of transfer-function matrices by output feedback

Abstract: A procedure is presented for the synthesis of multi-input multi-output linear time-invariant control systems using output feedback and if necessary a dynamic device. This additional dynamic part has the structure of a reduced order observer, but its order and parameters are determined rather to achieve a resultant closed-loop transfer matrix than to produce an estimate for unaccessible state variables or for linear functions of state variables. The given method allows in a simple manner for incorporation of additional design specifications relating to control effort and sensitivity properties.