Showing papers on "Transfer function published in 2000"

Nonlinearity in Structural Dynamics: Detection, Identification and Modelling

Abstract: Summary chapter and guidelines on nonlinear procedures: Flow diagrams. Why not dynamical systems theory. Summary of linear system theory: Continuous-time. Discrete-time. Dynamic testing of linear and nonlinear structures: Simple procedures for detecting nonlinearity in dynamic testing. Sine, Chirp, Random, Impulse etc. Linearisation. Correlations-coherence. FRFs of linear and nonlinear systems: Harmonic balance. Averaging methods. Nyquist plots. Carpet plots. MDOF systems. Hilbert transform - a practical approach: Definition in terms of odd/even functions. Time-frequency domain definitions. Computation - fast method. Correction terms. Principal component analysis. Corehence. Damping estimation (Khalid's work). Linearisation from random testing. Spectral moments. Hilbert transform - a complex analytical approach: Contour integrals. Titchmarsh's theorem. Artificial noncausality. Correction for asymptotic behaviour. Viscous v. Hysteretic damping - exponential integrals. Pole-zero decomposition - estimation without truncation. Restoring force surfaces and direct parameter estimation: Masri/Caughey theory. Link models/Khalids approach. Application requirements - integration/differentiation of data. Least-squares estimation: Normal equations. Orthogonal estimator. SVD. Recursive LS. - forgetting factors. Discrete-time methods: NARMAX. AVD. Model validity. Functional series: Volterra series. Existence, uniqueness, convergence. Connection with Green's functions - calculation - symmetries. Fliess/Lamnabhi power series approach. Wiener series - high-dimensional correlations - Volterra limit. Higher order FRFs/Transfer functions: Harmonic probing. Interpretaton. SDOF/MDOF systems. Hypercurve fitting (S. Gifford). Convergence revisited (Dr Lee). Neural networks: Multi-layer perceptrons. Radial basis functions. Modelling nonlinear systems. Dynamics neurons. Networks as nonlinear dynamical systems. Classification of nonlinear systems: Pattern recognition/feature extraction. Wigner-Ville distribution. Wavelet transform. Neural networks. FRFs for classification SDOF/MDOF. Nonlinear least-squares: Piecewise-linear systems. Hysteretic systems. Yar/Hammond - GA parameter estimation. Gradient descent - shock absorber model.

Out of control because of harmonics-an analysis of the harmonic response of an inverter locomotive

Abstract: Presents a method to use linear analysis to capture the frequency coupling of nonlinear and time-varying components. System stability is analyzed by connecting the harmonic transfer functions of the different component models. This facilitates an object-oriented approach to modeling, which supports reuse of models. An analysis of the complete railway system is, of course, difficult. Several locomotives can be moving along the power distribution line at the same time, and depending on the distance between them, the interaction changes. The power consumption also changes, depending on operating modes. During normal operation, energy is consumed from the network, but as modern locomotives use electrical braking, the power flow changes direction during deceleration, and energy is delivered back to the grid. The inverter trains are not passive systems. The converters are controlled with only limited system knowledge (local measurements of currents and voltages), making analysis and control design an even bigger challenge.

Output regulation for linear distributed parameter systems

Abstract: This work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator, in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system. In particular it is shown that the full state feedback and error feedback regulator problems are solvable, under the standard assumptions of stabilizability and detectability, if and only if a pair of regulator equations is solvable. For linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in Francis (1997) and Isidori and Byrnes (1990). We also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function. Examples are given of periodic tracking, set point control, and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system.

A novel current tracking method for active filters based on a sinusoidal internal model

Abstract: A new current control method based on the internal model principle in control theory is proposed. It introduces a sinusoidal internal model into the control system. It does not use any coordinate transformations. The method can be used for tracking an arbitrary number of harmonics; a DC component or a fundamental frequency component signal. It is applied to a single-phase PWM inverter and active filter. The validity is confirmed by simulation and experimental results.

Comprehensive theory of dispersion in graded-index optical fibers

Abstract: This paper presents a theoretical investigation on the dispersion in graded-index silica glass fibers under overfilled launching with equal excitation of modes. This theory incorporates both chromatic effect and modal contribution which takes not only the modal delay into account but also the distributed loss and mode-coupling. Random microbends are considered to be the most dominant source of coupling. All index perturbations and intrinsic core diameter variations are assumed to be negligible, but they could readily be included without changing the basic structure of the model. The 3-dB bandwidth is analyzed through the study of the fiber transfer function which introduces the wavelength and modal effects as two separate filter functions. The formal derivation of the chromatic transfer function is analytical. On the other hand, the modal transfer function is obtained by numerically solving the power flow equation in the frequency domain using Crank-Nicholson method. As an application, the results are illustrated showing, in particular, the influence of the fiber core/outside diameters, for the first time.

Robust H/sub 2//H/sub /spl infin// filtering for linear systems with error variance constraints

Abstract: In this correspondence, we consider the robust H/sub 2//H/sub /spl infin// filtering problem for linear perturbed systems with steady-state error variance constraints. The purpose of this multiobjective problem is to design a linear filter that does not depend on the parameter perturbations such that the following three performance requirements are simultaneously satisfied. (1) The filtering process is asymptotically stable. (2) The steady-state variance of the estimation error of each state is not more than the individual prespecified value. (3) The transfer function from exogenous noise inputs to error state outputs meets the prespecified H/sub /spl infin// norm upper bound constraint. We show that in both continuous and discrete-time cases, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like equations/inequalities. We present both the existence conditions and the explicit expression of desired robust filters. An illustrative numerical example is provided to demonstrate the flexibility of the proposed design approach.

Introduction to fractional linear systems. Part 1. Continuous-time case

Abstract: In the paper, the class of continuous-time linear systems is enlarged with the inclusion of fractional linear systems. These are systems described by fractional differential equations. It is shown how to compute the impulse, step, and frequency responses from the transfer function. The theory is supported by definitions of fractional derivative and integral, generalisations of the usual. An introduction to fractal signals as outputs of fractional differintegrators is presented. It is shown how to define a stationary fractal.

Linear dynamic modeling of a uni‐axial servo‐hydraulic shaking table system

Abstract: This paper focuses on the development of a linear analytical model (even though servo-hydraulic actuation systems are inherently non-linear, especially for large amplitude simulations — near the performance capacity of the system — linearized models proved experimentally to be quite effective overall in capturing the salient features of shaking table dynamics) of a uni-axial, servo-hydraulic, stroke controlled shaking table system by using jointly structural dynamics and linear control theory. This model incorporates the proportional, integral, derivative, feed-forward, and differential pressure gains of the control system. Furthermore, it accounts for the following physical characteristics of the system: time delay in the servovalve response, compressibility of the actuator fluid, oil leakage through the actuator seals and the dynamic properties of both the actuator reaction mass and test structure or payload. The proposed model, in the form of the total shaking table transfer function (i.e. between commanded and actual table motions), is developed to account for the specific characteristics of the Rice University shaking table. An in-depth sensitivity study is then performed to determine the effects of the table control parameters, payload characteristics, and servovalve time delay upon the total shaking table transfer function. The sensitivity results reveal: (a) a potential strong dynamic interaction between the oil column in the actuator and the payload, and (b) the very important effect of the servovalve time delay upon the total shaking table transfer function. Copyright © 2000 John Wiley & Sons, Ltd.

Adaptive digital correction of analog errors in MASH ADCs. I. Off-line and blind on-line calibration

Abstract: Cascaded delta-sigma (MASH) modulators for higher order oversampled analog-to-digital conversion rely on precise matching of contributions from different quantizers to cancel lower order quantization noise from intermediate delta-sigma stages. This first part of the paper studies the effect of analog imperfections in the implementation, such as finite gain of the amplifiers and capacitor ratio mismatch, and presents algorithms and architectures for digital correction of such analog imperfections, as well as gain and spectral distortion in the signal transfer function. Digital correction is implemented by linear finite-impulse response (FIR) filters, of which the coefficients are determined through adaptive off line or on-line calibration. Of particular interest is an on-line "blind" calibration technique, that uses no reference and operates directly on the digital output during conversion, with the only requirement on the unknown input signal that its spectrum be bandlimited. Behavioral simulations on dual-quantization oversampled converters demonstrate near-perfect adaptive correction and significant improvements in signal-to-quantization-noise performance over the uncalibrated case, using as few as 5 FIR coefficients. An alternative on line adaptation technique using test signal injection and experimental results from silicon are presented in the second part, in a companion paper.

Transfer function of current modulator in PWM converters with current-mode control

Abstract: Several different expressions have been derived in previous publications for the transfer function of the current modulator used in pulsewidth modulated (PWM) dc-dc power converters with current-mode control. These expressions give results higher than the measured ones and exhibit many other problems, e.g., one expression gives an infinite value when no slope compensation is used. This paper presents a derivation for the transfer function of the current modulator used in PWM converters with fixed-frequency, trailing-edge modulation, peak-current-mode control for two cases: without and with slope compensation. In addition, feedforward terms are also derived.

Sensitivity of automatic control systems

Abstract: Preface Parametric Models State Variables and Control System Parameters Parametric Models of Control Systems Sensitivity Functions and their Applications Finite-Dimensional Continuous Systems Finite-Dimensional Continuous Systems Depending on a Parameter Second Lyapunov's Method in Sensitivity Theory Sensitivity on Infinite Time Intervals Sensitivity Analysis of Self-Oscillating Systems in the Time Domain Sensitivity of Non-Autonomous Systems Sensitivity of Solutions of Boundary Value Problems Finite-Dimensional Discontinuous Systems Sensitivity Equations for Finite Dimensional Discontinuous Systems Sensitivity Equations for Relay Systems Sensitivity Equations for Pulse and Relay-Pulse Systems Discontinuous Systems Given by Operator Models Operator Parametric Models of Control Systems Operator Models of Discontinuous Systems Sensitivity of Operator Models Sensitivity Equations of Relay and Pulse Systems Non-Time Characteristics Sensitivity of Transfer Function and Frequency Response of Linear Systems Sensitivity of Zeros and Poles Sensitivity of Eigenvalues and Eigenvectors of Linear Time Invariant Control Systems Sensitivity of Integral Quality Indices Indirect Characteristics of Sensitivity Functions Sensitivity Invariants Sensitivity Invariants of Time Characteristics Root and Transfer Function Sensitivity Invariants Sensitivity Invariants of Frequency Responses Sensitivity Invariants of Integral Estimates Sensitivity Invariants for Gyroscopic Systems Sensitivity of Mathematical Programming Sensitivity of Linear Programming Problems Sensitivity of Optimal Solutions of Non-Linear Programming Problems Sensitivity of a Simplest Variational Problem Sensitivity of Variational Problems with Flexible Boundaries and Corner Points Sensitivity of Variational Problems on Conditional Extremum Applied Sensitivity Problems Direct and Inverse Problems of Sensitivity Theory Identification of Dynamic Systems Distribution of Parameter Tolerance Synthesis of Insensitive Systems Numerical Solution of Sensitivity Equations

Evaluation of an algorithm for the assessment of the MTF using an edge method.

Abstract: An algorithm to calculate the presampling modulation transfer function (MTF) of an imaging system from an angled edge image has its own inherent transfer function. Factors such as the angle of the sampling aperture to the edge, registration of edge function profiles using the determined edge angle, differentiation, smoothing, and folding all combine to produce the frequency response of the algorithm. In this work, the profile registration transfer function accounting for an error in the determined edge angle has been derived. This has been incorporated with other, previously reported, algorithm component transfer functions to fully characterize the MTF calculation algorithm. When registering profiles, small errors in the edge angle determination were found to result in large errors in the MTF, as the misalignment errors increase with the number of profiles. For example, registering 50 profiles a 0.07 degree error in a 7 degree edge angle (1% error) produces a 36% error in the MTF at the system cutoff frequency f=f(c) when profiles are oversampled at a frequency f(s)=8f(c)(f(c) is defined as the maximum frequency reproducible without aliasing when sampling at the limiting system Nyquist frequency f(s) = 2f(c)). These results highlight the importance of quantifying the transfer function of the algorithm used to determine an imaging system modulation transfer function. The MTF calculation algorithm and the transfer function analysis have been incorporated into a Windows-based software program to be made available for general use.

Introduction to fractional linear systems. Part 2. Discrete-time case

Abstract: In the paper, the class of discrete linear systems is enlarged with the inclusion of discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how io compute the impulse response and transfer function. Fractal signals are introduced as output of special linear systems: fractional differaccumulators, systems that can be considered as having fractional poles or zeros. The concept of fractional differaccumulation is discussed, gencralising the notions of fractal and lif noise, and introducing two kinds of fractional differaccumulated stochastic proccss: hyperbolic, resulting from fractional accumulation (similar to the continuous-time casc), and parabolic noise, resulting from fractional differencing.

Radiation modal expansion: Application to active structural acoustic control

Abstract: This paper demonstrates active structural acoustic control using multiple input/output adaptive sensoriactuators combined with radiation filters and a feedback control paradigm. A new method of reduced order modeling/design of radiation filters termed radiation modal expansion (RME) is presented. For the experiments detailed in this paper, the RME technique reduced the modeling of the radiation matrix from 400 transfer functions to 6 transfer functions (multiplied by a constant transformation matrix). Experimental results demonstrate reductions of radiated sound power on the order of 5 dB over the bandwidth of 0–800 Hz.

Fundamentals of Signals and Systems Using the Web and MATLAB

Abstract: Preface 1 FUNDAMENTAL CONCEPTS 1.1 Continuous-Time Signals 1.2 Discrete-Time Signals 1.3 Systems 1.4 Examples of Systems 1.5 Basic System Properties 1.6 Chapter Summary Problems 2 TIME-DOMAIN MODELS OF SYSTEMS 2.1 Input/Output Representation of Discrete-Time Systems 2.2 Convolution of Discrete-Time Signals 2.3 Difference Equation Models 2.4 Differential Equation Models 2.5 Solution of Differential Equations 2.6 Convolution Representation of Continuous-Time Systems 2.7 Chapter Summary Problems 3 THE FOURIER SERIES AND FOURIER TRANSFORM 3.1 Representation of Signals in Terms of Frequency Components 3.2 Trigonometric Fourier Series 3.3 Complex Exponential Series 3.4 Fourier Transform 3.5 Spectral Content of Common Signals 3.6 Properties of the Fourier Transform 3.7 Generalized Fourier Transform 3.8 Application to Signal Modulation and Demodulation 3.9 Chapter Summary Problems 4 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS 4.1 Discrete-Time Fourier Transform 4.2 Discrete Fourier Transform 4.3 DFT of Truncated Signals 4.4 FFT Algorithm 4.5 Application to Data Analysis 4.6 Chapter Summary Problems 5 FOURIER ANALYSIS OF SYSTEMS 5.1 Fourier Analysis of Continuous-Time Systems 5.2 Response to Periodic and Nonperiodic Inputs 5.3 Analysis of Ideal Filters 5.4 Sampling 5.5 Fourier Analysis of Discrete-Time Systems 5.6 Application to Lowpass Digital Filtering 5.7 Chapter Summary Problems 6 THE LAPLACE TRANSFORM AND THE TRANSFER FUNCTION REPRESENTATION 6.1 Laplace Transform of a Signal 6.2 Properties of the Laplace Transform 6.3 Computation of the Inverse Laplace Transform 6.4 Transform of the Input/Output Differential Equation 6.5 Transform of the Input/Output Convolution Integral 6.6 Direct Construction of the Transfer Function 6.7 Chapter Summary Problems 7 THE z-TRANSFORM AND DISCRETE-TIME SYSTEMS 7.1 z-Transform of a Discrete-Time Signal 7.2 Properties of the z-Transform 7.3 Computation of the Inverse z-Transform 7.4 Transfer Function Representation 7.5 System Analysis Using the Transfer Function Representation 7.6 Chapter Summary Problems 8 ANALYSIS OF CONTINUOUS-TIME SYSTEMS USING THE TRANSFER FUNCTION REPRESENTATION 8.1 Stability and the Impulse Response 8.2 Routh-Hurwitz Stability Test 8.3 Analysis of the Step Response 8.4 Response to Sinusoids and Arbitrary Inputs 8.5 Frequency Response Function 8.6 Causal Filters 8.7 Chapter Summary Problems 9 APPLICATION TO CONTROL 9.1 Introduction to Control 9.2 Tracking Control 9.3 Root Locus 9.4 Application to Control System Design 9.5 Chapter Summary Problems 10 DESIGN OF DIGITAL FILTERS AND CONTROLLERS 10.1 Discretization 10.2 Design of IIR Filters 10.3 Design of IIR Filters Using MATLAB 10.4 Design of FIR Filters 10.5 Design of Digital Controllers 10.6 Chapter Summary Problems 11 STATE REPRESENTATION 11.1 State Model 11.2 Construction of State Models 11.3 Solution of State equations 11.4 Discrete-Time Systems 11.5 Equivalent State Representations 11.6 Discretization of State Model 11.7 Chapter Summary Problems APPENDIX A BRIEF REVIEW OF COMPLEX VARIABLES APPENDIX B BRIEF REVIEW OF MATRICES BIBLIOGRAPHY INDEX

Method and apparatus for passive acoustic source localization for video camera steering applications

Abstract: A real-time passive acoustic source localization system for video camera steering advantageously determines the relative delay between the direct paths of two estimated channel impulse responses. The illustrative system employs an approach referred to herein as the “adaptive eigenvalue decomposition algorithm” (AEDA) to make such a determination, and then advantageously employs a “one-step least-squares algorithm” (OSLS) for purposes of acoustic source localization, providing the desired features of robustness, portability, and accuracy in a reverberant environment. The AEDA technique directly estimates the (direct path) impulse response from the sound source to each of a pair of microphones, and then uses these estimated impulse responses to determine the time delay of arrival (TDOA) between the two microphones by measuring the distance between the first peaks thereof (i.e., the first significant taps of the corresponding transfer functions). In one embodiment, the system minimizes an error function (i.e., a difference) which is computed with the use of two adaptive filters, each such filter being applied to a corresponding one of the two signals received from the given pair of microphones. The filtered signals are then subtracted from one another to produce the error signal, which is minimized by a conventional adaptive filtering algorithm such as, for example, an LMS (Least Mean Squared) technique. Then, the TDOA is estimated by measuring the “distance” (i.e., the time) between the first significant taps of the two resultant adaptive filter transfer functions.

A linearized electrohydraulic servovalve model for valve dynamics sensitivity analysis and control system design

Abstract: This paper presents the derivation of a linearized model for flapper-nozzle type two-stage electrohydraulic servovalves from the nonlinear state equations The coefficients of the linearized model are derived in terms of the valve physical parameters and fluid properties explicitly, and are useful for valve design and sensitivity analysis When using this model structure to fit experimental frequency response data, the results render closer agreement than when using existing low order linear models This model also suggests important servovalve dynamic properties such as the nonminimum phase zero and the transfer function relative degree, and how they relate to the valve component arrangement Because of the small modeling errors over a wide frequency range, a high bandwidth control system can be designed A robust performance controller is designed and implemented to demonstrate the utility of the model

Preserving positive realness through discretization

Abstract: It is shown that a discrete positive real transfer function is obtained from a positive real continuous one of relative order zero being strictly stable poles via discretization by a sampler and zero-order hold device provided that the direct input-output transmission gain is sufficiently large. Also, a discrete positive real transfer function may be obtained from a stable continuous one of relative order zero and high direct input-output gain which possess simple complex conjugate critically stable poles even in the case that this one is not positive real. For that purpose, the use of an appropriate phase lag or phase lead compensating network for the continuous transfer function may be required to ensure positive realness of the discrete transfer function.

Robust power system stabiliser

Abstract: Power system stabilisers (PSS) are usually implemented by feeding a speed signal through a supplementary loop that comprises a proper phase lead. The design parameters of this loop are load dependent. Thus, they have to be adjusted at each operating condition. A simple robust PSS is designed that can properly function over a wide range of operating conditions and extend the machine loadability. The lead compensator design is achieved by drawing the root loci for a finite number of extreme characteristic polynomials. Such polynomials are obtained, using the Kharitonov theorem, to reflect wide loading conditions on characteristic equation coefficients. For this purpose the explicit analytical forms for the coefficients of the system transfer functions are derived. Simulation results illustrate the effectiveness of the proposed stabiliser as it is applied to the original nonlinear differential equations describing system dynamics under wide loading conditions at lagging and leading power factors.

Imaging properties of scanning holographic microscopy

Abstract: Scanning heterodyne holography is an alternative way of capturing three-dimensional information on a scattering or fluorescent object We analyze the properties of the images obtained by this novel imaging process We describe the possibility of varying the coherence of the system from a process linear in amplitude to a process linear in intensity by changing the detection mode We illustrate numerically the properties of the three-dimensional point-spread function of the system and compare it with that of a conventional imaging system with equal numerical aperture We describe how it is possible, by an appropriate choice of the reconstruction algorithm, to obtain an ideal transfer function equal to unity up to the cutoff frequency, even in the presence of aberrations Some practical implementation issues are also discussed

Dynamic Analysis of Harmonics in Electrical Systems

Abstract: Frequency domain analysis and design of power systems is complicated in the presence of harmonics, switching dynamics, nonlinearities, unbalances, and for systems with mixed ac/dc dynamics. The reason is that linearization of the system does not lead to a time invariant system, but a system with periodically time varying dynamics, which implies that there is coupling between different frequencies. Often one has to rely on simplifying assumptions and simulation. The thesis uses linear time periodic (LTP) models to analyze power systems. The harmonic transfer function (HTF) for LTP systems is introduced. Using the HTF, the system can be treated as an infinitely dimensional linear time invariant system, which means that the system, under certain convergence conditions, can be analyzed using the well developed theory for LTI systems. The thesis contains four papers with power system applications. Paper I describes the modeling and analysis of networks including components with switching dynamics, such as diodes and thyristors. An algorithm for parameter estimation from experimental data is presented. Papers II and III treats modeling and analysis of single-phase railway systems. The modeling of the locomotives is performed in collaboration with industry. Paper IV treats analysis and control aspects of a converter for grid connection of a micro-turbine used for distributed power generation. This is a three-phase application done in collaboration with the industry. (Less)

Multistep linear predictors-based blind identification and equalization of multiple-input multiple-output channels

Abstract: Channel estimation and blind equalization of multiple-input multiple-output (MIMO) communications channels is considered using primarily the second-order statistics of the data. Such models arise when single receiver data from multiple sources is fractionally sampled (assuming that there is excess bandwidth) or when an antenna array is used with or without fractional sampling. We consider the estimation of (partial) channel impulse response and design of finite-length minimum mean-square error (MMSE) blind equalizers. We extend the multistep linear prediction approach to MIMO channels where the multichannel transfer function need not be column reduced. Moreover, we allow infinite impulse response (IIR) channels as well as the case where the "subchannel" transfer functions have common zeros. In the past, this approach has been confined to SIMO finite impulse response (FIR) channels with no common subchannel zeros. A related existing approach applicable to MIMO channels is restricted to FIR column-reduced systems with equal length subchannels. In our approach, the knowledge of the nature of the underlying model (FIR or IIR) or the model order is not required. Our approach works when the "subchannel" transfer functions have common zeros, as long as the common zeros are minimum-phase zeros. The sources are recovered up to a unitary mixing matrix and are further "unmixed" using higher order statistics of the data. Illustrative computer simulation examples are provided.