Showing papers on "Transfer function published in 2005"

A novel approach to the modeling of the indoor power line channel part I: circuit analysis and companion model

Abstract: Multiconductor Transmission Line (MTL) theory is utilized here for modeling the transfer function of power cables in the indoor environment. This approach allows us to determine a circuit model that well characterizes the underlying physics of signal propagation over power-line (PL) cables and that also allows us to account for particular wiring practices common in residential and business environments. In Part II of this work, we will show how the proposed approach allows one to compute a priori and in a deterministic fashion the transfer function of any PL link by using two-port transmission matrices, as commonly done for telephone channel modeling. In this two-part work we will cross several layers of abstraction following a bottom-up approach: starting from the definition of circuit models in this paper, we will arrive at a method for the computation of the transfer function of an indoor PL link in Part II of this work. Moreover, as discussed in Part II, the approach followed here allows us to unveil some special properties of the PL channel that were never reported earlier, such as the symmetry of the transfer function.

Modeling the closed-current loop of PWM boost DC-DC converters operating in CCM with peak current-mode control

Abstract: This paper derives the transfer function from error voltage to duty cycle, which captures the quasi-digital behavior of the closed-current loop for pulsewidth modulated (PWM) dc-dc converters operating in continuous-conduction mode (CCM) using peak current-mode (PCM) control, the current-loop gain, the transfer function from control voltage to duty cycle (closed-current loop transfer function), and presents experimental verification. The sample-and-hold effect, or quasi-digital (discrete) behavior in the current loop with constant-frequency PCM in PWM dc-dc converters is described in a manner consistent with the physical behavior of the circuit. Using control theory, a transfer function from the error voltage to the duty cycle that captures the quasi-digital behavior is derived. This transfer function has a pole that can be in either the left-half plane or right-half plane, and captures the sample-and-hold effect accurately, enabling the characterization of the current-loop gain and closed-current loop for PWM dc-dc converters with PCM. The theoretical and experimental response results were in excellent agreement, confirming the validity of the transfer functions derived. The closed-current loop characterization can be used for the design of a controller for the outer voltage loop.

Application of a sinusoidal internal model to current control of three-phase utility-interface converters

Abstract: Three-phase voltage-source converters are used as utility interfaces. In such a case, the converter line currents are required to track sinusoidal references synchronized with the utility grid without a steady-state error. In this paper a current control method based on a sinusoidal internal model is employed. The method uses a sine transfer function with a specified resonant frequency, which is called an S regulator. The combination of a conventional proportional-integral (PI) regulator and an S regulator is called a PIS regulator. The PIS regulator ensures that the steady-state error in response to any step changes in a reference signal at the resonant frequency and 0 Hz reduces to zero. An experiment was carried out using a 1-kVA prototype of three utility-interface converters, a voltage-source rectifier, an active power filter, and static synchronous compensator. Almost perfect current-tracking performance could be observed.

New modified Smith predictor scheme for integrating and unstable processes with time delay

Abstract: The paper extends a recently published Smith predictor scheme for controlling integrating and unstable processes with time delay, which results in a simpler control structure and improved tuning capacities for reference inputs and load disturbances. In the proposed scheme, a proportional controller is subtly employed to stabilise the setpoint response, and then an H2 optimal controller is analytically designed for setpoint tracking. To obtain the integral-squared-error (ISE) performance objective, a practically desired disturbance rejection transfer function is proposed to design the disturbance estimator in the inner closed loop of the proposed control structure. Essentially, the proposed control structure gives two-degrees-of-freedom (2DOF) control and correspondingly the setpoint and load disturbance responses can each be tuned conveniently by a single control parameter. Hence the setpoint response is decoupled from the load disturbance response, and both can be quantitatively estimated in terms of the proposed analytical tuning procedures. Simulation examples are included to show the superiority of the proposed method.

Optical vector network analyzer for single-scan measurements of loss, group delay, and polarization mode dispersion

Abstract: We present a method for measuring the complete linear response, including amplitude, phase, and polarization, of a fiber-optic component or assembly that requires only a single scan of a tunable laser source. The method employs polarization-diverse swept-wavelength interferometry to measure the matrix transfer function of a device under test. We outline the theory of operation to establish how the transfer function is obtained. We demonstrate the enhanced accuracy, precision, and dynamic range of the technique through measurements of several components.

Compensation voltage control in dynamic voltage restorers by use of feed forward and state feedback scheme

Abstract: This paper discusses the control of the compensation voltages in dynamic voltage restorers (DVR). It first analyzes the power circuit of a DVR system in order to come up with appropriate control limitations and control targets for the compensation voltage control. Based on this power stage analysis, a combined feed forward and state feedback control structure for the compensation voltages of DVRs is developed. This paper also discusses the time delay problems inherent in the digital control system of a DVR. Digital control systems normally have control delay from the sampling period, the switching frequency of the inverter, the sensor transmission time, etc. The control delay increases the dimension of the system transfer function. This makes the control system more unstable. This paper analyzes the control performance related with the control delay, closed loop damping factor, and the output filter parameters in DVR systems. Based on the control system analysis, design guidelines are proposed for the control gains and the inverter switching frequency of DVRs. The proposed theory is verified by an experimental DVR system with a full digital controller.

Network model for MIMO systems with coupled antennas and noisy amplifiers

Abstract: This work presents a framework for the analysis of mutually-coupled antennas in a multiple-input multiple-output system. The approach uses network theory to formulate the transfer matrix relating the signals input to the transmit antennas to the signals at the output of the receiver front end. This transfer function includes the coupled transmit and receive antennas, the multipath propagation channel, the receiver matching network, and a realistic noise model for the receive amplifiers. Application of the formulation to coupled dipole antennas characterized using full-wave electromagnetic analysis illustrates the performance gains possible from matching the coupled antenna/receive amplifier subsystem for minimum noise figure as compared to matching for maximum signal power transfer.

Cardinal exponential splines: part II - think analog, act digital

Abstract: By interpreting the Green-function reproduction property of exponential splines in signal processing terms, we uncover a fundamental relation that connects the impulse responses of allpole analog filters to their discrete counterparts. The link is that the latter are the B-spline coefficients of the former (which happen to be exponential splines). Motivated by this observation, we introduce an extended family of cardinal splines-the generalized E-splines-to generalize the concept for all convolution operators with rational transfer functions. We construct the corresponding compactly supported B-spline basis functions, which are characterized by their poles and zeros, thereby establishing an interesting connection with analog filter design techniques. We investigate the properties of these new B-splines and present the corresponding signal processing calculus, which allows us to perform continuous-time operations, such as convolution, differential operators, and modulation, by simple application of the discrete version of these operators in the B-spline domain. In particular, we show how the formalism can be used to obtain exact, discrete implementations of analog filters. Finally, we apply our results to the design of hybrid signal processing systems that rely on digital filtering to compensate for the nonideal characteristics of real-world analog-to-digital (A-to-D) and D-to-A conversion systems.

Compact reduced-order modeling of weakly nonlinear analog and RF circuits

Abstract: A compact nonlinear model order-reduction method (NORM) is presented that is applicable for time-invariant and periodically time-varying weakly nonlinear systems. NORM is suitable for model order reduction of a class of weakly nonlinear systems that can be well characterized by low-order Volterra functional series. The automatically extracted macromodels capture not only the first-order (linear) system properties, but also the important second-order effects of interest that cannot be neglected for a broad range of applications. Unlike the existing projection-based reduction methods for weakly nonlinear systems, NORM begins with the general matrix-form Volterra nonlinear transfer functions to derive a set of minimum Krylov subspaces for order reduction. Moment matching of the nonlinear transfer functions by projection of the original system onto this set of minimum Krylov subspaces leads to a significant reduction of model size. As we will demonstrate as part of comparison with existing methods, the efficacy of model reduction for weakly nonlinear systems is determined by the achievable model compactness. Our results further indicate that a multipoint version of NORM can substantially improve the model compactness for nonlinear system reduction. Furthermore, we show that the structure of the nonlinear system can be exploited to simplify the reduced model in practice, which is particularly effective for circuits with sharp frequency selectivity. We demonstrate the practical utility of NORM and its extension for macromodeling weakly nonlinear RF communication circuits with periodically time-varying behavior.

Scattering Systems with Several Evolutions and Multidimensional Input/State/Output Systems

Abstract: The one-to-one correspondence between one-dimensional linear (stationary, causal) input/state/output systems and scattering systems with one evolution operator, in which the scattering function of the scattering system coincides with the transfer function of the linear system, is well understood, and has significant applications in H∞ control theory. Here we consider this correspondence in the d-dimensional setting in which the transfer and scattering functions are defined on the polydisk. Unlike in the onedimensional case, the multidimensional state space realizations and the corresponding multi-evolution scattering systems are not necessarily equivalent, and the cases d = 2 and d > 2 differ substantially. A new proof of Ando’s dilation theorem for a pair of commuting contraction operators and a new statespace realization theorem for a matrix-valued inner function on the bidisk are obtained as corollaries of the analysis.

Robust boundary control of an axially moving string by using a PR transfer function

Abstract: In this note, a scheme for the vibration suppression of a translating string using a positive real (PR) transfer function is investigated. The transverse vibration of the string is controlled by hydraulic touch-rolls located at the right end of the string. The mathematical model of the system, which consists of a hyperbolic partial differential equation (PDE) describing the dynamics of the moving string and an ordinary differential equation (ODE) for the actuator dynamics, is derived by using Hamilton's principle for translating continua. The transfer function of the proposed boundary controller is a nonproper but PR function. The asymptotic stability of the closed-loop system in the presence of output disturbance is proved.

Application of a sinusoidal internal model to current control of three-phase utility interface converters

Abstract: Three-phase voltage-source converters are used as a utility interface. In such a case, the converter line currents are required to track sinusoidal references synchronized with the utility grid without steady-state error. In this paper a current control method based on a sinusoidal internal model is employed. The method uses a sine transfer function with a specified resonant frequency, which is called an S compensator. The combination of a conventional PI compensator and an S compensator is called a PIS compensator. The PIS compensator ensures that the steady-state error in response to any step changes in a reference signal at the resonant frequency and zero hertz reduces to zero. An experiment was carried out using a 1-kVA prototype of three utility interface converters, a voltage-source rectifier, an active power filter, and STATCOM. Almost perfect current tracking performance can be observed. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(3): 54–61, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20064

Frequency-domain analysis of linear time-periodic systems

Abstract: In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature.

Adc transfer function providing improved dynamic regulation in a switched mode power supply

Abstract: A power supply comprises at least one power switch adapted to convey power between input and output terminals of the power supply, and a digital controller adapted to control operation of the at least one power switch responsive to an output measurement of the power supply. The digital controller comprises an analog-to-digital converter providing a digital error signal representing a voltage difference between the output measurement and a reference value, a digital filter providing a digital control output based on a sum of previous error signals and previous control outputs, an error controller adapted to modify operation of the digital filter upon an error condition, and a digital pulse width modulator providing a control signal to the power switch having a pulse width corresponding to the digital control output. The analog-to-digital converter further comprises a windowed flash analog-to-digital converter having a transfer function defining a relationship between the voltage difference and corresponding digital values. The transfer function provides a substantially linear region at a center of a corresponding error window, including a first step size in the center of the error window and at least one other step size in a peripheral region of the error window that is larger than the first step size. The first step size and the other step sizes may each reflect a linear relationship between the voltage difference and the corresponding digital values. Alternatively, the first step size reflects a linear relationship between the voltage difference and the corresponding digital values, and the other step sizes each reflect a non-linear relationship between the voltage difference and the corresponding digital values.

Control of Flexible Structures Governed by the Wave Equation Using Infinite Dimensional Transfer Functions

Abstract: A method of noncollocated controller design for flexible structures, governed by the wave equation, is proposed. First an exact, infinite dimension, transfer function is derived and its properties are investigated. A key element in that part is the existence of time delays due to the wave motion. The controller design consists of two stages. The first one is an inner collocated rate loop. It is shown that there exists a controller that leads to a finite dimensional plus delay inner closed loop, which is the equivalent plant for the outer loop. In the second stage an outer noncollocated position loop is closed. It has the structure of an observer-predictor control scheme to compensate for the response delay. The resulting overall transfer function is second order with arbitrarily assigned dynamics, plus delay.

Fourier Series for Accurate, Stable, Reduced-Order Models in Large-Scale Linear Applications

Abstract: A new method, Fourier model reduction, for obtaining stable, accurate, low-order models of very large linear systems is presented. The technique draws on traditional control and dynamical system concepts and utilizes them in a way which is computationally very efficient. Discrete-time Fourier coefficients of the large system are calculated and used to construct a reduced-order model that preserves stability properties of the original system. Many coefficients can be calculated, which results in a very accurate representation of the system dynamics, but only a single factorization of the large system is required. The resulting system can be further reduced using explicit formulae for balanced truncation. The method is applied to two computational fluid dynamic systems, which model unsteady motion of a two-dimensional subsonic airfoil and unsteady flow in a supersonic diffuser. In both cases, the new method is found to work extremely well. Results are compared to models developed using the proper orthogonal decomposition and Arnoldi method. In comparison with these widely used techniques, the new method is computationally more efficient, preserves the stability of the original system, uses both input and output information, and, for smooth transfer functions, is valid over a wide range of frequencies.

An efficient method to compute transfer function of a transformer from its equivalent circuit

Abstract: The dynamics of an electrical network can completely be described from the knowledge of its poles and zeros. Computation of poles and zeros of the transfer function (TF) of a transformer winding, represented as a coupled ladder network, involves solution of a large-sized equivalent circuit. This paper presents a novel solution based on state space analysis approach. It is shown, how the linearly transformed state space formulation, together with algebraic manipulations, can become useful. In the proposed formulation, symbolic variables (i.e., Laplace variable, s) are suitably manipulated, so as to render computations purely numerical. With this feature, there is practically no limit on the size of networks and topologies (including resistances to model losses) that can be represented. So, virtually any number of windings of a transformer can be considered, permitting a comprehensive analysis of winding behavior and its interactions, that was until now severely limited, by the simplifying assumptions imposed by existing methods.

Jointly nonlinear delta sigma modulators

Abstract: A signal processing system includes a jointly non-linear delta sigma modulator (1002). In one embodiment, the jointly non-linear delta sigma modulator includes a non-linear quantization transfer function, and the output of the delta sigma modulator is defined, at least in part, by a non-linear interrelationship of multiple noise-shaping filter state variables (SVi). A look-ahead delta-sigma modulator can be implemented as a noise shaping filter and a function generator. State variables of the noise shaping filter provide the input data from which the function generator determines a quantizer output signal. Latter state variables are more dominant in determining the quantizer output signal. Accordingly, earlier state variables can be approximated to a greater degree than latter state variables without significant compromise in quantization accuracy.

Patch Transfer Functions as a Tool to Couple Linear Acoustic Problems

Abstract: A method to couple acoustic linear problems is presented in this paper. It allows one to consider several acoustic subsystems, coupled through surfaces divided in elementary areas called patches. These subsystems have to be studied independently with any available method, in order to build a database of transfer functions called patch transfer functions, which are defined using mean values on patches, and rigid boundary conditions on the coupling area. A final assembly, using continuity relations, leads to a very quick resolution of the problem. The basic equations are developed, and the acoustic behavior of a cavity separated in two parts is presented, in order to show the ability of the method to study a strong-coupling case. Optimal meshing size of the coupling area is then discussed, some comparisons with experiments are shown, and finally a complex automotive industrial case is presented.

Performance analysis of general charge sampling

Abstract: This brief focuses on the performance analysis of general charge-sampling circuits for signal capture. The theoretical analysis in the brief can be applied not only for weak signal capture, but also for the normal signal sampling. Based on a general charge-sampling model, the transfer function, the noise performance, and the clock jitter tolerance are analyzed and compared to conventional voltage sampling. The results provide a theoretical basis for charge-sampling circuit design.

Frequency Domain Identification of Multi-Input, Multi-Output Systems Considering Physical Relationships between Measured Variables

Abstract: This paper presents a new frequency domain identification method for multi-input, multi-output (MIMO) systems. Based on experimentally determined frequency response function data, rational polynomial transfer function models of structural systems are identified. Known physical relationships between the measured variables are incorporated in this MIMO frequency domain identification method. The method has three stages: (1) an initial estimation model is generated using a linear least-squares method, (2) the Steiglitz–McBride method is applied to improve the initial estimation model, and (3) a maximum likelihood estimator is optimized using the Levenberg–Marquardt method. For verification of the method, two experimental studies are conducted using shaking table tests; one is the system identification of a smart base-isolated structure employing a magnetorheological (MR) damper, and the other is for an actively controlled two-story, bench-scale building employing an active mass driver. Using the developed me...

Digital broadcast signal receiving apparatus and method

Abstract: A signal receiving apparatus and method which is high in deduction accuracy of transfer characteristic and less in error rate during signal decoding. For each detection signal of a pilot carrier allotted in an OFDM symbol space, a transfer function thereof is calculated. The transfer function is subjected to two-dimensional Fourier transform as to impulse delay time and symbol frequency thereby generating a two-dimensional data space. A predetermined domain of the two-dimensional data space is extracted by a filter extracting domain. The data included in the extracted domain is subjected to two-dimensional inverse Fourier transform as to carrier frequency and symbol time, thereby generating a deduced transfer function.

Padé-Type Model Reduction of Second-Order and Higher-Order Linear Dynamical Systems

Abstract: A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order systems While this approach results in reduced-order models that are characterized as Pade-type or even true Pade approximants of the system's transfer function, in general, these models do not preserve the form of the original higher-order system In this paper, we present a new approach to reduced-order modeling of higher-order systems based on projections onto suitably partitioned Krylov basis matrices that are obtained by applying Krylov-subspace techniques to an equivalent first-order system We show that the resulting reduced-order models preserve the form of the original higher-order system While the resulting reduced-order models are no longer optimal in the Pade sense, we show that they still satisfy a Pade-type approximation property We also introduce the notion of Hermitian higher-order linear dynamical systems, and we establish an enhanced Pade-type approximation property in the Hermitian case

A robust control based solution to the sample-profile estimation problem in fast atomic force microscopy

Abstract: SUMMARY The atomic force microscope (AFM) is a powerful tool for imaging and manipulating matter at the nanoscale. An optimal control problem is proposed for the control of AFMs which includes the design of a sample-profile estimate signal in addition to the set-point regulation and resolution objectives. A new estimate signal for the sample profile is proposed and it is proved that the transfer function between the profile signal and the estimate signal is unity. The main contribution in comparison to existing designs is that there is no bandwidth limitation on estimation of sample profiles! Experimental results are presented to corroborate these results. Copyright # 2005 John Wiley & Sons, Ltd.

Linear turbo equalization analysis via BER transfer and EXIT charts

Abstract: In this paper, two analytical methods are presented to investigate the soft information evolution characteristics of a soft-input soft-output (SISO) linear equalizer and its application to the design of turbo equalization systems without the reliance on extensive simulation. Given the channel and a SISO equalization algorithm, one method explored is to analytically compute the bit-error rate (BER) of the SISO equalizer in two extreme cases (no and perfect a priori information) from which a BER transfer characteristic is estimated. The second approach is to compute the mutual information [a key parameter of the extrinsic information transfer (EXIT) chart] at the two end points of the EXIT function. Then, by modeling the SISO equalizer BER transfer and EXIT functions as linear, some of the behavior of linear turbo equalization, such as how the BER performance can be improved as iterations proceed, can be predicted. Further, soft information evolution characteristics of different linear SISO equalizers can be compared and the usefulness of iterative methods such as linear turbo equalization for a given channel can be determined. Compared with existing methods for generating EXIT functions, these predictive methods provide insight into the iterative behavior of linear turbo equalizers with substantial reduction in numerical complexity.

On the frequency scaling in continuous-time modeling

Abstract: When identifying continuous-time systems in the Laplace domain, it is indispensable to scale the frequency axis to guarantee the numerical stability of the normal equations. Without scaling, identification in the Laplace domain is often impossible even for modest model orders of the transfer function. Although the optimal scaling depends on the system, the model, and the excitation signal, the arithmetic mean of the maximum and minimum angular frequencies in the frequency band of interest is commonly used as a good compromise as shown in the following references: J. Schoukens and R. Pintelon, Identification of Linear Systems: A Practical Guideline to Accurate Modeling (London, U.K.: Pergamon), R. Pintelon and J. Schoukens, System Identification: A Frequency Domain Approach, (Piscataway, NJ: IEEE Press, 2001), and I. Kolla/spl acute/r, R. Pintelon, Y. Rolain, J. Schoukens, G. Simon, "Frequency domain system identification toolbox for Matlab: Automatic processes-From data to model," in Proc. 13th IFAC Symp. System Identification, Rotterdam, The Netherlands, Aug. 27-29, 2003, pp. 1502-1506. We show: 1) that the optimal frequency scaling also strongly depends on the estimation algorithm and 2) that the median of the angular frequencies is a better compromise for improving the numerical stability than the arithmetic mean.