Showing papers on "Transfer function published in 1996"

Supervisory control of families of linear set-point controllers - Part I. Exact matching

Abstract: This paper describes a simple "high-level" controller called a "supervisor" which is capable of switching into feedback with a SISO process, a sequence of linear positioning or set-point controllers from a family of candidate controllers so as to cause the output of the process to approach and track a constant reference input. The process is assumed to be modeled by a SISO linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the candidate controllers would solve the positioning problem if the transfer function of the process were to be one of the subclasses' members. Each subclass contains a "nominal process model transfer function" about which the subclass is centred. It is shown that in the absence of unmodeled process dynamics, the proposed supervisor can successfully perform its function even if process disturbances are present, provided they are bounded and constant.

Analysis and design of a multiple feedback loop control strategy for single-phase voltage-source UPS inverters

Abstract: This paper presents the analysis and design of a multiple feedback loop control scheme for single-phase voltage-source uninterruptible power supply (UPS) inverters with an L-C filter. The control scheme is based on sensing the current in the capacitor of the load filter and using it in an inner feedback loop. An outer voltage feedback loop is also incorporated to ensure that the load voltage is sinusoidal and well regulated. A general state-space averaged model of the UPS system is first derived and used to establish the steady-steady quiescent point. A linearized small signal dynamic model is then developed from the system general model using perturbation and small-signal approximation. The linearized system model is employed to examine the incremental dynamics of the power circuit and select appropriate feedback variables for stable operation of the closed-loop UPS system. Experimental verification of a laboratory model of the UPS system under the proposed closed-loop operation is provided for both linear and nonlinear loads. It is shown that the control scheme offers improved performance measures over existing schemes, It is simple to implement and capable of producing nearly perfect sinusoidal load voltage waveform at moderate switching frequency and reasonable size of filter parameters. Furthermore, the scheme has excellent dynamic response and high voltage utilization of the DC source.

Differential evolution design of an IIR-filter

Abstract: The task of designing an 18 parameter IIR-filter (IIR=infinite impulse response) which has to meet tight specifications for both magnitude response and group delay is investigated. This problem is usually tackled by specialized design methods and requires an expert in digital signal processing for its solution. The use of the general purpose minimization method differential evolution (DE), however, allows filter design with a minimum knowledge of digital filters.

Generation of transfer functions with stochastic search techniques

Abstract: This paper presents a novel approach to assist the user in exploring appropriate transfer functions for the visualization of volumetric datasets. The search for a transfer function is treated as a parameter optimization problem and addressed with stochastic search techniques. Starting from an initial population of (random or pre-defined) transfer functions, the evolution of the stochastic algorithms is controlled by either direct user selection of intermediate images or automatic fitness evaluation using user-specified objective functions. This approach essentially shields the user from the complex and tedious "trial and error" approach, and demonstrates effective and convenient generation of transfer functions.

Frequency response of sampled-data systems

Abstract: This paper introduces the concept of frequency response for sampled-data systems and explores some basic properties as well as its computational procedures. It is shown that 1) by making use of the lifting technique, the notion of frequency response can be naturally introduced to sampled-data systems in spite of their time-varying characteristics, 2) it represents a frequency domain steady-state behaviour, and 3) it is also closely related to the original transfer function representation via an integral formula. It is shown that the computation of the frequency response can be reduced to a finite-dimensional eigenvalue problem, and some examples are presented to illustrate the results.

Computing dominant poles of power system transfer functions

Abstract: This paper describes the first algorithm to efficiently compute the dominant poles of any specified high order transfer function. As the method is closely related to Rayleigh iteration (generalized Rayleigh quotient), it retains the numerical properties of global and ultimately cubic convergence. The results presented are limited to the study of low frequency oscillations in electrical power systems, but the algorithm is completely general.

An explicit RC-circuit delay approximation based on the first three moments of the impulse response

Abstract: Due to its simplicity, the ubiquitous Elmore delay, or first moment of the impulse response, has been an extremely popular delay metric for analyzing RC trees and meshes. Its inaccuracy has been noted however and it has been demonstrated that higher order moments can be mapped to dominant pole approximations (e.g. AWE) in the general case. The first three moments can be mapped to a two pole approximation, but stability is an issue and even a stable model results in a transcendental equation that must be iteratively evaluated to determine the delay. We describe an explicit delay approximation based on the first three moments of the impulse response. We begin with the development of a provably stable two pole transfer function/impedance model based on the first three moments (about s=0) of the impulse response. Then, since the model form is known, we evaluate the delay (any waveform percentage point) in terms of an analytical approximation that is consistently within a fraction of 1 percent of the "exact" solution for this model. The result is an accurate, explicit delay expression that will be an effective metric for high speed interconnect circuit models.

System Dynamics: An Introduction

Abstract: 1. Introduction. 2. Energy and Power Flow in State-Determined Systems. 3. Summary of One-Port Primitive Elements. 4. Formulation of System Models. 5. State Equation Formulation. 6. Energy Transducing System Elements. 7. Operational Methods for Linear Systems. 8. System Properties and Solution Techniques. 9. First- and Second-Order System Response. 10. General Solution of the Linear State Equations. 11. Solution of System Response by Numerical Simulation. 12. The Transfer Function. 13. Impedance-Based Modeling Methods. 14. Sinusoidal Frequency Response of Linear Systems. 15. Frequency Domain Methods. Appendix A - Introduction to Matrix Algebra. Appendix B - Complex Numbers. Appendix C - Partial Fraction Expansion of Rational Functions.

System identification using nonstationary signals

Abstract: The conventional method for identifying the transfer function of an unknown linear system consists of a least squares fit of its input to its output. It is equivalent to identifying the frequency response of the system by calculating the empirical cross-spectrum between the system's input and output, divided by the empirical auto-spectrum of the input process. However, if the additive noise at the system's output is correlated with the input process, e.g., in case of environmental noise that affects both system's input and output, the method may suffer from a severe bias effect. We present a modification of the cross-spectral method that exploits nonstationary features in the data in order to circumvent bias effects caused by correlated stationary noise. The proposed method is particularly attractive to problems of multichannel signal enhancement and noise cancellation, when the desired signal is nonstationary in nature, e.g., speech or image.

Analytical delay models for VLSI interconnects under ramp input

Abstract: Elmore delay has been widely used as an analytical estimate of interconnect delays in the performance-driven synthesis and layout of VLSI routing topologies. However, for typical RLC interconnections with ramp input, Elmore delay can deviate by up to 100% or more from SPICE-computed delay since it is independent of rise time of the input ramp signal. We develop new analytical delay models based on the first and second moments of the interconnect transfer function when the input is a ramp signal with finite rise time. Delay estimates using our first moment based analytical models are within 4% of SPICE-computed delay, and models based on both first and second moments are within 2.3% of SPICE, across a wide range of interconnect parameter values. Evaluation of our analytical models is several orders of magnitude faster than simulation using SPICE. We also describe extensions of our approach for estimation of source-sink delays in arbitrary interconnect trees.

New methods to design an integral variable structure controller

Abstract: This paper presents two methods to design a single-input/single-output integral variable structure system. Once an overall transfer function is selected, two simple ways are presented to determine the required switching surface and the control function. The proposed methods not only avoid transforming the original plant into a companion form, but also enable the resulting control system to achieve the asymptotic tracking for a step reference signal and disturbance rejection for a bounded disturbance signal simultaneously. Two examples are given to illustrate the effectiveness of the proposed methods.

Sampling requirements for Volterra system identification

Abstract: Volterra systems generally produce-due to nonlinearity-an output signal with a higher frequency range when compared with the input signal. Hence, it seems necessary to sample the input and output signals at twice the maximum frequency of the output signal. The article shows that it is sufficient to sample at twice the maximum frequency of the input signal. A discrete-time Volterra system also produces the additional frequency components that appear-due to aliasing-at the sampled output of a continuous-time Volterra system with an equivalent transfer function.

Airy's functions implementation of the transfer-matrix method for resonant tunneling in variably spaced finite superlattices

Abstract: We improve the Airy's function version of the transfer-matrix method by presenting it in a form which is free of the common problems: numerical inefficiency for low-applied voltages and an inability to compute the energies of some quasi-bound states. In particular, we show that the transfer-function method can be used to study the negative-energy resonances which do not affect the tunneling transmission coefficient. Since this approach is based on the exact solution of Schrodinger's equation within the effective-mass approximation, it can be used to verify other computational methods used in the theory of resonant tunneling. After mathematical errors present in some of the earlier applications of the Airy's functions method are removed, an excellent agreement is reached between the transmission coefficient, energies of the bound and quasi-bound states, and I-V characteristics of the finite superlattices computed by different techniques. The proposed version of the transfer-matrix method is used to investigate the effective-barrier symmetry in electrically biased double-barrier structures.

Identification of finite impulse response models : Methods and robustness issues

Abstract: In model predictive control one often needs a finite impulse response (FIR) or step response model of the process. Several algorithms have been proposed for the direct identification of these nonparsimonious models (least-squares and biased algorithms such as regularized least squares and partial least squares). These algorithms are compared from several points of view: the closeness of the fit to the true model, the level of robust stability provided by the identified model, and the actual control performance obtained using the identified models. Although there are conveniences in directly identifying such nonparsimonious models (i.e., they can fit any complex dynamic system; there is no need for model structure selection), there are many disadvantages. In comparison with identifying parsimonious transfer function models by prediction error methods and then obtaining the impulse response from them, even the best direct FIR identification methods will generally provide much worse results or require much ...

Imaging system transfer function control method and apparatus

Abstract: Accurately measuring and controlling the system transfer function of an imaging system (408), by eliminating interference from aliases. An image is captured of an image primitive (406) with a uniaxial pattern, oriented at an angle (701, 702) to the primary axes of a sampling array. In order to accurately measure the system transfer function, a two-dimensional frequency representation is computed (53). The aliased components of the representation are separated from the unaliased components by translation in frequency (53) along the axis perpendicular to the axis of the image primitive (406). Accurate measurement of the system transfer function (58) makes it possible to accurately control the system transfer function.

Stability and Controllability of Euler-Bernoulli Beams With Intelligent Constrained Layer Treatments

Abstract: This paper studies the stability and controllability of Euler-Bernoulli beams whose bending vibration is controlled through intelligent constrained layer (ICL) damping treatments proposed by Baz (1993) and Shen (1993, 1994). First of all, the homogeneous equation of motion is transformed into a first order matrix equation in the Laplace transform domain. According to the transfer junction approach by Yang and Tan (1992), existence of nontrivial solutions of the matrix equation leads to a closed-form characteristic equation relating the control gain and closed-loop poles of the system. Evaluating the closed-form characteristic equation along the imaginary axis in the Laplace transform domain predicts a threshold control gain above which the system becomes unstable. In addition, the characteristic equation leads to a controllability criterion for ICL beams. Moreover, the mathematical structure of the characteristic equation facilitates a numerical algorithm to determine root loci of the system. Finally, the stability and controllability of Euler-Bernoulli beams with ICL are illustrated on three cantilever beams with displacement or slope feedback at the free end.

Modern control systems engineering

Abstract: ntroduction. METHODS AND CONCEPTS. Transfer Function Approach. State Space Approach. Stability. Controllability and Observability. ANALYSIS AND DESIGN: Transient and Steady State Responses. Root Locus Technique. Time Domain Controller Design. Frequency Domain Controller Design. Control System Theory Overview.

The application of two-dimensional signal transformations to the analysis and synthesis of structural excitations observed in acoustical scattering

Abstract: Acoustic scattering from air-filled, elastic shells submerged in water is an important problem in applied science. The excitations of interest yield a set of physically distinct components to the impulse response of a shell. The components form a natural basis for all signals which can be observed in acoustical scattering experiments from the shell via temporal convolution with some chosen input signal. The Fourier transform (FT) of the impulse response of a shell yields its transfer function, which is also called the form function. We study two types of shells in this paper: a spherical shell, and a finite, ribbed, cylindrical shell with endcaps. Utilizing several different two-dimensional (2-D) signal transformations, we can decompose the response of the shells. The resulting 2-D images allow for a striking visual decomposition of the responses into their distinct components. In the case of the spherical shell, a virtually exact theory exists that allows for analytic synthesis of the shell response into its components. However, for the more complex cylindrical shell, the theory for the direct scattering problem is not nearly so mature. Yet, we can still decompose experimentally-obtained shell responses into their distinct components via signal synthesis techniques applied to the 2-D transforms.

Locating transformer faults through sensitivity analysis of high frequency modeling using transfer function approach

Abstract: The online condition monitoring of power transformer insulation can give early warning of electrical failure and could prevent catastrophic losses. Transfer function analysis offers the additional advantage of fault identification and location. High frequency resonance in a transformer can be modeled by analogue distributed winding concepts. Every transformer has an unique transfer function independent of the shape of the input waveform and can be evaluated through sweep and impulse tests. Results show that this transfer function changes by winding deformation, displacement, ground leakage, local breakdown and partial discharges etc. Digital simulation of impulse and variable frequency transient responses together with their fast Fourier transform spectral analysis are used in this paper to identify transformer faults and characterize their influence on transfer function. Sliding faults through the winding revealed changes in the transfer function to help locate the fault's location. This paper contributes to the development of a high frequency transformer model capable of studying faults including partial discharges, deriving condition assessment of a previously untested transformer from the varied characteristic plots to assess remaining life of a power transformer.

Mechatronics : Electronic Control Systems in Mechanical Engineering

Abstract: Preface 1. Mechatronics 2. Sensors and transducers 3. Signal conditioning 4. Data presentation systems 5. Pneumatic and hydraulic systems 6. Mechanical actuation systems 7. Electrical actuation systems 8. Basic system models 9. System models 10. Dynamic responses of systems 11. System transfer functions 12. Frequency response 13. Closed loop controllers 14. Digital logic 15. Microprocessors 16. Assembly language 17. C language 18. Input/output systems 19. Programmable logic controllers 20. Digital communications 21. Fault finding 22. Design and mechatronics Appendix: The Laplace transform Further information Answers Index

Quadrature signal conversion device

Abstract: In a receiver two sigma delta modulators (13, 19) are used to convert a pair of analog quatradure signals into digital quadrature signals. In such sigma delta modulators the quantisation noise is shifted into a frequency region in which no signal is present. In order to improve the noise reduction without increasing the order of the filters (15, 17) a cross coupling between the filters (15, 17) is made. Due to this cross coupling it is possible to obtain complex poles and zeros in the noise transfer function which do not have to appear in complex conjugate pairs, resulting in an increase of the noise suppression in one specified frequency range.

State-space synthesis of oscillators based on the MOSFET square law

Abstract: The authors present a design methodology on pure CMOS VLSI technology, which exploits the square law relationship between gate voltage and drain current in a saturated MOS transistor to implement state equations derived from a given transfer function. The process is illustrated with the design of an differential integrator.

Power spectral density specifications for high-power laser systems

Abstract: This paper describes the use of Fourier techniques to characterize the transmitted and reflected wavefront of optical components. Specifically, a power spectral density (PSD), approach is used. High power solid-state lasers exhibit non-linear amplification of specific spatial frequencies. Thus, specifications that limit the amplitude of these spatial frequencies are necessary in the design of these systems. Further, NIF optical components have square, rectangular or irregularly shaped apertures with major dimensions up to 800 nm. Components with non-circular apertures can not be analyzed correctly with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. A more complete and powerful representation of the optical wavefront can be obtained by Fourier analysis in 1 or 2 dimensions. The PSD is obtained from the amplitude of frequency components present in the Fourier spectrum. The shape of a resultant wavefront or the focal spot of a complex multi-component laser system can be calculated and optimize using PSDs of the individual optical components which comprise the system. Surface roughness can be calculated over a range of spatial scale-lengths by integrating the PSD. FInally, since the optical transfer function of the instruments used to measure the wavefront degrades at high spatial frequencies, the PSD of an optical component is underestimated. We can correct for this error by modifying the PSD function to restore high spatial frequency information. The strengths of PSD analysis are leading us to develop optical specifications incorporating this function for the planned National Ignition Facility.

Optimal sizing and placement of piezo-actuators for active flutter suppression

Abstract: The purpose of this work is to design an active control system for flutter suppression of a laminated plate wing model using segmented piezo-actuators. We describe investigations pertaining to the optimal size, thickness and locations of piezo-actuators on a laminated plate-wing structure for flutter suppression. The analysis for the laminated composite wing model is conducted by the Ritz solution technique, which represents the displacement on the plate in terms of power series in spanwise and chordwise directions. The active control system design for flutter suppression requires the equation of motion to be expressed in a linear time-invariant state-space form. The doublet-lattice method is used to compute unsteady aerodynamic forces, which are approximated as the transfer functions of the Laplace variable by the minimum-state method combined with an optimization technique. To design the control system, linear quadratic regulator theory with output feedback is considered in this study. The feedback control gains are obtained by solving coupled nonlinear matrix equations via numerical optimization routines. The optimal geometry of piezo-actuators which minimizes the control performance index is determined by the optimization technique referred to as the sequential linear programming method. The numerical result shows a substantial saving in control effort compared with the initial model.

/spl gamma/-passive system and its phase property and synthesis

Abstract: In this paper the concept of passivity is generalized from the viewpoint of the rate of energy dissipation, introducing a new supply rate with an index /spl gamma/. A stabilizability result for nonlinear systems is obtained using the argument of the supply rate and the dissipative inequality. In the case of linear systems, it is shown that the index /spl gamma/ can be used as a measure of phase of transfer functions, which provides a phase curve shaping method. A stability result of a feedback system involving a /spl gamma/-positive real system is also obtained and its effectiveness is shown by an example. Finally, a design method of /spl gamma/-passive system is discussed using a bilinear transformation of nonlinear systems, called Cayley-transform.

A new two-dimensional squint mode SAR processor

Abstract: This paper extends the processing capability of the wide angle synthetic aperture radar (WASAR) algorithm (1992) to synthetic aperture radar (SAR) data acquired with the radar beam directed with an offset angle (squint angle) from the zero Doppler direction. The key point of this work is the analytical evaluation of the system transfer function for the squinted geometry via the stationary phase method. The range dependence of this new transfer function is compensated in two steps: a phase multiplication and a modified version of the basic fractional Fourier transform (FT). The performance of the extended algorithm is demonstrated by experiments with real and simulated data.