Showing papers on "Transfer function published in 1990"

Towards a theory of early visual processing

Abstract: We propose a theory of the early processing in the mammalian visual pathway. The theory is formulated in the language of information theory and hypothesizes that the goal of this processing is to recode in order to reduce a generalized redundancy subject to a constraint that specifies the amount of average information preserved. In the limit of no noise, this theory becomes equivalent to Barlow's redundancy reduction hypothesis, but it leads to very different computational strategies when noise is present. A tractable approach for finding the optimal encoding is to solve the problem in successive stages where at each stage the optimization is performed within a restricted class of transfer functions. We explicitly find the solution for the class of encodings to which the parvocellular retinal processing belongs, namely linear and nondivergent transformations. The solution shows agreement with the experimentally observed transfer functions at all levels of signal to noise.

Adaptive inverse control

Abstract: Adaptive control is seen as a two part problem control of plant dynamics and control of plant noise. The two parts are treated separately. An unknown plant will track an input command signal if the plant is driven by a controller whose transfer function approximates the inverse of the plant transfer function. An adaptive inverse identification process can be used to obtain a stable controller even if the plant is nonminimum phase. A model reference version of this idea allows system dynamics to closely approximate desired reference model dynamics. No direct feedback is used except that the plant output is monitored and utilized in order to adjust the paramters of the controller. Control of internal plant noise is accomplished with an optimal adaptive noise canceller. The canceller does not affect plant dynamics but feeds back plant noise in a way that minimizes plant output noise power. Key words. Adaptive control modeling identification inverse modeling noise cancelling deconvolution adaptive inverse control.© (1990) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Frequency response of linear time periodic systems

Abstract: A frequency response for linear time periodic (LTP) systems that exploits the one-to-one map induced by geometrically periodic signals is developed. This map is described by an integral operator, based on the GP (geometrically periodic) test input, and a generalized harmonic balance approach, based on an EMP (exponentially modulated periodic) input. The singular values or principal gains of the LTP operator are discussed, and the LTP principal gain diagram is described. Directional properties of the LTP operator are discussed, and notions of the domain and range spaces are presented. The framework of linear operators described has lead to the development of a comprehensive open-loop analysis theory for LTP systems, including a characterization of poles, transmission zeros, and their directional properties. >

Invariant properties of automotive suspensions

Abstract: Dynamic systems which are composed of interconnected sub-systems are subject to dynamic 'constraint equations' which are independent of the nature of the interconnections. A dynamic constraint equation is developed for a quarter car model of an automotive suspension. It is shown that only one of the three transfer functions (acceleration, suspension deflection and tyre deflection) can be independently specified and that the first two contain 'invariant points' at frequencies within the frequency range of interest. These constraint equations lead to conclusions with respect to trade-offs between the three transfer functions. Improvements in all three can be obtained near the unsprung natural frequency; however, severe trade-offs are shown to exist at all other frequencies. (A) (Author/TRRL)

New approach to sampled-data control systems-a function space method

Abstract: The author presents a novel framework for hybrid sampled-data control systems. Instead of considering the state only at sampling instants, the author introduces a function piece during the sampling period as the state and gives an infinite-dimensional model with such a state space. This provides the advantage that sampled-data systems with built-in intersample behavior can be regarded as linear, time-invariant, discrete-time systems. As a result, the approach makes it possible to introduce such time-invariant concepts as transfer functions, poles, and zeros even in the presence of the intersample behavior. In particular, tracking problems can be studied in this setting in a simple and unified way, and stationary ripples are completely characterized as a mismatch between the intersample reference signal and transmission zero directions. >

Practical repetitive control system design

Abstract: The author considers two basic problems with repetitive control: the tight stability condition and the poor noise characteristics. He presents three techniques for a practical repetitive controller design: stabilizing compensation by an inverse phase system, band limitation of the control, and smoothing of the control signal over periods of repetitive operation. >

Gravity anomaly separation by wiener filtering

Abstract: We introduce a gravity anomaly separation method based on frequency‐domain Wiener filtering. Gravity anomaly separation can be effected by such wavelength filtering when the gravity response from the geologic feature of interest (the signal) dominates one region (or spectral band) of the observed gravity field’s power spectrum. The Wiener filter is preferable to a conventional band‐pass filter because geologic information from the study area can be incorporated to a greater extent in specifying the filter’s transfer function. Our method differs from previous Wiener filtering schemes in that it provides, through direct modeling of known geology (e.g., outcrop and borehole data), a more objective estimate of the signal power spectrum required for defining the transfer function of the filter. We illustrate the technique first with synthetic data, and then with a field example from the southern Paradox basin. The Paradox basin example reveals the limitation inherent to all wavelength filtering which results f...

Crosstalk analysis of interconnection lines and packages in high-speed integrated circuits

Abstract: A novel approach for the analysis of crosstalk, propagation delay, and pulse distortion of interconnects in high-speed integrated circuits, packages, and circuit boards is presented. Based on frequency-domain modal analysis, a set of formulas is derived to describe the voltage and current transfer functions of coupled interconnects with arbitrary linear termination impedances and used to obtain analytical expressions for the time-domain waveforms for lossless multiconductors interconnection lines. The weak-coupling assumption is found to be only marginally valid. In a typical interconnection configuration, the secondary coupling of the disturbed line on the original signal line substantial and must be taken into account for accurate prediction of the waveforms. Simulation results are given to illustrate the influence of the layout parameters of the interconnects and the rise or fall times of the source signal. It is shown that ground conductors need to be placed on both sides of each of the signal lines to reduce crosstalk effectively. However, the presence of the ground conductors increases the layout complexity and results in more severe waveform distortion for the signal on the active line. >

Optimal finite precision implementation of a state-estimate feedback controller

Abstract: Expressions are derived for the sensitivity and the roundoff noise gain of the closed-loop transfer function of a system when the state estimate feedback controller is implemented with a finite word length and when the computations are performed in finite precision. This allows one to compare the sensitivity and noise gain over all equivalent state-variable implementations of the observer plus controller. The set of state-space models minimizing either the sensitivity or the roundoff noise gain is computed. Simulations compare the performance of the optimal implementations with respect to companion forms and a particular delta model. >

Analysis and Design of Repetitive Control Systems using the Regeneration Spectrum

Abstract: The absolute and relative stability of continuous-time SISO repetitive control systems is examined here using a function of frequency termed the regeneration spectrum. The regeneration spectrum is easily computed and is related to important of the characteristic root distribution of such systems, for large values of the time delay. The regeneration spectrum is combined with other frequency domain measures of control system performance such as the sensitivity and complementary sensitivity functions to obtain improved insight into the trade-offs in repetitive control system design. The result is a more rational approach to repetitive control system design and is illustrated by an example.

Robust identification of transfer functions in the s- and z-domains

Abstract: A frequency-domain maximum-likelihood estimator (MLE) for estimating the transfer function of linear continuous-time systems developed by J. Schoukens et al. (1988) assumes independent Gaussian noise on both the input and the output coefficients. A Gaussian frequency-domain MLE for transfer functions of linear continuous or discrete time invariant systems in an errors-in-variables model is presented. It is demonstrated that most of the properties of the estimator remain unchanged when it is applied to measured input and output Fourier coefficients corrupted with non-Gaussian errors. The result is a robust Gaussian frequency-domain estimator that is very useful for the practical identification of linear systems. The theoretical results are verified by simulations and experiments. >

Frequency analysis of time-interval-modulated switched networks

Abstract: A Fourier analysis of the time-interval-modulated switched networks is undertaken using time-varying system theory. The result is a linearized describing function approach which determines the small-signal control-to-output (fundamental Fourier component) frequency response. The proposed algorithm is general and exact, and the results are developed in closed form. The intended application area is that of switching DC-to-DC converters, where use of the algorithm is demonstrated in deriving an exact analytical expression for the control-to-output transfer function of pulse-width-modulated converters. Experimental results are presented, verifying the modeling technique. >

Spectral factorization and LQ-optimal regulation for multivariable distributed systems

Abstract: A necessary and sufficient condition is proved for the existence of a bistable spectral factor (with entries in the distributed proper-stable transfer function algebra 𝒜-) in the context of distributed multivariable convolution systems with no delays; a by-product is the existence of a normalized coprime fraction of the transfer function of such a possibly unstable system (with entries in the algebra ℬ of fractions over 𝒜-). We next study semigroup state-space systems SGB with bounded sensing and control (having a transfer function with entries in ℬ) and consider its standard LQ-optimal regulation problem having an optimal state feedback operator K0. For a system SGB, a formula is given relating any spectral factor of a (transfer function) coprime fraction power spectral density to K0; a by-product is the description of any normalized coprime fraction of the transfer function in terms of K0. Finally, we describe an alternative way of finding the solution operator K0 of the LQ-problem using spectral factor...

Multichannel signal processing for data communications in the presence of crosstalk

Abstract: Transceiver designs for multiple coupled channels typically treat the crosstalk between adjacent twisted pairs as random noise uncorrelated with the transmitted signal. The authors propose a transmitter/receiver pair that compensates for crosstalk by treating an entire bundle of twisted pairs as a single multi-input/multi-output channel with a (slowly varying) matrix transfer function. The proposed transceiver uses multichannel adaptive FIR filters to cancel near- and far-end crosstalk, and to pre- and postprocess the input/output of the channel. Linear pre- and postprocessors that minimize mean squared error between the received and transmitted signal in the presence of both near- and far-end crosstalk are derived. The performance of an adaptive near-end crosstalk canceller using the stochastic gradient (least-mean-square) transversal algorithm is illustrated by numerical simulation. Plots of mean squared error versus time and eye diagrams are presented, assuming a standard transmission line model for the channel. A signal design algorithm that maps a vector input bit stream to a stream of channel symbol vectors is also presented and illustrated explicitly for s simple model of two coupled channels. >

Surface Scatter Phenomena: A Linear, Shift-Invariant Process

Abstract: Empirical experimental scattering data from conventional optical surfaces is shown to exhibit shift-invariant behavior with respect to incident angle when plotted in direction cosine space. This implies the existence of a surface transfer function that completely characterizes the scattering properties of the surface, and permits the application of linear systems theory and Fourier techniques in modeling the scattering effects of optical surfaces. A theoretical basis for this behavior is illustrated by showing that scalar diffraction phenomena (conical diffraction from gratings) is shift-invariant with respect to incident angle only in direction cosine space, and surface roughness can be considered to be composed of a superposition of sinusoidal phase gratings. The fact that many optical surfaces of interest deviate from this shift-invariant behavior does not invalidate the usefulness of the linear systems formalism. The ideal behavior of a shift-invariant scattering process can still be used for making engineering calculations and retained as the reference from which scattering from real surfaces is compared. This is completely analogous to the universally accepted transfer function characterization of imaging systems in spite of the fact that few real imaging systems are isoplanatic (no field-dependent aberrations).

Pole-placement power system stabilizers design of an unstable nine-machine system

Abstract: Power system stabilizers (PSS) are designed for an unstable nine-machine system. Participation factors are used to select the sites and number of stabilizers. An efficient pole-placement method is developed with straightforward formulation and a reduced computation requirement. The design not only ensures the exact pole-placement of the unstable mechanical modes, but also improves the dampings of the poorly damped mechanical modes, resulting in a well-coordinated damping for the entire system. >

Real-time integration and differentiation of analog signals by means of digital filtering

Abstract: The performance of digital infinite impulse response (IIR) integrators and differentiators, calculated by means of a maximum likelihood estimator for transfer functions, is compared with that of their finite impulse response (FIR) counterparts and that of classical numerical integration and differentiation. An original design method that generates stable and reduced-order IIR filters in the complex domain (amplitude as well as phase constraints) is presented. In contrast to common opinion, it is shown that it is possible to design easy realizable IIR integrators and differentiators with an arbitrary small amplitude and phase error. Although there is no FIR alternative for IIR integrators, both FIR and IIR methods give competitive results for differentiators. It is shown that, owing to the design of pure delay filters, the (optimal) fractional delay integrators and differentiators can be used in case the original waveform and one (or more) of its (higher order) derivatives and (or) integrals are required. >

Multiscale system theory

Abstract: A system theory based on the homogeneous dyadic tree as a possible foundation for a multiscale system theory and multiscale statistical signal processing is developed. Multiscale representations, including wavelet transforms, homogeneous trees, shift operations, and transfer functions, are discussed. It is shown that the homogeneous tree possesses strange geometric properties that have the following consequence: the double role played by the classical z-transform, namely, encoding transfer function and defining stationarity, is split between two different objects-the shifts to encode transfer functions (these are not isometries) and the translations to define stationarity (these are not easily expressed by shifts). Two system theories are sketched that emphasize each of these two different objects. Finally, a notion of stationary stochastic processes is introduced. >

Bi-impulse response design of isotropic quadratic filters

Abstract: The bi-impulse response of a 1-D or 2-D quadratic Volterra filter is introduced as a mathematical tool able to completely describe the nonlinear operator. The conditions that must be satisfied in order to obtain isotropic input/output relations are studied. The result is a formal framework that allows simple but effective operators (particularly for image enhancement and preprocessing) to be designed and a deeper insight into the properties of Volterra filters to be acquired. Examples of design and of the performance obtained by processing natural and synthetic images are presented. >

Digital control of active magnetic bearings

Abstract: Theoretical relationships are developed to relate the characteristics of a controller transfer function to the stiffness and damping properties of an active magnetic bearing for machine rotors. Both proportional and derivative feedback are shown to be necessary for closed-loop system stability, and, for the ideal case, bearing stiffness and damping properties are shown to be simple linear functions of the proportional and derivative feedback gain constants, respectively. The flexibility of a digitally controlled magnetic bearing is demonstrated by the implementation of algorithms which include second-derivative and integral feedback. Second-derivative feedback is shown to be effective at extending the usable bandwidth of the digital controller, and integral feedback rejects rotor position error in the presence of static loads. The relationship between controller sampling rate and bearing performance is investigated, and it is shown that increased sampling rate and increased amounts of second-derivative feedback have similar effects on the bearing properties. >

Identification of transfer functions with time delay and its application to cable fault location

Abstract: A Gaussian frequency-domain maximum likelihood estimator (MLE) to estimate the transfer function of linear continuous-time systems with time delay is presented. The stochastic framework is an errors-in-variables model, which means that the input as well as the output of the system is disturbed with noise. The estimator is applied to a practical measurement problem, namely the estimation of the location of discontinuities, e.g. faults in electrical cables from a reflectogram. Experimental results for coaxial lines show that it is possible to identify simultaneously the location of the discontinuity and a rational approximation of the generator mismatch, the fault impedance, and some of the cable parameters. >

Sigma delta modulator with distributed prefiltering and feedback

Abstract: A separate filter circuit is inserted between the D/A converter and the summing junction in the feedback path of a conventional sigma delta modulator. This additional filter allows control of the quantization noise transfer function profile independently of the forward signal transfer function. By proper tailoring of the transfer functions a third or higher order modulator can be constructed without instability developing.

A New Algorithm for the Real Structured Singular Value

Abstract: A new algorithm is presented for computing a tight lower bound for Doyle's Structured Singular Value (SSV) in the case of real uncorrelated parameter uncertainty. The algorithm has several desirable features: it consists entirely of simple matrix algebra operations; it iterates on only one variable; and it returns the actual values of the "worst-case" parameters, not just their size. Unlike other algorithms for the real SSV, it does not require the computing of convex hulls or other difficult geometric constructs. This lower bound is conjectured to be exactly equal to the real SSV for a wide class of matrices. The new algorithm has wide applications for control system design; several types of control system robustness tests are identified. A numerical example is given for a 6 by 6 complex matrix.

Frequency tracking using constrained adaptive notch filters synthesised from allpass sections

Abstract: New constrained adaptive notch filter structures are proposed. These structures are synthesised from allpass filter sections, which are realised as structurally lossless bounded real functions with a minimum number of delay elements and multipliers. Both structures admit orthogonal tuning of their notch frequency and bandwidth. Frequency tracking is achieved simply by the evaluation of a function of a filter parameter. Connections are shown with the structures used by other workers. Signal enhancement outputs are obtained from both structures and their signal-to-noise improvement ratios are given. The mirror-image pair of polynomials present in a real allpass transfer function is shown to provide a significant simplification in the generation of the necessary gradient terms used in parameter adaptation. Simulations are included to verify the performance of these structures when they are used to track both single and multiple sinusoids in additive broadband noise.

Adaptive recursive state-space filters using a gradient-based algorithm

Abstract: To aid in the search for better adaptive filter structures, a method is presented to obtain the gradients required to adapt general state-space filters. Unfortunately, the number of computations for this general case is quite high. To reduce the number of computations, two new state-space adaptive filters are introduced. One application where these new structures are shown to be useful is in oversampled filtering where an estimate of the final pole locations is known and the adaptive filter is required only to fine-tune the transfer function. It is shown that for this type of application, the new adaptive structures can have much improved adaptation rates and roundoff noise performance as compared to the corresponding direct-form realizations. >

A methodology for building thermal dynamics studies and control applications

Abstract: A methodology is presented for a unified approach to building thermal control studies and building energy analysis. The same detailed building thermal models are used for energy calculations and for thermal control studies. Laplace transfer functions for the building are obtained by means of thermal network models that include both distributed parameter elements, such as thermal mass, and lumped elements, such as the room air thermal capacitance. For detailed models for which an analytical solution is not feasible, the s-domain transfer functions are obtained through a modified least squares polynomial fit to the discrete frequency responses. Laplace transfer functions are also used for HVAC system and control components. Transient thermal control studies are performed by means of a numerical Laplace transform inversion technique. Typical studies with the methodology led to the following results: A separation of building thermal dynamics into short-term and long-term dynamics for convective loads begins at frequencies of about 35 cycles per day (period 41 minutes), with the room air thermal capacitance being important only for the short-term, high-frequency thermal dynamics. Air temperature sensor time constants are shown to have a substantial effect on room temperature response to setpoint changes, such as an increase of 50% inmore » the settling time (with P-1 control) when the sensor time constant is increased from 30 s to 60 s.« less

Parametric System Identification on Logarithmic Frequency Response Data

Abstract: Gradient search methods that fit the parameters of a user-defined transfer function model to experimental Logarithmic frequency response data are presented. The methods match a model based on physically significant parameters, including natural frequencies of poles and zeroes and damping ratios of complex poles and zeroes. The algorithms construct and utilize their own analytical gradient descent functions, based on the desired model. One method attempts to fit both log magnitude and phase, while another identifies a minimum phase transfer function model from only log magnitude frequency response data. The performance of the log magnitude algorithm is shown to be superior to traditional methods using non-logarithmic frequency response data, including those used in commercially available frequency response analyzers. The algorithms are shown to perform well, especially for systems with lightly-damped dynamics.