Showing papers on "Transfer function published in 1985"

Structured uncertainty in control system design

Abstract: This paper reviews control system analysis and synthesis techniques for robust performance with structured uncertainty in the form of multiple unstructured perturbations and parameter variations. The structured singular value, µ, plays a central role. The case where parameter variations are known to be real is considered.

Asymptotic variance expressions for identified black-box transfer function models

Abstract: Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-type models. Expressions for the variances of the transfer function estimates are derived, that are asymptotic both in the number of observed data and in the model orders. The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise. The factor of proportionality is the ratio of model order to number of data. This result is independent of the particular model structure used. The result is applied to evaluate the performance degradation due to variance for a number of typical model uses. Some consequences for input design are also drawn.

A photon dose distribution model employing convolution calculations.

Abstract: A three-dimensional photon beam calculation is described which models the primary, first-scatter, and multiple-scatter dose components from first principles Three key features of the model are (1) a multiple-scatter calculation based on diffusion theory, (2) the demonstration of the modulation transfer function of the radiation dose transport process, and (3) the use of the finite fast Fourier transform to perform the required convolutions The results of calculations for cobalt-60 in a homogeneous phantom are used to verify the accuracy of the model

Asymptotic properties of black-box identification of transfer functions

Abstract: The problem of estimating the transfer function of a linear, stochastic system is considered. The transfer function is parametrized as a black box and no given order is chosen a priori. This means that the model orders may increase to infinity when the number of observed data tends to infinity. The consistency and convergence properties of the resulting transfer function estimates are investigated. Asymptotic expressions for the variances and distributions of these estimates are also derived for the case that the model orders increase. It is shown that the variance of the transfer function estimate at a certain frequency is asymptotically given by the noise-to-signal ratio at that frequency mulliplied by the model-order-to-number-of-data-points ratio.

Robustness of discrete-time direct adaptive controllers

Abstract: The problem of preserving stability of discrete-time adaptive controllers in spite of reduced-order modeling and output disturbances is addressed in this paper. Conditions for global stability (convergence of the tracking error with bounded signals) are derived for a discrete-time pole-zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals. Following an input-output perpective, the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors, respectively, and its stability is studied using the sector stability and passivity theorems. First the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure. In this L 2 -framework, it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed-loop transfer function verifies certain conicity conditions. The convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed. The results are further extended to a broader class of L_{\infty} disturbances and reference inputs.

Theory and application of an extended horizon self‐tuning controller

Abstract: A robust version of the self-tuning regulator is developed. The regulator, which requires relatively little knowledge of system characteristics (estimated order of transfer function polynomials and an upper bound for transportation delays), has been shown to yield stable control and convergence for linear, time-invariant systems. Simulations and practical tests on a large pilot-scale process have shown that the inclusion of a variable forgetting factor and an “extended horizon” control criterion provides the regulator with a sufficient degree of robustness and flexibility to perform well in a nonlinear time-varying environment. The regulator makes use of intuitively easy-to-understand concepts and leaves few degrees of freedom for the potential user. Furthermore, extensive experiments and simulation studies have shown it to be insensitive to choice of initial conditions and dynamic characteristics set by the user.

A Transfer-Function Approach to Linear Time-Varying Discrete-Time Systems

Abstract: In the first part of the paper a transfer-function approach is developed for the class of linear time-varying discrete-time systems. The theory is specified in terms of skew (noncommutative) rings of polynomials and formal power series, both with coefficients in a ring of time functions. The transfer-function matrix is defined to be a matrix whose entries belong to a skew ring of formal power series. It is shown that various system properties, such as asymptotic stability, can be characterized in terms of the skew-ring framework. In the last part of the paper, the transfer-function framework is applied to the study of feedback control. New results are obtained on assignability of system dynamics by using dynamic output feedback and dynamic state feedback. The results are applied to the control of an armature-controlled do motor with a variable loading.

A Frequency Domain Approach to Water Quality Modeling in Groundwater: Theory

Abstract: A method for the analysis of complex temporal variations of environmental tracers or pollution time series in groundwater is examined using spectral analysis and linear filter theory for stationary stochastic processes. The interpretation of solute fluctuations subject to a time varying source is accomplished via frequency domain solutions to stochastic differential equations for three widely applied transport models: (1) a lumped parameter or linear reservoir model; (2) convective (advective) transport in a curvilinear flow field; and (3) convective-dispersive transport in a uniform flow field. Frequency domain solutions are presented in terms of the theoretical transfer function and phase spectra which describe the amplitude attenuation and phase lag between frequencies in the input and output. A comparison of the frequency response of the three models indicates that the unique filtering characteristics of each may provide a diagnostic tool for matching the appropriate theory to a sampled water quality “signal.” A procedure is suggested for parameter estimation which involves comparison of the theoretical and field estimated transfer function and phase spectra.

Time-variant filtering of signals in the mixed time frequency domain

Abstract: A new approach to the problem of time-variant filtering is presented. This approach is based upon the generation of the mixed time-frequency representation (MTFR) of a signal, multiplication of that representation by a time-frequency function H(ω,t), and obtaining a filtered output by an inverse operation. The resultant filter is linear if the time-frequency representation used is the complex spectrogram. In contrast, the filter is nonlinear if the Wigner distribution function is used. Not every function of two variables is an allowed MTFR of a signal; some conditions must be satisfied. If the function produced by the product of the signal MTFR and the filter function is not an allowed MTFR, an approximation based on projection onto the space of allowed MTFR functions is investigated. This approximation yields a filtered function whose MTFR is as close as possible (in the least-squared sense) to the desired.

Linear model of brain electrical activity--EEG as a superposition of damped oscillatory modes

Abstract: EEG time series were modeled as an output of the linear filter driven by white noise. Parameters describing the signal were determined in a way fulfilling the maximum entropy principle. Transfer function and the impulse response function were found. The solutions of the differential equations describing the system have the form of the damped oscillatory modes. The representation of the EEG time series as a superposition of the resonant modes with characteristic decay factors seems a valuable method of the analysis of the signal, since it offers high reduction of the data to the few parameters of a clear physiological meaning.

A decomposition theorem and its implications to the design and realization of two-dimensional filters

Abstract: It is shown that an arbitrary rational 2-D transfer function can be expanded in first order terms, each one of which is a function of only one of the two variables. This method leads naturally to reconfigurable filters with great modularity and parallelism, which can realize any rational transfer function up to a given order.

Dynamic error compensating process controller

Abstract: A process control apparatus has a controller for performing a control operation including an integral operation for a set point signal supplied to a process and an output signal from the process and for generating a control signal to the process, and a reference model which has a desired transfer function of a control system and which receives the set point signal. The process control apparatus further has a first subtractor for subtracting the output signal of the reference model from the output signal of the process, an output error compensator for performing a control operation including an integral operation for the output error and for generating a compensation signal in such a manner that the output error becomes zero, and a second subtractor for subtracting the compensation signal from the output control signal of the controller.

Some Extensions of Loop Transfer Recovery

Abstract: In this paper, new conditions for regulator loop transfer recovery (LTR) of minimum phase, non-square, left-invertible, full- or reduced-order observer-based multivariable feedback control systems are derived. It is proved that these conditions are satisfied asymptotically by either the full- or the reduced-order Kalman filters that assume fictitious process noise at the input in the design model. These results eliminate the need for artificially squaring a non-square system and extend the theory to reduced-order observer-based LOG designs. The results are illustrated by a numerical example.

Linear system reduction by impulse energy approximation

Abstract: A method is given for linear system reduction which is a more general form of the Routh method. The reduced models retain stability, and a fuller contribution is made to the impulse response energy of the reduced system by appropriate selection of retained alpha and beta parameters. It requires no more computation than the Routh method and can be presented in a compact tabular form. Examples are given to illustrate the method.

Adaptive multipath delay estimation

Abstract: Two algorithms are proposed for the continuous tracking of multipath delay. The first is an efficient method for adaptively tracking the secondary peak in the autocorrelation function caused by multipath. In principle, it is equivalent to the correlation method commonly used in practice. The second is an adaptive inverse filter which can exactly remove the multipath transfer function. The methods use an adaptive delay line interpolated by a first-order filter. The interpolation coefficient is explicitly estimated using the recursive Gauss-Newton (RGN) algorithm often used for recursive system identification.

Modelling the transfer function in medium bandwidth radio channels during multipath propagation

Abstract: A method to compute the effects of a multipath propagation channel on a line-of-sight link consists in establishing a statistical model of the channel transfer function. It is then possible to compute the outage time previsions for various communication systems, or to compare these systems by means of their signatures. To carry out this method, it is first necessary to choose a representation model of the transfer function, then to establish on an experimental basis the joint statistics of the model parameters. The authors discuss the various steps in the construction and validation of such a model and compare several proposed models from the point of view of their applications. These points are illustrated by means of results from thepacem Iexperiment.

Transfer function model order and parameter estimation

Abstract: . A distributed lag model with a rational transfer function is considered. We have demonstrated that the C-table can be used to determine the orders of the rational transfer function and the Pade table can be used to estimate the parameters of an identifiable transfer function. In case the model is not uniquely identified, the C-table reduces possible competing models to only a few for further examination. Pade approximant gives consistent initial values for possibly more efficient iterative procedures to estimate the coefficients of the identified model. Some asymptotic results on the estimation of the C-table and the Pade table are given. A few examples are presented to demonstrate the effectiveness of the method.

Some considerations for estimator-based compensator design

Abstract: In this paper some criteria are presented for dividing the closed-loop system poles of a feedback system between the estimator and the controller when using an estimator-based compensator The criteria are based on frequency response considerations, but are related to some well-known facts in the time domain It is well known, for example, that the closed-loop system poles are the poles of the estimator in union with the controller poles It is also well known that the time response of the closed-loop plant states due to a command depends only on the closed-loop control poles, and the response of the estimate error depends only on the closed-loop estimator poles In the frequency domain, the following can be said: the open-loop compensator transfer function from the sensor measurement to the control and the closed-loop transfer function from the sensor measurement to the system output are both independent of how the closed-loop poles are distributed between the controller and the estimator, but the closed

Coupled wave analysis of multiple waveguide systems: The discrete harmonic oscillator

Abstract: Planar arrays of coupled synchronous waveguides are analyzed with regard to full power transfer between the outermost guides. It is shown analytically, that in an N -guide synchronous system the coupling coefficients have to be tapered parabolically, in agreement with previous empirical results; the propagation constants of this system are equi-spaced. We prove that full transfer indeed occurs and determine the coupling length of the system. The mode interference picture provides a physical interpretation of the full transfer phenomenon. This multiple waveguide system is a discrete analog of the quantum mechanical harmonic oscillator.

Efficient and accurate multiparameter analysis of linear digital filters using a multivariable feedback representation

Abstract: The fundamental property of bilinearity is exploited, to develop a unifying concept, for the analysis of the effects of large-scale changes in the coefficients of a digital filter. This makes use of a multivariable feedback representation of the filter. The transfer matrix of this multivariable system has the inherent property that, it can be directly evaluated for all possible coefficient vectors, from its value for a given coefficient vector. Based on this concept, computationally efficient and numerically reliable algorithms are derived for performing two tasks: (i) to evaluate accurately the complex frequency transfer function for arbitrary values of the network coefficients, and (ii) to compute feasible values of the coefficients for which the magnitude and phase of the frequency response satisfy prescribed bounds. These can be used in existing computer-aided filter design and optimization tools to improve their quality and efficiency as well as to develop new optimization techniques. An application of these algorithms to the discrete coefficient optimization problem for a PCM low-pass filter is illustrated. It is also shown that the proposed techniques are .superior to existing methods of symbolic analysis, repeated network analyses, and Taylor approximations.

Charge-domain integrated circuits for signal processing

Abstract: A new class of integrated circuits called charge-domain device has been developed for performing enhanced monolithic signal processing. All signal-processing operations are accomplished by splitting, routing and combining charge packets, thus overcoming many of the limitations of alternative devices such as charge-coupled device (CCD) split-electrode transversal filters and switched capacitor filters. Charge manipulation techniques are described which allow poles as well as zeros of a transfer function to be implemented efficiently, leading to infinite impulse response monolithic filters suitable for high-frequency applications. Several test filters, including a narrowband 8-pole bandpass filter, are demonstrated. These charge-domain devices are useful in applications ranging from radio IF to radar to video signal processing with a high level of integration achievable on a single charge-domain integrated circuit.