Transfer Functions Of Linear Systems Research Articles

The CONTSID Toolbox: A Matlab Toolbox for Continuous-Time System Identification

This paper presents the CONTSID toolbox for the identification of continuous-time transfer function or state-space models for linear time-invariant SISO and MIMO systems from sampled input/output data. The acronym CONTSID stands for CONtinuous-Time System IDentification toolbox. It has been designed as an addon to the Mathwork's system identification toolbox and has been given a similar setup. The toolbox is a collection of m-files and operates exclusively in the command line mode. It comprises most of the direct parametric continuous-time model identification methods from a discrete-time set of measurements, both classical ones as the state-variable filter method and more recent ones as subspace-based methods. The toolbox also includes tools for evaluating the estimated model properties.

Control of Chua's circuit with a cubic nonlinearity via nonlinear linearization technique

This paper addresses the controlling chaos problem of a cubic variant for the original Chua's circuit. A conventional input-output transfer function of a linearized system and a nonlinear linearization technique for a nonlinear system are also presented. According to analytical results, at equilibrium, the notion of local phase-minimality of the nonlinear system is equivalent to that of the linear system's transfer function. Our results also demonstrate that the controlled Chua's circuit, while considering a certain state as the system output, is an input-output linearizable minimum-phase system. In addition, nonlinear control laws are derived such that each state asymptotically tracks its corresponding desired trajectory while maintaining the boundedness of all signals inside the system.

Nonparametric estimation of transfer functions: rates of convergence and adaptation

The paper deals with estimating the transfer functions of stable linear time-invariant systems under stochastic assumptions. We adopt a nonparametric minimax approach for measuring the estimation accuracy. The quality of an estimator is measured by its worst case error over a family of transfer functions. The families with polynomially and exponentially decaying impulse response sequences are considered. We establish nonasymptotic upper bounds on the accuracy of the least squares estimator for finite impulse response approximation. It is shown that the attainable estimation accuracy is determined essentially by the rate at which the true impulse response tends to zero. Lower bounds on the estimation accuracy are presented. An adaptive estimator which does not exploit any a priori information about the true system, is developed.

Using nullors for realisation of inverse transfer functions and characteristics

A general method is proposed for obtaining the inverse transfer function (for linear dynamic systems) and the inverse transfer characteristic (for nonlinear resistive circuits). The presented method makes use of nullors, known to be the most important active circuit elements. The procedure, initially introduced to obtain the system inversion for circuits already containing nullors, can easily be extended to any general circuit.

Adaptive Filters for Real-Time System Identification and Control

An adaptive Ž lter or a neural network concept has been used to develop an algorithmfor real-time system identiŽ cation and control. The algorithmpermits not only identiŽ cation of transfer functions of linear structural systems but also extraction of modal parameters such as natural frequencies, damping ratios, and mode shape coefŽ cients in real time. Because the algorithm is capable of identifying a single mode at a time, bandpass Ž lters are employed to make it work properly for systems with multiplemodes. The algorithmhas been implemented in a digital signal processor-based data acquisition and control system for the system identiŽ cation and control experiments with the U.S. Naval Research Laboratory space truss. It was experimentally demonstrated that the algorithmwas capable of identifying modal parameters of the truss accurately by using a truss tip-mounted accelerometer as a sensor and a piezoceramic active strut as a disturbance source. The algorithmwas also successfully employed to conduct active vibration suppression and performance monitoring of the feedback controller by using the active strut and a collocated force transducer.

Rational Multiple Criterion Approximation and Rational Complex Approximation by Differential Correction-Type Algorithms

This work shows how to extend the differential correction algorithm (a well-known technique for rational minimax approximation of real functions) to handle simultaneous minimax approximation of magnitude and phase of complex-valued functions defined on the unit circle of the complex plane. The proposed procedure enjoys global convergence to local best approximants with poles only inside the unit circle. Hence, the approximants obtained can be used as transfer functions of causal and stable linear systems, and the proposed technique can be profitably applied to digital filter design. The differential correction strategy can also be applied to rational complex approximation, and can also be extended to the case of multidimensional rational functions, retaining the properties of the one-dimensional case. This ability to produce stable transfer functions is of special interest in the multidimensional case.

A Simple and Quick Technique for the Determination of Transfer Functions of Linear Mechanical Systems

Usual methods for the determination of the transfer functions of mechanical systems consisting of linear elements (i.e. mass, spring and damper), are practical only for simple cases. In a complicated system with many elements, the process is tedious and error-prone. In this work, with the aid of a simple model which easily transfers the system from time domain into the Laplace domain, the general forms of the transfer functions of the system have been derived. In this report, three general forms of such systems are discussed and examples are considered. The advantages of this method in addition to its simplicity are that the transfer functions provide numerators and denominators (characteristic equations) separately; the formulae are easily applicable in digital computer programs; and finally, the method can be used for academic purposes (for example, for quick problem-checking by the instructor).

A new nonparametric method for linear system phase recovery from bispectrum

For input signals with nonzero third order moment, the phase of a linear system transfer function can be identified from the bispectrum of its output signal. Instead of using partial bispectrum phase information which is more sensitive to noises and measurement errors, a new nonparametric method is proposed to utilize all the available bispectrum phase information. The proposed new method is computationally simple. It does not require finding the pseudo-inverse of a gigantic matrix as some existing methods do. Its effectiveness is demonstrated through computer simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Transfer Functions of Regular Linear Systems. Part I: Characterizations of Regularity

Transfer Functions of Regular Linear Systems. Part I: Characterizations of Regularity

Transfer functions of regular linear systems. I. Characterizations of regularity

We recall the main facts about the representation of regular linear systems, essentially that they can be described by equations of the form x ˙ ( t ) = A x ( t ) + B u ( t ) \dot x(t) = Ax(t) + Bu(t) , y ( t ) = C x ( t ) + D u ( t ) y(t) = Cx(t) + Du(t) , like finite dimensional systems, but now A, B and C are in general unbounded operators. Regular linear systems are a subclass of abstract linear systems. We define transfer functions of abstract linear systems via a generalization of a theorem of Fourés and Segal. We prove a formula for the transfer function of a regular linear system, which is similar to the formula in finite dimensions. The main result is a (simple to state but hard to prove) necessary and sufficient condition for an abstract linear system to be regular, in terms of its transfer function. Other conditions equivalent to regularity are also obtained. The main result is a consequence of a new Tauberian theorem, which is of independent interest.

New matrix method for multipoint Padé approximation of transfer functions

Abstract A new way of formulating a multipoint Pade approximant of a linear system transfer function is given. It is seen to be very flexible and computationally efficient. The expansion points can be a mixture of real, complex, purely imaginary and multiple points with no complex arithmetic required. The underlying idea of the method is to convert the rational approximation problem into one of polynomial approximation. This results in simple matrix multiplications and the solution of a set of linear equations to derive the reduced model. Examples are given to demonstrate the application of the technique.

110 Transfer function of linear discrete time-varying systems via non-cummutative algebra

110 Transfer function of linear discrete time-varying systems via non-cummutative algebra

A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling

A new method for the prediction of chatter in milling is presented. The dynamics of the milling process are described by a set of differential-difference equations with time varying periodic coefficients. The stability of this system is examined using Fourier analysis and basic properties of the parametric transfer functions of linear periodic systems. The resulting characteristic equation is of infinite order and has constant coefficients. Its truncated version is used to determine the limit of stability employing standard techniques of control theory. The proposed method is applied to a theoretical example and a practical milling system.

Fast inversion of transient calibration responses of arbitrary digital seismograph systems

Abstract A FORTRAN computer program intended for the identification of transfer functions of linear dynamic systems by stabilized inversion of preprocessed experimental transient responses is presented. Optimal nonequidistant resampling based on the limit value theorem of the Laplace transform is used to reduce the length of the response without loss of high- or low-frequency information. The effect of both preprocessing and reduction of the response is to stabilize the process of inversion and to accelerate it dramatically. The performance of the approach, developed with a special view to routine applications in observational seismology, is demonstrated on examples of identifying transfer functions of broad-band, intermediate-band, and short-period seismography. The examples convincingly demonstrate the usefulness of including weighted a priori information in the inversion of calibration signals with a poor signal-to-noise ratio.

Optimal model reduction by multipoint Padé approximation

A novel method of obtaining optimal reduced-order models of linear system transfer functions is presented. It uses the popular multipoint Padé approximation technique in an iterative way to generate efficiently the optimal models. Central to the method is a new way of calculating Padé approximants about many points by reducing them to equivalent Taylor series approximants. Optimal reduced-order models for impulse and step inputs are considered, and it is seen how the method may be extended to ramp and other polynomial inputs. Numerical examples are given to demonstrate the method.

Transfer Function of Linear Discrete Time-Varying Systems via Non-Commutative Algebra

Abstract In this paper, we pay attention to linear systems (∑) described by difference:equations with nonconstant coefficients. Here, we show that it is also possible to define, like in the continuous case, an isomorphism between the difference equation of (∑) and the non-commutative polynomials of ∇ where ∇ is the difference operator. In this case, the operator ζ (delay) acts on the time-varying coefficients. We precise the association rules for serial systems from the computation rules over rational “skew” fractions.

Properties of linear continuous dynamical system transfer function parameters estimates obtained by the method of auxiliary variables

The present paper considers a constant-parameter estimation al~orithm for an analog transfer function by discrete observations fof the object's input and output variables. The algo­ rithm is bas~d on supplementary variables and least-squares meth­ ods. It. is assumed, that the order of (,he transfer fUllction is known and the derh~tive~ of the input and output variables are nOI1- measurable. The supplementary variables and their derivatives are constructed from dicrete observations of the input and output vari­ ables by applying a numerically realized analog filter. Investigation results for the estimate properties are presented. The results were obtained by the method of statistical sim ulation. •

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

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. >

Linear systems analysis of cutaneous Type I mechanoreceptors

Linear system transfer functions of Type I mechanoreceptor domes in hairy skin were extracted for study. The system input, defined in units of indentation depth, was a punctate, 85 Hz bandlimited colored noise indenting stimulus. The system output was a dome's afferent AP event stream. After digitally low-pass filtering the AP event stream to prevent aliasing, transfer and coherence function estimates were generated from spectral and cross spectral estimates of the sampled input and output signals. Transfer function magnitudes (receptor sensitivity) beyond 10 Hz could be well fit by a fractional exponent (0.35 +/- 0.10) of frequency, indicating fractional order differentiation. Transfer function phases were near 120 degrees for frequencies less than 10 Hz and decreased progressively beyond 10 Hz. Coherence function estimates were low as a result of inherent nonlinearities, primarily rectification. Single dome results closely matched those reported by French and Kuster [6] for the tactile spine of the cockroach, suggesting that in terms of spectral sensitivity the receptors have similar transduction mechanisms. However, nonlinear systems modeling techniques are required for a more complete system characterization.

Remarks on the moduli space of SU(2) monopoles and Toda flow

Rational functions of degreek which parametrize the moduli space of SU(2)k-monopoles, can be regarded as transfer functions for certain linear dynamical systems. It is shown that a time shift for linear systems induces a finite nonperiodic complexk×k Toda flow on the parameter space of generic SU(2)k-monopoles. Thus, there exists an integrable flow of the Toda type over the moduli space of SU(2) monopoles.