Laplace Transfer Function Research Articles

A new set of piecewise constant orthogonal functions for the analysis of linear SISO systems with sample-and-hold

The present work searches for a suitable set of orthogonal functions for the analysis of control systems with sample-and-hold ( S/H). The search starts with the applicability of the well known block pulse function (BPF) set and uses an operational technique by defining a block pulse operational transfer function ( BPOTF ) to analyse a few control systems. The results obtained are found to be fairly accurate. But this method failed to distinguish between an input sampled system and an error sampled system. To remove these limitations, another improved approach was followed using a sample-and-hold operational matrix, but it also failed to come up with accurate results. Further, the method needed a large number of component block pulse functions leading to a much larger amount of storage as well as computational time. To search for a more efficient technique, a new set of piecewise constant orthogonal functions, termed sample-and-hold functions (SHF), is introduced. The analysis, based upon a similar operational technique, in the SHF domain results in the same accuracy as the conventional z-transform analysis. Here, the input signal is expressed as a linear combination of sample-and-hold functions; the plant having a Laplace transfer function G(s) is represented by an equivalent sample-and-hold operational transfer function ( SHOTF ), and the output in the SHF domain is obtained by means of simple matrix multiplication. This technique is able to do away with the laborious algebraic manipulations associated with the z-transform technique without sacrificing accuracy. Also, the accuracy does not depend upon m and the presented method does not need any kind of inverse transformation. A few linear sample-and-hold SISO control systems, open loop as well as closed loop, are analysed as illustrative examples. The results are found to match exactly with the z-transform solutions. Finally, an error analysis has been carried out to estimate the upper bound of the mean integral squared error (m.i.s.e.) of the SHF approximation of a function f(t) of Lebesgue measure.

Determination of Seismograph System Transfer Functions By Inversion of Transient and Steady-State Calibration Responses

The methods and software tools for the identification of the low-frequency portion of seismograph system transfer functions from transient (Dirac or step-impulse) calibration responses and of the high-frequency portion from steady-state (sinusoidal) calibration data are described. The presented procedures allow fast in-site determination of the overall Laplace transfer function of the analog stages of arbitrary seismograph systems. The developed identification software, which may also be employed for determining transfer functions in PAZ (polesandzeros) format from steady-state calibration data given graphically or in the form of FAP (frequency-amplitude-phase) triplets, has been made publicly available on the INTERNET. The paper is expected to prove useful especially for seismologists faced with the problem of specifying reliable calibration headers for digital upgrades of standard-class analog seismographs, for non-standard feedback-controlled seismograph systems, or for seismometric channels comprising inverse or simulation filters.

Coprime factorization design of a novel maglev presser foot controller

The problem of adverse presser foot dynamics affecting seam quality is addressed, and a novel control solution is proposed. The dynamics of a controlled sewing system are derived from first principles. The standard lockstitch sewing system with a novel maglev control mechanism is expressed both as a fourth order nonlinear state space model and as a Laplace transfer function. Using the linearized model, coprime factorization is used to find all stabilizing controllers. A controller producing a desired time domain response is then chosen. The resulting system demonstrates that adverse presser foot dynamics can be controlled and a desired sewing force can be maintained at all times during fabric feeding and stitch formation.

The zero-order hold equivalent transfer function for a time-delayed process

An explicit expression is derived for the zero-order hold equivalent z transfer function associated with the Laplace transfer function Gp(s)exp(−(r + α)Ts), where T is the sampling period, r is a positive integer or zero and 0α1 Vector-matrix generating rules are given for the numerator polynomial N(z, α) and structural relations between its coefficients are derived by invoking a ‘correspondence principle’. Approximate root locus analysis is given for N(z, α) under the assumption that T is chosen so that, for all i = 1,..., n the relation | pi T | ≪ 1 is satisfied, where p I, are the poles of G p(s).

Applying System Identification using Commercially Available Software and Hardware

System identification methods are now incorporated into several commercially available products, including two MATLAB Toolboxes and a number of frequency response analyzers. This paper reports on the performance of the two MATLAB Identification Toolboxes on two different applications, and on the performance of curve fitting algorithms used to obtain a Laplace transfer function from a measured frequency response on two commercial FFT analyzers.

A methodology for integrated building— HVAC system thermal analysis

This paper presents an integrated methodology for thermal analysis of buildings and their HVAC systems. The methodology is based on the use of Laplace transfer functions for the buildings, its heating-cooling system and control components. These transfer functions can be used for building thermal control studies, frequency domain analysis and energy analysis. Laplace transfer functions for the building are obtained by means of thermal network models that include both distributed parameter elements such as thermal mass, lumped elements such as the room light-weight contents, and which represent radiant exchanges accurately. 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 obtained by inversion of the system admittance matrix. Fourth order polynomials provide accuracies of approximately 1%. The methodology is applied to obtain both air temperature and operative temperature transfer functions. Laplace transfer functions are also used for HVAC system and control components. Transient thermal control studies are performed by means of an efficient numerical Laplace transform inversion technique. Building heating/cooling load calculations are performed by means of discrete Fourier series techniques.

A time domain method for the identification of dynamic parameters of structures

When using classic frequency methods, the identification of the modal parameters of a structure frequently fails in the event of high damping ratios and close modal frequencies, especially if associated with noisy measurements. This paper shows how, in such cases, time domain methods result in a correct and unbiased identification for a large range of parameter values, generally with a reduced sampling set of measures. The first part gives a short review of the mathematical framework. Formulations of the Laplace transfer function and z-transfer function are developed, resulting in a procedure for retrieving mechanical matrices of mass, damping stiffness. In the second part the z-transfer function is used to define the ARMA model of a structure. It is well-known in the field of automatics, that due to measurement noise, the least squares time domain estimates of the ARMA parameters are usually biased. An adaptive procedure for statistical estimation of the ARMA parameters with elimination of that bias is presented. Finally, the performances and limitations of the above procedure are determined by means of a large sequence of numerical simulations. The regions for correct identification in terms of damping ratio, sampling frequency and noise level are determined.

On narrow pulse duty cycle networks—analysis of a variable tuning twin-T notch filter

General considerations of a special category of periodically switching networks defined here as narrow pulse duty cycle networks is presented. With the aid of a suitable z-transformation a narrow pulse duty cycle twin-T notch filter is analysed using its linear Laplace transfer function. The conditions for zeroing the transfer function of the network are found and it is also proved that the notch frequency is proportional to the parametric switching frequency, The whole frequency characteristic can be moved along the frequency axis by varying the switching frequency.

A Q-matrix implementation of the Boxer and Thaler Z-form method

Application of the impulse invariance technique to z -transformation of certain Laplace transfer functions can be difficult if the function is not reduced to a constituent partial fraction form. This may be overcome by use of the z -form method, originally proposed by Boxer and Thaler [1]. However, the technique often requires a substantial amount of algebraic manipulation. Q -matrix methods are widely employed for such applications involving the bilinear transformation and substantially reduce the required amount of manipulation. This paper presents a general method for the formation and application of a z -form Q -matrix.

A Digital Transfer Matrix for Fuel Pin Heat Transfer

A method for rapid numerical simulation of transient radial heat transfer in nuclear fuel pins is presented. The method is based on a z-transfer matrix formulation of the transient conduction equations and assumes constant physical properties. The elements of the z-transfer matrix are obtained from Laplace transfer functions that are polynomial approximations to the exact equations over a specifiable frequency band, weighted to a better fit in the least-squares sense for frequencies for which inputs are expected to have higher amplitudes than for frequencies for which amplitudes of inputs are expected to be lower. Examples that demonstrate the method suitable for a large number of the transients encountered in plant dynamic analysis are presented.

Model reduction of continuous and discrete multivariable systems by moments matching

Algorithms for the calculation of the moments of multiple-input-multiple-output continuous-data and discrete-data systems are derived. Moments matching is used to reduce the order of the Laplace transfer functions and the z-transfer functions in matrix form. Examples with satisfactory results are given to illustrate the power of the method.

A Digital Transfer Matrix Approach to Distributed System Simulation

A method for rapid numerical simulation of transients in distributed-parameter systems is presented. The method is based on a z-transfer matrix formulation of the system equations and assumes linearity and time invariant physical properties. The elements of the z-transfer matrix are obtained from Laplace transfer functions which are polynomial approximations to the exact equations over a specifyable frequency band, weightable to be a better fit in the leastsquares sense for frequencies for which inputs are expected to have higher amplitudes than for frequencies for which amplitudes of inputs are expected to be lower. An example is presented which demonstrates the method to be very suitable for the analysis of the dynamics of distributed systems.

Torsional Stability Analysis of a Gas-Turbine Powered Helicopter Drive System

The torsional stability of a closed-loop dynamic system is evaluated. The system is a typical transport helicopter speed governor, gas-turbine engine and drive train. This is compared with the stability of a similar system in which a nonlinear coupling is included in the drive train, to determine if the coupling will increase the torsional stability of the system [1]. This nonlinear coupling is designed to isolate torsional vibrations in the rotor. The two systems are first linearized, using a decoupled rotor model for the ZTS coupling, and expressed in the form of Laplace transfer functions. Then a Bode Analysis is conducted and gain and phase margins are compared for the two systems. The nonlinear systems are numerically simulated to determine the time response and frequency response to excitation. The ZTS coupling design considered is found to be effective in stabilizing the previously unstable helicopter drive system.

Determination of the time-domain equivalents of higher-order Laplace transfer functions by analog computation

In the theory of optimal inventory control, a class of com plex Laplace transforms arises for which the theoretist needs to know the form and shape of the time domain equivalents. Several methods have been used to obtain these time domain equivalents. In this paper simulation by analog computer has been used, and a low-order approximation of higher-order transfer functions has been simulated. The accuracy of this low-order approximation has been de termined by use of time domain plots.

Transient plane wave magnetic field attenuation through an infinite plate using a simplified laplace transform function

The Laplace transfer function for the magnetic field vector of a plane traveling wave impinging on a single semi-infinite metallic plate is found to have real poles, which permits restatement of the transfer function in the form of an infinite product. It is shown that the significant poles of the infinite product have periodicity of (n\pi)^{2}) to within a few hundredths of a percent for a wide range of physical constants. A further practical assumption permits using only the first 10 terms of the infinite product. The resultant simplified transfer function indicates that the single, semi-infinite plate shielding geometry is analogous to a finite number of cascaded low-pass filters with similar roll-off characteristics. Several curves of steady-state attenuation as a function of frequency are plotted using the original closed form transfer function and these curves correlate closely with those predicted by the simplified transfer function. In particular, the similar roll-off characteristics of the different samples of metal plates, the low-frequency asymptotic values of attenuation, and the relative 3-dB attenuation points are all accurately predicted by the simplified transfer function, which relates these points directly to the physical parameters of the metal plate and the dielectric on both sides. A sample calculation of the transient response shows that the peak magnetic intensity of an impulsive wave is attenuated approximately 260 dB for a \frac{1}{4} inch thick steel plate.