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The purpose of this paper is to propose a new method for mathematical modeling of the buck dc‐dc converter in discontinuous conduction mode (DCM). By using the presented modeling method, the analysis of the transient and the steady states of the buck dc‐dc converter can be performed.

The proposed method is based on the two Laplace and Z transforms. In the proposed method, at first, the equations of the inductor current and the capacitor voltage are obtained as the power switch is on and off. Then by using the Laplace and Z transforms, the obtained equations are solved and the relations of the inductor current and the output voltage are obtained. In the proposed method, the Laplace transform is used for determining of the general relations of the inductor current and the output voltage. Also the Z‐transform is used as a tool for determining the initial values of the inductor current and the output voltage.

The transient and the steady state response of the dc‐dc converter is analyzed by the proposed method. By using the Z‐transform, the transient response of the converter and the effect of the elements of the converter on the time constant of the transient response are investigated. In addition, the effect of the elements of the converter and the load resistance on the electrical parameters of the converter such as the output voltage ripple and the inductor current ripple are investigated.

The proposed method in this paper is a suitable method for mathematical modeling of dc‐dc converters. The acernote of this method is that it can be used in both transient and steady state response, analysis of the dc‐dc converters. By using the final value theorem of the Z‐transform, the steady state response of the converter is investigated. Also by using this transform, the time constants of the transient response of the converter are determined. Finally, the results of the theoretical analysis are compared with the results of simulation in PSCAD/EMTDC and also the experimental results to prove the validity of the presented subjects.

The purpose of this paper is to suggest a new analytical methodology for transient analysis of DC‐DC power converters. The closed‐form solution obtained following this methodology is suitable both for design of passive elements of the converter and for the development of control techniques.

The methodology is based on a mixed use of Laplace transform and z‐transform. The expressions of variables of the set of equations, characteristic of a DC‐DC converter, are first evaluated in the Laplace domain for the generic switching interval. The solutions obtained are then z‐transformed in order that they match in each contiguous time interval, to form the complete transient response.

The new solution methodology allows the analytical determination of time constants of DC‐DC converters, also in presence of large duty‐cycle variations. Moreover, it is possible to evaluate easily the influence of passive elements on converter's behaviour, without several numerical simulations.

The analytical solution of linear systems is well known both in transient and in steady‐state conditions. However, when there is an infinite number of poles in the Laplace transform of the input signals, such as the case of switching power converters, the inversion in a closed form of the Laplace transform of the solution can be cumbersome. The methodology presented tries to overcome this problem by using an approach based on the z‐transform. Operating in this way, a closed‐form solution can be obtained both in transient and in steady‐state conditions, for all the main topologies of switching power converters. The procedure has been explained in detail for the sample case of boost DC‐DC converters.

Novel necessary and sufficient existence conditions for convolution inverses of real finite sequences are derived. These conditions are obtained with the aid of well known conditions expressed in terms of the Fourier and z‐transforms. The conditions given in the paper imply suitable algorithms, which are convenient for checking the existence of convolution inverses of any real finite sequences.

Lalwani et al. devised a controllable state-space model for a general APVIOBPCS production and inventory system. However, their procedure did not cater for production delays of other than one time unit. The authors have sought to devise a model that allows for any value of production delay.

A discrete z transform model of APVIOBPCS inventory is obtained using conventional algebra and converted to a state-space model using a reachable control formulation. This is then analysed to produce an analytic expression for the eigenvalues and then the general stability solution is derived from the unit circle condition.

This model allows a state-space model conversion from a discrete time input-output model using an exponential production delay with no loss of generality and is fully controllable and observable. Stability of these models can be obtained from the system eigenvalues and agrees with the authors' previously published stability boundaries using transform models.

The system is described by a linear control model of the production process and does not include production limits or other resource limitations. It does not include any past history of sales demand and responses.

This work allows a model to be implemented in a spreadsheet of APVIOBPCS PIC that can be used for any production delay and can be modified to include different sales smoothing procedures.

This present model is an extension and improvement of the model devised by Lalwani, in that it allows more accurate modelling of inventory production systems by permitting a more flexible selection of delay parameter values, closer to those of real systems.

A recent supplement to the journal of the Czechoslovak Association for Cybernetics, Kybernetika, Vol. 24, 1988, pp. 3–24, which was published under the auspices of the Czechoslovak Academy of Sciences, was concerned with the use of the multidimensional z‐transform in the solution of partial difference equations. Written by Dr Jiri Gregor it gives a survey of (generalised) multidimensional z‐transform (n‐D‐z transform) method and its use in the solution of linear partial difference equations with constant coefficients, as well as systems of such equations, whose solutions the author calls sequences. He says that this theory is aimed at forming a basis of multidimensional digital system theory which attracted wide and increasing attention in the last decade.

We present a combined or mixed method for the dynamic analysis of thin‐walled structures, based on the superposition of beam and shell strains and displacements. Polynomial or exact shape functions are used for the interpolation of the shell displacements, while discrete degrees of freedom are introduced instead of the generalized von Karman coefficients. Special attention has been given to the integration schemes, because of the combined beam and shell behaviour of the considered structures. The stability and accuracy of the four‐point integration scheme are studied by using the z‐transform. The method is applied to thin‐walled pipes and is also compared to the von Karman approach.

The modelling and analysis of robotic assembly cells and production lines usually relies on sophisticated software packages designed to simulate the operation of systems normally represented by mathematically intractable network notations. Describes how a mathematical transform normally used in the design of digital filters can be utilized in conjunction with a very simple network notation to provide an easy‐to‐use tool applicable to both manual and computer analysis of production systems.

The purpose of this paper is to design a tool for IIR digital filters obtained from analog prototypes, which preserves simultaneously the amplitude and the group delay response.

A new s-to-z transform is developed based on a second order formula used for numerical integration of differential equations. Stability of the newly obtained transfer functions in the z-domain is proved to be preserved. Distortions introduced by the new transform into the original amplitude and group delay responses are studied.

The new formula, when implemented to all-pole prototypes, exhibits lower selectivity than the original while reducing the pass-band group delay distortions. In the same time its structure is importantly simpler than the functions obtained by the well-known bilinear transform. When implemented to a prototype having “all kinds” of transmission zeros the resulting filter has almost ideally the same characteristic as the prototype.

The new transform may be used exclusively to synthesize even order filters. The new function is twice the order of the analog prototype. This kind of transformations are used to design IIR digital filters only. Low-pass transfer functions were studied being prototypes for all other cases.

This is a new result never mentioned in the literature. Its effectiveness is confined to a niche problem when simultaneous sharp selectivity and low group delay distortions are sought.

The objective of this work is to develop a model that can be used for simulation of different parameters including price, subjected to different control strategies.

The entire supply chain can be modelled by combining the transfer function into a closed loop system. The transfer function of each entity in the supply chain can be obtained by using the control theory tools. The model can be approximated as a linear discrete system with various operating constants, like lead time, price, order policy and supply.

The continuous replenishment ordering policy for a distribution node in a supply chain was analyzed using the z-transform. Characteristic equations of the closed loop transfer function are obtained. The bullwhip (BW) effect is analyzed. Study proves that the BW effect is in evitable if the standard heuristic ordering policy is employed with demand forecasting; also the paper analysed price supply trade-off for dynamic demand and supply. Simulation results show that BW is less in PI and simple p-only with cascade control. Robust control and PD, PID control results are not shown in this literature, and it is subject to further research.

Research is original, it can be applicable in today's dynamic world, due to globalization, it is necessary to have a automated machine that can handle most of supply chain decision.

The purpose of this paper is to study the 2D hybrid linear model, which is a method of describing both continuous‐ and discrete‐time dynamics in one system. Singularity of 2D hybrid linear models is a newly occurred problem and a very important question is how to compute the solution of the singular 2D hybrid linear model.

Computation of the solution of mentioned system is based on Laplace transform, Z‐transform and shifting algorithm. The inverse Laplace transform and inverse Z‐transform are used in two cases.

In this paper, a class of 2D singular hybrid linear systems is introduced. Two methods for computation of solutions of the singular hybrid system with nonzero boundary conditions are proposed. Both methods are illustrated by the examples.

Presented methods are a new way for computing the solution of singular 2D hybrid linear systems.