Z-transform Research Articles

Is the transfer function method reliable in a European building context? A theoretical analysis and a case study in the south of Italy

The available tools for dynamic simulation of the buildings thermal behaviour are manifold, and the most modern ones, known as TRNSYS, are founded upon the use of the Z-transform (ZT) set also called transfer function method (TFM). The transfer function method (TFM), recommended by American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE), is one of the most modern tools available to solve heat transfer problems in building envelopes and environments. TFM utilises Z-transforms to solve the equation system that describes the heat transfer in a multi-layered wall. Due to an analogy with an electric circuit, it is possible to write the equation system in a matrix suitable to be solved by computer. The authors have investigated TFM mathematical features, especially concerning the reliability and the quality of the thermal dynamic simulations. Using some basilar control systems tools such as plots, step response and model validation, results show clearly that, for a massive building, a simple application of TFM very often fails. The target of the work was to identify an automatic procedure able to optimise the reliability of the simulation by selecting and using in a more correct way poles and the residuals of the transfer functions.

Errata to "Z-transform implementation of the perfectly matched layer for truncating fdtd domains"

Errata to "Z-transform implementation of the perfectly matched layer for truncating fdtd domains"

Laplace transform and Z-transform: unification and extension

Laplace transform and Z-transform: unification and extension

1H, 13C and 15N Resonance Assignments for the Z Domain of Staphylococcal Protein A at pH* 6.5 and Temperature of 30 deg. C

1H, 13C and 15N Resonance Assignments for the Z Domain of Staphylococcal Protein A at pH* 6.5 and Temperature of 30 deg. C

Design and Sensitivity Analysis of Input Shaping Filter in the Z-domain

Input shaping method is to convolute input shaper, which is sequence of impulses, with reference input command not to excite the natural frequency of system. To reduce residual vibration for the ch ange of frequency, the number of impulses should be increased. Until now, amplitudes and time interval of those has been searched from the derivative of residual vibration. However, if time interval of impulses is fixed as the half of vibration period of system, input shaper H(z) in z-domain becomes (I-pz-1)n/K in which increasing n is the mean that robustness for change of parameter is improved. Also, design of many types of input shapers in z-domain is very easy because sensitivity curve is displayed with H(z)zn100. In the z-domain, EI(Extra-Insensitive) input shaper could be designed without solving nonlinear simultaneous equations as design in continuous time domain. In addition to, the design possibility of input shaper for a damped system was shown.

Stability Analysis of a Class of Interconnected Systems

There exists a class of systems that is characterized by having a so called regular cellular structure or homogeneous interconnection. In this note, the bilateral Z-Transform is used to obtain a mathematical model parametrized by z and it is shown that the stability properties of the system can be more easily investigated by a simple test applied to the parametrized model. The analysis is illustrated via three examples: the heat equation, the Euler-Bernoulli beam, and decentralized control of a countably infinite string of interconnected mass-spring-damper systems.

Thermogenesis: Comparative study of several deconvolution methods in time-invariant calorimetry

A comparative analysis of the performance of different deconvolution methods is presented. This includes harmonic analysis (HA), inverse filtering (IF), dynamic optimization (DO), optimal control (OC) and Z-transform (ZT). The methods are applied on simulated thermograms corresponding to time-invariant representative models of heat conduction calorimeters. The results suggest that: (1) IF and ZT are the simplest methods and give the best reconstructions of the heat power; (2) HA spends more computing time and memory space to achieve a similar quality in the thermogenesis; and (3) DO and OC, with the same expense in memory and time as HA, give much more inaccurate results when the power dissipation lasts a long time. On the other hand, it should be noted that to the present, IF and, conceptually, ZT and OC may be generalized to time-varying calorimetry.

A Method for Determining the Autocoyariance Function of A Box-Jenkins Forecasting Model

Abstract A method is presented for finding closed form expressions of the autocovariance function of a Box-Jenkins forecasting model. This method is based on the filter impulse response and its Z-transform, the transfer function. The bilateral Z-transform of the autocovariance function is obtained from the transfer function, and is inverted after a partial fraction expansion. One example is worked out in detail and a summary of solutions for a number of cases is given.

Further comments on "On the evaluation ofsum _ {n=0} ^∞ n^{k} x^{n}with applications to Z transforms"

Further comments on "On the evaluation ofsum _ {n=0} ^∞ n^{k} x^{n}with applications to Z transforms"

On the modified Z-transform of shifted functions

On the modified Z-transform of shifted functions

A theorem on the modified z-transform

A theorem on the modified z-transform

Vyjádření transformace z Carsonovou-Laplaceovou transformací

Vyjádření transformace z Carsonovou-Laplaceovou transformací

The Z transform of a product of two functions

The Z transform of a product of two functions