The constant value of the heat power P has been forced on the sys-tem. The value of the heat flux has been equal to 160Wfor all cop-per elements which correspond to the passage current with anintensity equal to 400 A. The temperature of stabilization has beenthen equal to approximately 350 C. The value of the heat flux hasbeen equal to 136W (the current intensity 48 A and stabilizationtemperature about 300 C) for all kanthal elements.The elements have been situated in the heating test channelwith dimensions 1.2 0.6 0.6 m. The channel walls have beenisolated using the glass wool and the base of the channel has beenthe copper plate with 1 mm thickness. The measuring position hasbeen situated in a closed space with the possibility of ventilationand with stable conditions of the surroundings.3. The methods of the analysisThe investigation of the many phenomenon is carried out withusage of the signal theory [21,22]. The based usage of this methodcarried out in this theory is: electronics, telecommunications andelectro techniques. But also the thermal processes research maybe in the analogical way investigated as the analysis of the conver-sion of the signal corresponding to the transferred thermal energy.It is usually the continuous signal of the discrete time, because thecontinuous signal is transformed to discrete during the sampling.The description of the dynamic, e.g. the heat exchanger, is thenthe choosing of the best mathematical model, corresponding to thesignal transforming in the investigated process. The input variableor system of input variables (input signals) are chosen as well asthe output variable or system of output variables (output signals)is chosen. The character of their dependencies, represented bythe linear system of the equations is analyzed using different tools.The basic way driving to object dynamic determines is descrip-tion of the transfer function G(s) form. It is the Laplace’s transformsratio: the output signal y(t) course to input signal x(t) course:GðsÞ¼ YðsÞXðsÞð1ÞThe methods offered in MATLAB and in System Identification Toolboxin particularly, give the possibility of very precise description of themodel, reproducing the physical course of the signal. In this wayfrom the form of the model some can conclude about character of the process which effected this specific transformation of the sig-nals (information and/or energy) [23,24].First of all character of this process is determined by the form ofthe transfer function G(s). It is the quotient of the two polynomialsand during the description of the model in the MATLAB it is firstdetermined for the discrete value z as a G(z) (because of the sam-pling). Then, after the way of transforming into the continuoustime domain is established, the continuous transfer function G(s)is determined.The character of the polynomials in the denominator and thevalues of the poles enable to find out the character of the all trans-fer function and from that of the examined process. If the poles areonly real, then transfer function represents the inertial character.But if the poles are also complex (conjugate) then the investigatedphenomenon have an oscillatory character. The character of theprocess described on the base of the transfer function form mightbe next analyzed using different tools. One of them is the investi-gation of the STEP characteristic and then presentation of this char-acteristic on the diagram. It often gives the first, graphical view ofthe dependencies describing process dynamics in the investigatedmodel. The STEP characteristic can indice on the inertial or oscilla-tory character of the examined model and is often used in the pres-ent analysis.The linear discretized models prepared on the base of the mea-surements have various presentations in the MATLAB System Iden-tification Toolbox: as the Parametric Models and Process Models.Their precision in physical phenomenon description has been val-uated using two general criterions: Final Prediction Error (FPE) andFIT (represented in window Model Output). The values of the FITand of the FPE are calculated from the formulas:FIT ¼ 1 yÞ2þþðyn yÞ2q0B @1C A 100FPE ¼ n þ kn k1n½ðy1 ym1Þ2þþðyn ymnÞ2 ð2Þwhere: y1, ..., yn – the values of the measurements, ym1, ..., ymn –the values calculated from the model, n – the number of the exper-imental points, k – the number of the model coefficients.The character of the reaction of the model to the step function(the STEP characteristic curve) has been investigated for the bestmodels (with the maximum of the FIT and the minimum of theFPE). The transfer function or/and the step function are generallyused in automatics in order to investigate the dynamics of the ele-ments. But the difficulties in their interpretation have been causedthe necessity to examine them in the different measuring position.4. The examples of results and discussion
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