4.1. The plate heat exchangerThe dynamic properties of the system model have been investi-gated by the using of the transfer function in the form:GðsÞ¼ YðsÞUðsÞð3Þwhere U(s) and Y(s) are respectively the Laplace transform of thefunction u(t) of the input signal (for the exchanger – the tempera-ture of the working agent by the side of the collectors) and the func-tion y(t) of the output signal (for the exchanger – the temperatureof the heated water flowing out from the exchanger).The models (parametric and non-parametric) which have beenevaluated in respect to their fitting (max FIT and min FPE) and nextusing for their STEP characteristic curve analysis have not had al-ways the unique physical interpretation. For instance, the bestmodel for the measurements (FIT = 89.95; FPE = 0.73) from mea-suring position in Budy Grabskie on the 12th May 2002 is the para-metric model BJ 33341 [25] with the difference equation:yðtÞ¼ BðqÞFðqÞuðtÞþ CðqÞDðqÞeðtÞwhereB(q) = 0.06688 q 1  0.1018 q 2+ 0.03492 q 3C(q) = 1 + 1.202 q 1+ 0.6656 q 2+ 0.009221 q 3D(q) = 1 + 0.4833 q 1  0.5618 q 2  0.8304 q 3F(q)=1   0.5138 q 1  1.02 q 2  0.3519 q 3+ 0.886 q 4.This model and the some next models (with less quality of fit-ting) have STEP characteristic astatic. But the physical phenome-non is bounded from above.The physical correct STEP has been found for model P2Z (FIT82.48, FPE 6.45) with transfer function in form:GðsÞ¼ K1 þ Tz  sð1 þ T1  sÞð1 þ T2  sÞð4Þwhere K = 0.37575, T1 = 30995, T2 = 117.24, Tz = 48981.The courses of STEP characteristic for both of the models arepresented in Fig. 5.
4.2. The shell-and-tube heat exchangerThe transient states of the exchanger: start-up (Ro1, Ro2, ...)orshut-down (Za1, Za2, ...) have only been used in this analysis. The example of the investigated variables courses for the data file Ro3is presented in the Fig. 6.The non-stability of the all heat exchanger parameters lastingnear an hour can be observed on these diagrams. The apparatuswith such a high thermal inertia (depending on their dimensions)in the non-steady states have a very unstable work, in spite ofmonitoring and the instantaneous work correction caused by theoperator. It also indicates on the necessity of the thorough exchan-ger dynamic investigation in the non-steady states, because theycan significantly cause on their usage time. The work on the non-steady states and all the more the oscillations can significantlycause shortening of the usage time of the apparatus.The output variable – outlet water temperature wt course ispresented in Fig. 6a and the input variables – water flow (wf),steam flow (sf), steam pressure (sp) and steam temperature (st)courses are presented in Fig. 6b–e. All this input variables havebeen used for an analysis, but the strong correlations (Table 5) be-tween pairs of them complicate the precise investigation the influ-ence of the particularly variable on the output. The analysis hasbeen carried out for this reason for all the variables separatelyand the SISO (Single Input Single Output) model has been createdfor each of theminstead ofMISO (Multi Input Single Output)modelfor all of them.The maximum of FIT parameter and the minimum of FPEparameter have indicated the best model as for the previous mod-els. This procedure was carried out for the different heat exchangerstart-up data files (in this paper presented for Ro3 and Ro5) andthen obtained models have been compared in their structure andthe values of the parameters.4.2.1. Models for water flow (wf)The model P2ZU, with the transfer function in the form:GðsÞ¼ K ð1 þ Tz  sÞð1 þ 2  f  x  s þ x2  s2Þð5Þhas been the best model for the data file Ro3, but for the Ro5 themodel P3U with the G(s) having the form:GðsÞ¼ Kð1 þ 2  f  x  s þ x2  s2Þð1 þ T3  sÞð6ÞThe parameters of the transfer function and the fitting of themodels are compared in the Table 2 and the courses of STEP char-acteristic are presented in the Fig. 7 (Fig. 7a for Ro3 and Fig. 7b forRo5).4.2.2. Models for the steam flow (sf)The best models for the remaining input variables are presentedfor the same data files (Ro3 and Ro5) as for the pw in order to com-pare them. The model P3ZU with the form of the transfer function:GðsÞ¼ K ð1 þ Tz  sÞð1 þ 2  1  x  s þ x2  s2Þð1 þ T3  sÞð7Þhas been the best model for both of the data files (Ro3 and Ro5). Theparameters are presented in the Table 3 and the STEP courses in theFig. 7c (for Ro3) and Fig. 7d (for Ro5).The structure of the model is the same in both examples but thecharacter of the STEP characteristic is different. This difference isthe result of the parameter f value. If the value of f is greater than1(f > 1) then STEP indicates the inertial character of the phenom-enon (Fig. 7c). If f < 1 then that character is oscillatory (Fig. 7d).4.2.3. Models for steam pressure (sp)The steam pressure sp in the heat exchanger is measured as thenegative pressure. The sub atmospheric pressure induces steamsuction in the exchanger. The structure of the models and alsothe character of their variability, given by the STEP, have indicatedthe greater persification for this variable. The best models are:P3ZU with transfer function form (7) for Ro3, P2Z with transferfunction form (4) for Ro5. The parameters of these models are gi-ven in the Table 4 and the STEP characteristics in the Fig. 8a (forRo3) and in the Fig. 8b (for Ro5).The observed STEP courses have been indicated the inertialcharacter of the phenomenon and for the Fig. 8a the not-mini-mal-phase. The increasing of the output signal is for the negativeTable 2The transmittance parameters values in models for wf.Data file K x f T3 Tz FIT FPE direction oppositely to the input signal for this case. This depen-dence occurs in some models for these variables in the other datafiles also.4.2.4. The coefficients of the correlation between the input variablesThe coefficients of the correlation between the investigated in-put variables: wf, sf, sp and st have been computed. Their values aregiven in the Table 5. for the pairs of variables and for different datafiles The high value of the correlation coefficient between variablesin the pairs for all data files was found for the sp and st variables(the last row of the table indicated with a gray colour). The analysisfor the variable sp has been omitted for this reason.4.2.5. Models for the steam temperature (st)The transfer function of the heat exchanger is the most fre-quently used in the literature (e.g. [26,27]) in the operational form(3) in which Y(s) denotes the Laplace transform of the function y(t)– temperature outlet for the exchanger and U(s) – the Laplacetransform of the function u(t) – temperature inlet for the exchan-ger. The investigation of the dependences between both of thesetemperatures as a dependences between the output signal wtand the input signal st seems to be for this reason a standard andthe most important examination of an heat exchanger dynamics(if the automatics methods are using).The best fitted model for the investigated exchanger and for thepresented data files (Ro3 and Ro5) has been taken the model P2ZUwith the transfer function of a form (5). 换热器动力学英文文献和中文翻译(4):http://www.751com.cn/fanyi/lunwen_42712.html