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Measurement of control behaviour of steam generators
Measurement of Control Behaviour of Steam Generators R:QUACK and A. SCHNEIDER pipe loop M. This enthalpy increase we take as the exit value X of our calculation section, which thus extends from the flow of coal in the feeder to the heat flow in the boiler. This section might well appear far too long and complicated for calculation, for it comprises a variety of phenomena, including the free fall of the coal from the feeder to the mill; the whirling motion of the coal in the mill combined with grinding and partial drying; the separation of coarse-grained and finegrained material in the sifter; pneumatic transport between grinding mill, sifter and burner, with numerous instances of acceleration, delay, mixing and separation; the chemical reaction between coal dust and air of combustion with its attendant phenomena of drying, degassing, gasification, ignition, chief reaction, dissociation and after-combustion; finally, the heat transfer in the flame space and the pipe system. Nevertheless we propose to describe this whole area with its numerous occurrences by the following simple function (frequency response curve) - T , .p F= e 1 1 + T1·p This is to say, we are trying to describe the total behaviour of this calculation section as the serial arrangement of a transport time (dead time Tt!) with a storage phenomenon (storing time T!). The admissibility of this simplifying assumption needs to be checked by measurements on actual plant.
Subdividing Control of Steam Generator into Several Sections It is desirable to calculate in advance the control behaviour of a steam power plant from its constructional data. To this end the plant is subdivided into separate sections, the behaviour of which is capable of approximate analytical description, under simplifying assumptions such as constancy of material properties or constant heat flow within a section. The admissibility of such simplifying assumptions can be tested by measuring the control behaviour in actual systems and by comparing the result with that of theoretical calculation. Hence, in subdividing the plant into sections for separate calculation it is advisable to bear in mind that the respective entrance and exit values of these sections should be measurable. As an example of a calculation section let us take a coal dust heating equipment in which the grinding mill contains a blower conducting the dust into the plant (the air stream being constant). From the coal bunker A the coal goes through the feeder B to the grinding mill C. The revolving speed of feeder B is variable and represents the entrance value Y of our calculation section. The grinding mill C which at the same time acts as a ventilator blows the ground coal into the sifter D. Whereas the coarse-grained part falls back into the mill C, the finely ground coal dust flies through pipeline E to the coal dust burners F. The coal dust is burnt in the flame space G, the molten ash contents flowing off through the opening H. The hot heating gas enters in between the pipes I into the space K where they give up radiant heat to the boiler heating plane L. The heat flow of the gas stream can be measured by the enthalpy increase of a small water stream flowing through the
Evaluation of Measurements of Control Behaviour Curve A (Figure 2) shows a measured transfer function for the
L K
x-
lSS\\S\S\i
C~=~TiTir= Feeler of measuring M
device
Figure 1.
Computing area feeder-radiation heat space
329
1842
R. QUACK AND A. SCHNEIDER
Control alteration
10 Control adjustment time 15 sec
o
50
25
To
sec
measuring device
Alteration of heating intensity 1·0 0·8
~
Curve A
• .--;;:::;;;::;--.----
/""
Curve B '----..,/"'__.. ,/' 06
Curve /
02 /
•
o
1.1e =17sec; liMe =3-5 sec
/ /
/
/ / /
Control distance
r------, ,-----.,
L ____ '
I
Figure 3.
75
consideration, with the aid of Duhamel's integraJ1, curve B (Figure 2) results, which would have been obtained if the coal flow could have been altered leapwise. (b) Curve B (Figure 2), in addition to the time behaviour of our control section, also contains the time behaviour of the heat flow measurement. Figure 3 shows the construction of the heat flow measuring device. To what extent the time behaviour of the heat flow measuring device can depend on the arrangement of water temperature measurement is shown in Figure 4. The two models investigated differ only with regard to the resistance thermometers. One of these, in a conventional protective casing, is several times slower than the other with directly exposed feeler. Figure 4 contains, apart from the respective transfer functions, also the representation of the time behaviour of the whole heat flow measuring device as a frequency response equation; the
LT~n~£!:.t~i~'!..J
50
Measuring device
Conlrol
-fkC~~H~J+Hlli;H0;HII
/"
25
Tl =60sec; Ttl =5·5 sec
7 . . . "7
,
04
/
100
125
Heatflow feeler for boilers. Water flow is set to a constant value and water heat measured
I
L _____ ..J
150
175
sec
Figure 2. Correction of a measured transfer function: A measured transfer function; B after correction to zero time; C additional correction as to time behaviour of measuring device
area feeder to radiant heat space. According to this curve it appears as if our section had a considerable dead time, amounting to about 25 sec, and that it consists not merely of one storage space but of several, serially arranged. Two points have to be considered, however: (a) In theory the transfer function represents the answer to a set discontinuity function. Yet in the practice of the control experiment the entrance value (coal flow) can only be varied with the finite adjusting time of the feeding device. In the present case adjusting time was 15 sec. If this is taken into
e- 2·S p
F.meas.-- 1 -+2p-
Correlated outlet temperature alteration 10
08
- .-
/-
_
1 _____ ------•. - - -
• 04
F. 02
e- 3 ·Sp
--1+17p
mea.-
30
40
50
60
70 sec
Figure 4. Time behaviour of the heat flow measuring device for two models of resistance thermometers. The model above is of3 mm diam, 60 mm long, the platinum wire being covered only by thin glazing
330
1843
MEASUREMENT OF CONTROL BEHAVIOUR OF STEAM GENERATORS
time behaviour of the device using the more responsive resistance thermometer chiefly depends on circulating time and heat storage in the pipe loop. From curve B (Figure 2), which corresponds to the serial arrangement of the control section and the measuring device, curve C (Figure 2), representing the time behaviour of the control area only, can be calculated!. On comparing the two curves A and C it will be seen how important it was to apply the corrections. The proper dead time of the control section, which is of special significance for attaining the practical optimum of control efficiency, amounts to only about 5·5 sec. This agrees with a fair degree of accuracy with actual time of transport (free fall from feeder to mill, pneumatic transport mill-sifter-burner-burner spaceradiant heat space). The storage time constant T! = 60 sec also largely corresponds to actual storage time in grinding mill and sifter, as can be computed from the constructional data 2 , 3. For control purposes the influence of storage time can, as is known, be diminished simply by altering the mill air stream, should this be desirable. We notice, therefore, that transport in the pipelines and storage in mill and sifter predominantly determine the time behaviour of the total area from feeder to radiant heat space and that the influence of all the remaining phenomena may be disregarded. For the actual computation of the interdependent curves A, Band C it may be mentioned that, if an analogue computer is not available, it is useful to start from a probable curve C' and to compute the curves B' and A' from it. After two to three iterations satisfactory agreement of curve A' with the real curve A is generally obtained, wherewith the desired curve C = C' is then also found. Experimental Determination of the Frequency Response In the preceding example the transfer function of a control section had been measured. Generally this is possible only where larger temporary deviations from the set control value are admissible. In investigating the control behaviour of high-
temperature steam superheaters larger deviations are undesirable because of the stability of materials and the sensitivity of the steam turbines. In drawing up position curves according to the frequency response method smaller deviations from the set value are usually sufficient. The evaluation, as hitherto common, by comparing recording strips 4,5 is rendered difficult, however, by the inevitable variation of magnitudes measured due to various disturbances. For the case of these variations being of statistical significance Schiifer 6 has suggested a simplified method of evaluation which does not require graphical recording of entrance and exit values. The SGS apparatus (Figure 5), which we constructed according to this suggestion, has proved the usefulness of this method of evaluation.
Figure 5. Frequency response recording apparatus SGS (SchiiferGass-Schneider). Below the sine-cosine jill1ction generator, above the curve-recording device
Figure 6 shows the overall arrangement. The sine potentiometer shifts the entrance value Y of the control distance under
Work
Counter
>
MeaSUring
apparatus
Qj
u
Imaginary
C
'"
U; is
o'-
c
LL..-+J
o u
Trans. m l s s l o n - r i i l gear Rectifier
.
III
o
u
y
Control
Figure 6. Block diagram of the frequency response recording apparatus SGS. RC frequency 35-175 Hz; gear ratios 2: 1; 1 :2'5; 1 :6'25; 1 :24; duration of periods can be set, infinitely variable, from 8·6 sec 10 34·3 min (w = 0,0188-0,000076 sec-I)
331
1844
R. QUACK AND A. SCHNEIDER
~J
'"'"
1·0
t
o
y
I
I 1
-----.
I
I
I
I I
001
01
w-
I
I
I
t
I
+
1·0
0 Measured values -Theor. behaviour
i..,, tQ]R,m,g;o.,y
C
L ______ l-_____ l Figure 7.
Calibrating device for frequency response recording equipment
- - - - - - - - - - - - - - - - - - - ' , Cooler 1
SI
I_~
r---- J \,.----.
r--
J
J
I
I J
L--~~--_4----r.x~~
Air intake-
220 V
sine impulse generator
Transmitter
Control valve
Cooling water ~ 10V sin I-----_......--------------------~--__f.----....J
'-----------' ± lOV cos Figure 8.
Counters
Application of the frequency response recording apparatus superheater of a boiler
332
1845
10
the steam cooler and sleam
MEASUREMENT OF CONTROL BEHAVIOUR OF STEAM GENERATORS investigation in the form of its sine and also directs two signals differing from each other by 90° to the tension coils of two a.c. counters. The current coils of these counters are charged with the exit value X of the control distance, so that-as Schiifer has proved-after a sufficient number of periods one of the counters indicates the real coordinate, the other the imaginary coordinate of the locus curve point belonging to the respective frequency. For calibrating and checking this device we are using the hydraulic control distance shown in Figure 7, the frequency response curve of which can be pre-calculated with easy methods from the constructional data. From a uniform water stream A a changing water stream B is diverted by shutter B which is moved to and fro in the form of the sine (= entrance value Y), so that the water level X (= exit value) in container C is also subject to pulsating changes. The sine generator producing sine and cosine impulses is indicated by D in the block diagram-the calibrating line on the right-hand side of Figure 7 shows good agreement between computation and experiment. Figure 8 demonstrates the use of the new device on an actual example, the control behaviour of surface hot steam cooler 2 and of the adjoining terminal superheater S Ill. The sine impulse generator shifts the pneumatic regulation of the cooling water control valve and sends sine and cosine impulses to two sets of counters. This example demonstrates a further advan-
tage of the SGS apparatus. In investigating complicated control distances by a simultaneous use of several counters the frequency response of the total control field and of its separate sections can be determined without a great deal of evaluating work. A separate paper will report the results of these experiments and their comparison with the theoretical findings of Profos 7 • References 1 2 3
4
5
6
7
OLDENBOURG, R. C. and SARTORIUS, H. Dynamik selbsttiitiger Regelungen. 1951 (2nd ed.). Munich; Oldenbourg SCHNEIDER, A. Das regeldynamische Verhalten von Einblasekohlemiihlen. Regelungstechnik. 1957. Munich; Oldenbourg SCHNEIDER, A. Das regeldynamische Verhalten von Kohlenstaubfeuerungen. Ph.D. thesis 1959. Stuttgart, Technische Hochschule STURMER, W. Regelung des Dampfdruckes eines Trommelkessels durch Anderung der Feuerungsleistung. Ph.D. thesis 1959. Stuttgart, Technische Hochschule SPLIETHOFF, H. Das Regelverhalten leistungsgeregelter Zwangsdurchlauf-Dampferzeuger. Ph.D. thesis 1959. Stuttgart, Technische Hochschule SCHAFER, O. and FEISEL, W. Ein verbessertes Verfahren zur Frequenzganganalyse industrieller Regelstrecken. Regelungstechnik 3 (1955) 225 PROFOS, P. Dynamik der Uberhitzerregelung. Regelungstechnik 6 (1958) 239
Summary The combustion and boiler system of a steam power plant consists measure the flow of mass and/or energy between the various units of a combination of several non-linear elements. To allow pre- such as grinding, burning, heat transfer, evaporation and superheatcalculation of the control response of the whole system the behaviour ing. The paper describes experimental equipment used and measures of each part of it should be known. To this end it is necessary to to eliminate disturbances during the course of the experiments. Sommaire Differentes parties d'une chaudiere sont composees par la combinaison debit de la masse ou de I'energie entre les differentes unites. Ce de plusieurs elements non lineaires. Pour permettre le calcul de la rapport decrit un equipement experimental utilise et essaye d'eliminer reponse du systeme de commande, le comportement de chacune des les perturbations pendant la duree des mesures. parties doit etre connue. Pour cela, il est necessaire de mesurer le Zusammenfassung Feuerung und Dampfkessel eines Kraftwerkes bestehen aus Mahlung, Verbrennung, Warmeiibertragung, Verdampfung und mehreren nichtlinearen E1ementen. Urn das Regelverhalten der Uberheizung. Der Bericht beschreibt einige Versuchseinrichtungen, die wir dazu Gesamtanlage vorausberechnen zu konnen, muB man das Verhalten jedes Teiles der Anlage kennen. Dazu muB man den Stoff benutzten, sowie unsere Bemiihungen, den EinfluB von StOrungen bzw. EnergiefluB zwischen den Anlageteilen messen, also zwischen wahrend der Versuche zu eliminieren.
DISCUSSION N. I. DAVYDOV (U.S.S.R.) How many oscillation cycles of the input value have to be applied for obtaining one point of the amplitude-phase characteristic ? R. QUACK, in reply. This depends on the relation between the noise level and the amplitude of the sinusoidal signal. Under normal conditions the first approximation can be obtained approximately after eight cycles, a more accurate value is obtained after 20 cycles. A. NAUMOV (U.S.S.R.) For what purpose have the dynamic characteristics been used which you obtained experimentally? R. QUACK, in reply. The main purpose of the work was to calculate the dynamic characteristics of the equipment based on its design and dimensions. In such calculations it is always necessary to simplify the picture of the physical phenomena which take place in reality and to disregard some design details of the equipment. The best method of verification of such calculations is to compare the results with the experimentally determined dynamic characteristics of similar units which are in operation. We found that the method of experimental study
of the dynamic characteristics of plants proposed by Professor Schiifer is fully suitable for such a purpose. The second task was to improve the quality of the regulation and in order to do this it was necessary to know the dynamic properties of the plant.
T. VAMOS (Hungary) How is the non-linearity taken into consideration? R. QUACK, in reply. In recording the dynamic characteristics the amplitude of the oscillations of the input signal was chosen to be a small value (this can be done by means of the Schafer-Gass-Schneider instrument), so as to reduce the effect of the non-linearity. The influence of non-linearities can be evaluated as follows: if, for a constant load level but different amplitudes of the input signal, and for a constant amplitude but different loads, approximately the same frequency characteristic is obtained, the non-linearity of the system can be disregarded. If, however, greatly differing frequency characteristics are obtained it can be concluded that the system contains considerable non-linearities. In this case the non-linearity has to be approximated by a linear equation selecting the coefficients in relation to the load or to the amplitude of the signal.
333
1846
Subdividing Control of Steam Generator into Several Sections It is desirable to calculate in advance the control behaviour of a steam power plant from its constructional data. To this end the plant is subdivided into separate sections, the behaviour of which is capable of approximate analytical description, under simplifying assumptions such as constancy of material properties or constant heat flow within a section. The admissibility of such simplifying assumptions can be tested by measuring the control behaviour in actual systems and by comparing the result with that of theoretical calculation. Hence, in subdividing the plant into sections for separate calculation it is advisable to bear in mind that the respective entrance and exit values of these sections should be measurable. As an example of a calculation section let us take a coal dust heating equipment in which the grinding mill contains a blower conducting the dust into the plant (the air stream being constant). From the coal bunker A the coal goes through the feeder B to the grinding mill C. The revolving speed of feeder B is variable and represents the entrance value Y of our calculation section. The grinding mill C which at the same time acts as a ventilator blows the ground coal into the sifter D. Whereas the coarse-grained part falls back into the mill C, the finely ground coal dust flies through pipeline E to the coal dust burners F. The coal dust is burnt in the flame space G, the molten ash contents flowing off through the opening H. The hot heating gas enters in between the pipes I into the space K where they give up radiant heat to the boiler heating plane L. The heat flow of the gas stream can be measured by the enthalpy increase of a small water stream flowing through the
Evaluation of Measurements of Control Behaviour Curve A (Figure 2) shows a measured transfer function for the
L K
x-
lSS\\S\S\i
C~=~TiTir= Feeler of measuring M
device
Figure 1.
Computing area feeder-radiation heat space
329
1842
R. QUACK AND A. SCHNEIDER
Control alteration
10 Control adjustment time 15 sec
o
50
25
To
sec
measuring device
Alteration of heating intensity 1·0 0·8
~
Curve A
• .--;;:::;;;::;--.----
/""
Curve B '----..,/"'__.. ,/' 06
Curve /
02 /
•
o
1.1e =17sec; liMe =3-5 sec
/ /
/
/ / /
Control distance
r------, ,-----.,
L ____ '
I
Figure 3.
75
consideration, with the aid of Duhamel's integraJ1, curve B (Figure 2) results, which would have been obtained if the coal flow could have been altered leapwise. (b) Curve B (Figure 2), in addition to the time behaviour of our control section, also contains the time behaviour of the heat flow measurement. Figure 3 shows the construction of the heat flow measuring device. To what extent the time behaviour of the heat flow measuring device can depend on the arrangement of water temperature measurement is shown in Figure 4. The two models investigated differ only with regard to the resistance thermometers. One of these, in a conventional protective casing, is several times slower than the other with directly exposed feeler. Figure 4 contains, apart from the respective transfer functions, also the representation of the time behaviour of the whole heat flow measuring device as a frequency response equation; the
LT~n~£!:.t~i~'!..J
50
Measuring device
Conlrol
-fkC~~H~J+Hlli;H0;HII
/"
25
Tl =60sec; Ttl =5·5 sec
7 . . . "7
,
04
/
100
125
Heatflow feeler for boilers. Water flow is set to a constant value and water heat measured
I
L _____ ..J
150
175
sec
Figure 2. Correction of a measured transfer function: A measured transfer function; B after correction to zero time; C additional correction as to time behaviour of measuring device
area feeder to radiant heat space. According to this curve it appears as if our section had a considerable dead time, amounting to about 25 sec, and that it consists not merely of one storage space but of several, serially arranged. Two points have to be considered, however: (a) In theory the transfer function represents the answer to a set discontinuity function. Yet in the practice of the control experiment the entrance value (coal flow) can only be varied with the finite adjusting time of the feeding device. In the present case adjusting time was 15 sec. If this is taken into
e- 2·S p
F.meas.-- 1 -+2p-
Correlated outlet temperature alteration 10
08
- .-
/-
_
1 _____ ------•. - - -
• 04
F. 02
e- 3 ·Sp
--1+17p
mea.-
30
40
50
60
70 sec
Figure 4. Time behaviour of the heat flow measuring device for two models of resistance thermometers. The model above is of3 mm diam, 60 mm long, the platinum wire being covered only by thin glazing
330
1843
MEASUREMENT OF CONTROL BEHAVIOUR OF STEAM GENERATORS
time behaviour of the device using the more responsive resistance thermometer chiefly depends on circulating time and heat storage in the pipe loop. From curve B (Figure 2), which corresponds to the serial arrangement of the control section and the measuring device, curve C (Figure 2), representing the time behaviour of the control area only, can be calculated!. On comparing the two curves A and C it will be seen how important it was to apply the corrections. The proper dead time of the control section, which is of special significance for attaining the practical optimum of control efficiency, amounts to only about 5·5 sec. This agrees with a fair degree of accuracy with actual time of transport (free fall from feeder to mill, pneumatic transport mill-sifter-burner-burner spaceradiant heat space). The storage time constant T! = 60 sec also largely corresponds to actual storage time in grinding mill and sifter, as can be computed from the constructional data 2 , 3. For control purposes the influence of storage time can, as is known, be diminished simply by altering the mill air stream, should this be desirable. We notice, therefore, that transport in the pipelines and storage in mill and sifter predominantly determine the time behaviour of the total area from feeder to radiant heat space and that the influence of all the remaining phenomena may be disregarded. For the actual computation of the interdependent curves A, Band C it may be mentioned that, if an analogue computer is not available, it is useful to start from a probable curve C' and to compute the curves B' and A' from it. After two to three iterations satisfactory agreement of curve A' with the real curve A is generally obtained, wherewith the desired curve C = C' is then also found. Experimental Determination of the Frequency Response In the preceding example the transfer function of a control section had been measured. Generally this is possible only where larger temporary deviations from the set control value are admissible. In investigating the control behaviour of high-
temperature steam superheaters larger deviations are undesirable because of the stability of materials and the sensitivity of the steam turbines. In drawing up position curves according to the frequency response method smaller deviations from the set value are usually sufficient. The evaluation, as hitherto common, by comparing recording strips 4,5 is rendered difficult, however, by the inevitable variation of magnitudes measured due to various disturbances. For the case of these variations being of statistical significance Schiifer 6 has suggested a simplified method of evaluation which does not require graphical recording of entrance and exit values. The SGS apparatus (Figure 5), which we constructed according to this suggestion, has proved the usefulness of this method of evaluation.
Figure 5. Frequency response recording apparatus SGS (SchiiferGass-Schneider). Below the sine-cosine jill1ction generator, above the curve-recording device
Figure 6 shows the overall arrangement. The sine potentiometer shifts the entrance value Y of the control distance under
Work
Counter
>
MeaSUring
apparatus
Qj
u
Imaginary
C
'"
U; is
o'-
c
LL..-+J
o u
Trans. m l s s l o n - r i i l gear Rectifier
.
III
o
u
y
Control
Figure 6. Block diagram of the frequency response recording apparatus SGS. RC frequency 35-175 Hz; gear ratios 2: 1; 1 :2'5; 1 :6'25; 1 :24; duration of periods can be set, infinitely variable, from 8·6 sec 10 34·3 min (w = 0,0188-0,000076 sec-I)
331
1844
R. QUACK AND A. SCHNEIDER
~J
'"'"
1·0
t
o
y
I
I 1
-----.
I
I
I
I I
001
01
w-
I
I
I
t
I
+
1·0
0 Measured values -Theor. behaviour
i..,, tQ]R,m,g;o.,y
C
L ______ l-_____ l Figure 7.
Calibrating device for frequency response recording equipment
- - - - - - - - - - - - - - - - - - - ' , Cooler 1
SI
I_~
r---- J \,.----.
r--
J
J
I
I J
L--~~--_4----r.x~~
Air intake-
220 V
sine impulse generator
Transmitter
Control valve
Cooling water ~ 10V sin I-----_......--------------------~--__f.----....J
'-----------' ± lOV cos Figure 8.
Counters
Application of the frequency response recording apparatus superheater of a boiler
332
1845
10
the steam cooler and sleam
MEASUREMENT OF CONTROL BEHAVIOUR OF STEAM GENERATORS investigation in the form of its sine and also directs two signals differing from each other by 90° to the tension coils of two a.c. counters. The current coils of these counters are charged with the exit value X of the control distance, so that-as Schiifer has proved-after a sufficient number of periods one of the counters indicates the real coordinate, the other the imaginary coordinate of the locus curve point belonging to the respective frequency. For calibrating and checking this device we are using the hydraulic control distance shown in Figure 7, the frequency response curve of which can be pre-calculated with easy methods from the constructional data. From a uniform water stream A a changing water stream B is diverted by shutter B which is moved to and fro in the form of the sine (= entrance value Y), so that the water level X (= exit value) in container C is also subject to pulsating changes. The sine generator producing sine and cosine impulses is indicated by D in the block diagram-the calibrating line on the right-hand side of Figure 7 shows good agreement between computation and experiment. Figure 8 demonstrates the use of the new device on an actual example, the control behaviour of surface hot steam cooler 2 and of the adjoining terminal superheater S Ill. The sine impulse generator shifts the pneumatic regulation of the cooling water control valve and sends sine and cosine impulses to two sets of counters. This example demonstrates a further advan-
tage of the SGS apparatus. In investigating complicated control distances by a simultaneous use of several counters the frequency response of the total control field and of its separate sections can be determined without a great deal of evaluating work. A separate paper will report the results of these experiments and their comparison with the theoretical findings of Profos 7 • References 1 2 3
4
5
6
7
OLDENBOURG, R. C. and SARTORIUS, H. Dynamik selbsttiitiger Regelungen. 1951 (2nd ed.). Munich; Oldenbourg SCHNEIDER, A. Das regeldynamische Verhalten von Einblasekohlemiihlen. Regelungstechnik. 1957. Munich; Oldenbourg SCHNEIDER, A. Das regeldynamische Verhalten von Kohlenstaubfeuerungen. Ph.D. thesis 1959. Stuttgart, Technische Hochschule STURMER, W. Regelung des Dampfdruckes eines Trommelkessels durch Anderung der Feuerungsleistung. Ph.D. thesis 1959. Stuttgart, Technische Hochschule SPLIETHOFF, H. Das Regelverhalten leistungsgeregelter Zwangsdurchlauf-Dampferzeuger. Ph.D. thesis 1959. Stuttgart, Technische Hochschule SCHAFER, O. and FEISEL, W. Ein verbessertes Verfahren zur Frequenzganganalyse industrieller Regelstrecken. Regelungstechnik 3 (1955) 225 PROFOS, P. Dynamik der Uberhitzerregelung. Regelungstechnik 6 (1958) 239
Summary The combustion and boiler system of a steam power plant consists measure the flow of mass and/or energy between the various units of a combination of several non-linear elements. To allow pre- such as grinding, burning, heat transfer, evaporation and superheatcalculation of the control response of the whole system the behaviour ing. The paper describes experimental equipment used and measures of each part of it should be known. To this end it is necessary to to eliminate disturbances during the course of the experiments. Sommaire Differentes parties d'une chaudiere sont composees par la combinaison debit de la masse ou de I'energie entre les differentes unites. Ce de plusieurs elements non lineaires. Pour permettre le calcul de la rapport decrit un equipement experimental utilise et essaye d'eliminer reponse du systeme de commande, le comportement de chacune des les perturbations pendant la duree des mesures. parties doit etre connue. Pour cela, il est necessaire de mesurer le Zusammenfassung Feuerung und Dampfkessel eines Kraftwerkes bestehen aus Mahlung, Verbrennung, Warmeiibertragung, Verdampfung und mehreren nichtlinearen E1ementen. Urn das Regelverhalten der Uberheizung. Der Bericht beschreibt einige Versuchseinrichtungen, die wir dazu Gesamtanlage vorausberechnen zu konnen, muB man das Verhalten jedes Teiles der Anlage kennen. Dazu muB man den Stoff benutzten, sowie unsere Bemiihungen, den EinfluB von StOrungen bzw. EnergiefluB zwischen den Anlageteilen messen, also zwischen wahrend der Versuche zu eliminieren.
DISCUSSION N. I. DAVYDOV (U.S.S.R.) How many oscillation cycles of the input value have to be applied for obtaining one point of the amplitude-phase characteristic ? R. QUACK, in reply. This depends on the relation between the noise level and the amplitude of the sinusoidal signal. Under normal conditions the first approximation can be obtained approximately after eight cycles, a more accurate value is obtained after 20 cycles. A. NAUMOV (U.S.S.R.) For what purpose have the dynamic characteristics been used which you obtained experimentally? R. QUACK, in reply. The main purpose of the work was to calculate the dynamic characteristics of the equipment based on its design and dimensions. In such calculations it is always necessary to simplify the picture of the physical phenomena which take place in reality and to disregard some design details of the equipment. The best method of verification of such calculations is to compare the results with the experimentally determined dynamic characteristics of similar units which are in operation. We found that the method of experimental study
of the dynamic characteristics of plants proposed by Professor Schiifer is fully suitable for such a purpose. The second task was to improve the quality of the regulation and in order to do this it was necessary to know the dynamic properties of the plant.
T. VAMOS (Hungary) How is the non-linearity taken into consideration? R. QUACK, in reply. In recording the dynamic characteristics the amplitude of the oscillations of the input signal was chosen to be a small value (this can be done by means of the Schafer-Gass-Schneider instrument), so as to reduce the effect of the non-linearity. The influence of non-linearities can be evaluated as follows: if, for a constant load level but different amplitudes of the input signal, and for a constant amplitude but different loads, approximately the same frequency characteristic is obtained, the non-linearity of the system can be disregarded. If, however, greatly differing frequency characteristics are obtained it can be concluded that the system contains considerable non-linearities. In this case the non-linearity has to be approximated by a linear equation selecting the coefficients in relation to the load or to the amplitude of the signal.
333
1846