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Solution of a microprocessor controlled blown film production line
copyright © IFAC PRP 4 Automation, Ghent, Belgium 1980
SOLUTION OF A MICROPROCESSOR CONTROLLED BLOWN FILM PRODUCTION LINE K. Malik, V. Lev and Z. MatouSek Rubber and Plastics Technology Research Institute, Gottwaldov, Czechoslovakia
Abstract.A procedure is presented for the develop~ent of a mIcroprocessor controlled plastics blown film production line. The solution of the line design is based on an analytical ~odel, which has been used to select the line parameters to be controlled and action control ele~ents of the process. Both the analytical model and tLe experiulental Ulethod used are discussed, since both have been e~ployed in solving the line. Also, relationship between input and output parameters has been established. The para~eters with less influence on the process have been excluded from the model. A multidi~ensional regression ~odel with parameters estimated during the process has been e~ployed as an identification method. The regression model has been developed by the Infor~tion Theory and Auto~tion Institute of the Czechoslovak Acade~ of Sciences in Prague. The solution has been applied in designing a blown-fil~ production line, tLe prototype of which is currentlJ being built. Keywords. Analytical model; stochastic model; microprocessor control; plastics industry; blown-fil~ production line. INTRODUCTION In plastics processing industry the computer or microprocessor controlled production line are still rather rare. This may be due to rather a short existence of the plastics processing industry and also due to rather great co~plexity of macrostructure of raw materials processed. For this reason a large number of processes have not yet been described analytically and verified experimentally. Nevertheless, there are already so~e technologies that have been investigated more thorougruy and are, therefore, und~r stood well enough to per~it their major improvement. One of the routes leading to such improvements is ~ king use of the potentials offered by microprocessors. Among the well understood processes are, for instance, injection moulding, extrusion and also fil~ blowing, the latter being the subject of our study. BLO~~-FILM
Technology hesearch Institute /V6GPT/ in about 1975. The SUbsequent work on the project was divided into the following stages: Selection of factors having influence on the blowing process and establishing their effect, Ten factors we~e cLosen, namely fl.lm th1ckness, f1.lm ther~l properties, film environmental te~perature, initial material temperature and some others, such as cooling air flow velocity § both inside and outside the bUbble, internal air pressure, etc. Based on an analytical solution, para~eters were established to be considered in calculating the process and other parameters important for the process control. Fil~ lay-flat width and fil~ gauge were selected as controlled parameters while film take-off speed, bubble internal air pressure, ril~ blow-up ration, cooling air parameters and some others, as will be shown, were chosen as action control eleJlents. An analytical ~odel has been developed, with the aid of which results as presented further on were 9btained. The ~odel, discussed 1.0 greater detail by Malik et al /1978a/, describes a process outlined
PhODUCTION LINE
The idea to control a tubular fil& production line by a microprocessor originated at the hubber and Plastics 103
104
K. Ma11k, V. Lev and Z. Matousek
schematically in Fig. 1.
is described by the following equations: r it (x*)
=8tf' - ~ ri (x*) +B( x*
-
ri (x*) =. E[cos h(
r* (x*) = R 2
lt
-
~*)r~
('r
1
+
(x*) (2) + 1
(3) r x*) _ cLcOS h (-==--x* --g-........... ( 4)
e (x*) r'*' = tg
=
/~
~
-2
~o
x*> 0 x*= 0
(6)
x*< 0 (7)
where the new dimensionless quantities are: X* is frost line distance; £ is constant and R* is blow-up ratio.
Fig. 1
Diagram of plastics film blowing process
analytical model, based on the work by Petrie /1974/ and Pearson and Petrie /1970/, takes into account changes of the di~eDBionless film thickness s* as given by the relationship ~he
ds* = _ ~ [2r,* dx* 4 r* + (F* + r*l p* )
+
29'
+
q* sec 2 'f
~Jt~
(1)
where the diJlel.lsionless quanti ties denote the following: x* is distance, r* is instantaneous bubble radius, ~* is fil~ density, F* is film take-off force, p* is air pressure inside the bUbble, 'P is bubble curvature angle and v* is kinematic viscosity. The change in the dimensionless radius of the bubble in x* direction
The model is completed with equations describing changes in film temperature in the take-up direction d ~ /dx*, changes in coefficients of heat transfer both inside and outside the film bUbble, (x"*") sad ~ *2 (x*), equations for temperature dependencas of mechanical parameters such as density ~*, specific heat c* and dynamic viscosity~*, and equations for changes in temperature of the cooling air d v ok/dxf equations for changes of air pressure inside the bubble and equations for film die-swell. To solve the equations a D 22 DATA SAAB computer was used. The above ~odel was tested experimentally by Malik et al /1978b/.
oCi
Based on the preceding stages, line design has been prQp~ The line ~et-up is shown in Fig. 2. The line comprises a Trusioma extruder /GDh/, a spiral flow channel extrusion head, internal and external cooling systeills, gauging, take-off and wind-Up equip~ent. The output is over 300 kg per hour of low density PE film.
Microprocessor Controlled Blown Film Production Line
At present, a prototype of the line is manufactured. Tt.Le last part of tile project is the Qf the line micrQp~ cessor control s~sten which will be described in greater detail further on. As it has already been said, to develop an efficient and reliable control syste~ the technological process to be controlled sho~d be thoroughly understood: both the structure of the object controlled and effects of each para~eter. Such knowledge permits to determine the number of key variables to be controlled and also to evaluate the process in economic ter~. Besides, the control system should be considered as an integral part of the entire technological process. develop~ent
The process control consists essentially in simulating behaviour of the controlled Object on a suitable model capable of providing information - according to a selected algorithm - on the necessity to take steps to achieve the pre-set target. Both conventional control systeillS and up-to-date control techniques are based on identical concepts.They differ from each other in the ~eans employed to create the model and in the capability of such model to approximate more or less accurately the behaviour of the controlled object. Microprocessor control systems ~ke possible to establish complex models capable of approximating a real process with relatively great precision. In such systems, however, the model must be treated mathematically. Two fundamental techniques can be used to describe the illodel in mathematical terms. ~rhe first metr.1od is an analytical one. It is based on application of physical laws and is valid under the assumption tl"!at the behaviour of the controlled Object can be described, provided its structure is known, by mathe~atical equations. The control parameters are selected from among design and process variables. Models obtaineu by using analytical methods are largely deteL~inistic in nature and are formed to a great extent by a set of partial differential non-linear equations. The second method allowing to create a simplified mathewatical model based on a set of measure&ents is an experi~en tal approach. In this case the structure is given by the type of model used. In order to achieve useable accuracy statistical ~ethods are frequently e~uployed for data evaluation and models produced in this way are, therefore, largely stochastic.
105
The above division of methods that are used in identification of controlled objects is merely a certain convention since in reality both theoretical and experimental approaches make mutual use of their respective apparatuses. The model derived by theoretical analysis must be assessed and verified by experi~ental ~ans and, vice versa, an experiment cannot be conducted without a theoretical preparation. Experiment evaluation must be consistent with theoretical conclusions. however, when the analytical model is used for process control, a discrepancy occurs frequently between the time required to solve a set of equations a~d the necessity to control the process in real ti~e. This leads partly to linearization of equations, partl~ to simplification of the set of equations to ordinary differential equations or to reduction of the number of the model parameters. As a result the model li~ted in this way cannot be used for control any more, due to its inability to approximate the behaviour of the cont~olled object with sufficient accuracy. Out of models obtained in experimental manner those permitting quick solution and acceptable approximation error are frequently selected. On establishing the required parameters and determining analytically their weights an experimental model has been chosen at VdGPT. As the whole process is rather extensive from teChnical cybernetics point of View, only a part of film blowing, cool1ng and take-up has been selected in the first stage. Changes caused by the extruder in this section of the manufacturing process are conaidered as surface variables both ~easurable and unLIleasurable. It should be noted that tfie parameters monitored in the film production are both of qualitative and quantitative nature. Therefore, both these features, consistent with certain weight coefficients, should be taken i~to account in tte process control. The quantitative indicator is the amount of material processed per hour provided the maxi~um throughput capacity of the Whole line is used without impairing the required product quality. ~ualitative indices are the film geometric di~cnsions with the closest tolerances, film collapsing temperature and mecllanical, optical or other filJl properties.
106
K. Ma11k, V. Lev and Z. Matousek
The above "quantitative and qualitative para~eters as well as process optimization are object of our project. Based on this, selection can be made of input and output quantities which are interrelated in tile process in manner described by the analytical solut~on. As inputs film take-up v~10c1ty,.vo~~e flow ra~e of cooling 81r both 1ns1de and outs1de tIle fil~ bubble and the amount of air exhausted fro~ inside the bubble were selected. Outputs are film thickness, film lay-flat gauge and filJl properties. The process itself is further affected by surface variables, which we cannot or do not want to control and which frequently cannot even be measured. These can be melt viscosity, mass flow rate of melt, rheologicsl, mechanic~l and therillophysical characteristics of the material both in solid state and in Jlelt. In addition, tIle surface variables m~ also comprise melt temperature 1n front of the extruder head and screw speed. The most significant are variations in those quantities that, in terms of process control, are considered constant.
The identification procedure is shown in a block diagram in Fig. 3
u
=f
(n, v, Ql' ~, Q3,Jm, Pm' K, R,-t t)
d
=g
-
~
~
1
DATA OBTAINED BY MEASURING
-
NOISE
I DATA TREATMENT
I
~ MODEl STRUCTURE
1
1 PARAMETER ESTIMATION
Functional dependences between inputs and outputs can be described by the relationships
s
y
PROCESS
-
e
, \4~ l
~ -
MODEL
(8) ~
(n, v, Ql' Q2' Q3' D, J'm, Pm,6 p ' Ko, tJ
(9)
where n are screw revolutions, n is a constant, ~ is fil~ take-off speed, Ql'.~' Q1 is cooling air flow rate, 11'. :lS Jlel't temperature, J is a ctfustant, #in is pressure fn front of extruder head, £ is constant, ~ ~re physical pr?pWr~ies of melt, x 15 constant, t :lS t~~e and d is ?il~ lay-flat wIdth. In order to set up a mathematical illO~el experimentally parameters th1S ~del must be established.
of In other words, the object to be controlled has to be identified. In selecting the identification metIlod, stochastic-type model capable of approximating dynamic behaviour of the controlled syste~ with mini~um erro~ ~a~ assumed. ~i~ultaneously, poss1b111ty for creat1ng an adaptive model capable of chanbing its parameters according to changes in the real process was investigated. ~uch changes may result for instance from rheological properties of the ~te rial uSE;d, etc.
Fig. 3 3lock diagram of identification procedure The set of input /U/ and output /y/ data loaded with illeasurement and transfer errors, is treated and transformed into a form required and sUbsequently put into an identification algorithm. The model structure is given by the mathematical model used. The parameters are estimated on the basis of the data measured and the magnitUde of deviation between the real output and that of the model. ~ our case.multidimensional regress10n model w1th parameters estimated during the process has been chosen. Ihe algorith~ of this identification method applying 8 square root filter has been developed by the Information Theory and Autoillation Institute of ~he Czechoslovak Acade~ of Sciences 1n Prague by V. Peterka /1975, 1976/.
Microprocessor Controlled Blown Film Production Line
The model is described by equation
107
CONCLUSIONS
/10/. Yr
:8
w~ere y~is
pT
Zcr
+
eT
(10)
output quantities vector,
P is transp?sed matrix of parameters, Z~vector
of 1nput and output quantities having the following form:
Z crT _[-T -T -T -T _T - U!, Y'r-l' Uef-l' ••• , Yr-n' ur.] '~Tis vector of input quan-
t1i~e6, aris vector of deviations between the actual process output and t~at ?f the model, L is sa~pling t1Jle l.ndex.
This model serves as a basis of a control syatem for creating a control algorithm. ~o far, the proposed ~o del has been tested by simulating the entire closed control loop on the syste~ model.
DISCUSSION The above results represent a further step towards a microprocessor controlled blown-film production line developed by vUGPT. At the present stage, the line is being illanufactured. The l1.ne prototype is expected to be co~~let~d i~ 1961. Whe~ put into operat10n 1t wlll be poss1ble to verify the validity of the proposed model and, if the need arises, to ~ke all the necessary corrections, should any larger deviation3 between the real process and the ~odel be revealed These deviations ~ be caused by· the necessity to simplify the ~odel due to a considerable co~plexity of the real process. Also, so~e of the parameters included in the model appear rather difficult to measure. This is particulary true of the relationship between the Jl8teriE1I properties and the material molecular structure. Also, certain problems may occur in determining the magnitude of tlle film take-up force which acts on the Jlaterif.ll and affects not only the process but also properties of the final product. Film die-swell too, is rather hard to ~easure. ' Neither measuring of temperature in the transparent thin fil~ is easy. All tL.is 'JlB.y result in various errors snd deviations. On the other hand, satisfactory agree~ent between the results of experimental illeasurements carried out so far and the calculations made with the aid of the ~odel plus availability of co~paratively enough tiille for further work justify our o;timism in achieving the final goal.
An analytical model used as a basis for the development of a ~cro~ro cessor controlled blown fil~ l10e has partially been presented. In addition, a stochastic model has been described, which completes the analytical one and is essential for the process control proper. Based on the models employed, a prototype line has been designed and is currently under construction. AlSO, possible causes are suggested for departures of the results obtained on the actual equipment from those calculated by using the model. The results presented here are not final since the work continues.
REFERENCES Malik, K., J. V1~ek and F. Tomis (!978a). Losung des KUhlvorgangs wahrenol der Herstellung von Plastfolien nach dem Extrusionsblasverfahren. Plaste und Kautschuk, £2, 331 - 333. Petrie, C.J.~. (1974). Mathematical modelling of heat transfer in film blowing a case study. Plastics & Polymers, 42, 259 - 2b47 Pearson, J.h.A., and C:J.S. Petrie (1970). A fluid - meChanical anal sis of tiLe film-blowing proc~ss. Plastics & Poly~ers, 38, 85 - 94. Malik, K., J. Vlcek and F. To~s (1978b). S~udium chlazeni vyfukovanYch folii z PE. Plasty a Kau~ukt 15L 6 - 8. Peterka, (~·(5). A square root filter for real-ti~e multivariate regression. Kvbernetika, 11, 53 - 67. PeterKB, v. (1976). IV. I?AC - Symposium Iaentification and s~s tem Para ter Est1mation. T 1lisi. 14.2.
v.
K. Malik, V. Lev and Z. Matousek
108
"--. ~.lt7---1L...-----I.L.t::======::::t::======:j~
Fig. 2
Blown
fil~
production line
SOLUTION OF A MICROPROCESSOR CONTROLLED BLOWN FILM PRODUCTION LINE K. Malik, V. Lev and Z. MatouSek Rubber and Plastics Technology Research Institute, Gottwaldov, Czechoslovakia
Abstract.A procedure is presented for the develop~ent of a mIcroprocessor controlled plastics blown film production line. The solution of the line design is based on an analytical ~odel, which has been used to select the line parameters to be controlled and action control ele~ents of the process. Both the analytical model and tLe experiulental Ulethod used are discussed, since both have been e~ployed in solving the line. Also, relationship between input and output parameters has been established. The para~eters with less influence on the process have been excluded from the model. A multidi~ensional regression ~odel with parameters estimated during the process has been e~ployed as an identification method. The regression model has been developed by the Infor~tion Theory and Auto~tion Institute of the Czechoslovak Acade~ of Sciences in Prague. The solution has been applied in designing a blown-fil~ production line, tLe prototype of which is currentlJ being built. Keywords. Analytical model; stochastic model; microprocessor control; plastics industry; blown-fil~ production line. INTRODUCTION In plastics processing industry the computer or microprocessor controlled production line are still rather rare. This may be due to rather a short existence of the plastics processing industry and also due to rather great co~plexity of macrostructure of raw materials processed. For this reason a large number of processes have not yet been described analytically and verified experimentally. Nevertheless, there are already so~e technologies that have been investigated more thorougruy and are, therefore, und~r stood well enough to per~it their major improvement. One of the routes leading to such improvements is ~ king use of the potentials offered by microprocessors. Among the well understood processes are, for instance, injection moulding, extrusion and also fil~ blowing, the latter being the subject of our study. BLO~~-FILM
Technology hesearch Institute /V6GPT/ in about 1975. The SUbsequent work on the project was divided into the following stages: Selection of factors having influence on the blowing process and establishing their effect, Ten factors we~e cLosen, namely fl.lm th1ckness, f1.lm ther~l properties, film environmental te~perature, initial material temperature and some others, such as cooling air flow velocity § both inside and outside the bUbble, internal air pressure, etc. Based on an analytical solution, para~eters were established to be considered in calculating the process and other parameters important for the process control. Fil~ lay-flat width and fil~ gauge were selected as controlled parameters while film take-off speed, bubble internal air pressure, ril~ blow-up ration, cooling air parameters and some others, as will be shown, were chosen as action control eleJlents. An analytical ~odel has been developed, with the aid of which results as presented further on were 9btained. The ~odel, discussed 1.0 greater detail by Malik et al /1978a/, describes a process outlined
PhODUCTION LINE
The idea to control a tubular fil& production line by a microprocessor originated at the hubber and Plastics 103
104
K. Ma11k, V. Lev and Z. Matousek
schematically in Fig. 1.
is described by the following equations: r it (x*)
=8tf' - ~ ri (x*) +B( x*
-
ri (x*) =. E[cos h(
r* (x*) = R 2
lt
-
~*)r~
('r
1
+
(x*) (2) + 1
(3) r x*) _ cLcOS h (-==--x* --g-........... ( 4)
e (x*) r'*' = tg
=
/~
~
-2
~o
x*> 0 x*= 0
(6)
x*< 0 (7)
where the new dimensionless quantities are: X* is frost line distance; £ is constant and R* is blow-up ratio.
Fig. 1
Diagram of plastics film blowing process
analytical model, based on the work by Petrie /1974/ and Pearson and Petrie /1970/, takes into account changes of the di~eDBionless film thickness s* as given by the relationship ~he
ds* = _ ~ [2r,* dx* 4 r* + (F* + r*l p* )
+
29'
+
q* sec 2 'f
~Jt~
(1)
where the diJlel.lsionless quanti ties denote the following: x* is distance, r* is instantaneous bubble radius, ~* is fil~ density, F* is film take-off force, p* is air pressure inside the bUbble, 'P is bubble curvature angle and v* is kinematic viscosity. The change in the dimensionless radius of the bubble in x* direction
The model is completed with equations describing changes in film temperature in the take-up direction d ~ /dx*, changes in coefficients of heat transfer both inside and outside the film bUbble, (x"*") sad ~ *2 (x*), equations for temperature dependencas of mechanical parameters such as density ~*, specific heat c* and dynamic viscosity~*, and equations for changes in temperature of the cooling air d v ok/dxf equations for changes of air pressure inside the bubble and equations for film die-swell. To solve the equations a D 22 DATA SAAB computer was used. The above ~odel was tested experimentally by Malik et al /1978b/.
oCi
Based on the preceding stages, line design has been prQp~ The line ~et-up is shown in Fig. 2. The line comprises a Trusioma extruder /GDh/, a spiral flow channel extrusion head, internal and external cooling systeills, gauging, take-off and wind-Up equip~ent. The output is over 300 kg per hour of low density PE film.
Microprocessor Controlled Blown Film Production Line
At present, a prototype of the line is manufactured. Tt.Le last part of tile project is the Qf the line micrQp~ cessor control s~sten which will be described in greater detail further on. As it has already been said, to develop an efficient and reliable control syste~ the technological process to be controlled sho~d be thoroughly understood: both the structure of the object controlled and effects of each para~eter. Such knowledge permits to determine the number of key variables to be controlled and also to evaluate the process in economic ter~. Besides, the control system should be considered as an integral part of the entire technological process. develop~ent
The process control consists essentially in simulating behaviour of the controlled Object on a suitable model capable of providing information - according to a selected algorithm - on the necessity to take steps to achieve the pre-set target. Both conventional control systeillS and up-to-date control techniques are based on identical concepts.They differ from each other in the ~eans employed to create the model and in the capability of such model to approximate more or less accurately the behaviour of the controlled object. Microprocessor control systems ~ke possible to establish complex models capable of approximating a real process with relatively great precision. In such systems, however, the model must be treated mathematically. Two fundamental techniques can be used to describe the illodel in mathematical terms. ~rhe first metr.1od is an analytical one. It is based on application of physical laws and is valid under the assumption tl"!at the behaviour of the controlled Object can be described, provided its structure is known, by mathe~atical equations. The control parameters are selected from among design and process variables. Models obtaineu by using analytical methods are largely deteL~inistic in nature and are formed to a great extent by a set of partial differential non-linear equations. The second method allowing to create a simplified mathewatical model based on a set of measure&ents is an experi~en tal approach. In this case the structure is given by the type of model used. In order to achieve useable accuracy statistical ~ethods are frequently e~uployed for data evaluation and models produced in this way are, therefore, largely stochastic.
105
The above division of methods that are used in identification of controlled objects is merely a certain convention since in reality both theoretical and experimental approaches make mutual use of their respective apparatuses. The model derived by theoretical analysis must be assessed and verified by experi~ental ~ans and, vice versa, an experiment cannot be conducted without a theoretical preparation. Experiment evaluation must be consistent with theoretical conclusions. however, when the analytical model is used for process control, a discrepancy occurs frequently between the time required to solve a set of equations a~d the necessity to control the process in real ti~e. This leads partly to linearization of equations, partl~ to simplification of the set of equations to ordinary differential equations or to reduction of the number of the model parameters. As a result the model li~ted in this way cannot be used for control any more, due to its inability to approximate the behaviour of the cont~olled object with sufficient accuracy. Out of models obtained in experimental manner those permitting quick solution and acceptable approximation error are frequently selected. On establishing the required parameters and determining analytically their weights an experimental model has been chosen at VdGPT. As the whole process is rather extensive from teChnical cybernetics point of View, only a part of film blowing, cool1ng and take-up has been selected in the first stage. Changes caused by the extruder in this section of the manufacturing process are conaidered as surface variables both ~easurable and unLIleasurable. It should be noted that tfie parameters monitored in the film production are both of qualitative and quantitative nature. Therefore, both these features, consistent with certain weight coefficients, should be taken i~to account in tte process control. The quantitative indicator is the amount of material processed per hour provided the maxi~um throughput capacity of the Whole line is used without impairing the required product quality. ~ualitative indices are the film geometric di~cnsions with the closest tolerances, film collapsing temperature and mecllanical, optical or other filJl properties.
106
K. Ma11k, V. Lev and Z. Matousek
The above "quantitative and qualitative para~eters as well as process optimization are object of our project. Based on this, selection can be made of input and output quantities which are interrelated in tile process in manner described by the analytical solut~on. As inputs film take-up v~10c1ty,.vo~~e flow ra~e of cooling 81r both 1ns1de and outs1de tIle fil~ bubble and the amount of air exhausted fro~ inside the bubble were selected. Outputs are film thickness, film lay-flat gauge and filJl properties. The process itself is further affected by surface variables, which we cannot or do not want to control and which frequently cannot even be measured. These can be melt viscosity, mass flow rate of melt, rheologicsl, mechanic~l and therillophysical characteristics of the material both in solid state and in Jlelt. In addition, tIle surface variables m~ also comprise melt temperature 1n front of the extruder head and screw speed. The most significant are variations in those quantities that, in terms of process control, are considered constant.
The identification procedure is shown in a block diagram in Fig. 3
u
=f
(n, v, Ql' ~, Q3,Jm, Pm' K, R,-t t)
d
=g
-
~
~
1
DATA OBTAINED BY MEASURING
-
NOISE
I DATA TREATMENT
I
~ MODEl STRUCTURE
1
1 PARAMETER ESTIMATION
Functional dependences between inputs and outputs can be described by the relationships
s
y
PROCESS
-
e
, \4~ l
~ -
MODEL
(8) ~
(n, v, Ql' Q2' Q3' D, J'm, Pm,6 p ' Ko, tJ
(9)
where n are screw revolutions, n is a constant, ~ is fil~ take-off speed, Ql'.~' Q1 is cooling air flow rate, 11'. :lS Jlel't temperature, J is a ctfustant, #in is pressure fn front of extruder head, £ is constant, ~ ~re physical pr?pWr~ies of melt, x 15 constant, t :lS t~~e and d is ?il~ lay-flat wIdth. In order to set up a mathematical illO~el experimentally parameters th1S ~del must be established.
of In other words, the object to be controlled has to be identified. In selecting the identification metIlod, stochastic-type model capable of approximating dynamic behaviour of the controlled syste~ with mini~um erro~ ~a~ assumed. ~i~ultaneously, poss1b111ty for creat1ng an adaptive model capable of chanbing its parameters according to changes in the real process was investigated. ~uch changes may result for instance from rheological properties of the ~te rial uSE;d, etc.
Fig. 3 3lock diagram of identification procedure The set of input /U/ and output /y/ data loaded with illeasurement and transfer errors, is treated and transformed into a form required and sUbsequently put into an identification algorithm. The model structure is given by the mathematical model used. The parameters are estimated on the basis of the data measured and the magnitUde of deviation between the real output and that of the model. ~ our case.multidimensional regress10n model w1th parameters estimated during the process has been chosen. Ihe algorith~ of this identification method applying 8 square root filter has been developed by the Information Theory and Autoillation Institute of ~he Czechoslovak Acade~ of Sciences 1n Prague by V. Peterka /1975, 1976/.
Microprocessor Controlled Blown Film Production Line
The model is described by equation
107
CONCLUSIONS
/10/. Yr
:8
w~ere y~is
pT
Zcr
+
eT
(10)
output quantities vector,
P is transp?sed matrix of parameters, Z~vector
of 1nput and output quantities having the following form:
Z crT _[-T -T -T -T _T - U!, Y'r-l' Uef-l' ••• , Yr-n' ur.] '~Tis vector of input quan-
t1i~e6, aris vector of deviations between the actual process output and t~at ?f the model, L is sa~pling t1Jle l.ndex.
This model serves as a basis of a control syatem for creating a control algorithm. ~o far, the proposed ~o del has been tested by simulating the entire closed control loop on the syste~ model.
DISCUSSION The above results represent a further step towards a microprocessor controlled blown-film production line developed by vUGPT. At the present stage, the line is being illanufactured. The l1.ne prototype is expected to be co~~let~d i~ 1961. Whe~ put into operat10n 1t wlll be poss1ble to verify the validity of the proposed model and, if the need arises, to ~ke all the necessary corrections, should any larger deviation3 between the real process and the ~odel be revealed These deviations ~ be caused by· the necessity to simplify the ~odel due to a considerable co~plexity of the real process. Also, so~e of the parameters included in the model appear rather difficult to measure. This is particulary true of the relationship between the Jl8teriE1I properties and the material molecular structure. Also, certain problems may occur in determining the magnitude of tlle film take-up force which acts on the Jlaterif.ll and affects not only the process but also properties of the final product. Film die-swell too, is rather hard to ~easure. ' Neither measuring of temperature in the transparent thin fil~ is easy. All tL.is 'JlB.y result in various errors snd deviations. On the other hand, satisfactory agree~ent between the results of experimental illeasurements carried out so far and the calculations made with the aid of the ~odel plus availability of co~paratively enough tiille for further work justify our o;timism in achieving the final goal.
An analytical model used as a basis for the development of a ~cro~ro cessor controlled blown fil~ l10e has partially been presented. In addition, a stochastic model has been described, which completes the analytical one and is essential for the process control proper. Based on the models employed, a prototype line has been designed and is currently under construction. AlSO, possible causes are suggested for departures of the results obtained on the actual equipment from those calculated by using the model. The results presented here are not final since the work continues.
REFERENCES Malik, K., J. V1~ek and F. Tomis (!978a). Losung des KUhlvorgangs wahrenol der Herstellung von Plastfolien nach dem Extrusionsblasverfahren. Plaste und Kautschuk, £2, 331 - 333. Petrie, C.J.~. (1974). Mathematical modelling of heat transfer in film blowing a case study. Plastics & Polymers, 42, 259 - 2b47 Pearson, J.h.A., and C:J.S. Petrie (1970). A fluid - meChanical anal sis of tiLe film-blowing proc~ss. Plastics & Poly~ers, 38, 85 - 94. Malik, K., J. Vlcek and F. To~s (1978b). S~udium chlazeni vyfukovanYch folii z PE. Plasty a Kau~ukt 15L 6 - 8. Peterka, (~·(5). A square root filter for real-ti~e multivariate regression. Kvbernetika, 11, 53 - 67. PeterKB, v. (1976). IV. I?AC - Symposium Iaentification and s~s tem Para ter Est1mation. T 1lisi. 14.2.
v.
K. Malik, V. Lev and Z. Matousek
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Fig. 2
Blown
fil~
production line