JPH09123251A - Film thickness control device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To make the entire profile of a film thickness uniform in a short time by using a specific state formula for a PI control calculation performed by each of controllers outputting a calorific value command to a specific heater installed in a die gap. SOLUTION: A thickness measurement value of a film at a spot corresponding to each of heaters is supplied to each of N-pieces of PI-type controllers provided on an adjustment heater. These PI-type controllers calculate a deviation of the thickness measurement value of the film at a spot corresponding to each of the heaters and the set thickness value, and enters a command for the heat generation of a heater to the heater. Here, the N pieces of PI-type controllers use control gains expressed by state formulae I, II including their respective PI control calculations.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a film thickness control device used for a blown film product and a biaxially stretched film manufacturing device.

[0002]

2. Description of the Related Art FIG. 8 shows a structure of a film manufacturing apparatus by a method called an inflation molding method. In the figure,
Reference numeral 1 is an extruder for discharging molten resin. The molten resin from the extruder 1 is spread by a cylindrical die 2 along the circumferential direction of the die and discharged as a sheet-shaped resin from a die gap 3 at the upper end of the die. It

The resin sheet discharged from the cylindrical die 2 is cooled and solidified by the air from the air supplier 4 and stretched by the air pressure supplied from the air supplier 5 to form a film 6 having a tensile strength. Molded. The film 6 is wound by a winder 11 via a guide roll 7 and a nip roll 8.

One of the factors that determine the quality of the wide film product produced as described above is to make the thickness profile uniform in the film width direction. A lip heater system is one of the highly accurate thickness control means for that purpose. In this lip heater system, a large number of thickness adjusting heaters 9 are embedded at equal intervals along the circumference of a cylindrical die 2 that discharges molten resin in a sheet shape, and the heating value of each heater 9 is adjusted. The resin viscosity is changed by adjusting the resin flow rate through the die gap 3, thereby making the resin discharge amount distribution in the die circumferential direction uniform and making the film thickness uniform. The film thickness profile is measured by a thickness gauge 10 that reciprocates along the circumference of the film.

In this lip heater system, the heat generated by one heater is diffused in the circumferential direction of the die due to the heat conduction of the die portion in which the heater is embedded, and is changed to the film thickness at the position corresponding to the adjacent heater. It has an interfering effect of shutting down.

On the other hand, the unevenness of the resin flow velocity along the circumferential direction caused by the non-uniformity of the flow velocity resistance of the molten resin in the die, the heating value of each adjustment heater 9 is adjusted and the distribution thereof is uniform. Adjust it so that it is At this time, in order to adjust the film thickness at a certain position, not only the heat generation amount of the heater 9 corresponding to the thickness changing position but also the plurality of adjacent heaters 9 in consideration of the above-described interference effect between the heater 9 and the film thickness. The calorific value of must be adjusted at the same time.

Generally, in a film manufacturing apparatus, several tens or more heaters 9 are attached in the circumferential direction of the die, and in order to realize a uniform film thickness along the circumferential direction of the die, the tens of these heaters are required. It is necessary to adjust the above heaters 9 at the same time.

Conventionally, the operator sees the measured values of the thickness profile along the circumferential direction of the die and adjusts a plurality of heater heat generation amounts by trial and error, or it corresponds to a certain heater 9. One of the second operation methods is adopted in which the film thickness at the portion to be detected is detected, and the deviation from the set value of the thickness is input to the PI type controller for automatic control.

[0009]

However, the above-mentioned first problem
In the above operating method, an operator adjusts a plurality of heater heat generation amounts by trial and error in accordance with the degree of skill, so that it takes a long time to realize a good film thickness profile.

Also in the second operation method described above, the PI action is caused by the interference between the heater heat generation amount and the film thickness.
The shape controllers interfere with each other to make it difficult to stably control the entire film thickness profile, or it takes a lot of time for the film thickness to converge stably.

The present invention has been made in view of the above-mentioned circumstances, and an object of the present invention is to make an interference action between a plurality of heater heat generation amounts and film thickness irrespective of skill level of an operator. In consideration of the above, it is an object of the present invention to provide a film thickness control device capable of performing stable automatic control so that the entire film thickness profile becomes uniform in a shorter time.

[0012]

Means for Solving the Problems That is, the present invention provides an extruder for discharging a molten resin, a die for expanding the molten resin from the extruder and discharging it as a sheet resin through a die gap, and a die for discharging from this die. A film thickness control device used in a film manufacturing device having a cooler for cooling and solidifying a sheet-shaped resin to be formed into a film, and a winder for winding the film formed by the cooler, N (N: an integer of 2 or more) heaters installed at regular intervals in the die gap so that the sheet-shaped resin discharged from the die has a uniform resin velocity distribution. A thickness meter that measures the thickness profile of the corresponding film, and a measurement value of the thickness meter that corresponds to a specific heater among the N heaters and a preset film thickness setting And N PI controllers that output a heat generation amount command to the specific heater by PI control calculation, and the PI control calculation performed by each of the N PI controllers is in the above state. Control gains k _P and k _I expressed by equations (1) and (2)
It is characterized by using.

With such a structure, in consideration of the interference effect between the heat values of the heaters and the film thickness, the film thickness profile is automatically and stably maintained so that the entire film thickness profile becomes uniform in a shorter time. You will be able to control.

[0014]

An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 exemplifies the structure in the case where the present invention is applied to a film manufacturing apparatus using an inflation film molding method. Since the structure is basically the same as that shown in FIG. The same reference numerals are given and the description thereof is omitted.

However, the thickness gauge 10 is provided in N (N: integer of 2 or more) according to the number of the heaters 9 for adjusting the thickness, and the thickness of the film at the location corresponding to each heater 9 measured by these thickness gauges 10. The measured values of are supplied to N PI type controllers 12 individually provided in the thickness adjusting heater 9.

As shown in the control system of FIG. 2, the PI type controller 12 has a deviation ei between the measured value of the film thickness yi and the set value ri of the film corresponding to a certain heater 9.
= Ri-yi is calculated and the heater heat value command is input to the heater 9.

When the proportional gain of the PI controller 12 is k _P and the integral gain is k _I , these gains k _P ,
k _I is from the circulation of the input and output relationship in the blown film thickness control, common the same gain value k _P, and those using k _I, figure interference process with multiple heater heating value and a number of the film thickness Block P of

The process of obtaining the proportional gain k _P and the integral gain k _I in each PI controller 12 having the above-mentioned configuration will be described.

When the N sets of thickness adjusting heaters 9 are arranged at equal intervals along the circumference of the die, the heat generated by a certain heater 9 reaches the film thickness of the portion corresponding to the adjacent heater 9 as described above. Since it has an interfering effect of changing it, the interval of the heaters 9 is narrowed in order to perform the thickness control with high accuracy, but it is considered that this also causes the above-mentioned interfering effect easily. However, normally, the heat generated by a certain heater 9 is at most 2 each on both sides.
It can be considered that the thickness of a portion corresponding to each heater changes on the film. Therefore, there are only five heaters that affect the arbitrary thickness measurement point, including the heater at the corresponding position.

From the above, N sets of heater heat generation amounts u ₁ , u ₂ , ..., U _N are input, and N sets of film thickness measurement values y ₁ , y ₂ , ..., Y _N are output. The dynamic characteristics of the control model can be represented by the following transfer function matrix. That is,

(Equation 7)

The transfer function g ₁ (s) gives the change in thickness at the film position corresponding to the heater that has changed the amount of heat generation, and g
₂ (s) gives a thickness change at the film position corresponding to the heater next to the heater that has changed the heat generation amount. Above (8)
The 0 element in the first row of the transfer function matrix of the equation is the thickness measurement value y ₁
Is due to the process of the control model that is not affected by the heater heat generation amount u ₄ , ..., U _N−2 , and the 0 element in other rows has the same meaning.

Since the transfer function matrix of the above equation (8) is a cycle of transfer functions g ₁ , g ₂ , and g ₃ , first, a system of 1 input and 3 outputs [g ₁ , g ₂ , g ₃ ] ^t (T: Inversion value)
The minimum realization state equation expression of is calculated and expressed as follows. That is,

(Equation 8)

At this time, the state equation of the N-input N-output system expressed by the above equation (8) can be expressed as follows based on the matrices A, B and C. That is,

(Equation 9)

[0025]

(Equation 10)

For the control system shown in FIG. 2, the control inputs u ₁ , u ₂ , ..., U _N can be expressed by the following equation. That is,

[Equation 11]

Further, in consideration of simplicity and practicality, if the PI controller 12 is a controller having the same PI control discipline for each input, the integral gain k _I has the following diagonal structure. That is,

(Equation 12)

Therefore, the following quadratic form evaluation function is adopted. That is,

(Equation 13)

Next, the optimum control gains k _P and k of the PI type controller 12 that minimize the evaluation function J in the above equation (23).
_Ask for _I.

The controlled object is represented by the above equations (11) and (12), while the control input is determined by the above equation (22). Therefore, with respect to the integral element of the PI type controller 12, If a new state variable x _Ii is introduced, (11), (1
The following equation of state is obtained from equation (2). That is,

[Equation 14]

Using the above symbols, the state equation expression of the N-input N-output control system can be expressed by the equations (24) to (28) as follows. That is,

(Equation 15)

[0032]

(Equation 16)

When the above equations (32) and (33) are substituted into the equation (31), the state equation of the closed loop system is as follows. That is,

[Equation 17]

At this time, the evaluation function J of the above equation (23) is expressed by the following equation. That is,

(Equation 18)

The equations (43) and (44) are added to the equation (45).
Substituting the expression gives

[Equation 19]

[0036]

(Equation 20)

[0037]

(Equation 21)

At this time, the matrix T ^-1 ST is converted into a block diagonal matrix represented by the following equation. That is,

(Equation 22)

It is shown below that the above equation (56) is obtained by the transformation matrix T of the above equation (54). Here, for simplification, Ai in the above equation (53) is a scalar, that is, n.
= 1 and N is an even number. The matrix S can be expressed by the following equation. That is,

(Equation 23)

[0040]

(Equation 24)

However, the above (58), (63), (6)
The following equation is established by the equation 5). That is,

(Equation 25)

By the way, it is not difficult to show that the next N vectors are independent. That is,

(Equation 26)

[0043]

[Equation 27]

When Ai is an n × n matrix, the transformation matrix T
It is already described that is given by the above equations (54) and (55). Further, it can be seen that the transformation matrix T in the equation (54) is determined without depending on the block matrix Ai to be controlled.

From the above, the procedure for determining the control gains k _P and k _I is as follows. That is, (S1) The transformation matrix T is obtained by the above equation (54).

(S2) Determine the initial values of the control gains k _P and k _I.

(S3) From the transformation matrix T, the above (3
The matrix of Expression 9) is decomposed into a block diagonal matrix, and the above Expression (49) is solved for each block diagonal matrix to obtain a block diagonal matrix solution Pd.

(S4) From the transformation matrix T, the solution Pd =
(P ⁻¹ ) ^t · Pd · P ⁻¹ is obtained.

(S5) An inverse matrix is obtained for each block diagonal matrix obtained in (S3) to obtain an inverse matrix of block diagonal matrix type.

(S6) Inverse matrix solution by the transformation matrix T

[Equation 28]

Is obtained.

(S7) The evaluation function J is obtained from the above equations (50) and (51).

(S8) Gains k _P and k _I for making the evaluation function J smaller are obtained by the simplex method.

(S9) Returning to (S2), the gains k _P and k _I that minimize the evaluation function J are determined by iterative calculation.

(S10) By confirming the positive definiteness of the obtained solution P, the stability of the entire closed loop system using the determined gains k _P and k _I is confirmed.

With the above procedure, the control gains k _P and k _I
By determining, the optimum control gains k _P and k _I of the PI controller 12 can be reliably obtained in a shorter time.

Next, a case where the procedure shown in S1 to S10 is applied to an actual die will be described.

(I) Example of Application to Cylindrical Die First, the case of application to the cylindrical die 2 as shown in FIG. 1 will be described.

Assuming application by the lip heater type,
Transfer function g, which is an element of the transfer function matrix according to the above equation (8), in which the heater heat value is input and the film thickness is output
₁ (s), g ₂ (s) and g ₃ (s) are given by the following equations. That is,

(Equation 29)

At this time, the degree n of the state equation of the above equation (9) is n = 6, and the matrix “A (here, for convenience sake)” of the above equations (31) and (34) is 56 ×. 56
Will be next. Therefore, the weight matrix

[Equation 30]

On the other hand, the optimum control gains k _P and k _I obtained by the procedure shown in S1 to S10 are k _P = 14.13, k _I = 0.21 (79).

FIG. 3 shows a simulation result when the parameter values of these control gains k _P and k _I are used. FIG. 3 shows the time response of the film thickness and the heat value of the heater when all the thickness setting values are increased stepwise in increments of 1 μm. Since the input / output relationship of the heater calorific value and the film thickness is cyclically similar at all thickness points, the time response of the film thickness and the heater calorific value is the same in all thickness control systems.

It was also found that the values of the obtained control gains k _P and k _I hardly changed even if the number N of thickness control points was increased. Therefore, even if the number N of thickness control points is large, the control gain k _p , K _I could be calculated in a very short time.

(II) Example of application to T-shaped die In a biaxially stretched film manufacturing apparatus or a non-stretched film manufacturing apparatus, a T-shaped die 20 having a structure shown in FIG. 4 is used. The figure (A) shows the structure of the die lip part, and the figure (B) shows the arrangement state of the adjustment heater. 21 is a die body, 22 is a die heater, 23 is a manifold,
24a, 24b are left and right lips, 25a, 25b
Is a heater for adjusting the left and right sides, 26 is a resin sheet, 27
Is a casting roller.

In the T-shaped die 20 having such a structure, as shown in FIG.
As shown in (B), the adjustment heaters 25a and 25b are linearly arranged, and the resin sheet 26 is discharged from the die 20 into a flat surface.

The film thickness control model for the T-shaped die 20 is the matrix element C at the upper right and lower left of the matrix of the above equation (16).
It is equivalent to that ₂ and C ₃ become a zero matrix. Therefore,
The application conditions of the gain calculation method described in S1 to S10 are not satisfied, and the optimum gain calculation method cannot be applied. However, even in the case of the T-shaped die 20, the upper right and lower left matrix elements C ₂ and C ₃ of the equation (16) were intentionally added to obtain the optimum control gains k _P and k _I by this method. This control gain k
A thickness control simulation calculation in the T-shaped die 20 was performed using _P and k _I.

FIGS. 5 and 6 are simulation results of the T-shaped die 20 in which the number of thickness control points N = 8, and the film thickness when all the thickness setting values are increased in steps of 1 μm ( FIG. 5 shows the time response of the heater heat generation amount (FIG. 6). Due to the symmetry, the time response shows the case where the number of thickness control points N = 1 to 4. The response at the thickness control points N = 5 to 8 is equal to the response at N = 4-1.

In the discrete time control with the control period Ts = 20 seconds, the control gains k _P and k _{I used} were k _P = 19.36, k _I = 0.36 (80). If PI type controllers are used for the thickness control points at both ends of the T-shaped die 20, two P thickness control points (N = 1, 2, N = 7, 8) at both ends of the corresponding die are used as P controllers. did. An offset occurs at the two thickness control points on both ends of the die, but the thickness control at the middle point (N = 3 to 6) is well performed.

FIG. 7 shows the time response characteristic in the discrete time control with the cylindrical die when the same parameter value of the control gain as in FIGS. 5 and 6 shown in the equation (80) is used.

The film thickness time response at the midpoint of FIG. 6 (N = 3-6) is almost equal to the time response for the cylindrical die. From this, it is understood that the control gains summarized in S1 to S10 described above are effective for the thickness control in the T-shaped die by overcoming the modeling error.

In the above embodiment, the case where the invention is applied to the apparatus for producing an inflation-molded film is illustrated, but the present invention is not limited to this, and it can be applied to a biaxially stretched film producing apparatus or the like. Of course.

[0072]

As described above in detail, according to the present invention, regardless of the degree of skill of the operator, the effect of interference between the heat value of each heater and the film thickness is taken into consideration, and It is possible to provide a film thickness control device capable of performing stable automatic control so that the entire film thickness profile becomes uniform.

[Brief description of the drawings]

FIG. 1 is a diagram showing a configuration of a film manufacturing apparatus according to an embodiment of the present invention.

FIG. 2 is a diagram showing a system configuration of each PI controller of FIG.

FIG. 3 is a diagram illustrating a simulation result of film thickness control performance in the cylindrical die according to the same embodiment.

FIG. 4 is a diagram showing a configuration of a T-shaped die according to the same embodiment.

FIG. 5 is a diagram showing an example of a simulation result of film thickness control performance in the T-die according to the same embodiment.

FIG. 6 is a diagram illustrating a simulation result of film thickness control performance in the T-shaped die according to the same embodiment.

FIG. 7 is a diagram illustrating a simulation result of film thickness control performance in a cylindrical die using the same control gain as in FIGS. 5 and 6 according to the same embodiment.

FIG. 8 is a diagram showing a configuration of a film manufacturing apparatus using a conventional inflation molding method.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Extruder 2 ... Cylindrical die 3 ... Die gap 4, 5 ... Air supply machine 6 ... Film 7 ... Guide roll 8 ... Nip roll 9 ... Thickness adjusting heater 10 ... Thickness gauge 11 ... Winding machine 12 ... PI type control Container 20 ... T-shaped die 21 ... Die main body 22 ... Die heater 23 ... Manifold 24a, 24b ... Lip, 25a, 25b ... Adjustment heater 26 ... Resin sheet 27 ... Casting roller

Claims (1)

[Claims] 1. An extruder for discharging a molten resin, a die for expanding the molten resin from the extruder and discharging it as a sheet resin through a die gap, and a sheet resin discharged from the die for cooling and solidification. A film thickness control device used in a film manufacturing apparatus having a cooling machine for molding as a film and a winding machine for winding a film molded by the cooling machine, wherein the sheet-shaped resin discharged from the die is N heaters (N: an integer of 2 or more) installed at regular intervals in the die gap so as to obtain a uniform resin velocity distribution, and a film thickness profile corresponding to each of the N heaters are measured. And a control deviation between the film thickness set value set in advance and the measured value of the thickness meter corresponding to a specific heater among the N heaters, and PI control is performed. And N PI controllers for outputting a heat generation amount command to the specific heater by calculation, and PIs performed by the N PI controllers respectively.
The film thickness control device is characterized in that the control calculation is expressed by the following equations (1) and (2). (Equation 1) (Equation 2) (Equation 3) (Equation 4) (Equation 5) (Equation 6)