Abstract: In control of a cooling water-injection type interstand cooling unit for the finishing mill, for controlling with higher precision a strip temperature on a delivery side of the finishing mill and decreasing the frequency of increasing/decreasing a cooling spray flow, an interstand cooling controller 1 comprises a preset control section 11 controlling an amount of a cooling spray flow of each of interstand cooling units 7a to 7d in a finishing mill 2 so that an FDT (finishing mill delivery strip temperature) of a strip 3 becomes identical to a desired target temperature, predicting the FDT with a strip temperature prediction model 18 before the strip is cooled by cooling water, and calculating the amount of the cooling spray flow of the interstand cooling unit based on the predicted FDT to thereby generate a preset control output; a dynamic control section 12 acquiring a state quantity of the strip under rolling and calculating a change amount of the cooling spray flow based on the state quantity to thereby generate a dynamic control output; and, an interstand cooling command generation section 13 generating and outputting an interstand cooling command from the preset control output and the dynamic control output.
1. An interstand cooling controller for a finishing mill which is provided with a plurality of stands, an interstand cooling unit capable of cooling down a strip under rolling by injecting cooling water between the stands, a finishing mill entry strip temperature measurement section for measuring a finishing mill entry strip temperature which is a temperature of the strip on an entry side of the finishing mill, and a finishing mill delivery strip temperature measurement section for measuring a finishing mill delivery strip temperature which is a temperature of the strip on a delivery side of the finishing mill, the interstand cooling controller controlling an amount of a cooling spray flow of the interstand cooling unit so that the finishing mill delivery strip temperature becomes identical to a desired target temperature, comprising: a preset control section provided with a strip temperature prediction model for predicting the finishing mill delivery strip temperature in relation to the cooling by means of the cooling water and configured to predict the finishing mill delivery strip temperature with the strip temperature prediction model before the strip is cooled by the cooling water and calculate an amount of a cooling spray flow of the interstand cooling unit based on the predicted finishing mill delivery strip temperature to thereby generate a preset control output; a dynamic control section configured to acquire a state quantity of the strip which has been cooled by the interstand cooling unit while being rolled by the finishing mill, and to calculate a change amount of the cooling spray flow based on the acquired state quantity to generate a dynamic control output; and an interstand cooling command generation section configured to generate an interstand cooling command from the preset control output and the dynamic control output and to output the interstand cooling command to the interstand cooling unit. 2. The interstand cooling controller according to claim 1, wherein said dynamic control section comprises: an finishing mill entry strip temperature deviation correction section configured to generate and output a change amount of the cooling spray flow capable of suppressing influence on the finishing mill delivery strip temperature, of a deviation between an assumed finishing mill entry strip temperature which is assumed for the finishing mill entry strip temperature upon generation of the preset control output and an actual measurement finishing mill entry strip temperature obtained through actual measurement during rolling; a speed deviation correction section configured to generate and output a change amount of the cooling spray flow capable of suppressing the influence on the finishing mill delivery strip temperature, of a deviation between an assumed strip speed which is assumed upon generation of the preset control output and an actual measurement strip speed obtained through actual measurement during rolling; an finishing mill delivery strip temperature deviation correction section configured to generate and output a change amount of the cooling spray flow for reducing the deviation between the target temperature and an actual measurement finishing mill delivery strip temperature obtained through actual measurement during rolling; and a dynamic control output generation section configured to generate a dynamic control output by selectively using respective outputs of the finishing mill entry strip temperature deviation correction section, the speed deviation correction section, and the finishing mill delivery strip temperature deviation correction section.
3. The interstand cooling controller according to claim 2, wherein said dynamic control section further comprises an influence coefficient table including: a first influence coefficient table storing the influence on the finishing mill delivery strip temperature, of a change in the amount of the cooling spray flow; a second influence coefficient table storing the influence on the finishing mill delivery strip temperature, of a change in the finishing mill entry strip temperature; and a third influence coefficient table storing the influence on the finishing mill delivery strip temperature, of a change in the strip speed on the delivery side of the finishing mill, and wherein an influence coefficient which each of said finishing mill entry strip temperature deviation correction section, said speed deviation correction section, and said finishing mill delivery strip temperature deviation correction section uses when generating the change amount of the cooling spray flow is acquired from said influence coefficient table. 4. The interstand cooling controller according to claim 2 or 3, wherein said dynamic control section is capable of holding an output of said finishing mill entry strip temperature deviation correction section at predetermined timings so that a lock-on value is thereafter maintained to be constant, and wherein said holding timings are set to a time point when an output corresponding to the first computation for generating the change amount is performed in the finishing mill entry strip temperature deviation correction section, or to a time point when said finishing mill delivery strip temperature detection is started.
5. The interstand cooling controller according to claim 4, wherein said dynamic control output generation section is configured to selectively use the output of each of said finishing mill entry strip temperature deviation correction section, said speed deviation correction section, and said finishing mill delivery strip temperature deviation correction section, based on position information of the strip under rolling, so that in a state where the finishing mill entry strip temperature has been detected for the strip and the strip has entered into the finishing mill but the finishing mill delivery strip temperature is not yet detected, a value obtained by adding the outputs of the finishing mill entry strip temperature deviation correction section and the speed deviation correction section is output, and that in a state where said finishing mill delivery strip temperature has been detected for the first time but the strip has not yet escaped from the finishing mill, a value obtained by adding the output or the lock-on value of the finishing mill entry strip temperature deviation correction section, the output of the speed deviation correction section, and the output of the finishing mill delivery strip temperature deviation correction section is output.
6. The interstand cooling controller according to claim 2, wherein a plurality of gains is prepared to be used in calculation for generating the change amount of the cooling spray flow in said finishing mill delivery strip temperature deviation correction section so that one of the plurality of gains is selected based on said strip speed.
7. The interstand cooling controller according to claim 1, wherein a model error of the strip temperature prediction model is predicted from an actual result of the control by said dynamic control section so that a prediction result of the model error is reflected in the finishing mill delivery strip temperature prediction by the strip temperature prediction model in the preset control section.
8. The interstand cooling controller according to claim 7, further comprising: an adaptive control amount calculation section capable of calculating an adaptive control amount based on a deviation between the target temperature and the actual measurement finishing mill delivery strip temperature, a deviation between the assumed finishing mill entry strip temperature and the actual measurement finishing mill entry strip temperature, a deviation between the assumed strip speed and the actual measurement strip speed, the output of the finishing mill delivery strip temperature deviation correction section, the lock-on value of the output of the finishing mill entry strip temperature deviation correction section, and the output of the speed deviation correction section, which are detected or calculated with respect to a plurality of parts of the strip of which the tail end is determined to have escaped the finishing mill, and an adaptive control section capable of correcting the target temperature with the adaptive control amount of said adaptive control amount calculation section to thereby calculating a target temperature for finishing mill delivery strip temperature prediction, wherein the target temperature for finishing mill delivery strip temperature prediction calculated by said adaptive control section is used when predicting the finishing mill delivery strip temperature by the strip temperature prediction model. 9. An interstand cooling control method for a finishing mill which is provided with a plurality of stands, an interstand cooling unit capable of cooling down a strip under rolling by injecting cooling water between the stands, a finishing mill entry strip temperature measurement section for measuring a finishing mill entry strip temperature which is a temperature of the strip on an entry side of the finishing mill, and a finishing mill delivery strip temperature measurement section for measuring a finishing mill delivery strip temperature which is a temperature of the strip on a delivery side of the finishing mill, the interstand cooling control method controlling an amount of a cooling spray flow of the interstand cooling unit so that the finishing mill delivery strip temperature becomes identical to a desired target temperature, wherein: the method is configured to perform a control combined of preset control and dynamic control, in which the preset control predicts the finishing mill delivery strip temperature before the strip is cooled by the cooling water by using a strip temperature prediction model for predicting the finishing mill delivery strip temperature in relation to the cooling by means of the cooling water, so as to be performed with a preset control output obtained by calculating an amount of a cooling spray flow of the interstand cooling unit based on the predicted finishing mill delivery strip temperature, and in which the dynamic control acquires a state quantity of the strip which has been cooled by the interstand cooling unit while being rolled by the finishing mill, so as to be performed with a dynamic control output obtained by calculating a change amount of the cooling spray flow based on the acquired state quantity. 10. The interstand cooling control method according to claim 9, wherein said dynamic control output includes a finishing mill entry strip temperature deviation correction output which is a control output of a change amount of the cooling spray flow capable of suppressing the influence on the finishing mill delivery strip temperature, of a deviation between an assumed finishing mill entry strip temperature which is assumed when generating the preset control output of the finishing mill entry strip temperature and an actual measurement finishing mill entry strip temperature obtained through actual measurement during rolling, and wherein the finishing mill entry strip temperature deviation correction output is held at predetermined timings so that a lock-on value is thereafter maintained to be constant. 11. The interstand cooling control method according to claim 10, wherein the holding timings are set to a time point when an output corresponding to the first computation for the finishing mill entry strip temperature deviation correction output is performed, or to a time point when the finishing mill delivery strip temperature detection is started.
Field of the invention
The present invention relates to control of interstand cooling carried out by water injection between stands in order to adjust a strip temperature on a delivery side of a finishing mill during hot rolling to a predetermined target temperature.
Description of Related Art
During hot rolling, finishing rolling is performed to adjust the shape or dimension of a strip on a finishing mill having a plurality of stands. Moreover, in the finishing mill, cooling is performed to adjust a finishing mill delivery strip temperature (a strip temperature on a delivery side of the finishing mill; hereinafter appropriately referred to as "FDT") to a predetermined target temperature. The cooling is generally performed in the finishing mill by an interstand cooling unit provided at each location between the stands by injecting cooling water in spray state to a strip under rolling. In such a cooling process, it is necessary to control an injection amount of the cooling water in order to control the FDT based on its relation with the target temperature, and interstand cooling control is performed therefor. Specifically, an interstand cooling controller is
provided, and the injection amount of the interstand cooling unit is controlled by the interstand cooling controller based on the FDT and the like so that the FDT becomes identical to the target temperature.
As for the interstand cooling control, techniques as disclosed in JP-A-10-43811, JP-A-2006-159261, JP-A-10-94814, and JP-A-7-75816, for example, are known. According to "Hot Finishing Mill Delivery Strip Temperature Control Method" of JP-A-10-43811, cooling control is performed on an injection number n of a strip coolant unit, which is preliminarily set prior to starting the cooling, by changing the injection number to an injection number (n+Δn) with an increment of An in accordance with a FDT measurement result so that the FDT becomes identical to the target temperature. In such a cooling control process, at timings where a decrease in a strip speed is expected, when An is positive, the positive An is forcibly set to zero so that the cooling is performed with an injection number of n, while when An is negative, the cooling is performed with an injection number of (n+Δn).
According to "Hot-Rolled Strip Manufacturing Method" of JP-A-2006-159261, cooling is started after a top end of a rolling material is bitten into the last stand by keeping track of the top end of the rolling material to thereby achieve a high precision of rolling temperature control and obtain a hot-rolled strip with very small grain diameter.
According to "Method For Controlling
Finishing Mill Delivery Strip Temperature Of Hot-Rolled Metal Strip" of JP-A-10-94814, a strip under rolling is virtually divided in a longitudinal direction into sections, and an injection amount and an injection timing are calculated for each of the sections after division based on a finishing mill entry strip temperature and a delivery time of the strip so that an FDT of each section becomes identical to a target value.
According to "Automated Control Of Water Injection Between Stands" of JP-A-7-75816, when water injection is performed between stands of a finishing mill so that a FDT becomes identical to a target value, a temperature change during a finishing process of a strip is calculated based on a preset temperature prediction model and an actual result parameter for each part, and water injection control is performed based on a calculation result.
The FDT in the finishing mill has an influence on the quality or shape of the resulting strip. For this reason, in the interstand cooling control, it is desired to achieve a high precision so that the FDT becomes identical to the target temperature as much as possible. Moreover, it is desired to perform control with high precision in a state where the frequency of increasing/decreasing the cooling spray flow is suppressed as much as possible.
In this respect, the conventional control techniques described above cannot be said sufficient. For example, in the control technique of JP-A-10-43811, the injection number is chanqed by using only feedback control based on an actually measured FDT so as to control the FDT to be identical to the target temperature. Thus, deterioration of the temperature precision (the precision of FDT to target temperature) is inevitable in the top end of the strip in which the effect of the feedback control is not reflected. Moreover, the control technique of JP-A-10-43811 does not take into consideration a case where a finishing mill entry strip temperature (a strip temperature on an entry side of a finishing mill; hereinafter appropriately referred to as "FET"), which is assumed in calculation for determining the injection number n prior to starting the cooling process, is different from an actually measured FET during rolling. For this reason, when the assumed FET differs from the actually measured FET, there is a possibility that the temperature precision deteriorates depending on a predetermined influence coefficient. Furthermore, in the control technique of JP-A-10-43811, although it is possible to cope with a change in the strip speed which is preliminarily scheduled by computation prior to cooling, it is difficult to cope with a change in the strip speed which cannot be predicted on a controller side, such as a change in the speed resulting from an
operator's manual manipulation. There is a possibility that the temperature precision deteriorates upon occurrence of such a change in the speed.
In the control technique of JP-A-2006-159261, although it is possible to reflect the effect of the control even in the top end of the strip because it tracks the top end of the strip, since it does not take sufficient consideration the fluctuation in the FET or the strip speed, there is a possibility that the temperature precision deteriorates upon occurrence of a change in the FET or the strip speed.
In view of individually controlling the temperature of respective parts of the strip for each of the virtually divided sections, the control technique of JP-A-10-94814 can be said to be an effective method in the conventional tandem rolling in which the strip temperature decreases in the longitudinal direction of the strip and cyclic temperature disturbances, which are often called skids, overlap at a time point where it enters into the finishing stand; however, the control technique is not suitable for so-called mini-hot tandem rolling. The mini-hot tandem rolling is a direct charge type rolling process for directly rolling a hot slab immediately after being cast in a continuous casting equipment, in which a slab maintained at constant temperature in a tunnel furnace is directly subjected to coarse rolling and then to finishing rolling. In such a mini-hot
tandem rolling process, a decrease in the temperature in the longitudinal direction of the strip is not great, and the skid temperature disturbances do not occur. Therefore, when the control technique of JP-A-10-94814 is applied to the mini-hot tandem rolling process, there is a fear that the control configuration thereof is unnecessarily complicated, that the temperature variations corresponding to the FDT of the strip overlap with one another in response to operations of changing the cooling spray flow for each section, and thus, the overlapping temperature variations act as a disturbance to winding temperature control in a later process, and that the frequency of increasing/decreasing the cooling spray flow increases unnecessarily.
In the control technique of JP-A-7-75816, since the water injection control is only performed based on the calculation results on the temperature variations of the strip during the finishing process based on the preset temperature prediction model or the actual result parameters, there is a possibility that the temperature precision deteriorates in response to the change in the actual FET or strip speed.
Brief Summary of the Invention
The present invention has been made in view of the above circumstances, and an object of the present invention is to provide an interstand cooling
controller and a control method therefor capable of achieving a higher temperature precision and suppressing the frequency of increasing/decreasing a cooling spray flow as much as possible.
In order to attain the object, according to an aspect of the present invention, there is provided an interstand cooling controller in a finishing mill which is provided with a plurality of stands, an interstand cooling unit capable of cooling down a strip under rolling by injecting cooling water between the stands, a finishing mill entry strip temperature measurement section for measuring a finishing mill entry strip temperature which is a temperature of the strip on an entry side of the finishing mill, and a finishing mill delivery strip temperature measurement section for measuring a finishing mill delivery strip temperature which is a temperature of the strip on a delivery side of the finishing mill, the interstand cooling controller controlling a cooling spray flow of the interstand cooling unit so that the finishing mill delivery strip temperature becomes identical to a desired target temperature, comprising: a preset control section provided with a strip temperature prediction model for predicting the finishing mill delivery strip temperature in relation to the cooling by means of the cooling water and configured to predict the finishing mill delivery strip temperature with the strip temperature prediction model before the strip is
cooled by the cooling water and calculate an amount of a cooling spray flow of the interstand cooling unit based on the predicted finishing mill delivery strip temperature to thereby generate a preset control output; a dynamic control section configured to acquire a state quantity of the strip which has been cooled by the interstand cooling unit while being rolled by the finishing mill and calculate a change amount of the cooling spray flow based on the acquired state quantity so as to generate a dynamic control output; and an interstand cooling command generation section configured to generate an interstand cooling command from the preset control output and the dynamic control output to output the interstand cooling command to the interstand cooling unit.
The interstand cooling controller performs a combination of preset control which is based on preliminary prediction by a strip temperature prediction model and dynamic control which is based on a state quantity of a strip under rolling, whereby a deficient range of the preset control is compensated by the dynamic control and a burden of the dynamic control is reduced by the preset control. Owing to such a configuration, it is possible to control with higher precision than the conventional technique of JP-A-10-43811, JP-A-2006-159261, or JP-A-7-75816, and to more decrease the cooling spray flow increase/decrease frequency than the conventional technique of, for
example, JP-A-10-94814.
The interstand cooling controller according to a preferred embodiment of the present invention has such a configuration that the dynamic control section comprises: a finishing mill entry strip temperature deviation correction section configured to generate and output a change amount of the cooling spray flow capable of suppressing influence on the finishing mill delivery strip temperature, of a deviation between an assumed finishing mill entry strip temperature which is assumed for the finishing mill entry strip temperature upon generation of the preset control output and an actual measurement finishing mill entry strip temperature obtained through actual measurement during rolling; a speed deviation correction section configured to generate and output a change amount of the cooling spray flow capable of suppressing the influence on the finishing mill delivery strip temperature, of a deviation between an assumed strip speed which is assumed upon generation of the preset control output and an actual measurement strip speed obtained through actual measurement during rolling; a finishing mill delivery strip temperature deviation correction section configured to generate and output a change amount of the cooling spray flow for reducing the deviation between the target temperature and an actual measurement finishing mill delivery strip temperature obtained through actual measurement during
rolling; and a dynamic control output generation section configured to generate the dynamic control output by selectively using respective outputs of the finishing mill entry strip temperature deviation correction section, the speed deviation correction section, and the finishing mill delivery strip temperature deviation correction section. According to such an embodiment, since correction of the finishing mill entry strip temperature deviation and correction of the strip speed deviation are performed as feedforward control, the dynamic control becomes more effective.
The interstand cooling controller according to a preferred embodiment of the present invention has such a configuration that the dynamic control section further comprises an influence coefficient table including: a first influence coefficient table storing the influence on the finishing mill delivery strip temperature, of a change amount in the cooling spray flow; a second influence coefficient table storing the influence on the finishing mill delivery strip temperature, of a change in the finishing mill entry strip temperature; and a third influence coefficient table storing the influence on the finishing mill delivery strip temperature, of a change in the strip speed on the delivery side of the finishing mill, wherein an influence coefficient which each of the finishing mill entry strip temperature deviation
correction section, the speed deviation correction section, and the finishing mill delivery strip temperature deviation correction section uses when generating the change amount of the cooling spray flow is acquired from the influence coefficient table. According to such an embodiment, the operation of generating a change amount of the cooling spray flow can be performed in a more efficient manner.
The interstand cooling controller according to a preferred embodiment of the present invention has such a configuration that the dynamic control section is capable of holding an output of the finishing mill entry strip temperature deviation correction section at predetermined timings so that it is thereafter a lock-on value maintained to be constant, and that the holding timings are set to a time point when an output corresponding to the first computation for generating the change amount is output in the finishing mill entry strip temperature deviation correction section, or to a time point when the finishing mill delivery strip temperature detection is started.
In the case of a direct charge type mini-hot tandem rolling process, the finishing mill entry strip temperature variation is small in the longitudinal direction of the strip, and as long as the control by the finishing mill entry strip temperature deviation correction section is performed only until a time point, or its neighboring time point, when the rolling
for one strip is started, it can be said that there is no substantial influence on the control precision even when the control output thereof is used thereafter. Such an embodiment is based on such characteristics of the mini-hot tandem rolling process and is capable of more decreasing the cooling spray flow amount increase/decrease frequency by locking the output of the finishing mill entry strip temperature deviation correction section to a fixed lock-on value.
The interstand cooling controller according to a preferred embodiment of the present invention has such a configuration that the dynamic control output generation section is configured to selectively use the output of each of the finishing mill entry strip temperature deviation correction section, the speed deviation correction section, and the finishing mill delivery strip temperature deviation correction section, based on position information of the strip under rolling, so that in a state where the finishing mill entry strip temperature has been detected for the strip and then the strip has entered into the finishing mill but the finishing mill delivery strip temperature is not yet detected, a value obtained by adding the outputs of the finishing mill entry strip temperature deviation correction section and the speed deviation correction section is output, and that in a state where the finishing mill delivery strip temperature has been detected for the first time but the strip has not yet
escaped from the finishing mill, a value obtained by adding the output, or the lock-on value thereof, of the finishing mill entry strip temperature deviation correction section, the output of the speed deviation correction section, and the output of the finishing mill delivery strip temperature deviation correction section is output. According to such an embodiment, the control can be performed in accordance with the rolling state and thus higher precision control can be preformed in a more efficient manner.
The interstand cooling controller according to a preferred embodiment of the present invention has such a configuration that a plurality of gains is prepared to be used in calculation for generating the change amount of the cooling spray flow in the finishing mill delivery strip temperature deviation correction section so that one of the plurality of gains is selected based on the strip speed. According to such an embodiment, when the strip speed is in the course of accelerating, the control can be performed in a stable manner with relatively smaller gain, while after the strip speed has reached the stabilized condition and the rolling has been stabilized, the control can be performed with good responsiveness with larger gain, whereby higher precision control can be performed in a more efficient manner.
The interstand cooling controller according to a preferred embodiment of the present invention has
such a configuration that a model error of the strip temperature prediction model is predicted from an actual result of the control by the dynamic control section so that a prediction result of the model error is reflected in the finishing mill delivery strip temperature prediction by the strip temperature prediction model in the preset control section.
A preset control error (a model error) of a recently rolled strip generally has high correlation with a preset control error expected in a subsequently rolled strip. The adaptive control in the above embodiment focuses on such characteristics of the preset control error, and by performing the adaptive control, it is possible to indirectly compensate the model error of the strip temperature prediction model. In this way, it is possible to reduce a control error resulting from not obtaining accordance between the strip temperature prediction model and actual cooling phenomenon, thereby enabling more precise control.
The interstand cooling controller according to a preferred embodiment of the present invention has such a configuration that the interstand cooling controller further comprises an adaptive control amount calculation section capable of calculating an adaptive control amount based on a deviation between the target temperature and the actual measurement finishing mill delivery strip temperature, a deviation between the assumed finishing mill entry strip temperature and the
actual measurement finishing mill entry strip temperature, a deviation between the assumed strip speed and the actual measurement strip speed, the output of the finishing mill delivery strip temperature deviation correction section, the lock-on value of the output of the finishing mill entry strip temperature deviation correction section, and the output of the speed deviation correction section, which are detected or calculated with respect to a plurality of parts of the strip of which the tail end is determined to have escaped the finishing mill, and an adaptive control section capable of correcting the target temperature with the adaptive control amount by the adaptive control amount calculation section to thereby calculate a target temperature for finishing mill delivery strip temperature prediction, and that the target temperature for finishing mill delivery strip temperature prediction calculated by the adaptive control section is used when predicting the finishing mill delivery strip temperature by the strip temperature prediction model. According to such an embodiment, it is possible to more effectively compensate the model error.
In order to attain the object, according to another aspect of the present invention, there is provided an interstand cooling control method in a finishing mill which is provided with a plurality of stands, an interstand cooling unit capable of cooling down a strip under rolling by injecting cooling water
between the stands, a finishing mill entry strip temperature measurement section for measuring a finishing mill entry strip temperature which is a temperature of the strip on an entry side of the finishing mill, and a finishing mill delivery strip temperature measurement section for measuring a finishing mill delivery strip temperature which is a temperature of the strip of a delivery side of the finishing mill, the interstand cooling control method controlling an amount of a cooling spray flow of the interstand cooling unit so that the finishing mill delivery strip temperature becomes identical to a desired target temperature, wherein: the method is configured to perform a combination of preset control and dynamic control in which the preset control predicts the finishing mill delivery strip temperature before the strip is cooled by the cooling water by using a strip temperature prediction model for predicting the finishing mill delivery strip temperature in relation to the cooling by means of the cooling water, so as to be performed with a preset control output obtained by calculating an amount of a cooling spray flow of the interstand cooling unit based on the predicted finishing mill delivery strip temperature, and in which the dynamic control acquires a state quantity of the strip which has been cooled by the interstand cooling unit while being rolled by the finishing mill so as to be performed with a dynamic
control output obtained by calculating a change amount of the cooling spray flow based on the acquired state quantity.
The interstand cooling control method according to a preferred embodiment of the present invention has such a configuration that the dynamic control output includes a finishing mill entry strip temperature deviation correction output which is a control output of a change amount of the cooling spray flow capable of suppressing the influence on the finishing mill delivery strip temperature, of a deviation between an assumed finishing mill entry strip temperature which is assumed when generating the preset control output of the finishing mill entry strip temperature and an actual measurement finishing mill entry strip temperature obtained through actual measurement during rolling, and that the finishing mill entry strip temperature deviation correction output is held at predetermined timings so as to be a lock-on value which is maintained to be constant thereafter.
The interstand cooling control method according to a preferred embodiment of the present invention has such a configuration that the holding timings are set to a time point when an output corresponding to the first computation for the finishing mill entry strip temperature deviation correction output is output, or to a time point when the finishing mill delivery strip temperature detection
is started.
In accordance with the present invention, it is possible to achieve higher temperature precision and lower cooling spray flow increase/decrease frequency in an interstand cooling unit of a finishing hot rolling mill.
Brief description of the several views of the drawing
Fig. 1 is a diagram illustrating a configuration of an interstand cooling controller according to a first embodiment of the present invention.
Fig. 2 illustrates an example of a target temperature table.
Fig. 3 illustrates an example of a speed table.
Fig. 4 illustrates an example of a standard flow pattern table.
Fig. 5 illustrates a flow of operations in preset control.
Fig. 6 is a diagram illustrating an example of a configuration of a dynamic control section.
Fig. 7 illustrates an example of a first influence coefficient table.
Fig. 8 illustrates an example of a second influence coefficient table.
Fig. 9 illustrates an example of a third influence coefficient table.
Fig. 10 illustrates a flow of operations of a feedback control activation timing generation section.
Fig. 11 illustrates a flow of operations of a feedback gain selection section.
Fig. 12 illustrates a flow of operations of a tracking section.
Fig. 13 illustrates a flow of operations of a dynamic control output generation section.
Fig. 14 is a graph illustrating an example of an output of the dynamic control output generation section.
Fig. 15 is a diagram illustrating a
configuration of an interstand cooling unit according to a second embodiment of the present invention.
Fig. 16 illustrates a flow of operations of an adaptive control amount calculation section.
Fig. 17 illustrates a flow of operations of an adaptive control section.
Detailed description of the invention
Description of preferred embodiments of the present invention will be provided herein below in detail with reference to the accompanying drawings. The configuration of an interstand cooling controller 1 according to a first embodiment of the present invention is illustrated in Fig. 1 in relation to a finishing mill 2 which is a control subject. The interstand cooling controller 1 receives a variety of
signals from the finishing mill 2 and outputs control signals to the finishing mill 2. It is noted that, hereinafter, some "means" described below can be replaced with the "section" and be read as the "section".
The finishing mill 2 includes five stands Fl to F5 (hereinafter, sometimes denoted by only symbols while omitting "stand"). A strip 3 delivered from a non-illustrated coarse mill to the finishing mill 2 is moved from left to right in the drawing while being rolled by rolling rolls 4 in each of the stands Fl to F5. Moreover, the finishing mill 2 is provided with a finishing mill entry strip temperature gauge 5 as a finishing mill entry strip temperature measurement section for measuring an FET of the strip 3 and a finishing mill delivery strip temperature gauge 6 as a finishing mill delivery strip temperature measurement section for measuring an FDT of the strip 3, and is further provided with an interstand cooling unit 7.
The interstand cooling unit 7 is provided as interstand cooling units 7a to 7d for the stands Fl to F5 so as to correspond to each of the locations between Fl and F2, F2 and F3, F3 and F4, and F4 and F5, respectively. The interstand cooling units 7a to 7d inject a respective amount of cooling water in spray state in accordance with an interstand cooling command from the interstand cooling controller 1 to thereby cool down the strip 3. The purpose of interstand
cooling control is to correct with high precision the FDT measured by the finishing mill delivery strip temperature gauge 6 to be identical to a desired target temperature. The target temperature of the FDT is generally controlled to be constant at each part of the strip in the longitudinal direction but may be controlled to be different.
Next, a description of the interstand cooling controller 1 will now be provided herein below. The interstand cooling controller 1 includes a preset control means 11 configured to calculate an amount of an injection cooling spray flow of each of the interstand cooling units 7a to 7d before the strip 3 is cooled by the interstand cooling unit 7 and generate and output a preset control output; a dynamic control means 12 configured to acquire a variety of types of state quantities of the strip 3 such as a measurement temperature in the finishing mill delivery strip temperature gauge 6 during periods when the strip 3 is cooled by the interstand cooling units 7a to 7d while being rolled by the finishing mill 2 and generate and output a dynamic control output for changing the amount of the cooling spray flow under a real time condition; and an interstand cooling command generation means 13 configured to output an interstand cooling command for correcting the preset control output of the preset control means 11 with the dynamic control output of the dynamic control means 12, more specifically, the
interstand cooling command being obtained by adding the preset control output and the dynamic control output together, to the interstand cooling units 7a to 7d. A detailed description of the preset control means 11 and the dynamic control means 12 will be provided herein below.
First, a description of the preset control means 11 will be provided. As described above, the preset control means 11 functions to calculate an amount of the cooling spray flow of each of the interstand cooling units 7a to 7d before the strip 3 is cooled by the interstand cooling unit 7 and generate a preset control output. To realize such a function, the preset control means 11 is provided with a preset means 14 so that computation by a strip temperature prediction model 18 is performed by the preset means 14 based on information acquired from each of a target temperature table 15, a speed table 16, and a standard flow pattern table 17, whereby an amount of a cooling spray flow of each of the interstand cooling unit 7a to 7d, that is, an amount of a preset control cooling spray flow, can be determined prior to starting the cooling.
Referring to Fig. 2, an example configuration of the target temperature table 15 is illustrated. In the target temperature table 15 of this example, a target value of finishing mill delivery strip temperature is classified corresponding to a strip
grade (type of strip). The preset control means 11 identifies the strip grade of a coil which is subjected to rolling and acquires a corresponding target temperature from the target temperature table 15. For example, when the strip grade is SS400, the target strip temperature on the finishing mill delivery side is set to 900°C.
Referring to Fig. 3, an example configuration of the speed table 16 is illustrated. In the speed table 16 of this example, a speed of the strip 3 on a deliver side of the last stand (F5 in this embodiment) is classified into an initial speed, a normal speed, and a final speed corresponding to a strip grade, a strip thickness, and a strip width. Here, the initial speed is a strip speed when a top end of the strip is ejected from F5, the final speed is a strip speed when a tail end of the strip escapes out of F5, and the normal speed is a strip speed that is set to higher speed than the initial speed and the final speed when neither initial speed nor the final speed is set. The preset means 14 identifies the strip grade, the strip thickness, and the strip width of a coil which is subjected to rolling and acquires corresponding speed information from the speed table 16. For example, when the strip grade is SS400, the strip thickness is 3.0 to 4.0 mm, and the strip width is 1200 mm, the initial speed is set to 360 mpm, the normal speed to 700 mpm, and the final speed to 600 mpm, respectively. A
gradient of a speed change from the initial speed to the normal speed is determined as a value at which the FDT becomes constant under the same amount of the cooling spray flow, during periods when the preset means 14 performs computations for determining an amount of an interstand cooling spray flow. Moreover, the gradient from the normal speed to the final speed is determined based on facility limitations or an allowable range. When the strip speed on F5 delivery side is determined, a rotation speed of the rolling rolls 4 of F5 is determined, and moreover, from this value, a rotation speed of the rolling rolls of each of the other stands is determined based on a strip thickness ratio of each stand (a ratio of an entry side strip thickness to a delivery side strip thickness).
Referring to Fig. 4, an example configuration of the standard flow pattern table 17 is illustrated. In the standard flow pattern table 17 of this example, an initial value of an amount of a cooling spray flow used in computations for determining an amount of a cooling spray flow under the conditions of a strip grade, a strip thickness, and a strip width is stored for each interstand, and the initial value is a percentage to the amount of the maximum flow. For example, when the strip grade is SS400, the strip thickness is 3.0 to 4.0 mm, and the strip width is 1200 mm, the amount of the initial flow between Fl and F2 is set to 80 percent of the maximum flow, the amount of
the initial flow between F2 and F3 to 70 percent of that of the maximum flow, the amount of the initial flow between F3 and F4 to 50 percent of the maximum flow, and the amount of the initial flow between F4 and F5 to 0 percent of the maximum flow, respectively. Such contents of the standard flow pattern table 17 are obtained through simulation or actual rolling results so that an actual FDT becomes approximately identical to the target temperature under the initial strip speed and an FET assumed at the top end of the strip, and that a desired temperature decrease pattern accompanied by rolling is obtained in each stand.
Referring to Fig. 5, the flow of operations in preset control performed by the preset means 14 is illustrated. The preset control by the preset means 14 includes steps Sll to S16. At step Sll, a target temperature is acquired from the target temperature table 15 and an initial speed is acquired from the speed table 16. At step S12, a standard flow pattern is acquired from the standard flow pattern table 17. At step S13, calculations predicting an FDT using a strip temperature prediction model 18 are performed under the conditions acquired at step Sll or S12. In the strip temperature prediction model 18 predicting the FDT, it is necessary to perform calculations in which an FET (assumed FET) which is assumed for a strip which is from now on to be rolled by the finishing mill 2 is used as an initial value, and a variety of factors
such as heat radiation from a strip, convection heat conduction, processing heat generation accompanied by plastic deformation of rolling, contact conductive heat loss when a strip makes contact with rolling rolls, frictional heat generation by friction of a strip and the rolling rolls 4, or temperature drop in response to interstand cooling are expressed as numerical formulas and integrated. Respective calculation formulas have been studied in various ways and are described in detail, for example, in "Theories and Practical Applications of Strip Rolling" (The Iron And Steel Institute Of Japan; 1984) . As an example, a calculation formula of heat transfer coefficient by heat radiation is expressed as the following formula
(Formula Removed)
In this formula, a is the Stefan-Boltzmann constant (=4.88), s is a radiation ratio, Ta is an air temperature (°C), and Tsu is a strip surface temperature (°C) .
The strip is deprived of heat as represented by the formula (1) when the strip is moving between stands. In the case of cooling the strip, the strip is deprived of heat corresponding to an amount of a cooling spray flow as represented by a relational expression described, for example, in "Theories and Practical Applications of Strip Rolling." The total
amount of heat lost or gained by the respective factors is substituted with a heat transfer coefficient, and the amount of heat coming from and going to the strip during a predetermined period A is calculated. Based on a strip temperature before a lapse of A, the transfer amount of heat during A period is added or subtracted in accordance with the following formula (2) .
(Formula Removed)
In this formula, Tn is a present strip
temperature, Tn-1 is a strip temperature before A, ht is a heat transfer coefficient of strip top surface, hb is a heat transfer coefficient of strip bottom surface, p is a strip density, C is a specific heat of a strip, and B is a strip thickness.
In addition, when it is necessary to consider a heat transfer of the strip in a thickness direction, it can be calculated by solving a well-known heat equation. The heat equation is expressed by the following formula (3), and a method of calculating the difference by means of calculator is available from various documents.
(Formula Removed)
In this formula, A, is the thermal conductivity and T is the material temperature.
Such calculations are performed putting a clock on by several milliseconds during periods when the top end of the strip 3 escapes from F5 after being
bitten into Fl, whereby the FDT of the top end of the strip 3 is calculated.
Returning to Fig. 5, at step S14, a determination is made as to whether or not the FDT falls within a predetermined range (±a) of the target temperature. If it is higher than the target temperature, an operation of increasing the amount of the interstand cooling spray flow is performed, while if it is lower than the target temperature, an operation of decreasing the amount of the interstand cooling spray flow is performed. In other cases, the amount of the interstand cooling spray flow is maintained. The flow amount increase/decrease operation is generally performed by
increasing/decreasing the amount of the cooling spray flow in each interstand in a predetermined proportion, and if necessary, a method of increasing/decreasing the amount of the cooling spray flow in a particular stand may be used.
At step S15, a determination is made as to a termination condition. The event that the FDT falls within the predetermined range of the target temperature may be used as the termination condition, and the number of calculations repeated at step S13 or S14 may be applied to the termination condition.
At step S16, an acceleration factor for
accelerating the strip 3 to the normal speed defined in the speed table 16 is determined, and a speed pattern
of the strip 3 is settled. The acceleration factor Vr may be preliminarily defined as a constant and may be calculated by the following formula (4) based on an FET drop rate FETr from the top end of the strip 3. Vr=(∂V/dFDT) • (∂FDT/dFET) -AFETr .... (4) In this formula, (∂V/∂FDT) and (∂FDT/∂FET) are influence coefficients used in the dynamic control, description of which will be provided later. By the above calculations, the amount of the preset control cooling spray flow of each of the interstand cooling units 7a to 7d is determined for a strip which is from now on to be rolled by the finishing mill 2.
Next, a description of the dynamic control means 12 will now be provided. As described above, the dynamic control means 12 performs dynamic control for acquiring under a real time condition an actual result value such as a measurement temperature on the finishing mill delivery strip temperature gauge 6 during periods when the strip 3 is cooled by the interstand cooling unit 7 while being rolled by the finishing mill 2 to thereby change the amount of the cooling spray flow. That is, the dynamic control means 12 functions to more increase the FDT control precision (temperature precision) by performing the dynamic control that changes under a real time condition the amount of the preset control cooling spray flow output from the preset control means 11 based on an actual measurement FET (an FET detected by the finishing mill
entry strip temperature gauge 5 for the strip 3 under rolling) , an actual measurement strip speed (a strip speed calculated for the strip 3 under rolling from a rotation speed of the rolling rolls 4 of F5), and an actual measurement FDT (an FDT detected by the finishing mill delivery strip temperature gauge 6 for the strip 3 under rolling).
To realize such a function, the dynamic control means 12 is provided with a finishing mill entry strip temperature deviation correction means 21, a speed deviation correction means 22, a finishing mill delivery strip temperature deviation correction means 23, and a dynamic control output generation means 24. More specifically, such a dynamic control means 12 has a configuration as illustrated in Fig. 6. In the example of Fig. 6, in addition to the above respective functional portions, the dynamic control means 12 is further provided with an influence coefficient table 25, a feedback control activation timing generation means 26, a feedback gain selection means 27, and a tracking means 28. A detailed description of each of these elements will be provided herein below.
First, a description of the influence
coefficient table 25 will be provided. The influence coefficient table 25 is a table storing an influence coefficient used in calculation performed in each of the finishing mill entry strip temperature deviation correction means 21, the speed deviation correction
means 22, and the finishing mill delivery strip temperature deviation correction means 23, and includes a first influence coefficient table 25a storing the influence on the FDT, of a change in the amount of the cooling spray flow, a second influence coefficient table 25b storing the influence on the FDT, of a change in the FET, and a third influence coefficient table 25c storing the influence on the FDT, of a change in the strip speed on the last stand delivery side (F5).
Referring to Fig. 7, an example configuration of the first influence coefficient table 25a is illustrated. In the first influence coefficient table 25a of this example, ∂FDT/∂Q (°C), which is a numerical value corresponding to a change amount of FDT when the amount of the cooling spray flow is changed by a unit amount, is classified and stored corresponding to a strip grade, a strip thickness after rolling, and a stand. That is, referring to the first influence coefficient table 25a, for example, when the strip grade is a carbon steel (SS400) and the strip thickness is 2 mm or less, the ∂FDT/∂Q between Fl and F2 is 0.1°C, which indicates that the FDT increases or decreases by 0.1°C when the amount of the cooling spray flow is increased or decreased by a unit amount. Moreover, a strip speed on a delivery side of the finishing mill (hereinafter, appropriately referred to as "finishing mill delivery speed") may be added as the classification item.
Referring to Fig. 8, an example configuration of the second influence coefficient table 25b is illustrated. In the second influence coefficient table 25b of this example, ∂FDT/∂FET, which is a numerical value corresponding to a change amount of FDT when the FET measured by the finishing mill entry strip temperature gauge 5 is increased or decreased by 1°C, is classified and stored corresponding to a strip grade, a finishing mill delivery speed, and a strip thickness on a delivery side of the finishing mill (hereinafter, appropriately referred to as a finishing mill delivery thickness). That is, referring to the second influence coefficient table 25b, for example, when the strip grade is a carbon steel (SS400), the strip speed on F5 delivery side is 400 mpm or less, and the strip thickness is 2 mm or less, the dFDT/dFET is 0.02°C, which indicates that the FDT increases or decreases by 0.02°C when the measured value of the FET is increased or decreased by 1°C. Moreover, the table also indicates that the value of 3FDT/5FET increases as the finishing strip thickness increases; for example, when the strip speed on F5 delivery side is 400 mpm or less and the strip thickness is 7 mm or more, it indicates that 0.56°C change in the FDT corresponds to 1°C change in the FET.
Referring to Fig. 9, an example configuration of the third influence coefficient table 25c is illustrated. In the third influence coefficient table
25c of this example, ∂FDT/∂V, which is a numerical value corresponding to a change amount of FDT when the strip speed is increased or decreased by 1 mpm, is classified and stored corresponding to a strip grade, a finishing mill delivery speed, and a finishing mill delivery thickness. That is, referring to the third influence coefficient table 25c, for example, when the strip grade is a carbon steel (SS400), the strip speed on F5 delivery side is 400 mpm or less, and the strip thickness is 2 mm or less, the value of ∂FDT/∂V is 0.06°C, which indicates that 0.06°C change in the FDT corresponds to 1 mpm change in the strip speed.
Next, a description of the finishing mill entry strip temperature deviation correction means 21 will be provided herein below. The finishing mill entry strip temperature deviation correction means 21 is activated at regular intervals, and performs feedforward control (hereinafter, appropriately referred to as "FET-FF control" or "FET-FF") on the FET in order to correct a deviation between the actual measurement FET obtained from the finishing mill entry strip temperature gauge 5 and the assumed FET in the preset control process. That is, the FET deviation correction means 21 calculates an amount of a cooling spray flow capable of suppressing the influence on the FDT in relation to the deviation between the assumed FET in the preset control process and the actual measurement FET measured by the finishing mill entry
strip temperature gauge 5, and outputs the calculated amount of the cooling spray flow as a cooling command change amount ΔQi to each of the interstand cooling unit 7a to 7d. Here, Δq1 is expressed by the following formula (5).
(Formula Removed)
In this formula, Δq11 is a cooling spray flow change amount between Fl and F2, Δq12 is a cooling spray flow change amount between F2 and F.3, Δq13 is a cooling spray flow change amount between F3 and F4, and Aqi4 is a cooling spray flow change amount between F4 and F5.
Specifically, a deviation AFET between an assumed FET and an actual measurement FET is acquired, and any one of the interstand cooling units 7a to 7d is selected for compensating the influence of AFET, and thereafter, the influence coefficients (∂FDT/∂Q) and (∂FDT/∂FET) of a class corresponding to a present state are acquired from the first influence coefficient table 25a and the second influence coefficient table 25b, and a cooling spray flow change amount of a corresponding interstand (a change amount of a cooling spray flow of a corresponding interstand cooling unit 7) is calculated by the following formula (6).
(Formula Removed)
In this formula, Δq1i is a cooling spray flow change amount between FI and FI+I by FET-FF, GI is a constant (FET-FF gain), (∂FDT/∂Q)i is an influence
coefficient of a corresponding class extracted from the first influence coefficient table 25a in relation to the cooling spray flow change amount between FI and FI+I, and (∂FDT/∂FET) is an influence coefficient of a corresponding class extracted from the second influence coefficient table 25b.
Although the stand for compensating the AFET is generally selected preferentially from the entry side stand depending on whether the amount of the cooling spray flow will be changed or not, a selection method in which the stand is selected preferentially from the delivery side stand may be considered.
Next, a description of the speed deviation correction means 22 will be provided herein below. Similarly, the speed deviation correction means 22 is activated at regular intervals, and performs feedforward control (hereinafter, appropriately referred to as "V-FF control" or "V-FF") on the strip speed deviation in order to correct the strip speed deviation between the actual measurement strip speed and the assumed strip speed which is assumed from the speed table 16 during calculations for the preset control. That is, the speed deviation correction means 22 calculates an amount of a cooling spray flow capable of suppressing the influence on the FDT in relation to the deviation between the assumed strip speed in the preset control process and the actual measurement strip speed, and outputs the calculated amount of the cooling
spray flow as a cooling command change amount ΔQ2 to each of the interstand cooling unit 7a to 7d. Here, ΔQ2 is expressed by the following formula (7).
(Formula Removed)
In this formula, Aq2i is a cooling spray flow change amount between Fl and F2, Aq22 is a cooling spray flow change amount between F2 and F3, Aq23 is a cooling spray flow change amount between F3 and F4, and Aq24 is a cooling spray flow change amount between F4 and F5.
Specifically, a deviation AV between an assumed strip speed and an actual measurement strip speed is acquired, and any one of the interstand cooling units 7a to 7d is selected for compensating the influence of AV, and thereafter, the influence coefficients (∂FDT/∂Q) and (∂FDT/∂V) of a class corresponding to a present state are acquired from the first influence coefficient table 25a and the third influence coefficient table 25c, and a cooling spray flow change amount of a corresponding interstand is calculated by the following formula (8).
(Formula Removed)
In this formula, Aq2i is a cooling spray flow change amount between Fi_ and FI+I by V-FF, G2 is a constant (V-FF control gain), and (∂FDT/∂V) is an influence coefficient of a corresponding class extracted from the third influence coefficient table 25c.
Similarly, although the stand for
compensating the AV is selected preferentially from the entry side stand depending on whether the amount of the cooling spray flow will be changed or not, a selection method in which the stand is selected preferentially from the delivery side stand may be considered.
Next, a description of the finishing mill delivery strip temperature deviation correction means 23 will be provided herein below. Similarly, the FDT deviation correction means 23 is activated by the feedback control activation timing generation means 26, and performs feedback control (hereinafter, appropriately referred to as "FDT-FB control" or "FDT-FB") on the FDT in order to correct a deviation between the actual measurement FDT and the target temperature. That is, the FDT deviation correction means 23 calculates an amount of a cooling spray flow capable of decreasing the difference between the target temperature and the actual measurement FDT, and outputs the calculated amount of the cooling spray flow as a cooling command change amount ΔQ3 to each of the interstand cooling unit 7a to 7d. Here, ΔQ3 is expressed by the following formula (9).
(Formula Removed)
In this formula, Aq3i is a cooling spray flow change amount between Fl and F2, Δq32 is a cooling spray flow change amount between F2 and F3, Δq33 is a cooling spray flow change amount between F3 and F4, and Δq34 is
a cooling spray flow change amount between F4 and F5.
Specifically, a deviation ΔFDT between an actual measurement FDT and a target temperature is acquired, and any one of the interstand cooling units 7a to 7d is selected for compensating the AFDT, and thereafter, the influence coefficient (∂FDT/∂Q) of a class corresponding to a present state is acquired from the first influence coefficient table 25a, and a cooling spray flow change amount of a corresponding interstand is calculated by the following formula (10).
(Formula Removed)
In this formula, Δq3i is a cooling spray flow change amount between F± and Fi+1 by FDT-FB and G3 is a constant (FDT-FB control gain).
The stand for compensating the AFDT is
preferably selected preferentially from the downstream stand from the viewpoint of the responsiveness and control efficiency of the feedback control. However, there is a case where cooling the strip 3 after being rolled thin may have bad influence on the shape of the strip 3. In consideration of this respect, the stand may be selected preferentially from the entry side stand while sacrificing the responsiveness of the feedback control to some degree.
Next, a description of the feedback control activation timing generation means 26 will be provided herein below. As described above, the feedback control activation timing generation means 26 generates the
activation timings of the finishing mill delivery strip temperature deviation correction means 23. The flow of operations executed by the feedback control activation timing generation means 26 is illustrated in Fig. 10. The feedback control activation timing generation means 26 is timer-activated at intervals of several hundreds of milliseconds and performs the operations of steps 321 to S26. At step S21, a rotation speed of the rolling rolls 4 is acquired. At step S22, a strip speed calculated from the rotation speed acquired at step S21 is integrated to thereby calculate a movement amount of the strip. The strip speed can be easily calculated by conversion from the rotation speed of the rolling rolls 4 through computations using well-known forward slip ratio and backward slip ratio.
At step S23, a determination is made as to whether or not a strip part corresponding to a control amount change has passed through the finishing mill delivery strip temperature gauge 6, that is, whether or not a strip part disposed right below the interstand cooling unit (any one or some of the interstand cooling units 7a to 7d) subjected to a cooling spray flow amount change has passed through the finishing mill delivery strip temperature gauge 6. Such a determination is made at timings where the amount of the interstand cooling spray flow is changed by the FDT-FB control. If the determination result of step S23 is negative, the process ends, while if the result
is positive, the flow proceeds to step S24.
At step S24, a determination is made as to whether or not a predetermined period has lapsed. Here, the predetermined period is a period corresponding to a period (usually 1 to 2 seconds) passed after a cooling spray flow amount change command has been issued to the interstand cooling unit 7 until the corresponding amount of the cooling spray flow is reflected in the cooling of the strip 3. If the determination result of step S24 is negative, the process ends, while if the result is positive, the flow proceeds to step S25.
At step S25, an activation signal is output to the finishing mill delivery strip temperature deviation correction means 23. Then, the integrated value for strip movement amount calculation is cleared at step S26 and the process ends.
Next, a description of the feedback gain selection means 27 will be provided herein below. The feedback gain selection means 27 determines the constant G3 in the formula (10) by selecting one from a plurality of gain values prepared in advance. The selection and determination is performed based on the stability of the strip speed. More specifically, when the strip speed has reached the maximum speed and transitions to a stabilized condition, it is defined to be stable, and when the strip speed is in a transitioning state (accelerating state) toward the
stabilized condition or a transitioning state (decelerating state) from the stabilized condition, it is defined to be unstable, and the gain is selected depending on the state stable or unstable. Similarly, the feedback gain selection means 27 is timer-activated at intervals of several hundreds of ms and performs the operations of steps S31 to S33 as illustrated in Fig. 11 illustrating the flow of the operations.
At step S31, the rotation speed of the rolling rolls 4 is acquired, and a determination is made as to whether or not the rotation speed has reached the maximum speed. If the rotation speed has not reached the maximum speed, the flow proceeds to step S32, and gain 1 (a first gain) is output as a FDT-FB control gain G3. On the other hand, if the rotation speed has reached the maximum speed, the flow proceeds to step S32, and gain 2 (a second gain) is output as the FDT-FB control gain G3. In general, the gain 1 is smaller than gain 2. By doing so, when the strip speed is in the course of accelerating, the FB control can be performed in a stable manner with relatively smaller gain, while after the strip speed has reached the stabilized condition and the rolling has been stabilized, the FB control can be performed with good responsiveness with larger gain.
Next, a description of the tracking means 28 will be provided herein below. The tracking means 28 acquires the rotation speed of the rolling rolls 4 and
outputs a strip top end position information for determining the operation contents of the dynamic control output generation means 24. The flow of the operations executed by the tracking means 28 is illustrated in Fig. 12. Similarly, the tracking means 28 is timer-activated at intervals of several hundreds of ms and performs the operations of steps S41 to S44. At step S41, the rotation speed of the rolling rolls 4 is acquired. At step S42, a strip speed calculated from the rotation speed acquired at step S41 is integrated to thereby calculate a movement amount of the strip. At step S43, a top end position of the strip 3 is calculated from the strip movement amount, and a determination is made based on the calculation result as to whether the top end of the strip 3 is positioned at the position of the finishing mill entry strip temperature gauge 5 or the position of the finishing mill delivery strip temperature gauge 6 and whether or not the top end of the strip 3 has escaped from the finishing last stand. At step S44, the determination result of step S43 is output to the dynamic control output generation means 24 as a status information.
Next, a description of the dynamic control output generation means 24 will be provided herein below. The dynamic control output generation means 24 generates a dynamic control command (a dynamic control output which is a command output for dynamically
controlling under a real time condition the amount of the cooling spray flow of each of the interstand cooling units la to 7d) by selectively using the output from each of the finishing mill entry strip temperature deviation correction means 21, the speed deviation correction means 22, and the finishing mill delivery strip temperature deviation correction means 23. More specifically, a control mode is determined based on information from the tracking means 28, and the output of the dynamic control means 12 is determined by switching the output from each of the finishing mill entry strip temperature deviation correction means 21, the speed deviation correction means 22, and the finishing mill delivery strip temperature deviation correction means 23 in accordance with the determination result.
Referring to Fig. 13, a flow of the operations executed by the dynamic control output generation means 24 is illustrated. In Fig. 13, the finishing mill entry strip temperature deviation correction means 21 is abbreviated to FET-FF control, the speed deviation correction means 22 to V-FF control, and the finishing mill delivery strip temperature deviation correction means 23 to FDT-FB, respectively. The dynamic control output generation means 24 is activated at regular intervals and performs the operations of steps S51 to S61.
At step S51, a control mode is determined.
Specifically, a determination is made as to whether the control mode belongs to 0, 1, or 2. Here, the control mode 0 is a state where the strip is not yet rolled, the control mode 1 is a state where the FET of the strip has been detected and the strip has entered into the finishing mill 2 but the FDT is not yet detected, and the control mode 2 is a state where the FDT has been detected for the first time but the strip has not escaped from the finishing mill 2.
When it is determined at step S51 that the control mode belongs to 0, the flow proceeds to step S52. At step S52, a determination is made as to whether or not the strip has entered into the finishing mill 2 and the FET detection has been started. When the FET detection has not been started, the process ends. On the other hand, when the FET detection has been started, the flow proceeds to step S53, where a value obtained by adding the outputs of the finishing mill entry strip temperature deviation correction means 21 and the speed deviation correction means 22 is output, and the control mode is set to 1 at step S54 and the process ends.
When it is determined at step S51 that the control mode belongs to 1, the flow proceeds to step S55. At step S55, a determination is made as to whether or not the top end of the strip has escaped from the finishing mill 2 and the FDT detection has been started. If the FDT has not been detected, the
flow proceeds to step S56, where similarly to step S53, a value obtained by adding the outputs of the finishing mill entry strip temperature deviation correction means 21 and the speed deviation correction means 22 is output, and the process ends. On the other hands, if the FDT detection has been detected, the flow proceeds to step S57, where a present output of the finishing mill entry strip temperature deviation correction means 21 is maintained (locked-on). Then, at step S58, a value obtained by adding three values of the lock-on value of the output of the finishing mill entry strip temperature deviation correction means 21, the output of the speed deviation correction means 22, and the output of the finishing mill delivery strip temperature deviation correction means 23 is output, and the control mode is set to 2 at step S59 and the process ends.
When it is determined at step S51 that the control mode belongs to 2, the flow proceeds to step S60. At step S60, a determination is made as to whether or not the strip has escaped from the finishing mill 2. If the strip has not yet escaped, the flow proceeds to step S61, where similarly to step S58, a value obtained by adding three values of the lock-on value of the output of the finishing mill entry strip temperature deviation correction means 21, the output of the speed deviation correction means 22, and the output of the finishing mill delivery strip temperature
deviation correction means 23 is output. If the strip has escaped from the finishing mill 2, the control mode is set to 0 at step S62 and the process ends. When the process ends, the dynamic control output generation means 24 waits for an entry of a next strip into the finishing mill 2 and repeats the same operations.
Referring to Fig. 14, an example output of the dynamic control output generation means 24 in one strip is illustrated with other signals. An output value Sg of the dynamic control output generation means 24 corresponds to the sum of an output value Sa of the finishing mill entry strip temperature deviation correction means 21, or a lock-on value SaL thereof, an output value Sb of the speed deviation correction means
22, and an output value Sc of the finishing mill
delivery strip temperature deviation correction means
23. The operation of the finishing mill entry strip
temperature deviation correction means 21 starts at
time tl and outputs an output value Sa. When the
finishing mill delivery strip temperature deviation
correction means 23 starts its operation at time t2,
the output of the finishing mill entry strip
temperature deviation correction means 21 is locked on
at time t3 (in this example, t3=t2), and a lock-on
value SaL which is maintained constant is output
thereafter. Then, the finishing mill delivery strip
temperature deviation correction means 23 outputs an
output value Sc which is recalculated at timings when
an FDT corresponding to the output is detected, and stops outputting the output value at t6 when the strip escapes from the finishing mill 2. During periods between time tl to time t6, the speed deviation correction means 22 repeats the operation at regular intervals. In the example of Fig. 14, a speed deviation occurs at time t4, and accordingly, the speed deviation correction means 22 starts outputting the output value Sb and stops outputting the output value Sb when the speed deviation is compensated at time t5.
Although in the present embodiment, the lock-on timings of the output of the finishing mill entry strip temperature deviation correction means 21 are set to the start timings of the FDT detection, that is, the start timings of the output of the finishing mill delivery strip temperature deviation correction means 23, the output corresponding to the first computation of the finishing mill entry strip temperature deviation correction means 21 may be locked on as it is. This is because in the case of a direct charge type mini-hot tandem rolling process, the FET variation is small in the longitudinal direction of the strip, and as long as the FET-FF control is performed only at a time point when the rolling for one strip is started, it can be said that there is no substantial effect on the precision of the FET-FF control even when the output of the FET-FF control at the rolling start time point is used thereafter. Such characteristics of the mini-hot
tandem rolling process serve as a premise of the effectiveness of the output lock-on of the finishing mill entry strip temperature deviation correction means 21.
The above-described output of the dynamic control output generation means 24, namely, the dynamic control output is added to the output from the preset control means 11 by the interstand cooling command generation means 13, whereby the interstand cooling command is generated from the interstand cooling command generation means 13 so as to be output to the interstand cooling units 7a to 7d.
Next, a description of a second embodiment according to the invention will be provided. The configuration of an interstand cooling controller 31 according to a second embodiment of the present invention is illustrated in Fig. 15 in relation to a finishing mill 2 which is a control subject. The interstand cooling controller 31 according to the present embodiment has similar configuration to that of the interstand cooling controller 1 according to the first embodiment, except that the interstand cooling controller 31 is further provided with an adaptive control amount calculation means 32 and an adaptive control means 33. Therefore, descriptions will be provided mainly for the adaptive control amount calculation means 32 and the adaptive control means 33, and the same components as the interstand cooling
controller 1 will be denoted by the same reference numerals as used in Fig. 1, and redundant description thereof will be omitted. Moreover, some of the components are not illustrated in Fig. 15.
The adaptive control amount calculation means 32 and the adaptive control means 33 function to perform adaptive control. Here, the adaptive control is a control method for predicting a model error (preset control error) of the strip temperature prediction model 18 in the preset control means 11 from an actual result of the control by the dynamic control means 12 so that a prediction result of the model error is reflected in FDT prediction calculation by the strip temperature prediction model 18 in the preset control means 11. An adaptive control amount (correction temperature) is calculated based on the actual control result of the dynamic control means 12. Then, the adaptive control amount is added to the target temperature obtained from the target temperature table 15, and a resulting temperature (the target temperature from the target temperature table 15 plus the adaptive control amount) is used as the FDT target temperature.
The adaptive control amount calculation means 32 performs the operations of steps S61 to S63 as illustrated in Fig. 16 illustrating the flow of the operations. At step S61, a determination is made as to whether the tail end of the strip 3 has escaped from the last stand (F5) of the finishing mill 2. If the
tail end of the strip 3 has not yet escaped, an operation of waiting for a tail end escape event is performed. When it is determined that the tail end of the strip 3 has escaped, the flow proceeds to step S62.
At step S62, AFDT which is a difference between a target temperature and an actual measurement FDT, AFET which is a difference between an assumed FET and an actual measurement FET in the preset control process, AV which is a difference between an assumed strip speed and an actual result strip speed in the preset control process, ΔQFDT-FB which is an output of the finishing mill delivery strip temperature deviation correction means 23, ΔQpET-FR-Lock which is a lock-on value of an output of the finishing mill entry strip temperature deviation correction means 21, and AQv-FF which is an output of the speed deviation correction means 22, detected or calculated after the output of the FET-FF control is locked on, are acquired with respect to a plurality of parts of the strip 3 of which the tail end is determined to have escaped the finishing mill.
At step S63, the respective values acquired at step S62 are averaged for the plurality of parts to be reset to ΔFDT, ΔFET, ΔV, ΔQFDT-FB, ΔQFET-FR-Lock/ and ΔQv-FF, and a preset control error Cerr-eq f°r the FDT conversion is calculated by the following formula (11), which is output to the adaptive control means 33 of the preset control means 11 as the adaptive control amount,
and the process ends.
(Formula Removed)
The adaptive control means 33 corrects the target temperature by using the adaptive control amount output from the adaptive control amount calculation means 32 to thereby calculate a target temperature for FDT prediction. Specifically, the target temperature for FDT prediction is calculated as "the target temperature from the target temperature table 15 plus the adaptive control amount." Such an adaptive control means 33 performs the operations of steps S71 and S72 as illustrated in Fig. 17 illustrating the flow of the operations. At step S71, a corresponding target temperature is acquired from the target temperature table 15. At step S72, the adaptive control amount from the adaptive control amount calculation means 32 is added to the target temperature acquired at step S71 to thereby calculate the target temperature for FDT prediction, and the target temperature for FDT prediction is delivered to the preset means 14.
A preset control error of an immediately rolled strip generally has high correlation with a preset control error expected in a subsequently rolled strip. The above-described adaptive control focuses on such characteristics of the preset control error, and by performing the adaptive control, it is possible to
indirectly compensate the model error of the strip temperature prediction model 18. In this way, it is possible to reduce a control error resulting from discrepancies between the strip temperature prediction model 18 and actual cooling phenomenon, thereby enabling more precise control.
Although the present invention has been described with respect to embodiments thereof, it should be appreciated that these embodiments are merely representative examples, and that the present invention may be embodied in various forms without departing from the spirit and scope thereof.
CLAIMS:
1. An interstand cooling controller for a finishing mill which is provided with a plurality of stands, an interstand cooling unit capable of cooling down a strip under rolling by injecting cooling water between the stands, a finishing mill entry strip temperature measurement section for measuring a finishing mill entry strip temperature which is a temperature of the strip on an entry side of the finishing mill, and a finishing mill delivery strip temperature measurement section for measuring a finishing mill delivery strip temperature which is a temperature of the strip on a delivery side of the finishing mill, the interstand cooling controller controlling an amount of a cooling spray flow of the interstand cooling unit so that the finishing mill delivery strip temperature becomes identical to a desired target temperature, comprising:
a preset control section provided with a strip temperature prediction model for predicting the finishing mill delivery strip temperature in relation to the cooling by means of the cooling water and configured to predict the finishing mill delivery strip temperature with the strip temperature prediction model before the strip is cooled by the cooling water and calculate an amount of a cooling spray flow of the interstand cooling unit based on the predicted finishing mill delivery strip temperature to thereby
generate a preset control output;
a dynamic control section configured to acquire a state quantity of the strip which has been cooled by the interstand cooling unit while being rolled by the finishing mill, and to calculate a change amount of the cooling spray flow based on the acquired state quantity to generate a dynamic control output; and
an interstand cooling command generation section configured to generate an interstand cooling command from the preset control output and the dynamic control output and to output the interstand cooling command to the interstand cooling unit. 2. The interstand cooling controller according to claim 1,
wherein said dynamic control section comprises:
an finishing mill entry strip temperature deviation correction section configured to generate and output a change amount of the cooling spray flow capable of suppressing influence on the finishing mill delivery strip temperature, of a deviation between an assumed finishing mill entry strip temperature which is assumed for the finishing mill entry strip temperature upon generation of the preset control output and an actual measurement finishing mill entry strip temperature obtained through actual measurement during rolling;
a speed deviation correction section
configured to generate and output a change amount of the cooling spray flow capable of suppressing the influence on the finishing mill delivery strip temperature, of a deviation between an assumed strip speed which is assumed upon generation of the preset control output and an actual measurement strip speed obtained through actual measurement during rolling;
an finishing mill delivery strip temperature deviation correction section configured to generate and output a change amount of the cooling spray flow for reducing the deviation between the target temperature and an actual measurement finishing mill delivery strip temperature obtained through actual measurement during rolling; and
a dynamic control output generation section configured to generate a dynamic control output by selectively using respective outputs of the finishing mill entry strip temperature deviation correction section, the speed deviation correction section, and the finishing mill delivery strip temperature deviation correction section.
3. The interstand cooling controller according to claim 2,
wherein said dynamic control section further comprises an influence coefficient table including:
a first influence coefficient table storing the influence on the finishing mill delivery strip
temperature, of a change in the amount of the cooling spray flow;
a second influence coefficient table storing the influence on the finishing mill delivery strip temperature, of a change in the finishing mill entry strip temperature; and
a third influence coefficient table storing the influence on the finishing mill delivery strip temperature, of a change in the strip speed on the delivery side of the finishing mill, and
wherein an influence coefficient which each of said finishing mill entry strip temperature deviation correction section, said speed deviation correction section, and said finishing mill delivery strip temperature deviation correction section uses when generating the change amount of the cooling spray flow is acquired from said influence coefficient table. 4. The interstand cooling controller according to claim 2 or 3,
wherein said dynamic control section is capable of holding an output of said finishing mill entry strip temperature deviation correction section at predetermined timings so that a lock-on value is thereafter maintained to be constant, and
wherein said holding timings are set to a time point when an output corresponding to the first computation for generating the change amount is performed in the finishing mill entry strip temperature
deviation correction section, or to a time point when said finishing mill delivery strip temperature detection is started.
5. The interstand cooling controller according to claim 4, wherein said dynamic control output generation section is configured to selectively use the output of each of said finishing mill entry strip temperature deviation correction section, said speed deviation correction section, and said finishing mill delivery strip temperature deviation correction section, based on position information of the strip under rolling, so that in a state where the finishing mill entry strip temperature has been detected for the strip and the strip has entered into the finishing mill but the finishing mill delivery strip temperature is not yet detected, a value obtained by adding the outputs of the finishing mill entry strip temperature deviation correction section and the speed deviation correction section is output, and that in a state where said finishing mill delivery strip temperature has been detected for the first time but the strip has not yet escaped from the finishing mill, a value obtained by adding the output or the lock-on value of the finishing mill entry strip temperature deviation correction section, the output of the speed deviation correction section, and the output of the finishing mill delivery strip temperature deviation correction section is output.
6. The interstand cooling controller according
to claim 2, wherein a plurality of gains is prepared to
be used in calculation for generating the change amount
of the cooling spray flow in said finishing mill
delivery strip temperature deviation correction section
so that one of the plurality of gains is selected based
on said strip speed.
7. The interstand cooling controller according
to claim 1, wherein a model error of the strip
temperature prediction model is predicted from an
actual result of the control by said dynamic control
section so that a prediction result of the model error
is reflected in the finishing mill delivery strip
temperature prediction by the strip temperature
prediction model in the preset control section.
8. The interstand cooling controller according
to claim 7, further comprising:
an adaptive control amount calculation section capable of calculating an adaptive control amount based on a deviation between the target temperature and the actual measurement finishing mill delivery strip temperature, a deviation between the assumed finishing mill entry strip temperature and the actual measurement finishing mill entry strip temperature, a deviation between the assumed strip speed and the actual measurement strip speed, the output of the finishing mill delivery strip temperature deviation correction section, the lock-on value of the
output of the finishing mill entry strip temperature deviation correction section, and the output of the speed deviation correction section, which are detected or calculated with respect to a plurality of parts of the strip of which the tail end is determined to have escaped the finishing mill, and
an adaptive control section capable of correcting the target temperature with the adaptive control amount of said adaptive control amount calculation section to thereby calculating a target temperature for finishing mill delivery strip temperature prediction,
wherein the target temperature for finishing mill delivery strip temperature prediction calculated by said adaptive control section is used when predicting the finishing mill delivery strip temperature by the strip temperature prediction model. 9. An interstand cooling control method for a finishing mill which is provided with a plurality of stands, an interstand cooling unit capable of cooling down a strip under rolling by injecting cooling water between the stands, a finishing mill entry strip temperature measurement section for measuring a finishing mill entry strip temperature which is a temperature of the strip on an entry side of the finishing mill, and a finishing mill delivery strip temperature measurement section for measuring a finishing mill delivery strip temperature which is a
temperature of the strip on a delivery side of the finishing mill, the interstand cooling control method controlling an amount of a cooling spray flow of the interstand cooling unit so that the finishing mill delivery strip temperature becomes identical to a desired target temperature, wherein:
the method is configured to perform a control combined of preset control and dynamic control, in which the preset control predicts the finishing mill delivery strip temperature before the strip is cooled by the cooling water by using a strip temperature prediction model for predicting the finishing mill delivery strip temperature in relation to the cooling by means of the cooling water, so as to be performed with a preset control output obtained by calculating an amount of a cooling spray flow of the interstand cooling unit based on the predicted finishing mill delivery strip temperature, and in which the dynamic control acquires a state quantity of the strip which has been cooled by the interstand cooling unit while being rolled by the finishing mill, so as to be performed with a dynamic control output obtained by calculating a change amount of the cooling spray flow based on the acquired state quantity. 10. The interstand cooling control method according to claim 9,
wherein said dynamic control output includes a finishing mill entry strip temperature deviation
correction output which is a control output of a change amount of the cooling spray flow capable of suppressing the influence on the finishing mill delivery strip temperature, of a deviation between an assumed finishing mill entry strip temperature which is assumed when generating the preset control output of the finishing mill entry strip temperature and an actual measurement finishing mill entry strip temperature obtained through actual measurement during rolling, and
wherein the finishing mill entry strip temperature deviation correction output is held at predetermined timings so that a lock-on value is thereafter maintained to be constant. 11. The interstand cooling control method according to claim 10, wherein the holding timings are set to a time point when an output corresponding to the first computation for the finishing mill entry strip temperature deviation correction output is performed, or to a time point when the finishing mill delivery strip temperature detection is started.
| # | Name | Date |
|---|---|---|
| 1 | 323-del-2009-gpa.pdf | 2011-08-21 |
| 2 | 323-del-2009-form-5.pdf | 2011-08-21 |
| 3 | 323-del-2009-form-3.pdf | 2011-08-21 |
| 4 | 323-del-2009-form-2.pdf | 2011-08-21 |
| 5 | 323-del-2009-form-18.pdf | 2011-08-21 |
| 6 | 323-del-2009-form-1.pdf | 2011-08-21 |
| 7 | 323-del-2009-drawings.pdf | 2011-08-21 |
| 8 | 323-del-2009-description (complete).pdf | 2011-08-21 |
| 9 | 323-del-2009-correspondence-others.pdf | 2011-08-21 |
| 10 | 323-del-2009-claims.pdf | 2011-08-21 |
| 11 | 323-del-2009-abstract.pdf | 2011-08-21 |
| 12 | 323-del-2009-323-del-2009-Form-3-(02-01-2013).pdf | 2013-01-02 |
| 13 | 323-del-2009-323-del-2009-Correspondence Others-(02-01-2013).pdf | 2013-01-02 |
| 14 | 323-del-2009-GPA-(11-03-2016).pdf | 2016-03-11 |
| 15 | 323-del-2009-Correspondecne Others-(11-03-2016).pdf | 2016-03-11 |
| 16 | 323-DEL-2009-FER.pdf | 2016-09-22 |
| 17 | Other Patent Document [18-11-2016(online)].pdf | 2016-11-18 |
| 18 | Petition Under Rule 137 [08-03-2017(online)].pdf | 2017-03-08 |
| 19 | Other Document [08-03-2017(online)].pdf | 2017-03-08 |
| 20 | Examination Report Reply Recieved [08-03-2017(online)].pdf | 2017-03-08 |
| 21 | Description(Complete) [08-03-2017(online)].pdf_150.pdf | 2017-03-08 |
| 22 | Description(Complete) [08-03-2017(online)].pdf | 2017-03-08 |
| 23 | Correspondence [08-03-2017(online)].pdf | 2017-03-08 |
| 24 | Claims [08-03-2017(online)].pdf | 2017-03-08 |
| 25 | Abstract [08-03-2017(online)].pdf | 2017-03-08 |
| 26 | 323-DEL-2009-HearingNoticeLetter.pdf | 2018-07-24 |
| 27 | 323-DEL-2009-FORM-26 [06-08-2018(online)].pdf | 2018-08-06 |
| 28 | 323-DEL-2009-Power of Attorney-090818.pdf | 2018-08-13 |
| 29 | 323-DEL-2009-Correspondence-090818.pdf | 2018-08-13 |
| 30 | 323-DEL-2009-Written submissions and relevant documents (MANDATORY) [21-08-2018(online)].pdf | 2018-08-21 |
| 31 | 323-DEL-2009-Response to office action (Mandatory) [11-09-2018(online)].pdf | 2018-09-11 |
| 32 | 323-DEL-2009-PatentCertificate13-09-2018.pdf | 2018-09-13 |
| 33 | 323-DEL-2009-IntimationOfGrant13-09-2018.pdf | 2018-09-13 |
| 34 | 323-DEL-2009-RELEVANT DOCUMENTS [07-03-2019(online)].pdf | 2019-03-07 |
| 35 | 323-DEL-2009-RELEVANT DOCUMENTS [09-03-2020(online)].pdf | 2020-03-09 |
| 36 | 323-DEL-2009-RELEVANT DOCUMENTS [17-08-2021(online)].pdf | 2021-08-17 |
| 37 | 323-DEL-2009-RELEVANT DOCUMENTS [10-09-2022(online)].pdf | 2022-09-10 |
| 38 | 323-DEL-2009-RELEVANT DOCUMENTS [21-08-2023(online)].pdf | 2023-08-21 |
| 1 | US5289867_02-09-2016.pdf |
| 2 | US3589160_02-09-2016.pdf |