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CN109189112B - Tension roller strip steel tension slip form control method and control device - Google Patents

Tension roller strip steel tension slip form control method and control device Download PDF

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CN109189112B
CN109189112B CN201811115019.5A CN201811115019A CN109189112B CN 109189112 B CN109189112 B CN 109189112B CN 201811115019 A CN201811115019 A CN 201811115019A CN 109189112 B CN109189112 B CN 109189112B
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tension
strip steel
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CN109189112A (en
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白锐
祁学鹏
王贺彬
孙丽颖
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Liaoning University of Technology
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    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D15/00Control of mechanical force or stress; Control of mechanical pressure
    • G05D15/01Control of mechanical force or stress; Control of mechanical pressure characterised by the use of electric means
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention provides a tension sliding mode control method and a control device for tension roller strip steel, and belongs to the field of industrial automation. The method comprises the following steps: step one, modeling tension of strip steel of a tensioning roller; step two, designing a tension sliding mode control method of the tension roller strip steel; compared with the traditional PID control method, the sliding mode control method can effectively overcome the control difficulties of nonlinearity, unknown external interference and the like of the tension roller strip steel tension; the invention relates to a tension sliding mode control device for tension roller strip steel, which takes Siemens S7-300 series PLC (CPU model 315-2 DP) as a master station, takes self-CPU distributed I/O ET200S (CPU model IM 151-7) as a slave station, and communicates with the master station through Profibus-DP field buses. The hardware design and the software design of the control device are completed.

Description

Tension roller strip steel tension slip form control method and control device
Technical Field
The invention designs a tension sliding mode control method and a control device for a tension roller strip steel, and belongs to the field of industrial automation.
Background
In the metallurgical production process, the accurate control of the tension of the strip steel of the tension roller is a key factor for ensuring the quality of the strip steel product and improving the production efficiency of the strip steel. Most of the existing strip steel tension control devices adopt PID control algorithm, so that the control precision is low and the control effect is not ideal.
Disclosure of Invention
The invention aims to design a sliding mode control method for tension of a tension roller strip steel, and compared with a traditional PID control method, the sliding mode control method can effectively overcome control difficulties such as nonlinearity of the tension roller strip steel tension, unknown external interference and the like; the invention also aims to design a tension roller strip steel tension sliding mode control device capable of realizing the sliding mode control method, which takes Siemens S7-300 series PLC (CPU model 315-2 DP) as a master station, and completes hardware design and software design of the control device.
In order to realize the development of an advanced control system for the tension of the strip steel of the tension roller, a state space model for the tension control of the strip steel of the tension roller is firstly established, a PLC sliding mode controller based on a sliding mode variable structure control theory is developed by utilizing an industrial automatic control architecture of Siemens company, and finally a strip steel tension sliding mode control device consisting of a PLC control system and an upper computer monitoring system is established.
The invention is realized by the following technical scheme:
a tension sliding mode control method of tension roller strip steel comprises the following steps:
step one, tension modeling of strip steel of tension roller
(1) Tensioning roller structure
According to the sequence of the strip steel passing through each roller, each driving roller is defined as No. 1, no. 2, no. 3 and No. 4 respectively; wherein the No. 1 roller and the No. 4 roller rotate anticlockwise, the No. 2 roller and the No. 3 roller rotate clockwise, v 0 For the upstream strip speed of the tensioning roller v 1 、v 2 、v 3 、v 4 The rotation linear speeds of the driving rollers are respectively; wherein v is 0 The size of (2) is determined by the upstream production process, detected by a measuring tool and is a known parameter; the magnitude of vi (i=1, …, 4) is controlled by the motors of the respective driving rollers, and is a variable parameter; f (F) 1 To tension the strip at the entrance of the tensioning roller, F 2 、F 3 And F 4 Respectively the strip steel tension between the driving rollers, F 5 Tension at the strip steel outlet of the tensioning roller; fi (i=1, …, 4) is adjusted by adjusting the rotational speed of the 4 driving rolls, the downstream strip tension F 5 Determined by downstream production equipment; l (L) 1 For the length of the strip at the inlet of the tension roller strip, L 2 、L 3 And L 4 The length of the strip steel between the driving rollers is respectively the fixed known parameter;
(2) Tension roller strip steel model establishment
In the tension control process of the tension roller strip steel, the electromagnetic moment T of each driving roller motor is regulated e,i (i=1, …, 4) to adjust the rotation speed of each roller, thereby controlling the tension F of the strip i (i=1, …, 4); definition T e,i For model input variables, define F i As the output variable of the model, the motor motion equation of the ith driving roller can be obtained as follows:
Figure BDA0001810323510000021
in the formula (1), J i For moment of inertia, ω, of the ith driving roller i For the angular velocity of the ith driving roller, T L,i The load moment of the ith driving roller motor; obtaining T L,i The mathematical relation formula between the tension of the same strip steel is as follows:
T L,i =(F i -F i+1 )×R i ,i=1,2,3,4 (2)
wherein R is i Is the radius of the ith driving roller;
the generation of the strip steel tension is caused by strip steel deformation, and in the running process of the tensioning rollers, the strip steel generates second flow difference due to the speed difference between the driving rollers, so that the strip steel tension is generated; the mathematical relation between the tension of the strip steel and the second flow difference of the strip steel is obtained as follows:
Figure BDA0001810323510000022
wherein k is i The elastic coefficient of the strip steel is calculated as follows:
Figure BDA0001810323510000031
wherein E is the elastic modulus of the strip steel, S is the cross-sectional area of the strip steel;
assuming that the linear speed of the driving roller is consistent with the speed of the strip steel attached to the surface of the roller body, the conversion relation between the flow speed of the strip steel in the tensioning roller and the angular speed of the driving roller is obtained by an angular speed linear speed conversion formula:
v i =ω i ×R i ,i=1,2,3,4 (5)
the tension dynamic mechanism model of the tension roller strip steel obtained by the combined type (1) - (5) is as follows:
Figure BDA0001810323510000032
deducing a state space expression of tension control of the strip steel of the tensioning roller according to a dynamic mechanism model of the tension control of the strip steel of the tensioning roller;
the state space vector x (t) is:
x(t)=[x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 ] T =[F 1 ω 1 F 2 ω 2 F 3 ω 3 F 4 ω 4 ] T
taking the control variable u (t) as: u (t) = [ u ] 1 u 2 u 3 u 4 ] T =[T e,1 T e,2 T e,3 T e,4 ] T
The output variable y (t) is: y (t) = [ y ] 1 y 2 y 3 y 4 ] T =[F 1 F 2 F 3 F 4 ] T
The state space expression for tension control of the tension roller strip steel can be obtained according to the formula (6) as follows:
Figure BDA0001810323510000041
in the formula (7), A, B, T is a state matrix, an input matrix and an output matrix of the system, and d is a known constant interference vector;
wherein:
Figure BDA0001810323510000042
Figure BDA0001810323510000043
step two, design of tension sliding mode control method of tension roller strip steel
Order the
Figure BDA0001810323510000044
Figure BDA0001810323510000045
Figure BDA0001810323510000051
The state matrix a may be sorted as:
Figure BDA0001810323510000052
order the
Figure BDA0001810323510000053
The input matrix B and the stationary disturbance vector d may be sorted as:
Figure BDA0001810323510000054
determining a control target to enable the strip steel tension to be the same as that of the strip steel
Figure BDA0001810323510000055
Follow tension set point->
Figure BDA0001810323510000056
Defining a sliding mode function as follows:
s=CE (8)
in the formula (8), the values of the variables are respectively:
s=[s 1 s 2 s 3 s 4 ] T
Figure BDA0001810323510000061
Figure BDA0001810323510000062
wherein e 1 =y d1 -y 1 ,e 2 =y d2 -y 2 ,e 3 =y d3 -y 3 ,e 4 =y d4 -y 4 ,c 1 >0,c 2 >0,c 3 >0,c 4 >0;
The derivative of the switching function s is obtained:
Figure BDA0001810323510000063
the control amount u (x) is obtained by a constant velocity approach law method
Figure BDA0001810323510000064
Where epsilon=diag [ epsilon ] 1234 ],sgn(s)=[sgn(s 1 )sgn(s 2 )sgn(s 3 )sgn(s 4 )] T
The control amount u (x) obtained by the combined type (7) - (10) is:
Figure BDA0001810323510000065
Figure BDA0001810323510000066
Figure BDA0001810323510000067
Figure BDA0001810323510000068
taking the Liapunov function as follows:
Figure BDA0001810323510000071
wherein v=diag [1, 1];
in order to verify the stable running of the tension controller of the obtained tension roller strip steel, the method for deriving the Liapunov function by the sliding mode is combined with a selected constant-speed approach method to obtain the following steps:
Figure BDA0001810323510000072
therefore, the designed sliding mode controller is verified to ensure that the system is asymptotically stable, so that the tension of the strip steel of the tension roller follows the tension set value.
The utility model provides a tensioning roller belted steel tension slipform controlling means, includes control module and control module, control module is connected with control module, and control module gives control module with the signal transmission who receives and shows on the control module, and control module gives control module with the signal transmission who sets for, through control module control tensioning roller.
Further, the control module comprises a master station and a slave station, wherein the master station selects Siemens S7-300 series PLC, and the model of the CPU is 315-2DP; the slave station selects a distributed I/O ET200S with a CPU, the model of the CPU is IM151-7, and the master station and the slave station communicate through a Profibus-DP field bus.
Further, the monitoring module selects an Activex control integrated in WinCC software, and comprises a parameter display interface, a tension setting interface, a state monitoring interface and an alarm report interface; the state monitoring interface is used for monitoring each parameter of the tension control model of the tension roller strip steel, the parameter display interface is used for displaying parameter information of each control object in the control module in real time, and changing a tension set value of the strip steel through the tension setting interface according to production specification change of the strip steel, and simultaneously, the real-time state detection of the strip steel tension and the alarm and alarm function in the tension control process are completed.
The beneficial effects of the invention are as follows: compared with the traditional PID control method, the sliding mode control method can effectively overcome the control difficulties of nonlinearity, unknown external interference and the like of the tension roller strip steel; the invention also aims to design a tension roller strip steel tension slip-form control device capable of realizing the slip-form control method, wherein the control device selects Siemens S7-300 series PLC (CPU model 315-2 DP) as a master station, and selects self-CPU distributed I/O ET200S (CPU model IM 151-7) as a slave station, and the master station and the slave station communicate through a Profibus-DP field bus. The hardware design and the software design of the control device are completed.
Drawings
FIG. 1 is a block diagram of a control system according to the present invention.
Fig. 2 is a schematic view of the structure of the tension roller of the present invention.
FIG. 3 is a flow chart of a control procedure of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific examples.
Examples
As shown in fig. 1-3, the slip form control method of tension of the tension roller strip steel of the invention comprises the following steps:
step one, tension modeling of strip steel of tension roller
(1) Tensioning roller structure
The invention takes a 4-shaft tensioning roller consisting of 4 driving rollers as an example to establish a tensioning roller strip steel tension control model. According to the sequence of the strip steel passing through each roller, each driving roller is defined as No. 1, no. 2, no. 3 and No. 4. Wherein the No. 1 roller and the No. 4 roller rotate anticlockwise, the No. 2 roller and the No. 3 roller rotate clockwise, v 0 For the upstream strip speed of the tensioning roller v 1 、v 2 、v 3 、v 4 Respectively are each driving rollerIs provided. Wherein v is 0 The size of (2) is determined by the upstream production process, can be detected by a measuring tool and is a known parameter; the magnitude of vi (i=1, …, 4) can be controlled by the motors of the respective driving rollers as variable parameters. F (F) 1 To tension the strip at the entrance of the tensioning roller, F 2 、F 3 And F 4 Respectively the strip steel tension between the driving rollers, F 5 Is the tension at the exit of the tension roller strip. Wherein Fi (i=1, …, 4) can be adjusted by adjusting the rotational speed of 4 driving rolls, the downstream strip tension F 5 Determined by downstream production equipment. L (L) 1 For the length of the strip at the inlet of the tension roller strip, L 2 、L 3 And L 4 The length of the strip steel between the driving rollers is respectively defined as a fixed known parameter when the annealing unit is designed.
(2) Tension roller strip steel model establishment
In the tension control process of the tension roller strip steel, the electromagnetic moment T of each driving roller motor is regulated e,i (i=1, …, 4) to adjust the rotation speed of each roller, thereby controlling the tension F of the strip i (i=1, …, 4). Definition T e,i For model input variables, define F i As the output variable of the model, the 4-axis tension roller strip steel tension control model is easy to see and is a typical multi-input multi-output model. Analyzing a tension control mechanism of the strip steel of the tension roller, neglecting the viscosity factor in the tension roller and the sliding between the strip steel driving rollers, and aiming at the ith driving roller, obtaining the motor motion equation of the ith driving roller as follows:
Figure BDA0001810323510000091
in the formula (1), J i For moment of inertia, ω, of the ith driving roller i For the angular velocity of the ith driving roller, T L,i Is the load moment of the ith driving roller motor. Ignoring minor factors such as dead weight of the strip steel and longitudinal pressure of the tension meter, T can be obtained L,i The mathematical relation formula between the tension of the same strip steel is as follows:
T L,i =(F i -F i+1 )×R i ,i=1,2,3,4 (2)
wherein R is i Is the radius of the ith driving roller.
The tension of the strip steel is generated by deformation of the strip steel, and in the running process of the tensioning rollers, the strip steel generates second flow difference due to the speed difference between the driving rollers, so that the tension of the strip steel is generated. The mathematical relation between the strip steel tension and the strip steel second flow difference can be obtained by neglecting the time delay in the strip steel deformation process, and the mathematical relation is as follows:
Figure BDA0001810323510000092
wherein k is i The elastic coefficient of the strip steel is calculated as follows:
Figure BDA0001810323510000093
wherein E is the elastic modulus of the strip steel, and S is the cross-sectional area of the strip steel.
Assuming that the linear speed of the driving roller is consistent with the speed of the strip steel attached to the surface of the roller body, the conversion relation between the flow speed of the strip steel in the tensioning roller and the angular speed of the driving roller is obtained by an angular speed linear speed conversion formula:
v i =ω i ×R i ,i=1,2,3,4 (5)
the tension dynamic mechanism model of the tension roller strip steel obtained by the combined type (1) - (5) is as follows:
Figure BDA0001810323510000101
and deducing a state space expression of tension control of the strip steel of the tensioning roller according to a dynamic mechanism model of the tension control of the strip steel of the tensioning roller.
The state space vector x (t) is:
x(t)=[x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 ] T =[F 1 ω 1 F 2 ω 2 F 3 ω 3 F 4 ω 4 ] T
taking the control variable u (t) as:
u(t)=[u 1 u 2 u 3 u 4 ] T =[T e,1 T e,2 T e,3 T e,4 ] T
the output variable y (t) is:
y(t)=[y 1 y 2 y 3 y 4 ] T =[F 1 F 2 F 3 F 4 ] T
the state space expression for tension control of the tension roller strip steel can be obtained according to the formula (6) as follows:
Figure BDA0001810323510000102
in equation (7), A, B, T is a state matrix, an input matrix, and an output matrix of the system, and d is a known constant interference vector.
Figure BDA0001810323510000111
Figure BDA0001810323510000112
Step two, design of tension sliding mode control method of tension roller strip steel
Order the
Figure BDA0001810323510000113
Figure BDA0001810323510000114
Figure BDA0001810323510000115
The state matrix a may be sorted as:
Figure BDA0001810323510000121
order the
Figure BDA0001810323510000122
The input matrix B and the stationary disturbance vector d may be sorted as:
Figure BDA0001810323510000123
determining a control target to enable the strip steel tension to be the same as that of the strip steel
Figure BDA0001810323510000124
Follow tension set point->
Figure BDA0001810323510000125
Defining a sliding mode function as follows:
s=CE (8)
in the formula (8), the values of the variables are respectively:
s=[s 1 s 2 s 3 s 4 ] T
Figure BDA0001810323510000126
Figure BDA0001810323510000131
wherein e 1 =y d1 -y 1 ,e 2 =y d2 -y 2 ,e 3 =y d3 -y 3 ,e 4 =y d4 -y 4 ,c 1 >0,c 2 >0,c 3 >0,c 4 >0;
The derivative of the switching function s is obtained:
Figure BDA0001810323510000132
the control amount u (x) is obtained by a constant velocity approach law method
Figure BDA0001810323510000133
Where epsilon=diag [ epsilon ] 1234 ],sgn(s)=[sgn(s 1 )sgn(s 2 )sgn(s 3 )sgn(s 4 )] T
The control amount u (x) obtained by the combined type (7) - (10) is:
Figure BDA0001810323510000134
Figure BDA0001810323510000135
Figure BDA0001810323510000136
Figure BDA0001810323510000137
taking the Liapunov function as follows:
Figure BDA0001810323510000138
wherein v=diag [1, 1].
In order to verify the stable running of the tension controller of the obtained tension roller strip steel, the method for deriving the Liapunov function by the sliding mode is combined with a selected constant-speed approach method to obtain the following steps:
Figure BDA0001810323510000141
therefore, the designed sliding mode controller is verified to ensure that the system is asymptotically stable, so that the tension of the strip steel of the tension roller follows the tension set value.
1-3, a sliding mode control scheme for tension of the strip steel of the tension roller is completed by using a PLC in a control system, and a sliding mode control algorithm is realized by using a PLC ladder diagram and a statement list language. The controller adopts a master-slave station structure, meets the centralized management, decentralized control and distributed control requirements of complex metallurgical industry, fully utilizes the program function block function of the Siemens PLC in the development of a sliding mode control program, and completes the process control of strip steel tension. The control signal and the feedback signal are transmitted in real time between the controller and the tensioning roller system, so that the system is kept in a state of dynamic response and stable control.
The monitoring system displays the parameter information of each main control object in the control system in real time by using the development software WinCC of the Siemens upper computer monitoring system, changes the tension set value of the strip steel according to the production specification change of the strip steel, and simultaneously completes the functions of real-time state detection of the tension of the strip steel, alarm and alarm in the tension control process, and the like. The method has the advantages that an Activex control integrated in WinCC software is fully utilized in the design of the monitoring interface, the monitoring interface is concise and attractive and convenient to operate on the basis of good function perfection of the whole monitoring system, and finally, a bottom layer driving program is called and configured to realize mutual communication of an upper computer, a PLC and a tensioning roller.
The tension roller strip steel tension control model comprises 8 state variables, namely the tension of each section of strip steel and the angular speed of each driving roller. The system contains 4 control variables, the values of which are provided by the PLC slipform controller in the control. The system contains 4 strip tension outputs and is provided as feedback signals to the PLC controller in the control system. The control objective of the whole tension control system is to enable the strip tension process value to stably follow the strip tension set value, and enable the control system to maintain good dynamic characteristics.
According to the control requirement of the control system, the software program development of the control system is designed to adopt a distributed program structure, different organization blocks and functional blocks are respectively selected to realize the control function of each part, and the control function is sequentially and successively called in the main organization block OB1 to meet the control requirement. In the development of a control program, the design and implementation of a sliding mode control algorithm of a PLC controller is a key part of the whole software design. Before programming, firstly, determining an I/O interface of a system, and distributing the I/O addresses of the system in a hardware configuration part according to a physical wiring mode of a control system and a working mode of each input/output module, wherein the obtained I/O distributed addresses of the system are shown in a table 1:
TABLE 1 control System I/O Address assignment Table
Figure BDA0001810323510000151
The operation flow chart of the PLC sliding mode control program is shown in fig. 3: when the PLC is in a working state, the information exchange with the control object is realized by accessing a process image storage area of the CPU system memory. The process mapping area is mainly divided into two parts, namely a process mapping input table and a process influence output table, wherein the process mapping input table is used for storing signal states of input modules, the process influence output table is used for temporarily storing output values of program execution results, and the output values can be transmitted to an actual output module after a scanning period is finished. And (3) using the circulation interrupt tissue block to complete the calculation of the error and the change rate thereof in the tension control process, sending the error and the change rate thereof to a sliding mode function for calculation, and obtaining a control signal u.
The tension roller strip steel tension control monitoring computer monitoring interface mainly comprises 4 parts, namely a state monitoring interface, a parameter display interface, a tension setting interface and an alarm report interface.
And each parameter of the tension roller strip steel tension control model can be monitored in the state monitoring interface, wherein the parameters comprise the rotation angle of each driving roller, the input torque of a control system, the set value of strip steel tension and a process value. Meanwhile, the state condition of the strip steel tension control process can be displayed in the state monitoring interface, when the strip steel tension is in a normal control state, the central shaft of the driving roller is green, and when the strip steel tension control is abnormal, the central shaft of the driving roller is red.
Entering a parameter display interface, wherein the parameter display interface can monitor the set value and the process value of the strip steel tension of each section, and the parameter display interface has the function of modifying the set value of the strip steel tension. And inputting a target tension set value in a column of 'please input a new strip steel tension set value' of any strip steel tension frame of the parameter display interface, and clicking a determination button to complete the modification of the strip steel tension set value. It should be noted that, since the adjustment of the set values of the strip tension in each section of the tension roller strip tension control model must satisfy a certain constraint condition, the resetting of the strip tension in the setting interface of which strip tension in the parameter display interface affects the overall strip tension control system.

Claims (4)

1. The tension sliding mode control method for the tension roller strip steel is characterized by comprising the following steps of:
step one, tension modeling of strip steel of tension roller
(1) Tensioning roller structure
According to the sequence of the strip steel passing through each roller, each driving roller is defined as No. 1, no. 2, no. 3 and No. 4 respectively; wherein the No. 1 roller and the No. 4 roller rotate anticlockwise, the No. 2 roller and the No. 3 roller rotate clockwise, v 0 For the upstream strip speed of the tensioning roller v 1 、v 2 、v 3 、v 4 The rotation linear speeds of the driving rollers are respectively; wherein v is 0 The size of (2) is determined by the upstream production process, detected by a measuring tool and is a known parameter; the magnitude of vi (i=1, …, 4) is controlled by the motors of the respective driving rollers, and is a variable parameter; f (F) 1 To tension the strip at the entrance of the tensioning roller, F 2 、F 3 And F 4 Respectively the strip steel tension between the driving rollers, F 5 Tension at the strip steel outlet of the tensioning roller; fi (i=1, …, 4) is adjusted by adjusting the rotational speed of the 4 driving rolls, the downstream strip tension F 5 Determined by downstream production equipment; l (L) 1 To be tensionedLength of strip at entrance of roll strip L 2 、L 3 And L 4 The length of the strip steel between the driving rollers is respectively the fixed known parameter;
(2) Tension roller strip steel model establishment
In the tension control process of the tension roller strip steel, the electromagnetic moment T of each driving roller motor is regulated e,i (i=1, …, 4) to adjust the rotation speed of each roller, thereby controlling the tension F of the strip i (i=1, …, 4); definition T e,i For model input variables, define F i As the output variable of the model, the motor motion equation of the ith driving roller can be obtained as follows:
Figure FDA0004149098380000011
in the formula (1), J i For moment of inertia, ω, of the ith driving roller i For the angular velocity of the ith driving roller, T L,i The load moment of the ith driving roller motor; obtaining T L,i The mathematical relation formula between the tension of the same strip steel is as follows:
T L,i =(F i -F i+1 )×R i ,i=1,2,3,4 (2)
wherein R is i Is the radius of the ith driving roller;
the generation of the strip steel tension is caused by strip steel deformation, and in the running process of the tensioning rollers, the strip steel generates second flow difference due to the speed difference between the driving rollers, so that the strip steel tension is generated; the mathematical relation between the tension of the strip steel and the second flow difference of the strip steel is obtained as follows:
Figure FDA0004149098380000021
wherein k is i The elastic coefficient of the strip steel is calculated as follows:
Figure FDA0004149098380000022
wherein E is the elastic modulus of the strip steel, S is the cross-sectional area of the strip steel;
assuming that the linear speed of the driving roller is consistent with the speed of the strip steel attached to the surface of the roller body, the conversion relation between the flow speed of the strip steel in the tensioning roller and the angular speed of the driving roller is obtained by an angular speed linear speed conversion formula:
v i =ω i ×R i ,i=1,2,3,4 (5)
the tension dynamic mechanism model of the tension roller strip steel obtained by the combined type (1) - (5) is as follows:
Figure FDA0004149098380000023
deducing a state space expression of tension control of the strip steel of the tensioning roller according to a dynamic mechanism model of the tension control of the strip steel of the tensioning roller;
the state space vector x (t) is:
x(t)=[x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 ] T =[F 1 ω 1 F 2 ω 2 F 3 ω 3 F 4 ω 4 ] T
taking the control variable u (t) as: u (t) = [ u ] 1 u 2 u 3 u 4 ] T =[T e,1 T e,2 T e,3 T e,4 ] T
The output variable y (t) is: y (t) = [ y ] 1 y 2 y 3 y 4 ] T =[F 1 F 2 F 3 F 4 ] T
The state space expression for tension control of the tension roller strip steel can be obtained according to the formula (6) as follows:
Figure FDA0004149098380000031
in the formula (7), A, B, T is a state matrix, an input matrix and an output matrix of the system, and d is a known constant interference vector;
wherein:
Figure FDA0004149098380000032
Figure FDA0004149098380000033
step two, design of tension sliding mode control method of tension roller strip steel
Order the
Figure FDA0004149098380000041
Figure FDA0004149098380000042
Figure FDA0004149098380000043
The state matrix a may be sorted as: />
Figure FDA0004149098380000044
Order the
Figure FDA0004149098380000045
The input matrix B and the stationary disturbance vector d may be sorted as:
Figure FDA0004149098380000046
determining a control target to enable the strip steel tension to be the same as that of the strip steel
Figure FDA0004149098380000047
Follow tension set point->
Figure FDA0004149098380000048
Defining a sliding mode function as follows:
s=CE (8)
in the formula (8), the values of the variables are respectively:
s=[s 1 s 2 s 3 s 4 ] T
Figure FDA0004149098380000051
Figure FDA0004149098380000052
wherein e 1 =y d1 -y 1 ,e 2 =y d2 -y 2 ,e 3 =y d3 -y 3 ,e 4 =y d4 -y 4 ,c 1 >0,c 2 >0,c 3 >0,c 4 >0;
The derivative of the switching function s is obtained:
Figure FDA0004149098380000053
the control amount u (x) is obtained by a constant velocity approach law method
Figure FDA0004149098380000054
Where epsilon=diag [ epsilon ] 1234 ],sgn(s)=[sgn(s 1 ) sgn(s 2 ) sgn(s 3 ) sgn(s 4 )] T
The control amount u (x) obtained by the combined type (7) - (10) is:
Figure FDA0004149098380000055
Figure FDA0004149098380000056
Figure FDA0004149098380000057
Figure FDA0004149098380000061
taking the Liapunov function as follows:
Figure FDA0004149098380000062
wherein v=diag [1, 1];
in order to verify the stable running of the tension controller of the obtained tension roller strip steel, the method for deriving the Liapunov function by the sliding mode is combined with a selected constant-speed approach method to obtain the following steps:
Figure FDA0004149098380000063
therefore, the designed sliding mode controller is verified to ensure that the system is asymptotically stable, so that the tension of the strip steel of the tension roller follows the tension set value.
2. The control device adopting the tension sliding mode control method of the tension roller strip steel according to claim 1, which is characterized in that: the tension roller comprises a monitoring module and a control module, wherein the control module is connected with the monitoring module, the control module transmits received signals to the monitoring module and displays the signals on the monitoring module, the monitoring module transmits set signals to the control module, and the tension roller is controlled by the control module.
3. The tension roller strip steel tension slip form control device according to claim 2, wherein: the control module comprises a master station and a slave station, wherein the master station selects Siemens S7-300 series PLC, and the model of CPU is 315-2DP; the slave station selects a distributed I/O ET200S with a CPU, the model of the CPU is IM151-7, and the master station and the slave station communicate through a Profibus-DP field bus.
4. The tension roller strip steel tension slip form control device according to claim 2, wherein: the monitoring module selects an Activex control integrated in WinCC software and comprises a parameter display interface, a tension setting interface, a state monitoring interface and an alarm report interface; the state monitoring interface is used for monitoring each parameter of the tension control model of the tension roller strip steel, the parameter display interface is used for displaying parameter information of each control object in the control module in real time, and changing a tension set value of the strip steel through the tension setting interface according to production specification change of the strip steel, and simultaneously, the real-time state detection of the strip steel tension and the alarm and alarm function in the tension control process are completed.
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