A sliding mode variable structure control method for a twenty-high rolling mill system

Abstract

The present invention belongs to the technical field of rolling mill vibration reduction, and specifically relates to a sliding mode variable structure control method for a twenty-roll mill system. It mainly establishes a six-degree-of-freedom nonlinear dynamic model of the twenty-roll mill system through a three-dimensional model of the twenty-roll mill system, and designs an SMC controller based on the sliding mode variable structure control principle to control the roll system of the twenty-roll mill system; in addition, the stability, existence and accessibility of the SMC controller are demonstrated by using the Lyapunov stability theory; at the same time, the time domain diagram, phase diagram, spectrum diagram and Poincaré cross-section diagram are used for simulation comparison to verify that the designed SMC controller can suppress the vertical vibration of the working rolls of the twenty-roll mill, thereby improving the stability of the system. The nonlinear vibration control method of the twenty-roll mill system provided by the present invention can effectively solve the problem that the modeling of the twenty-roll mill is complex and it is difficult to study its nonlinear vibration characteristics, and realize the study of the nonlinear vibration characteristics of the twenty-roll mill.

Description

Technical Field

[0001] The invention belongs to the technical field of rolling mill vibration reduction, and in particular relates to a sliding mode variable structure control method for a twenty-high rolling mill system. Background Art

[0002] In the field of heavy industrial machinery, plate and strip rolling mills occupy a pivotal position. As plate and strip rolling equipment develops towards large-scale, continuous, high-speed and intelligent, the dynamic effect of the rolling mill during the rolling process has also become prominent, and the problems caused by the vibration of the rolling mill have become more and more obvious, especially in the process of rolling extremely thin strips. The vibration of the rolling mill not only reduces the surface quality of the plate, but also threatens the safe operation of the rolling mill equipment and may even cause major equipment accidents. This phenomenon has become a problem that plagues the high-quality and efficient production of strip steel.

[0003] The vibration system of the twenty-high mill is a coupled nonlinear system. The state feedback control method can be used to deal with the control problem of the nonlinear system. However, the overall structure of the twenty-high mill is compact and complex. The existing modeling method cannot study the nonlinear vibration characteristics of the twenty-high mill. Therefore, there is a lack of theoretical basis for how to suppress the vibration of the twenty-high mill system. At present, the coupled vibration of the roll system of the twenty-high mill has an important impact on the production of ultra-thin strips. Due to the precision and complexity of the overall structure of the twenty-high mill, it is difficult for the existing technology to control the twenty-high mill. There is a lack of theoretical basis for how to suppress the vibration of the twenty-high mill system, and thus it is impossible to improve the quality of rolled products by reducing the coupled vibration of the roll system. Therefore, when using the twenty-high mill system for ultra-thin strip rolling, it is impossible to achieve vibration suppression of the twenty-high mill system, and it is also impossible to reduce the impact of the coupled vibration of the roll system on the quality of rolled products, and it is impossible to meet the quality requirements of rolled products.

[0004] Therefore, how to design a sliding mode variable structure control method for a twenty-high mill system to ensure effective and rapid suppression of the vibration of the twenty-high mill has become an urgent problem to be solved. Summary of the invention

[0005] In order to solve the above problems, we use a reasonable modeling method to study and analyze the nonlinear vibration characteristics of the twenty-high rolling mill system to provide a theoretical basis for suppressing its vibration. Based on this, the present invention provides a sliding mode variable structure control method for a twenty-high rolling mill system.

[0006] To achieve the above object, the present invention adopts the following technical scheme: a sliding mode variable structure control method for a twenty-high rolling mill system, including a three-dimensional model of the twenty-high rolling mill system, which includes the following steps: step 1: deleting all support roll structures in the three-dimensional model, retaining only the first intermediate roll, the second intermediate roll and the working roll, obtaining a six-roll system model, setting the roll systems in the six-roll system model to be in line contact, and obtaining a six-degree-of-freedom nonlinear dynamic model;

[0007] Step 2: Determine the target control gain based on the six-degree-of-freedom nonlinear dynamics model, and design the SMC controller according to the target control gain. The SMC controller is expressed as follows:

[0008] SMC Controller: ,

[0009] in, is the parameter matrix to be designed, C=[c1,c2,c3,c4,c5,c6], is the rolling mill vertical vibration displacement matrix, Φ is the rolling mill stiffness damping coefficient matrix, sgn is the symbolic function, is any positive number, is the sliding surface, c2 is the target control gain;

[0010] Step 3: In the SMC controller, the rolling mill vibration equation is converted into the system state equation, that is, the SMC controller is applied to the twenty-high rolling mill system, and the stability of the SMC controller is proved according to the Lyapunov stability theory, and the existence and accessibility of the SMC controller are demonstrated;

[0011] Step 4: Bring the rolling mill vibration equation and the system state equation into the MATLAB environment for simulation calculation, and simulate and analyze the amplitude control and stability before and after the SMC controller is applied. The time domain curve, spectrum curve, phase plane diagram and Poincaré cross-section diagram before and after the SMC controller is applied are obtained, and the control effect before and after the SMC controller is applied is verified.

[0012] Step 5: Connect a computer including a readable storage medium of the SMC controller to a control console of the twenty-high mill system to suppress the vertical vibration of the twenty-high mill system.

[0013] As a further supplement to the above technical solution, in step 2, the target control gain includes three indicators: sliding surface function, sliding mode switching function, and approach rate:

[0014] Sliding surface function: ,

[0015] Sliding mode switching function: ,

[0016] Approach rate: ,

[0017] in, is the sliding surface, is the parameter matrix, is the vertical vibration displacement matrix of the rolling mill, is the symbolic function, is the sliding mode gain and .

[0018] As a further supplementary explanation of the above technical solution, in step 1, the six-degree-of-freedom nonlinear dynamic model is:

[0019] ,

[0020] in, is the equivalent mass of the working roll, is the equivalent mass of the first left intermediate roller, is the equivalent mass of the first right intermediate roller, is the horizontal displacement of the working roll, is the vertical displacement of the working roll, is the horizontal displacement of the first left intermediate roller, is the vertical displacement of the first left intermediate roller, is the horizontal displacement of the first right intermediate roller, is the vertical displacement of the first right intermediate roller, is the equivalent contact linear stiffness between the working roll and the ultra-thin strip, is the equivalent contact nonlinear stiffness between the working roll and the ultra-thin strip, is the equivalent contact stiffness between the working roll and the first left intermediate roll, is the equivalent contact stiffness between the working roll and the first right intermediate roll, is the equivalent contact stiffness between the left first intermediate roller and the idler roller, is the equivalent contact stiffness between the first right intermediate roller and the idler roller, is the equivalent contact stiffness between the left first intermediate roller and the driving roller, is the equivalent contact stiffness between the right first intermediate roller and the driving roller, is the equivalent contact linear stiffness between the working roll and the ultra-thin strip, is the equivalent contact nonlinear damping between the working roll and the ultra-thin strip, is the contact angle between the working roll and the first intermediate roll, is the contact angle between the first intermediate roller and the driving roller, is the contact angle between the first intermediate roller and the idler roller, is the equivalent external incentive, For time, is the natural frequency of the external disturbance force, is the horizontal speed of the working roll, is the vertical speed of the working roll, is the horizontal speed of the first left intermediate roller, is the vertical speed of the first left intermediate roller, is the horizontal speed of the first right intermediate roller, is the vertical speed of the first right intermediate roller, is the horizontal acceleration of the working roll, is the vertical acceleration of the working roll, is the horizontal acceleration of the first left intermediate roller, is the vertical acceleration of the first left intermediate roller, is the horizontal acceleration of the first right intermediate roller, is the vertical acceleration of the first right intermediate roller.

[0021] As a further supplement to the above technical solution, in step 1, the structure of the six-degree-of-freedom nonlinear dynamic model is bilaterally symmetrical, and The horizontal initial displacement is zero, and the simplified six-degree-of-freedom nonlinear dynamic model can be obtained:

[0022] ,

[0023] The physical quantities in the simplified six-degree-of-freedom nonlinear dynamics model are dimensionlessly processed to obtain the dimensionless quantities corresponding to each physical quantity:

[0024] ,

[0025] in, , , , , , , , , , , , , , , , , is the dimensionless quantity of each physical quantity in the simplified six-degree-of-freedom nonlinear dynamic model, is the natural frequency of the working roll, is the natural frequency of the support roller in the horizontal direction, is the natural frequency of the support roller in the vertical direction, is the acceleration due to gravity;

[0026] Substituting the dimensionless quantities corresponding to each physical quantity into the simplified six-degree-of-freedom nonlinear dynamic model, the rolling mill vibration equation is obtained: .

[0027] As a further supplement to the above technical solution, in step 3, the SMC controller transforms the rolling mill vibration equation into a state space equation, and the state space equation is as follows:

[0028] ,

[0029] in, is the vertical vibration displacement of the working roll, is the first-order derivative of the vertical vibration displacement of the working roll, is the vertical vibration speed of the working roll, is the first-order derivative of the vertical vibration velocity of the working roll, is the horizontal displacement of the support roller, is the first-order derivative of the horizontal displacement of the support roller, is the horizontal speed of the support roller, is the first-order derivative of the horizontal velocity of the support roller, is the vertical displacement of the support roller, is the first-order derivative of the vertical displacement of the support roller, is the vertical speed of the support roller, is the vertical acceleration of the support roller, The force generated by the controller;

[0030] The SMC controller converts the state space equation into the system state equation, which is as follows:

[0031] ,

[0032] In the formula, , , , , .

[0033] As a further supplement to the above technical solution, in step 3, the stability of the SMC controller is demonstrated based on the Lyapunov stability theory:

[0034] Assume the Lyapunov equation: ,

[0035] Combining the sliding mode approach rate expression, the first-order derivative equation of the Lyapunov equation is obtained: ,

[0036] According to the second Lyapunov method, when When the time is right, Zhengding, Negative determination indicates that the system is stable; when Negative timing, Negative determination, Negative definite, indicating that the system is stable.

[0037] In step 3, the existence and reachability of the SMC controller are demonstrated as follows:

[0038] The linear sliding surface is used for design, and the sliding surface function expression is set as ,

[0039] Where, C=[c1,c2,c3,c4,c5,c6];

[0040] Set the sliding mode switching function to , the approach rate expression is ,

[0041] In the formula, is the sliding mode gain, which can be any positive number;

[0042] According to the approach rate expression, the following formula can be obtained:

[0043] ,

[0044] when , can be obtained And when ,have to ; Therefore, it can be proved that the SMC controller exists and can make any point in the state space approach the sliding surface through control. At the same time, when the system state is near the sliding surface, it can actually reach the sliding surface under different effects of the SMC controller, which proves the reachability of the controller.

[0045] As a further supplement to the above technical solution, according to the system state equation and sliding surface expression under the action of the SMC controller: ,

[0046] Combined with the approach rate expression, the actuation force expression is established: ,

[0047] Where: is the parameter matrix to be designed, C=[c1,c2,c3,c4,c5,c6], is the vertical vibration displacement matrix of the rolling mill, Φ is the stiffness damping coefficient matrix of the rolling mill, sgn is the sign function, is an arbitrary positive number, is the sliding surface, and c2 is the target control gain;

[0048] In order to reduce the complexity of the sliding surface, the vibration displacement and vibration velocity of the working roll are considered as observation values, and c3=c4=c5=c6=0 is set. The system characteristic equation under the intervention of the SMC controller is obtained according to the actuating force expression: ;

[0049] Where p is the Laplace operator, k 1-0 is the square of the natural frequency of the working roll,

[0050] In order to achieve rapid asymptotic stability of sliding mode motion, p=2 is taken, and we can get: ;

[0051] The rolling mill vibration equation and system state equation were brought into the MATLAB environment for simulation calculation respectively. The amplitude control and stability before and after the SMC controller were simulated and analyzed. The time domain curve, spectrum curve, phase plane diagram and Poincaré cross-section diagram before and after the SMC controller were obtained, verifying the control effect before and after the application of the SMC controller.

[0052] Compared with the prior art, the beneficial effects of the twenty-high mill system vibration control technology proposed in the present invention are mainly reflected in the following aspects:

[0053] 1. The present invention constructs a six-degree-of-freedom nonlinear dynamic model based on the three-dimensional model of the twenty-high rolling mill system and simplifies the twenty-high rolling mill system into a six-high system, which significantly improves the accuracy and efficiency of the vibration characteristics analysis of the rolling mill system. This simplification and modeling method makes the study of vibration characteristics more in-depth and accurate, and provides a solid foundation for the subsequent control strategy design.

[0054] 2. The present invention uses sliding mode control technology to design an SMC controller, converts the rolling mill vibration equation into a system state equation, and accurately controls the twenty-high rolling mill system based on the system state equation, which not only improves the control accuracy of the system, but also enhances the robustness of the system. This enables the rolling mill system to operate stably under various working conditions, greatly improving production efficiency and product quality.

[0055] 3. Based on Lyapunov stability theory and six-degree-of-freedom nonlinear dynamics model, the present invention conducts an in-depth stability analysis of the SMC controller and obtains the stability analysis results. At the same time, it also proves the existence and accessibility of the controller and provides an important theoretical basis for the design and optimization of the controller.

[0056] 4. The present invention provides a rich theoretical basis for vibration suppression of the rolling mill system by comprehensively analyzing the nonlinear vibration characteristics of the twenty-high rolling mill system from multiple angles such as time domain curves, spectrum curves, phase diagrams and Poincaré cross-sectional diagrams. This comprehensive analysis method makes the study of vibration characteristics more in-depth and comprehensive.

[0057] 5. The present invention reduces the influence of the roller system coupling vibration on the quality of rolled products by suppressing the vibration of the twenty-high rolling mill, and realizes the stable, efficient and high-quality production of ultra-thin strips. This not only improves the market competitiveness of the products, but also brings significant economic benefits to the enterprise.

[0058] 6. The present invention proposes a solution to the multi-state coupled vibration problem of the twenty-high mill roll system, reduces the amplitude of the system, improves product quality, and reduces the loss of vibration to the rolling equipment. At the same time, the present invention has the advantages of fast response, insensitivity to parameter changes and disturbances, no need for system online identification, simple physical implementation, etc., and is more suitable for wide promotion and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The following drawings are used to further understand the present invention and are a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0060] Figure 1 It is a structural schematic diagram of the six-degree-of-freedom nonlinear dynamic model in the present invention;

[0061] Figure 2 It is a schematic diagram of the working principle of the SMC controller in the present invention;

[0062] Figure 3 It is a schematic diagram of the time domain curve of the system before and after the controller is applied in the present invention;

[0063] Figure 4 It is a schematic diagram of the system spectrum curve before and after the controller is applied in the present invention;

[0064] Figure 5 A schematic diagram of a system phase curve before and after the controller is applied in the present invention;

[0065] Figure 6 This is a schematic diagram of the Poincaré cross section of the system before the controller is applied in the present invention;

[0066] Figure 7 It is a schematic diagram of the Poincaré cross section of the system after the controller in the present invention is applied. DETAILED DESCRIPTION

[0067] In order to further illustrate the technical solution of the present invention, the present invention is further described below through embodiments.

[0068] The vibration system of the twenty-high mill is a coupled nonlinear system. The state feedback control method can be used to deal with the control problem of the nonlinear system. However, the overall structure of the twenty-high mill is compact and complex. The existing modeling method cannot study the nonlinear vibration characteristics of the twenty-high mill. Therefore, there is a lack of theoretical basis for how to suppress the vibration of the twenty-high mill system. Therefore, when the twenty-high mill system is used for ultra-thin strip rolling, the vibration suppression of the twenty-high mill system cannot be achieved, and the influence of the coupled vibration of the roller system on the quality of the rolled products cannot be reduced, and the quality requirements of the rolled products cannot be met.

[0069] In order to solve the above problems, the present invention proposes a sliding mode variable structure control method for a twenty-high rolling mill system, including a three-dimensional model of the twenty-high rolling mill system, which includes the following steps: Step 1: Delete all support roll structures in the three-dimensional model, and only retain the first intermediate roll, the second intermediate roll and the working roll to obtain a six-roll system model, and set the rolls in the six-roll system model to be in line contact to obtain a six-degree-of-freedom nonlinear dynamic model;

[0070] Step 2: Determine the target control gain based on the six-degree-of-freedom nonlinear dynamics model. The target control gain includes three indicators: sliding surface function, sliding mode switching function, and approach rate:

[0071] Sliding surface function: ,

[0072] Sliding mode switching function: ,

[0073] Approach rate: ,

[0074] in, is the sliding surface, is the parameter matrix, is the vertical vibration displacement matrix of the rolling mill, is the symbolic function, is the sliding mode gain and ;

[0075] The SMC controller is designed according to the target control gain. The SMC controller is expressed as follows:

[0076] SMC Controller: ,

[0077] in, is the parameter matrix to be designed, C=[c1,c2,c3,c4,c5,c6], is the rolling mill vertical vibration displacement matrix, Φ is the rolling mill stiffness damping coefficient matrix, sgn is the symbolic function, is any positive number, is the sliding surface, c2 is the target control gain;

[0078] Step 3: In the SMC controller, the rolling mill vibration equation is converted into the system state equation, that is, the SMC controller is applied to the twenty-high rolling mill system, and the stability of the SMC controller is proved according to the Lyapunov stability theory, and the existence and accessibility of the SMC controller are demonstrated;

[0079] Step 4: Bring the rolling mill vibration equation and the system state equation into the MATLAB environment for simulation calculation, and simulate and analyze the amplitude control and stability before and after the SMC controller is applied. The time domain curve, spectrum curve, phase plane diagram and Poincaré cross-section diagram before and after the SMC controller is applied are obtained, and the control effect before and after the SMC controller is applied is verified.

[0080] Step 5: Connect a computer including a readable storage medium of the SMC controller to a control console of the twenty-high mill system to suppress the vertical vibration of the twenty-high mill system.

[0081] In the above embodiment, as shown in the attached Figure 1 As shown, the six-degree-of-freedom nonlinear dynamic model is:

[0082] ,

[0083] in, is the equivalent mass of the working roll, is the equivalent mass of the first left intermediate roller, is the equivalent mass of the first right intermediate roller, is the horizontal displacement of the working roll, is the vertical displacement of the working roll, is the horizontal displacement of the first left intermediate roller, is the vertical displacement of the first left intermediate roller, is the horizontal displacement of the first right intermediate roller, is the vertical displacement of the first right intermediate roller, is the equivalent contact linear stiffness between the working roll and the ultra-thin strip, is the equivalent contact nonlinear stiffness between the working roll and the ultra-thin strip, is the equivalent contact stiffness between the working roll and the first left intermediate roll, is the equivalent contact stiffness between the working roll and the first right intermediate roll, is the equivalent contact stiffness between the left first intermediate roller and the idler roller, is the equivalent contact stiffness between the first right intermediate roller and the idler roller, is the equivalent contact stiffness between the left first intermediate roller and the driving roller, is the equivalent contact stiffness between the right first intermediate roller and the driving roller, is the equivalent contact linear stiffness between the working roll and the ultra-thin strip, is the equivalent contact nonlinear damping between the working roll and the ultra-thin strip, is the contact angle between the working roll and the first intermediate roll, is the contact angle between the first intermediate roller and the driving roller, is the contact angle between the first intermediate roller and the idler roller, is the equivalent external incentive, For time, is the natural frequency of the external disturbance force, is the horizontal speed of the working roll, is the vertical speed of the working roll, is the horizontal speed of the first left intermediate roller, is the vertical speed of the first left intermediate roller, is the horizontal speed of the first right intermediate roller, is the vertical speed of the first right intermediate roller, is the horizontal acceleration of the working roll, is the vertical acceleration of the working roll, is the horizontal acceleration of the first left intermediate roller, is the vertical acceleration of the first left intermediate roller, is the horizontal acceleration of the first right intermediate roller, is the vertical acceleration of the first right intermediate roller.

[0084] Further, in step 1, the six-degree-of-freedom nonlinear dynamic model structure is bilaterally symmetrical, and The horizontal initial displacement is zero, and the simplified six-degree-of-freedom nonlinear dynamic model can be obtained:

[0085] ,

[0086] The physical quantities in the simplified six-degree-of-freedom nonlinear dynamics model are dimensionlessly processed to obtain the dimensionless quantities corresponding to each physical quantity:

[0087] ,

[0088] in, , , , , , , , , , , , , , , , , is the dimensionless quantity of each physical quantity in the simplified six-degree-of-freedom nonlinear dynamic model, is the natural frequency of the working roll, is the natural frequency of the support roller in the horizontal direction, is the natural frequency of the support roller in the vertical direction, is the acceleration due to gravity;

[0089] Substituting the dimensionless quantities corresponding to each physical quantity into the simplified six-degree-of-freedom nonlinear dynamic model, the rolling mill vibration equation is obtained: .

[0090] As attached Figure 2 As shown in the figure, the sliding mode variable structure control principle: As a variable structure control, sliding mode variable structure control belongs to nonlinear control method. The sliding surface is pre-set, and the state space is divided into two parts by the sliding surface. Any state of the system is regarded as a point in the state space, and different rates of approach to the sliding surface are adopted in different spaces. In the dynamic process, it changes purposefully and continuously according to the current state of the system (such as deviation and its derivatives of various orders, etc.). Under the action of the SMC controller, the system is forced to move according to the state trajectory of the predetermined "sliding mode", thereby reducing the amplitude of the twenty-high mill roll system. In step 3, the SMC controller transforms the mill vibration equation into a state space equation, and the state space equation is as follows:

[0091] ,

[0092] in, is the vertical vibration displacement of the working roll, is the first-order derivative of the vertical vibration displacement of the working roll, is the vertical vibration speed of the working roll, is the first-order derivative of the vertical vibration velocity of the working roll, is the horizontal displacement of the support roller, is the first-order derivative of the horizontal displacement of the support roller, is the horizontal speed of the support roller, is the first-order derivative of the horizontal velocity of the support roller, is the vertical displacement of the support roller, is the first-order derivative of the vertical displacement of the support roller, is the vertical speed of the support roller, is the vertical acceleration of the support roller, The force generated by the controller;

[0093] The SMC controller converts the state space equation into the system state equation, which is as follows:

[0094] ,

[0095] In the formula, , , , , .

[0096] In this embodiment, in step 3, the stability of the SMC controller is demonstrated based on the Lyapunov stability theory:

[0097] Assume the Lyapunov equation: ,

[0098] Combining the sliding mode approach rate expression, the first-order derivative equation of the Lyapunov equation is obtained: ,

[0099] According to the second Lyapunov method, when When the time is right, Zhengding, Negative determination indicates that the system is stable; when Negative timing, Negative determination, Negative definite, indicating that the system is stable.

[0100] In step 3, the existence and reachability of the SMC controller are demonstrated as follows:

[0101] The linear sliding surface is used for design, and the sliding surface function expression is set as ,

[0102] Where, C=[c1,c2,c3,c4,c5,c6];

[0103] Set the sliding mode switching function to , the approach rate expression is ,

[0104] In the formula, is the sliding mode gain, which can be any positive number;

[0105] According to the approach rate expression, the following formula can be obtained:

[0106] ,

[0107] when , can be obtained And when ,have to ; Therefore, it can be proved that the SMC controller exists and can make any point in the state space approach the sliding surface through control. At the same time, when the system state is near the sliding surface, it can actually reach the sliding surface under different effects of the SMC controller, which proves the reachability of the controller.

[0108] In summary, it can be proved that the SMC controller has accessibility and stability.

[0109] According to the system state equation and sliding surface expression under the action of SMC controller: ,

[0110] Combined with the approach rate expression, the actuation force expression is established: ,

[0111] Where: is the parameter matrix to be designed, C=[c1,c2,c3,c4,c5,c6], is the vertical vibration displacement matrix of the rolling mill, Φ is the stiffness damping coefficient matrix of the rolling mill, sgn is the sign function, is an arbitrary positive number, is the sliding surface, and c2 is the target control gain;

[0112] In order to reduce the complexity of the sliding surface, the vibration displacement and vibration velocity of the working roll are considered as observation values, and c3=c4=c5=c6=0 is set. The system characteristic equation under the intervention of the SMC controller is obtained according to the actuating force expression: ;

[0113] Where p is the Laplace operator, k 1-0 is the square of the natural frequency of the working roll,

[0114] In order to achieve rapid asymptotic stability of sliding mode motion, p=2 is taken, and we can get: ;

[0115] As attached Figures 3 to 7 As shown in the figure, the rolling mill vibration equation and the system state equation are respectively brought into the MATLAB environment for simulation calculation, and the amplitude control and stability in two cases before and after the SMC controller are simulated and analyzed. The time domain curve, spectrum curve, phase plane diagram and Poincaré cross-section diagram before and after the SMC controller are obtained, which verifies the control effect before and after the application of the SMC controller.

[0116] from Figure 3 It can be seen from the time domain curve that under the unstable operation state of the original system, the system reaches stability in about 1 second after the SMC controller is activated, and the original maximum displacement amplitude of vibration is stabilized from 2.0×10-6m to 1.0×10-6m. Figure 4 In the spectrum curve shown, the intervention of the SMC controller has significantly suppressed both the main resonance peak and the subharmonic resonance peak of the system. Figure 5 It can be seen from the phase plane diagram that under the action of the SMC controller, not only the unstable state of the original system is stabilized, but also the amplitude of the newly established stable periodic vibration is significantly reduced. Figure 6 and Figure 7The figure shows a Poincaré cross-section diagram. By comparison, it can be seen that before and after the SMC controller is applied, the system tends to a stable point from a chaotic scattered point, indicating that through the action of the controller, the vibration state of the system is controlled from an unstable state to a stable state, which further verifies the effectiveness of the designed controller in controlling the vibration of the working roll, and has a good control effect in improving the stability of the system.

[0117] In the above embodiments, the SMC controller is implemented by software, hardware, firmware or any combination thereof. When implemented by software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer programs or instructions. When the computer program or instruction is loaded and executed on a computer, the process or function described in the embodiment of the present application is executed in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, a terminal, a user device or other programmable device. The computer program or instruction may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer program or instruction may be transmitted from one website, computer, server or data center to another website, computer, server or data center by wired or wireless means. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium may be a magnetic medium, such as a floppy disk, a hard disk, or a tape; it may also be an optical medium, such as a digital video disc (DVD); it may also be a semiconductor medium, such as a solid state drive (SSD).

[0118] The above shows and describes the main features and advantages of the present invention. For those skilled in the art, it is obvious that the specific implementation of the present invention is not limited to the details of the above exemplary embodiments, and the creative ideas and design ideas of the present invention can be realized in other specific forms without departing from the spirit or basic features of the present invention, which should be equivalent to the protection scope disclosed in the technical solution of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the attached claims rather than the above description, and it is intended to include all changes within the meaning and scope of the equivalent elements of the claims in the present invention.

[0119] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A sliding mode variable structure control method for a twenty-high rolling mill system, comprising a three-dimensional model of the twenty-high rolling mill system, characterized in that: The following steps are included: Step 1: Delete all support roll structures in the three-dimensional model, and only keep the first intermediate roll, the second intermediate roll and the working roll to obtain a six-roll system model. Set the rolls in the six-roll system model to be in line contact to obtain a six-degree-of-freedom nonlinear dynamic model; The six-degree-of-freedom nonlinear dynamic model is: Among them, m1 is the equivalent mass of the working roll, m2 is the equivalent mass of the left first intermediate roll, m3 is the equivalent mass of the right first intermediate roll, x1 is the horizontal displacement of the working roll, z1 is the vertical displacement of the working roll, x2 is the horizontal displacement of the left first intermediate roll, z2 is the vertical displacement of the left first intermediate roll, x3 is the horizontal displacement of the right first intermediate roll, z3 is the vertical displacement of the right first intermediate roll, k1 is the equivalent contact linear stiffness between the working roll and the ultra-thin strip, is the equivalent contact nonlinear stiffness between the working roll and the ultra-thin strip, k2 is the equivalent contact stiffness between the working roll and the first left intermediate roll, k3 is the equivalent contact stiffness between the working roll and the first right intermediate roll, k5 is the equivalent contact stiffness between the first left intermediate roll and the idler roll, k6 is the equivalent contact stiffness between the first right intermediate roll and the idler roll, k4 is the equivalent contact stiffness between the first left intermediate roll and the drive roll, k7 is the equivalent contact stiffness between the first right intermediate roll and the drive roll, c1 is the equivalent contact linear stiffness between the working roll and the ultra-thin strip, is the equivalent contact nonlinear damping between the working roll and the ultra-thin strip, α is the contact angle between the working roll and the first intermediate roll, β is the contact angle between the first intermediate roll and the driving roll, γ is the contact angle between the first intermediate roll and the idler roll, Fcos(ωt) is the equivalent external excitation, t is the time, ω is the natural frequency of the external disturbance force, is the horizontal speed of the working roll, is the vertical speed of the working roll, is the horizontal speed of the first left intermediate roller, is the vertical speed of the first left intermediate roller, is the horizontal speed of the first right intermediate roller, is the vertical speed of the first right intermediate roller, is the horizontal acceleration of the working roll, is the vertical acceleration of the working roll, is the horizontal acceleration of the first left intermediate roller, is the vertical acceleration of the first left intermediate roller, is the horizontal acceleration of the first right intermediate roller, is the vertical acceleration of the first right intermediate roller; The structure of the six-degree-of-freedom nonlinear dynamic model is bilaterally symmetrical, and the horizontal initial displacement of m1 is zero, so a simplified six-degree-of-freedom nonlinear dynamic model can be obtained: The physical quantities in the simplified six-degree-of-freedom nonlinear dynamics model are dimensionlessly processed to obtain the dimensionless quantities corresponding to each physical quantity: Among them, ω0, τ, l, z'1, x'2, z'2, k 1-1 , k 1-2 , c 1-1 , k 2-1 , k 2-2 , k 3-1 , k 3-2 , F0, ω' is the dimensionless quantity of each physical quantity in the simplified six-degree-of-freedom nonlinear dynamic model, ω 10 is the natural frequency of the working roll, ω 20 is the natural frequency of the support roller in the horizontal direction, ω 30 is the natural frequency of the support roller in the vertical direction, g is the acceleration of gravity; Substituting the dimensionless quantities corresponding to each physical quantity into the simplified six-degree-of-freedom nonlinear dynamic model, the rolling mill vibration equation is obtained: Step 2: Determine the target control gain based on the six-degree-of-freedom nonlinear dynamics model, and design the SMC controller according to the target control gain. The target control gain includes three indicators: sliding surface function, sliding mode switching function, and approach rate: Sliding surface function: σ=CY, Sliding mode switching function: sgn(σ), Approach rate: Among them, σ is the sliding surface, C is the parameter matrix, Y is the vertical vibration displacement matrix of the rolling mill, sgn is the sign function, η is the sliding gain and η>0; The SMC controller is expressed as follows: SMC Controller: Among them, C is the parameter matrix to be designed, C = [c1, c2, c3, c4, c5, c6], Y is the vertical vibration displacement matrix of the rolling mill, Φ is the stiffness damping coefficient matrix of the rolling mill, sgn is the sign function, η is an arbitrary positive number, σ is the sliding surface, and c2 is the target control gain; Step 3: In the SMC controller, the rolling mill vibration equation is converted into the system state equation, that is, the SMC controller is applied to the twenty-high rolling mill system, and the stability of the SMC controller is proved according to the Lyapunov stability theory, and the existence and accessibility of the SMC controller are demonstrated; The stability demonstration of the SMC controller based on Lyapunov stability theory is as follows: Assume the Lyapunov equation: Combining the sliding mode approach rate expression, the first-order derivative equation of the Lyapunov equation is obtained: According to the second Lyapunov method, when σ is positive definite, sgn(σ) is positive definite. Negative definite, indicating that the system is stable; when σ is negative definite, sgn(σ) is negative definite, Negative determination indicates that the system is stable; The existence and reachability of the SMC controller are demonstrated as follows: The linear sliding surface is used for design, and the sliding surface function expression is set to σ=CY. Where, C = [c1, c2, c3, c4, c5, c6]; Assume the sliding mode switching function is sgn(σ), and use the approach rate expression as Where η is the sliding mode gain, which can be any positive number; According to the approach rate expression, the following formula can be obtained: When σ<0, we can get When σ>0, we get Therefore, it can be proved that the SMC controller has existence and can make any point in the state space approach the sliding surface through control. At the same time, when the system state is near the sliding surface, it can actually reach the sliding surface under different actions of the SMC controller, which proves the reachability of the controller. Step 4: Bring the rolling mill vibration equation and the system state equation into the MATLAB environment for simulation calculation, and simulate and analyze the amplitude control and stability before and after the SMC controller is applied. The time domain curve, spectrum curve, phase plane diagram and Poincaré cross-section diagram before and after the SMC controller is applied are obtained, and the control effect before and after the SMC controller is applied is verified. Step 5: Connect a computer containing a readable storage medium of the SMC controller to a control console of the twenty-high mill system to suppress the vertical vibration of the twenty-high mill system.

2. The sliding mode variable structure control method of a twenty-high rolling mill system according to claim 1, characterized in that: In step 3, the SMC controller transforms the rolling mill vibration equation into a state space equation, which is shown as follows: Among them, y1 is the vertical vibration displacement of the working roll, is the first-order derivative of the vertical vibration displacement of the working roll, y2 is the vertical vibration velocity of the working roll, is the first-order derivative of the vertical vibration velocity of the working roll, y3 is the horizontal displacement of the support roll, is the first-order derivative of the horizontal displacement of the support roller, y4 is the horizontal speed of the support roller, is the first-order derivative of the horizontal velocity of the support roller, y5 is the vertical displacement of the support roller, is the first-order derivative of the vertical displacement of the support roller, y6 is the vertical velocity of the support roller, is the vertical acceleration of the support roller, F a The force generated by the controller; The SMC controller converts the state space equation into the system state equation, which is as follows: where \(u(t)=F\) a , \(f(t)=F_0\cos(\omega t)\), \(Y = [y_1, y_2, y_3, y_4, y_5, y_6]\) T , 3. The sliding mode variable structure control method of a twenty-high rolling mill system according to claim 1, characterized in that: According to the system state equation and sliding surface expression under the action of SMC controller: Combined with the approach rate expression, the actuation force expression is established: Where: C is the parameter matrix to be designed, C = [c1, c2, c3, c4, c5, c6], Y is the vertical vibration displacement matrix of the rolling mill, Φ is the stiffness damping coefficient matrix of the rolling mill, sgn is the sign function, η is an arbitrary positive number, σ is the sliding surface, and c2 is the target control gain; In order to reduce the complexity of the sliding surface, the vibration displacement and vibration velocity of the working roll are considered as observation values, and c3 = c4 = c5 = c6 = 0 is set. According to the actuating force expression, the system characteristic equation under the intervention of the SMC controller is obtained: (c1-c2c 1-1 )pk 1- 0c2=0; Where p is the Laplace operator, k 1-0 is the square of the natural frequency of the working roll, In order to achieve rapid asymptotic stability of sliding mode motion, p = 2, we can get: c2=1; The rolling mill vibration equation and system state equation were brought into the MATLAB environment for simulation calculation respectively. The amplitude control and stability before and after the SMC controller were simulated and analyzed. The time domain curve, spectrum curve, phase plane diagram and Poincaré cross-section diagram before and after the SMC controller were obtained, verifying the control effect before and after the application of the SMC controller.

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