Plate glass online cutting method based on model predictive control

Abstract

The invention relates to the technical field of plate glass cutting, in particular to a plate glass online cutting method based on model predictive control. Comprising the steps of establishing a state space model of a cutting control system; carrying out difference on the state space model at adjacent time steps to obtain a change relation between a state vector and an input vector in the state space model, and outputting a control system state model; measuring and acquiring a space state vector of a sampling point of the cutting control system, calculating a future trajectory of the cutting control system by using the control system state model, and calculating a prediction state variable and prediction output of the cutting control system; and calculating to obtain an optimal control signal. According to the plate glass online cutting method based on model predictive control, the defects of traditional proportional integral (PI) control can be overcome, the response speed and stability of a glass cutting control system are improved, and the good real-time adjusting effect on the state of the cutting system can be achieved.

Description

Technical Field

[0001] The invention relates to the technical field of flat glass cutting, and in particular to an online cutting method for flat glass. Background Art

[0002] In the cold end production line of glass products, the online cutting of flat glass is an important part of the industrial automation production of glass products. Therefore, the reliability of glass cutting equipment greatly affects the production quality of glass products. A complete glass cutting system consists of a cross-cutting machine and a longitudinal cutting machine. The cross-cutting machine is used to control the length of the glass products, and the longitudinal cutting machine is used to control the width of the glass products. Cutting accuracy is particularly important in the production process of flat glass. The control method of the cutting machine is motion control. Its cutting wheel needs to make horizontal and vertical movements relative to the glass during the pulling process of the glass ribbon. It needs to be positioned to the corresponding position of the glass ribbon according to the production order for cutting. When facing multiple orders running at the same time, the cutting system needs to have high responsiveness, so the optimization control of the cutting system is very critical.

[0003] Traditional cutting system control methods generally use proportional integral (PI) control. Proportional integral linear controllers are widely used in industrial control because of their simple structure and easy implementation. However, the motion control system of the cutting machine is a complex nonlinear system. The traditional PI control method cannot solve the problem between rapidity and reliability. Therefore, when the glass ribbon is pulled at a fast speed, PI control has obvious defects and the real-time performance of the cutting machine control cannot be met. Summary of the invention

[0004] The purpose of the present invention is to provide a flat glass online cutting method based on model predictive control to solve the above technical problems;

[0005] The technical problem solved by the present invention can be achieved by adopting the following technical solutions:

[0006] A flat glass online cutting method based on model predictive control, comprising:

[0007] Step S1, establishing a state space model of a cutting control system;

[0008] Step S2, performing differentiation on the state space model at adjacent time steps, obtaining a change relationship between a state vector and an input vector in the state space model, and outputting a control system state model;

[0009] Step S3, measuring and acquiring the spatial state vector of the sampling point of the cutting control system, calculating the future trajectory of the cutting control system using the control system state model, and calculating the predicted state variables and predicted output of the cutting control system;

[0010] Step S4, setting a cost function, substituting the predicted output into the cost function, and calculating an optimal control signal.

[0011] Preferably, the expression of the state space model is:

[0012] x n (d+1)=A n x n (d)+B n u(d)

[0013] y(d)=C n x n (d)

[0014] where x n represents the state vector, d represents the sampling time, u represents the input vector, y represents the process output variable, A n Denotes the system dynamic coefficient, B n Indicates the input coefficient, C n Represents the output coefficient.

[0015] Preferably, in step S2, the state space model is subjected to differential calculation of adjacent time steps at the d+1th time and the dth time to obtain:

[0016] x n (d+1)-x n (d) = A n (x n (d)-(x n (d-1))+B n (u(d)-u(d-1))

[0017] The state vector x n The difference between the d+1th moment and the dth moment is expressed as,

[0018] Δx n (d+1)=x n (d+1)-x n (d)

[0019] The difference between the input vector u at the dth moment and the d-1th moment is expressed as,

[0020] Δu(d)=u(d)-u(d-1)

[0021] The spatial state equation is obtained in the difference form,

[0022] Δx n (d+1)=A n Δx n (d)+B n Δu(d)

[0023] The difference between the process output variable y at the d+1th moment and the dth moment is expressed as,

[0024] y(d+1)-y(d)=Cnx n (d+1)-Cnx n (d)

[0025] =C n Δx n (d+1)

[0026] =A n C n Δx n (d)+B n C n Δu(d)

[0028] Preferably, in step S2, the control system state model is obtained according to the expression of the difference between the process output variable y at the d+1th moment and the dth moment, and the expression is,

[0029]

[0030] Among them, n is a zero vector, when C=[o n 1], the matrix (ABC) is an augmented matrix.

[0031] Preferably, in step S3, the sampling point of the cutting control system is d i , the measured space state vector is x(d i ), the future trajectory of the cutting control system is expressed as,

[0032] Δu(d i ), Δu(d i +1), ......Δu(d i +T c -1)

[0033] Among them, T c is the control domain, representing the number of parameters required to track future trajectories.

[0034] Preferably, in step S3, the expression for predicting the state variable is,

[0035] x(d i +1|d i ), x(d i +2|d i ), ..., x(d i +m|d i ), ..., x(d i +TP|di )

[0036] Among them, x(d i +m|d i ) represents the space state vector x(d i ) in d i + The predicted state variable at point m, T P is the prediction depth, which indicates the number of predicted state variables.

[0037] Preferably, in step S3, the predicted state variable is calculated based on the control system state model, and the expression is:

[0038]

[0039] The predicted output is derived from the predicted state variables. The expression of the predicted output is,

[0040]

[0041] Define a vector:

[0042] Y=[y(d i +1|d i )y(d i +2|d i )y(d i +T P |d i )] T

[0043] ΔU=[Δu(d i )Δu(d i +1)Δu(d i +T C -1)] T

[0044] Among them, Y represents the output variable, ΔU represents the input variable, and the output definition vector is used to obtain

[0045] Y=Fx(d i )+λΔU

[0046] in,

[0048] Preferably, in step S4, the expected output is set to R p , the expression of the cost function is,

[0049]

[0050] Among them, Y represents the actual output, represents a diagonal matrix, where rw represents the weight coefficient of closed-loop control, represents the identity matrix;

[0051] The expression Y=Fx(d i )+λΔU is brought into the cost function to obtain

[0052]

[0053] Taking the derivative of ΔU, we get

[0054]

[0055] make When is zero, the optimal control signal is obtained, and the expression is:

[0056]

[0057] Preferably, it also includes step S6, executing the optimal control signal at the current moment, returning to execute step S3 when entering the next moment, obtaining the space state vector at the next moment, and re-predicting and calculating the optimal control signal based on the space state vector at the next moment.

[0058] Preferably, the cutting control system is centrally symmetrically arranged relative to the flat glass conveying roller.

[0059] Beneficial effects of the present invention: Due to the adoption of the above technical scheme, the flat glass online cutting method based on model predictive control of the present invention can overcome the defects of traditional proportional integral (PI) control, improve the response speed and stability of the glass cutting control system, play a good real-time adjustment role for the cutting system state, effectively reduce the failure rate of the cutting equipment, and ensure the stable operation of the glass cutting equipment BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 Schematic diagram of the steps of a flat glass online cutting method based on model predictive control in an embodiment of the present invention;

[0061] Figure 2 This is a model prediction control flow chart in an embodiment of the present invention;

[0062] Figure 3 Schematic diagram of the model predictive control algorithm in an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0064] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0065] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0066] A method for online cutting of flat glass based on model predictive control, such as Figure 1 As shown, including,

[0067] Step S1, establishing a state space model of a cutting control system;

[0068] Step S2, performing differentiation on the state space model at adjacent time steps, obtaining the change relationship between the state vector and the input vector in the state space model, and outputting the control system state model;

[0069] Step S3, measuring and acquiring the spatial state vector of the sampling point of the cutting control system, calculating the future trajectory of the cutting control system using the control system state model, and calculating the predicted state variables and predicted output of the cutting control system;

[0070] Step S4, setting a cost function, substituting the predicted output into the cost function, and calculating the optimal control signal.

[0071] Specifically, predictive control (MPC) predicts the future action of the system by establishing a mathematical model of the controlled object, and selects the most appropriate control action based on the optimization principle. It also has the characteristics of multi-objective control and rapid response, and has broad application prospects in flat glass cutting control systems.

[0072] The present invention proposes a flat glass online cutting method based on model predictive control, which has better dynamic characteristics than traditional proportional integral (PI) control, makes the control system more efficient and reliable, and can effectively improve the accuracy and stability of glass cutting equipment.

[0073] Specifically, the basis of model predictive control is the mathematical model of the controlled object. The cutting system is arranged in a centrally symmetrical manner relative to the flat glass transmission roller, so the state space model is adopted in the present invention. Through the known information of the system, the model-based predictive calculation is performed to obtain the predicted response for the next period of time. By evaluating the future response, the system is controlled to take corresponding actions.

[0074] The purpose of the present invention is to overcome the shortcomings of the proportional integral (PI) control method in the traditional cutting control system, and propose a flat glass online cutting method based on model predictive control, which can effectively improve the reliability and accuracy of glass cutting equipment, ensure the quality of flat glass cutting, and have good dynamic response performance.

[0075] In a preferred embodiment, the expression of the state space model is:

[0076] x n (d+1)=A n x n (d)+B n u(d) (1)

[0077] y(d)=C n x n (d) (2)

[0078] where x n represents the state vector, d represents the sampling time, u represents the input vector, y represents the process output variable, A n Denotes the system dynamic coefficient, B n Indicates the input coefficient, C n Represents the output coefficient.

[0079] In a preferred embodiment, in step S2, the state space model is subjected to differential calculations at adjacent time steps at the d+1th moment and the dth moment to obtain:

[0080] x n (d+1)-x n (d) = A n (x n (d)-(x n (d-1))+B n (u(d)-u(d-1)) (3)

[0081] The state vector x n The difference between the d+1th moment and the dth moment is expressed as,

[0082] Δx n (d+1)=x n (d+1)-x n(d) (4) The difference between the input vector u at the dth moment and the d-1th moment is expressed as,

[0083] Δu(d)=u(d)-u(d-1) (5) The spatial state equation in differential form is obtained,

[0084] Δx n (d+1)=A n Δx n (d)+B n Δu(d) (6)

[0085] The difference between the process output variable y at the d+1th moment and the dth moment is expressed as,

[0086] y(d+1)-y(d)=C n x n (d+1)-C n x n (d) (7)

[0087] =C n Δx n (d+1)

[0088] =A n C n Δx n (d)+B n C n Δu(d)

[0090] Specifically, the cutting control system is represented by the state space model, and the change of state is represented by differential calculation.

[0091] First, the spatial state model of the cutting control system is established as follows:

[0092] x n (d+1)=A n x n (d)+B n u(d) (1)

[0093] y(d)=C n x n (d) (2)

[0094] In the above formula, xn is the state vector, d is the sampling time, u is the input variable, y is the process output variable, A n , B n , C n is a coefficient that describes the relationship between state, input, and output. By performing differential calculations on adjacent time steps, we can obtain

[0095] x n (d+1)-xn (d) = A n (x n (d)-(x n (d-1))+B n (u(d)-u(d-1)) (3)

[0096] The difference between the state vector xn at time d+1 and time d can be expressed as:

[0097] Δx n (d+1)=x n (d+1)-x n (d) (4)

[0098] The difference between the input variable u at the dth moment and the d-1th moment can be expressed as:

[0099] Δu(d)=u(d)-u(d-1) (5)

[0100] Then equation (3) can be expressed as the differential form of the spatial state equation:

[0101] Δx n (d+1)=A n Δx n (d)+B n Δu(d) (6)

[0102] Then the difference between the process output variable y at time d+1 and time d can be expressed as:

[0103] y(d+1)-y(d)=C n x n (d+1)-C n x n (d) (7)

[0104] =C n Δx n (d+1)

[0105] =A n C n Δx n (d)+B n C n Δu(d)

[0106] In a preferred embodiment, in step S2, according to the expression of the difference between the process output variable y at the d+1th moment and the dth moment: Formula (7), the control system state model is obtained, which is expressed as follows:

[0107]

[0108]

[0109] Among them, n is a zero vector, when C=[o n 1], the matrix (ABC) is an augmented matrix.

[0110] In a preferred embodiment, in step S3, the sampling point of the cutting control system is d i , the measured spatial state vector is x(d i ), the future trajectory of the cutting control system is expressed as,

[0111] Δu(d i ), Δu(d i +1), ......Δu(d i +T c -1) (9)

[0112] Among them, T c is the control domain, representing the number of parameters required to track future trajectories.

[0113] Specifically, the prediction basis of model predictive control is the system model. Assume that the sampling point of the control system is di, and the spatial state vector x(d i ) is obtained through measurement, then the future control system trajectory is expressed as formula (9), where T c is the control domain, which represents the number of parameters required to track the future control trajectory. i ), the number of predicted future state variables is T P , T P Also called prediction depth.

[0114] The present invention is in the cutting control system sampling point d i The system status information is obtained through sensors or other measurement methods, such as position, speed, temperature and other state variables, and the control trajectory Δu(d i ), Δu(d i +1), ......Δu(d i +T c -1), that is, formula (9) is the future control input sequence generated based on the prediction model in the current state, each Δu(d j ) indicates that at sampling point d j The control action applied at T c is the control domain, which represents the number of parameters required to track the future trajectory or the length of the future control trajectory.

[0115] MPC uses the dynamic model of the system to predict the future system state and optimize the control input based on the current state x(d i) to predict the future state. In step S3, the current state x(d i ) measurements, predict future control input changes, and optimize on this basis to achieve the predetermined control objectives.

[0116] In a preferred embodiment, in step S3, the expression of the predicted state variable is:

[0117] x(d i +1|d i ), x(d i +2|d i ), ..., x(d i +m|d i ), ..., x(d i +T P |d i )(10)

[0118] Among them, x(d i +m|d i ) represents the space state vector x(d i ) in d i + The predicted state variable at point m, T P is the prediction depth, which indicates the number of predicted state variables.

[0119] In a preferred embodiment, in step S3, the predicted state variable is calculated based on the control system state model, and the expression is:

[0120]

[0121] The predicted output is derived from the predicted state variables. The expression of the predicted output is,

[0122]

[0123] Define a vector:

[0124] Y=[y(d i +1|d i )y(d i +2|d i )y(d i +T P ∣d i )] T (13)

[0125] △U=[△u(d i ) △u(d i +1) △u(d i +T C -1)] T (14)

[0126] Among them, Y represents the output variable, △U represents the input variable, and the output definition vector is used to obtain

[0127] Y=Fx(d i )+λ△U (15)

[0128] in,

[0129]

[0130] Specifically, define the vector:

[0131] Y=[y(d i +1|d i )y(d i +2|d i )y(d i +T P ∣d i )] T (13)

[0132] △U=[△u(d i ) △u(d i +1) △u(d i +T C -1)] T (14)

[0133] Formula (13) includes all output prediction values ​​in the prediction time domain, and formula (14) includes the control input changes at the current time and future time.

[0134] in,

[0135]

[0136] Where F and λ are matrices constructed through the state-space model, which relate the current state to the control input changes to obtain the predicted output. Contains the combination of matrix C and matrix A with multiple powers, forming the prediction time length T P A linear combination of related

[0137] In a preferred embodiment, in step S4, the expected output is set to R p , the expression of the cost function is,

[0138]

[0139] in, represents a diagonal matrix, where r w represents the weight coefficient of closed-loop control, represents the identity matrix;

[0140] The expression Y=Fx(d i )+λ△U is substituted into the cost function to obtain

[0141]

[0142] Taking the derivative of △U, we get

[0143]

[0144] make When is zero, the optimal control signal is obtained, and the expression is:

[0145]

[0146] Specifically, assuming that the following trajectory of the output vector is R_p, the cost function J is defined to represent the control target.

[0147]

[0148] in, represents a diagonal matrix, where r w represents the weight coefficient of closed-loop control. Substituting equation (15) into equation (18) yields:

[0149]

[0150] The above formula can be derived with respect to △U:

[0151]

[0152] when When , the optimal control signal of the cutting system can be obtained:

[0153]

[0154] Specifically, the present invention is based on the above algorithm analysis, such as Figure 2 , Figure 3 As shown, firstly, a mathematical model of the cutting system is established, and the sensor device of the cutting system itself is used to sample the state variables in real time, so as to obtain the spatial state model of the control system, thereby predicting the future control trajectory of the cutting system, and obtaining the future state variables and predicted output based on the predicted cutting control trajectory. Then, a cost function J is established, and △U is derived through function J, and the optimal control signal is obtained when the derivative is 0.

[0155] In a preferred embodiment, the method further includes step S6, executing the optimal control signal at the current moment, returning to step S3 at the next moment, obtaining the space state vector at the next moment, and re-predicting and calculating the optimal control signal based on the space state vector at the next moment.

[0156] Specifically, the present invention first predicts the following T through model predictive control P The cutting system state at the moment is further optimized after the optimization is completed at the current sampling moment d. Figure 2 As shown, at the next sampling moment, the optimization is performed forward using the same optimization method and optimization time domain, and the optimization is continuously rolled forward, i.e., rolling optimization.

[0157] During the optimization process, a closed-loop feedback is formed by introducing the state information of the system in the current prediction time domain, that is, the system error correction is performed.

[0158] In a preferred embodiment, the cutting control system is centrally symmetrically arranged relative to the flat glass conveying roller.

[0159] Specifically, the basis of model predictive control is the mathematical model of the controlled object. The cutting control system is arranged in a centrally symmetrical manner relative to the flat glass transmission roller. Therefore, the state space model is adopted in the present invention. Through the known information of the system, the model-based predictive calculation is performed to obtain the predicted response for the next period of time. By evaluating the future response, the control system can be controlled to take corresponding actions.

[0160] The flat glass online cutting method based on model predictive control of the present invention can overcome the defects of the traditional proportional integral (PI) control, improve the response speed and stability of the glass cutting control system, play a good real-time adjustment role for the cutting system state, effectively reduce the failure rate of the cutting equipment, and ensure the stable operation of the glass cutting equipment. The present invention has strong practicality and is easy to implement.

[0161] The above description is only a preferred embodiment of the present invention, and does not limit the implementation mode and protection scope of the present invention. For those skilled in the art, it should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the description and illustrations of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for online cutting of flat glass based on model predictive control, characterized in that: include, Step S1, establishing a state space model of a cutting control system; Step S2, performing differentiation on the state space model at adjacent time steps, obtaining a change relationship between a state vector and an input vector in the state space model, and outputting a control system state model; Step S3, measuring and acquiring the spatial state vector of the sampling point of the cutting control system, calculating the future trajectory of the cutting control system using the control system state model, and calculating the predicted state variables and predicted output of the cutting control system; Step S4, setting a cost function, substituting the predicted output into the cost function, and calculating an optimal control signal.

2. The method for online cutting of flat glass based on model predictive control according to claim 1, characterized in that: The expression of the state space model is, x n (d+1)=A n x n (d)+B n u(d) y(d)=C n x n (d) where x n represents the state vector, d represents the sampling time, u represents the input vector, y represents the process output variable, A n Denotes the system dynamic coefficient, B n Indicates the input coefficient, C n Represents the output coefficient.

3. The method for online cutting of flat glass based on model predictive control according to claim 2, characterized in that: In step S2, the state space model is subjected to differential calculation of adjacent time steps at the d+1th time and the dth time, and the following is obtained: x n (d+1)-x n (d)=A n (x n (d)-(x n (d-1))+B n (u(d)-u(d-1)) The state vector x n The difference between the d+1th moment and the dth moment is expressed as, △x n (d+1)=x n (d+1)-x n (d) The difference between the input vector u at the dth moment and the d-1th moment is expressed as, △u(d)=u(d)-u(d-1) The spatial state equation is obtained in the difference form, △x n (d+1)=A n △x n (d)+B n △u(d) The difference between the process output variable y at the d+1th moment and the dth moment is expressed as, y(d+1)-y(d)=C n x n (d+1)-C n x n (d) =C n △x n (d+1) =A n C n △x n (d)+B n C n △u(d)。 4. The method for online cutting of flat glass based on model predictive control according to claim 3, characterized in that: In step S2, the control system state model is obtained according to the expression of the difference between the process output variable y at the d+1th moment and the dth moment, and the expression is: Among them, n is a zero vector, when C=[o n 1], the matrix (ABC) is an augmented matrix.

5. The method for online cutting of flat glass based on model predictive control according to claim 1, characterized in that: In step S3, the sampling point of the cutting control system is d i , the measured space state vector is x(d i ), the future trajectory of the cutting control system is expressed as, △u(d i ),△u(d i +1),……△u(d i +T c -1) Among them, T c is the control domain, representing the number of parameters required to track future trajectories.

6. The method for online cutting of flat glass based on model predictive control according to claim 4, characterized in that: In step S3, the expression of the predicted state variable is, x(d i +1∣d i ),x(d i +2∣d i ),……,x(d i +m∣d i ),……,x(d i +T P ∣d i ) Among them, x(i+m|d i ) represents the space state vector x(d i ) in d i + The predicted state variable at point m, T P is the prediction depth, which indicates the number of predicted state variables.

7. The method for online cutting of flat glass based on model predictive control according to claim 6, characterized in that: In step S3, the predicted state variable is calculated based on the control system state model, and the expression is: The predicted output is derived from the predicted state variables. The expression of the predicted output is, Define a vector: Y=[y(d i +1∣d i ) y(d i +2∣d i ) y(d i +T P ∣d i )] T △U=[△u(d i ) △u(d i +1) △u(d i +T C -1)] T Among them, Y represents the output variable, △U represents the input variable, and the output definition vector is used to obtain Y=Fx(d i )+λ△U in, 8. The method for online cutting of flat glass based on model predictive control according to claim 7, characterized in that: In step S4, let the expected output be R p , the expression of the cost function is, Among them, Y represents the actual output, represents a diagonal matrix, where r w represents the weight coefficient of closed-loop control, represents the identity matrix; The expression Y=Fx(d i )+λ△U is brought into the cost function to obtain, Taking the derivative of △U, we get make When is zero, the optimal control signal is obtained, and the expression is:

9. The method for online cutting of flat glass based on model predictive control according to claim 1, characterized in that: The method further includes step S6, executing the optimal control signal at the current moment, returning to step S3 at the next moment, obtaining the space state vector at the next moment, and re-predicting and calculating the optimal control signal based on the space state vector at the next moment.

10. The method for online cutting of flat glass based on model predictive control according to claim 1, characterized in that: The cutting control system is centrally symmetrically arranged relative to the flat glass conveying roller.

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