JPH0259002B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Application Field] The present invention relates to a dimensional control method in continuous rolling of wire rods and steel bars. [Prior Art] Conventionally, there are the following examples of dimensional control methods for wire rods and steel bars. As a first example, “Plasticity and Processing” vol20, No.224
(1979-9), the deviation of the actual measured tension value from the target value is determined by direct tension detection in the steel bar mill, and the roll rotation speed is adjusted by the manipulated variable by taking into account the mutual influence between the stands. Proportional and integral control of the tension is performed. As a second example, as shown in Japanese Unexamined Patent Application Publication No. 128469/1983, using the influence coefficient of rolling reduction on the product width dimension, the product vertical dimension is determined by the roll reduction of the final stand of a common drive block mill for wire rods. The width of the product is proportionally controlled by the deviation of the actual measurement value from the target value by the reduction of the first stand. As a third example, as shown in Japanese Unexamined Patent Publication No. 57-88908, No. 1 of a finishing block mill for wire rods is shown.
By changing the relative speed between stand 1 and stands No. 2 to n, the tension between stands no. The product width is controlled according to the deviation of the value from the target value. In the method of the first example, the gain is determined by trial and error, and the optimization thereof is limited. In the method of the second example, the influence coefficient is a proportional gain, but the control performance is unknown. In the method of the third example, a specific method for determining the gain is not shown, and the control performance is unknown. [Problems to be Solved by the Invention] The present invention provides multivariable control with short settling time, zero offset, and good control performance for the exit height and exit width of the final stand in continuous rolling of wire rods and steel bars. is intended to do. [Means for Solving the Problem] The present invention uses the equation of state for rolling consisting of deformation, load, and temperature, and uses the roll rotation speed and roll gap as manipulated variables, and calculates the output side of the final stand of the target rolling mill group. In the method of controlling the height and exit width using state vector feedback based on the optimal regulator theory, the deviation of the roll gap in each stand that makes up the rolling mill row during continuous rolling of wire rods and bars by the rolling mill row. [((Actual measurement value) - (Reference value))/(Reference value of rolled material exit height)] as ΔS _i ^* , i=1, 2,...,n Deviation of forward tension of rolled material [((Actual measurement) value) - (reference value)) / (reference value of average deformation resistance)] as Δt _fj ^* , j = 1, 2,..., n-1 Deviation of roll rotation speed [(actual value) / (reference value) - 1] as ΔN _i ^* , i=1, 2,...,n Deviation of the cross-sectional height of the rolled material and the width of the rolled material at the exit side [(actual value)/(target value) - 1] as Δh _i ^* , Δb _i ^* , i = 1, 2, ..., n Deviations of the average temperature of the material at the entrance, the cross-sectional height of the rolled material at the entrance, and the width of the rolled material at the entrance [(Actual value) / (Reference value) - 1] as ΔT _ni ^* , ΔH _i ^* , ΔB _i ^* , i=1, 2,..., n Also, the height dimension of the rolled material at the exit side of the k-th stand and the width of the rolled material at the exit side, respectively. _The integral value of the _deviation of ^is expressed as _{∫Δh k} ^* dt _, ^∫Δb _k ^* dt ^, and _the state vector ^{x is} expressed _as
^* dt, ∫Δb _k ^* dt)′ (′ means transposed matrix) Output y=(Δh _i ^* , Δb _i ^* , Δt _fj ^* , ΔN _i ^* , ∫Δh _k ^* dt,
∫Δb _k ^* dt)' Input u = (dΔS _i ^* /dt, dΔN _j ^* /dt)' Disturbance w = (ΔT _ni ^* , ΔH _i ^* , ΔB _i ^* )'i=1, 2,... ，
n, j = 1, 2, ..., n-1 where k: stand number at which the height and width of the rolled material at the exit side are measured; n: the number of stands in the rolling mill row; Using the state equation dx/dt=Ax+Bu y=Cx, the optimal input u _ppt that minimizes the evaluation function J=∫ ^∞ ₀ (y′Qy+u′Ru)dt (Q, R are weight matrices) = −R ^{- 1} B'Px (matrix P is A'P+PA-PBR ^-1 B'P+C
'QC
= 0 solution), the height dimension and width dimension of the rolled material discharged from the final stand (nth stand) in the rolling mill row are controlled by state vector feedback. This is a dimensional control method for wire rod and steel bar rolling. [Here, the stand numbers i, j at the control input u = (dΔS _i ^* /dt, dΔN _j ^* /dt) are i = 0 to n, j
It is assumed that any combination can be taken within the range of =0 to n. When i = 0, the roll gap is not used as the manipulated variable. When j = 0, the roll rotation speed is not used as the manipulated variable. When j≠0, j = any one of 1 to n.
The stand is a pivot stand, and the roll rotation speed is not used as the manipulated variable. There is no case where i=0 and j=0 (in which case neither the roll gap nor the roll rotation speed is used as the manipulated variable in any of the stands 1 to n). ] [Operation] The present invention uses the evaluation function J=∫ ^∞ ₀ (y′Qy+u′Ru)dt
The optimal input u _ppt that minimizes the state vector feedback u _ppt = -R ^-1 B'Px (matrix P is A'P + PA - PBR ^-1 B'P
+
Since a plurality of inputs can be found simultaneously as solutions for C'QC=0, it is relatively easy to design a control system with good control performance. [Examples] Hereinafter, the present invention will be explained in detail based on Examples. When the nonlinear rolling model is linearized around the reference state (Table 2) and made dimensionless, the following state equation is obtained. Here, Δx is defined as a variation from the pass schedule value x ₀ , Δx ^* ≡ Δx/x ₀ . (However, ΔS ^* = ΔS/h, Δt _f ^* = Δt _f /k _fn ) Here, the definitions of the symbols are as follows. ΔS _i ^* : Deviation of the roll gap at the i-th stand ([(actual value) - (standard value)] / [standard value of the height of rolled material at the exit side of the stand]) ΔS _tj ^* : In front of the j-th stand Deviation of material tension at (output side of J-th stand) ([(actual measurement value) - (reference value)]/[average deformation resistance reference value of rolled material]) ΔN _j ^* : Roll rotation speed at j-th stand Deviation ([(actual value) - (reference value)] / [reference value]) Δh _i ^* : Deviation of material height at the exit side of the i-th stand ([(actual value) - (reference value)] / [Reference value]) Δb _i ^* : Deviation of material width at the exit side of the i-th stand ([(actual value) - (reference value)]/[reference value]) ΔT _ni ^* : Input side of the i-th stand Deviation of material average temperature at ([(actual value) - (reference value)]/
[Reference value]) ΔH _i ^* : Deviation of material height at the entry side of the i-th stand ([(actual value) - (reference value)]/[Reference value]) ΔB _i ^* : Deviation of the material height at the entry side of the i-th stand Deviation of material width on the side ([(actual value) - (reference value)] / [reference value]) dΔS _i ^* /dt: Time derivative of ΔS _i ^* dΔN _j ^* /dt: Time derivative of ΔN _j ^* x〓 =Ax+Bu+Dw (1) y=Cx+Ew (2) However, the state vector x, output y, input u, and disturbance w are as follows. x=(ΔS _i ^* , Δt _fj ^* , ΔN _j ^* )′ (3) y=(Δh _i ^* , Δb _i ^* , Δt _fj ^* , ΔN _j ^* )′ (4) u=(dΔS _i ^* /dt , dΔN _j ^* /dt)′ (5) w=(ΔT _ni ^* , ΔH _i ^* , ΔB _i ^* )′ (6) i=1 to n, j=1 to n-1, n: number of stands A, B, C, D, and E are matrices whose elements are partial differential coefficients of rolling characteristics. The delay formula between stands is ΔT _ni+1 ^* (t)=ΔT _ni ^* (t−t _di+1 )+Δ∫ ^t _t−td 〓
_i+1
∂T′ _ni ^* /∂tdt (7) Here, t is a certain time, and t _di+1 represents the time required for the material to be transferred from the i-th stand to the i+1-th stand. Further, Δ∫ ^t _t-td 〓 _i+1 ∂T′ _ni ^* /∂ _t dt represents the deviation of the average temperature drop of the mountain material from the i-th stand to the i+1-th stand. ΔH _i+1 ^* (t)=Δb _i ^* (t−t _di+1 ) (8) ΔB _i+1 ^* (t)=Δh _i ^* (t−t _di+1 ) (9) In 4-stand mill The values of matrices A to E in the standard state of rolling in Table 2 are as shown in Table 3.

【table】

【table】

[Table] A continuous-time control system was designed by applying optimal control theory to this system. In a linear control system, the influence of disturbances after dead time is not considered. Therefore, in order to take this into account, an influence coefficient was added and the state equation was changed as shown below. When integral control is provided for the exit height and width of the finishing stand, the state vector x, output y, and input u are set as follows. Here, the definitions of the symbols are as follows. ∫Δh ₄ ^* dt: Time integral value of the material height deviation Δh ₄ ^* at the exit side of the fourth stand ∫Δb ₄ ^* dt: Time integral value of the material width deviation Δb ₄ ^* at the exit side of the fourth stand Time integral value ΔS _i ^* : Deviation of the roll gap at the i-th stand ([(actual value) - (reference value)] / [reference value of the height of the rolled material at the exit side of the stand]) Δt _fj ^* : Deviation of the roll gap at the i-th stand Deviation of material tension at the front of the stand (exit side of the j-th stand) ([(actual value) - (reference value)]/[average deformation resistance reference value of rolled material]) ΔN _j ^* : at the j-th stand Deviation of roll rotation speed ([(actual value) - (reference value)] / [reference value]) Δh _i ^* : Deviation of material height at the exit side of the i-th stand ([(actual value) - (reference value) )] / [Reference value]) Δb _i ^* : Deviation of material width at the exit side of the i-th stand ([(actual value) - (reference value)] / [reference value]) ΔT _ni ^* : i-th stand Deviation of material average temperature at the entrance side ([(actual value) - (reference value)]/
[Reference value]) ΔH _i ^* : Deviation of material height at the entry side of the i-th stand ([(actual value) - (reference value)]/[Reference value]) ΔB _i ^* : Deviation of the material height at the entry side of the i-th stand Deviation of material width on the side ([(actual value) - (reference value)] / [reference value]) dΔS _i ^* /dt: Time derivative of ΔS _i ^* dΔN _j ^* /dt: Time derivative of ΔN _j ^* x= (ΔS _i ^* , Δt _fj ^* , ΔN _j ^* , ∫Δh ₄ ^* dt, ∫Δb ₄ ^*
dt)′ (10) y=(Δh _i ^* , Δb _i ^* , Δt _fj ^* , ΔN _j ^* , ∫Δh ₄ ^* dt,
∫Δb ₄ ^* dt)′ (11) u=(dΔS _i ^* /dt, dΔN _j ^* /dt)′ (12) Influence coefficients are added to matrices A, B, and C as follows. Here, the matrix adds to B the influence coefficient that the control input has on the time derivative of tension. b~ _i+1,j = ∂i+1Δt _fi ^* /∂ΔS _j ^* =a _i+4,j (16) b~ _i+4,j+4 = ∂i+1Δt _fi ^* /∂ΔN _j ^* =a _{i+ 4,j+7} (17
) Matrix C~ adds to C the influence coefficient of the roll gap on the exit height and exit width. C~ _i,j = ∂Δh _i ^* /∂ΔS _j ^* (18) C~ _i+4,j = ∂Δb _i ^* /∂ΔS _j ^* (19) The state equation for finding optimal control is x〓= Ax+Bu (20) y=Cx (21) In the system shown by equations (20) and (21), the optimal input u _ppt that minimizes the evaluation function J=∫ ^∞ ₀ (y′Qy+u′Ru)dt (22) is u _ppt = −R ⁻¹ B′Px (23). However, the matrix P is A'P+PA-PBR ^- 'B'P+C'QC
=0
(24) This is the solution of the Riccati equation shown by. Weight Q,
R was determined by repeating simulations. The results of control using the dimensional control method of the present invention are shown below. Here, Table 1 shows symbols of variables of physical quantities in continuous rolling of wire rods and steel bars. In a 4-stand mill, the average temperature of the material at the entrance of No. 1 stand, the height at the entrance, and the width at the entrance are ΔT _ni ^* = −0.055, ΔH _i
^* = ΔB _i ^* = 0.033 A case where the change occurs in a stepwise manner was studied.

〔Effect of the invention〕

As explained above, in the case of this embodiment according to the present invention, it has been revealed that the control using the integral type optimal regulator has excellent control performance as described below. (1) Tension control has short settling time and offset = 0.
(zero). (2) The height and width of the exit side of the finishing stand can be controlled to offset = 0 (zero). In this example, looperless continuous rolling was shown, but even when there is a looper between stands, if the equation of state is constructed using the relational expression between the looper height and the tension of the rolled material, the same result as in the above example can be obtained. Dimensional control is possible with this method.

[Brief explanation of drawings]

Figures 1 to 3 are illustrative diagrams of the step response of tension Δt _fj ^* , exit height Δh _i ^* , and exit width Δb _i ^* when the input is 0 (zero), and Figures 4 to 8 are Tension force Δt _fj ^* , exit height Δh i *, exit width Δb _i ^* , roll rotation speed ΔN _j ^* , roll gap ΔS _i ^* when integral control is used for _finishing ^stand exit height and exit width. FIG. 6 is an exemplary diagram of a step response.

Claims (1)

[Claims] 1. In continuous rolling of wire rods and steel bars by rolling mill rows, the deviation of the roll gap in each stand that makes up the rolling mill row [((Actual measurement value) - (Reference value))/(Rolled material output Standard value of side height)] is ΔS _i ^* , i = 1, 2, ..., n Deviation of forward tension of rolled material [((actual value) - (standard value)) / (standard value of average deformation resistance) ] as Δt _fj ^* , j=1, 2,..., n-1 Roll rotation speed deviation [(actual value)/(reference value)-1] as ΔN _i ^* , i=1, 2,..., n The deviation of the cross-sectional height of the rolled material and the width of the rolled material at the side [(actual value) / (target value) - 1] is Δh _i ^* , Δb _i ^* , i = 1, 2, ..., n Average temperature of the material on the inlet side , the deviations of the cross-sectional height of the rolled material at the entry side and the width of the rolled material at the entry side [(actual value)/(standard value) - 1] are expressed as ΔT _ni ^* , ΔH _i ^* , ΔB _i ^* , i= 1, 2,..., n Also, the integral values of the deviations of the height dimension of the rolled material at the outlet side and the width of the rolled material at the outlet side of the k-th stand are ∫Δh _k ^* dt, ∫Δb _k ^* dt _The ^{state vector} _{x is} ^expressed _as ^_ _{_} ^_ _{_}
^* dt, ∫Δb _k ^* dt)′ (′ means transposed matrix) Output y=(Δh _i ^* , Δb _i ^* , Δt _fj ^* , ΔN _i ^* , ∫Δh _k ^* dt,
∫Δb _k ^* dt)' Input u = (dΔS _i ^* /dt, dΔN _j ^* /dt)' Disturbance w = (ΔT _ni ^* , ΔH _i ^* , ΔB _i ^* )'i=1, 2,... ，
n, j = 1, 2, ..., n-1 where k: stand number at which the height and width of the rolled material at the exit side are measured; n: the number of stands in the rolling mill row; Using the state equation dx/dt=Ax+Bu y=Cx, the optimal input u _ppt that minimizes the evaluation function J=∫ ^∞ ₀ (y′Qy+u′Ru)dt (Q, R are weight matrices) = −R ^{- 1} B'Px (matrix P is A'P+PA-PBR ^-1 B'P+C
'QC
= 0 solution), the height dimension and width dimension of the rolled material discharged from the final stand (nth stand) in the rolling mill row are controlled by state vector feedback. A method for controlling the dimensions of a cross section of a rolled material during wire rod and steel bar rolling. [Here, the stand numbers i, j at the control input u = (dΔS _i ^* /dt, dΔN _j ^* /dt) are i = 0 to n, j
It is assumed that any combination can be taken within the range of =0 to n. When i = 0, the roll gap is not used as the manipulated variable. When j = 0, the roll rotation speed is not used as the manipulated variable. When j≠0, j = any one of 1 to n.
The stand is a pivot stand, and the roll rotation speed is not used as the manipulated variable. There is no case where i=0 and j=0 (in which case neither the roll gap nor the roll rotation speed is used as the manipulated variable in any of the stands 1 to n). ]