JPH0230766B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a tension control method for controlling the inter-stand tension to an arbitrary target value while keeping the looper angle of the looper between the stands of a continuous rolling mill substantially constant.

In a conventional tension control device that includes a looper between stands of a continuous rolling mill, the tension between the stands is controlled by causing a looper motor to generate a predetermined torque, and by changing the looper angle by changing the speed between the stands. However, in this system, the tension changes as the looper height changes, and the looper height changes as the tension changes, resulting in a so-called mutual interference system, which has a limit in controllability.

On the other hand, a state feedback control has been proposed in which the looper angular velocity, looper angle, tension, and disc speed difference between stands are used as state vectors, and the looper motor drive torque and the standard value of disc speed difference between stands are used as operation vectors (Japanese Patent Application Laid-Open No. 1983-1999-1). 23309). However, according to optimal control theory, this method constitutes feedback based only on proportional operation, and offset may occur if there is a relatively large steady disturbance or if the target tension changes over time. It is generally said that this reduces controllability.

This invention has been made in view of the above-mentioned circumstances, and its purpose is to provide a method for controlling tension between stands of a continuous rolling mill that does not cause offset by performing integral state feedback control. .

The method of this invention will be explained in detail below. Figure 1 shows the geometrical arrangement of the looper system in a general tension control system.
2 is a rear stand, each of which is equipped with a speed control device. 3 is a looper device, which includes a looper control device. 4 is a material to be rolled. Here, in order to simplify the explanation, the reference speed stand (pivot stand) for control is taken as the rear stage stand 2. Therefore, the height of the looper and the tension between the stands are affected by the peripheral speed of the roll of the front stage stand 1 and the torque of the looper motor.

The equation of motion of the looper is the reference angle θ ₀ of the looper,
The following equation is obtained by linear approximation around the reference value σ ₀ of the inter-stand tension and the reference target value T _refp of the looper torque.

d ² / dt ² (Δθ) = a ₁₁ d/dt (Δθ) + a ₁₂ (Δθ) + a ₁₃ (Δσ) + b ₁₁ (ΔT _ref ) ... (1) However, θ: looper angle σ: tension between stands T _ref : looper drive torque target value Δ: operator indicating the deviation around the reference value Each parameter in equation (1) is obtained as follows.

a ₁₁ =-g/JD ……(2) a ₁₂ =-g/J{σ ₀ (∂′K ₁ /∂θ)〓 _p + (∂′K ₂ /
∂θ)〓 _p }……(3) a ₁₃ =−g/JK ₁ (θ ₀ )……(4) b ₁₁ =g/J……(5) K ₂ (θ) = 2ρh ₀ B ₀ rcosθ√ ² + (−)
² + W _L arcos (θ + θ _G ) ...(7) However, g: Acceleration of gravity J: Rate of inertia of the looper r: Arm length of the looper ar: Arm length of the center of gravity of the looper c: Offset of the looper rotation axis from the path line Quantity l: 1/2 of the distance between stands θ _G : Offset angle of looper center of gravity D: Friction coefficient of looper axis h ₀ : Material plate thickness B ₀ : Material plate width ρ: Material density W _L : Looper weight and tension between stands The generation formula is expressed by the following formula.

Δσ=E/2l(∂K ₄ /∂θ)〓 ₀ Δθ＋ ^E _2l ∫ ^t _p Δv _M dt
...(8) However, K ₄ (θ) = 2√ ² + (-) ² ...(9) Δv _M = (1-f) Δv ...(10) E: Young's modulus Δv _M : Material speed difference f: Advancement rate of front stand material Δv: Front stand roll circumferential speed deviation Equation (8) is differentiated and linearized around the reference value to obtain the following equation.

d/dt(Δσ)=a ₃₁ d/dt(Δθ)+a ₃₄ Δv……(
11) However, a ₃₁ = E/2l(∂K ₄ /∂θ) 〓 _p ……(12) a ₃₄ = −E/2l(1+f) ……(13) On the other hand, the response of the main motor is first-order lag It is expressed as

d/dt (Δv) = a ₄₄ (Δv) + b ₄₂ (Δv _ref ) ... (14) However, a ₄₄ = -1/T ... (15) b ₄₂ = 1/T ... (16) T: Main motor time constant Δv _ref : Target value of the difference Δv between the roll peripheral speeds of the pivot stand and the dependent stand.Then, the following variables are defined here.

ΔZ〓=−∫ ^t ₀ Δθdt ……(17) ΔZσ=−∫ ^t _p Δσdt ……(18) Combining the above equations (1), (11), (14), (17), and (18), If we ignore the variation term of the target value, we get the following equation.

d/dtX=AX+BU...(19) However,
Z〓) ^T u = (ΔT _ref , ΔV _ref ) ^T A = a ₁₁ 1 a ₃₁ 0 0 0 a ₁₂ 0 0 0 -1 0 a ₁₃ 0 0 0 0 -1 0 0 a ₃₄ a ₄₄ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 B=b ₁₁ 0 0 0 0 0 0 b ₄₂ 0 0 0 0〓 | 〓 ^T That is, X is the state variable vector, U is the operation vector, and A and B are the coefficient matrices. show.

This invention takes into account the integral elements according to equations (17) and (18), and calculates the quadratic evaluation index J=∫ ^∞ _p (X ^T QX + U ^T RU) dt ... (20) where, Q: non-negative definite matrix R: Good responsiveness by finding U that minimizes the positive definite matrix,
In addition, tension control is performed that is resistant to steady disturbances and fluctuations in target tension.

Here, Q and R constitute evaluation criteria determined by the degree of emphasis placed on tension control accuracy, looper angle control accuracy, offset removal ability, and the like.

Now, equation (20) solves the Rikatsuchi type differential equation,
It can be minimized by finding the feedback matrix K. That is, it is optimal to feedback the manipulated variable according to the following equation.

U=KX...(21) In the above explanation, the pivot stand is installed on the rear stand 2, but the same method can be applied even when the pivot stand is installed on the front stand 1.

Next, an outline of a tension control device for carrying out the method of this invention will be explained with reference to FIG. Front and rear stands 1 and 2
are provided with mill speed control devices 11 and 12, respectively, and the looper device 3 is provided with a looper torque control device 13. Reference numeral 21 denotes a tension control device, which controls control reference values θ ₀ , σ ₀ , T _refp , v ₀ and equations (2) to (7), (9) to (10), and (12) to (13) in a steady state. ) and (15) to (16), the material specifications, equipment constants, etc. are given to this tension control device 21 in advance.
In addition, the looper device 3 is equipped with an inter-stand tension meter, a looper angle meter, and a looper angular velocity meter, and σ, θ, and d/dtθ are inputted to the tension control device 21, and v is input to the tension control device 21.
In this case, the pivot stand is the rear stage stand 2, and the main motor speed v _ref of the front stage stand 1 and the looper drive torque target value T _ref of the looper device 3 can be set from the tension control device 21.

The tension control operation using the above control device and measuring instrument is performed as follows. First, σ, θ, d/dt θ, v are measured, and the state vector X is determined by adding equations (17) and (18). Next, coefficient matrices A and B are determined using equations (1) to (16). Next, find the feed gain K that minimizes the evaluation index J in equation (20). The feedback gain K determines the weight that each element of the state vector gives to the main motor speed change amount and the looper motor torque change amount. Finally, the front stand roll circumferential speed deviation instruction value and looper drive torque obtained by equation (20) are set in the main motor and looper motor of the front stand, respectively. The above processing is performed at regular intervals.

By performing the above control, it is possible to control steady disturbances and changes in the tension target value without causing offsets.

FIG. 3 shows a comparison between the control characteristics according to the method of this invention and the control characteristics according to the invention described in the above-mentioned Japanese Patent Application Laid-Open No. 56-23309 (hereinafter referred to as the conventional method). This shows that offsets occur in the conventional method due to ramp-shaped disturbances, but the offsets can be absorbed by the integral type control of the present invention.

The method of this invention is as described above, and by performing integral state feedback control, it is possible to perform inter-stand tension force control that does not cause offset even if the disturbance is large or the target tension value is changed. . FIG. 4 shows the control status of the looper angle and tension when the control method of the present invention is used and when the method shown in FIG. 1 is used.

In the control method of the present invention shown in Fig. 4a, even when a step-like disturbance is applied, both the looper angle and the tension are controlled close to the target values, whereas the control method shown in Fig. 4b It can be seen that in the method shown in FIG. 1, a steep and large disturbance occurs in the tension, and the looper angle also fluctuates greatly, making it difficult for the looper angle to recover.

[Brief explanation of drawings]

Fig. 1 is an explanatory diagram of a general tension control system for explaining the method of this invention, Fig. 2 is a schematic explanatory diagram of a tension control device for carrying out the method of this invention, and Fig. 3
The figure is a diagram showing the response of the control system according to the method of the present invention in comparison with the conventional method. FIG. 4 is a diagram comparing and showing the control states of the looper angle and tension when the control method of the present invention is used and when the method shown in FIG. 1 is used. 1... Front stage stand, 2... Back stage stand, 3... Looper device, 11, 12... Mill speed control device, 13
...Looper torque control device, 21...Tension control device.

Claims (1)

[Scope of Claims] 1. A tension control device consisting of a looper torque control device and a mill speed control device arranged between the stands of a continuous rolling mill is provided to control the tension between the stands while controlling the looper angle to a constant value. In the inter-stand tension control method of a continuous rolling mill that controls the tension to a reference value, the angular deviation Δθ from the reference angle of the looper, the differential value d/dt (Δθ) of Δθ, the deviation Δσ of the inter-stand tension from the reference value, Difference Δv in roll peripheral speed between pivot stand and dependent stand, and time integral value ΔZ〓 of Δθ
and the time integral value ΔZ〓 of the inter _- stand tension deviation _Δσ are elements of _the state variable _vector , the equation of motion of the tension control system is expressed as a state equation of d/dtx=Ax+Bu by the coefficient matrices A and B, and where Q is a non-negative definite matrix and R is a positive definite matrix, J=∫ ^∞ _p (x ^T Qx+u ^T Find the operation vector u that minimizes the evaluation function Ru)dt, and the obtained ΔT _ref ,
A method for controlling tension between stands of a continuous rolling mill, characterized in that tension between stands is controlled by controlling a looper torque control device and a mill speed control device using Δv _ref .