KR950012385B1 - Thickness control method for cold earip - Google Patents

Abstract

The method controls the thickness of cold rolling steel plate by simultaneouly controlling multiple variables of roll gap and roll velocity.

Description

Cold Rolled Sheet Thickness Control Method

Figure 1a is a conceptual diagram showing the relationship between the thickness control device and the control object and appearance according to the rolling phenomenon between two adjacent stand in the thickness control system of a conventional continuous cold rolling mill,

FIG. 1B is a reference diagram showing a thickness control concept of FIG. 1A in a block diagram. FIG.

Figure 2a is an example showing a conventional loop forming Elcu control system related to the present invention,

Figure 2b is an embodiment showing a loop forming elcu controller according to the present invention.

3 is a reference diagram showing a singular value diagram used for performance analysis of a controller in a conventional multivariate control system.

Figure 4a is an embodiment of the elcu controller controller reflecting the modeling error to the plant entrance side according to the present invention,

4b is a reference diagram showing a singular value diagram of a closed loop transfer function satisfying stability-toughness in the present invention.

Figure 5a is a reference diagram showing the amount of residual plate thickness deviation and tension deviation caused by a conventional PI controller,

Figure 5b is a reference diagram showing the amount of residual plate thickness and tension deviation caused by a conventional standard Elcu controller,

Figure 5c is a reference diagram of the amount of residual plate thickness deviation and tension deviation generated by the loop-forming Elcu controller according to the present invention.

* Explanation of symbols for main parts of the drawings

1 cold rolled plate 3 roll gap adjusting device

4: roll speed adjusting device 6: rolling load measuring device

7: Plate thickness measuring device 8: Tension measuring device

9: AGC system 10: Plant

11: integrator

The present invention relates to a thickness control means of a cold rolled steel sheet, which particularly ensures good uniformity of thickness when manufacturing such a cold rolled steel sheet to control the thickness of the cold rolled steel sheet by a loop forming elcuum control that can be widely used in various precision devices. It is about a method.

Conventionally, cold rolling mills that produce cold rolled plates have been pursuing maximization of productivity due to the rapid expansion of large-scale manufacturing industry that creates mass demand for cold rolled steel sheets such as automobiles, construction, and home appliances. With the advent of the industry, great attention has been paid to the upgrading of cold rolled steel sheets, in particular to the uniformity of sheet thickness. In addition, the type and the thickness of the cold rolled steel sheet is also gradually becoming thinner than the conventional.

Such changes in production environment are difficult to meet various requirements such as high precision of plate thickness and production of various varieties with the rolling controller using the classical technique used in the past. Therefore, there is an urgent demand for the application of a new control method for the design of a high performance thickness control system that can satisfy the specifications required for producing such cold rolled steel sheets.

On the other hand, the thickness variation of the cold rolled steel sheet is caused by various factors such as poor thickness of the material to be rolled, eccentricity of the rolling mills, unevenness of the rolling conditions, and the factors causing such plate thickness variation are disturbances for the normal rolling conditions. . The most important purpose of the cold rolling automatic thickness controller (hereinafter referred to as AGC) is to produce a cold rolled steel sheet with a target thickness regardless of the presence of disturbance.

When the plate thickness deviation occurs due to the disturbance during rolling, the AGC controls the thickness deviation to be "0" through the controller based on the thickness deviation measured by the sensor. In particular, in a continuous cold rolling mill in which four to five stands are continuously arranged, the thickness of the specific stand does not affect the adjacent stand so that the plate thickness at the stand exit is maintained at the target value.

In addition, the AGC system of continuous cold rolling is a typical multi-input (multi-input) in which the control targets such as plate thickness, tension between the stand and rolling load, and control means such as roll gap and roll speed have strong coherence around the rolling mill. Multi-Output or MIMO) system. However, most AGC systems in use are designed based on the theory of single-input single-output (SISO) control.

SISO means controlling only the roll gap to reduce the plate thickness variation, or controlling only the roll speed to control the tension uniformly. However, in actual rolling, the thickness change may occur due to the adjustment of the roll gap, and the plate thickness is controlled by the cold rolling AGC, which is designed in the conventional SISO concept, because it is a complicated system in which the plate thickness is changed by the change of the tension.

The object of the present invention is to provide the stability of the uncertainty of the mathematical model, such as non-linearity of cold rolling, inaccuracy of rolling theory, and error in setup calculation, among the control theory applied to the conventional Automatic Gauge Control (AGC) system. As a thickness control method to compensate for the lack of toughness, it is applied to the cold rolling process to provide a cold rolling thickness control method that can reduce the thickness variation (hereinafter referred to as "plate thickness variation") generated in the longitudinal direction of the cold rolled steel sheet It is.

It is still another object of the present invention to provide a thickness control system for continuous cold rolling, which is a typical multivariate system of multi-input-multi-output, by using a new optimal control theory, the loop forming LQ (Linear Quadratic) control method. The present invention provides a cold rolling thickness control method that overcomes limitations of plate thickness control due to instability of mathematical models and improves the thickness of cold rolled sheet.

Prior to describing the cold rolling thickness control method of the present invention, first, the physical phenomenon of rolling centering on any i-stand in a conventional multi-stand continuous cold rolling machine will be described with reference to FIG.

In this case, if a steel plate having a plate thickness of H is rolled at a reduction ratio r to obtain a rolled plate 1 having a plate thickness of h, the interval between the upper and lower work rates 2 should be set to S, and the rolling speed is 1 stand. The front and rear tensions should be set to Vr to keep them within acceptable limits.

Plate thickness deviation if disturbance occurs during rolling at the set roll gap S and rolling speed Vr and affects the rolling system h and rear tension deviation T _b is generated. At this time, the AGC system 9 finely adjusts the roll gap adjusting device 3 and the roll speed adjusting device 4 of the rolling mill as control means at the same time in order to make the target plate thickness and tension constant regardless of the influence of disturbance. Will be. In Fig. 1 (a), reference numeral "5" denotes disturbance, "6" denotes a rolling load measuring apparatus, "7" denotes a sheet thickness measuring apparatus, and "8" denotes a tension measuring apparatus.

On the other hand, when the cold rolling thickness control system of FIG. 1 (a) is shown as a block diagram, it is the same as (b), and in this case, when an error occurs in the output due to the disturbance W, the rolling mill 10 driven in the initial setting state is AGC ( 9) feeds back a control input proportional to the error to control the error to be removed. At this time, mathematically expressing the rolling mill thickness control system of Figure 1 (b) is as follows.

χ _p (t) = A _p χ _p (t) + B _p U (t) + E _p ω (t) (1)

The time function (1) is also called a state space model of the thickness control system, and is a typical representation of the MIMO system. The variables χ _p , U and ω used in the transplantation represent the state variable vector, the control input variable vector and the disturbance variable vector, respectively, and A _p , B _p and E _p represent the relationship between the state variable, the input variable and the disturbance variable, respectively. It is a coefficient matrix determined from the specification and dynamic characteristics of the rolling mill.

By integrating the state space model equation (1) with time, the process of change of state variables during rolling can be known, and the variables of interest among state variables are used as output variables. The state variable in rolling is the plate thickness variation h, tension change T _b , rolling load variation P and the like, and control input variables include control means of roll gap and roll speed. The disturbances include plate thickness variations and roll eccentricities of rolled materials.

On the other hand, the AGC system 9, which is a feedback controller, obtains a value proportional to an output variable (or a deviation between the target value and the actual value of the output) and uses it as a feedback control input. Therefore, if the feedback control gain of the AGC system 9 is denoted by G, the feedback cancellation input U will be as follows.

U (t) = -Gχ _p (t) (3)

In the method of obtaining G, the conventional AGC regards the rolling phenomenon as the SISO system and controls the plate thickness of each stand by using only one of the roll gap and the roll speed. However, since the actual rolling phenomenon is a MIMO system, the roll gap and the rolling speed are reduced. At the same time, a control gain G that can be finely adjusted must be obtained.

One of the most widely known controllers of the MIMO system is the Elcu controller. Elcu controller is a control method that applies the minimum principle of the calculus of variations. It is a characteristic function called cost function with the conditional equation (1) that mathematically expresses the physical state of the plant. It is an optimal control technique to obtain the control amount U that can minimize.

In particular, the loop-forming Elcu controller is an advanced form of the Elcu controller. The multivariable control method is used to obtain the weighting matrices Q and the control weighted matrix R much more systematically than the standard Elcu control scheme. to be. Elcu controller has the advantage of always guaranteeing the nominal stability, and also has the feature that the performance of the control system depends on the method of determining the Q, R.

In the following, an Elcu controller using the loop forming technique generalized in selecting Q and R will be briefly described.

In general, the loop forming Elcu controller is integrated with the existing control system (FIG. 1 (b)) as shown in FIG. 2 (a) to reduce the steady-state error for command follow- ing performance and disturbance and to obtain the necessary degree of freedom for forming the loop. Add element 11. Therefore, the feedback control gain G and the control input U of the control system including the integral element 11 will be as follows.

G = [G _z G _y G _r ] (4)

U (t) = -G _z Z (t)-G _y y (t)-G _r χ _r (t) (5)

As we add the integral element, the state variables and coefficient matrices of state equation (1) are changed as follows.

In the above formula, gradually p denotes an existing control system in which the integral element 11 is not included, and Z denotes a state variable of the integral element.

On the other hand, the price function J of the loop forming ElQ controller described above is defined as follows using the state equation (1) as a constraint.

In the above equation, Q and R are the design parameters of the Elcu controller, and by appropriately selecting the matrix N calculated from the coefficient matrices A, B and C of the state equation and the unknown values n and ρ, the control gain G necessary for optimal control can be obtained. . The unknowns n and ρ can be easily determined by frequency characterization.

Frequency characteristic analysis, which is a method to investigate the frequency-domain performance of multivariable systems, is a method of analyzing the characteristics of the maximum and minimum singular values of the transfer function using a board diagram, and the transfer function is a controller. Dynamic function representing the input and output of a.

The loop forming Elcu controller according to the present invention is shown in FIG.

Here, the feedback control gain G _y (13) is connected between the control input variable B _p side summer (S ₂ ) and the input side summer (S ₁ ), which is directly connected to the integrator 11 and the integrator 11 in parallel. It consists of a transfer function equipped with a feedback control gain G _z 14. In addition, the transfer function at this time can be expressed by the following equation.

That is, G _LQ (S) = G (SI-A) ^-1 B (10)

Where S is the Laplace operator, A and B are constant matrices representing the relationships between variables in the state equation, and I is the unit matrix. The singular value of the matrix is expressed by σ [·], and the singular value of the transfer function 10 can be obtained from the following equation from the property of the matrix.

Where λ is the eigenvalue of the transfer function matrix G _LQ , and G _LQ ^H is the complex conjugate transpose matrix. If the propagation matrix G _LQ is an (nxm) matrix with rank k, then k characteristic values can be obtained, and only the maximum value σ _max [G _LQ ] and the minimum value σ _min [G _LQ ] are changed by changing the frequency. In this case, a singular value Bode plot can be obtained as shown in FIG.

In general, as shown in FIG. 3, satisfactory control performance can be obtained as the maximum singular value σ _max [G _LQ ] and the minimum specific value σ _min [G _LQ ] coincide in the low and high frequency _bands . In addition, responsiveness can be improved by increasing the crossover frequency (frequency at which the characteristic value becomes " 0 ") representing the operating point characteristic of the control target. However, increasing the crossover frequency requires very large control inputs, so care must be taken.

The matching of singular values in the low and high frequencies depends on the determination of the unknown n in Eq. (9), and the magnitude of the crossover frequency is determined by the size of ρ. Therefore, it can be seen that by appropriately selecting the unknowns n and ρ, it is possible to optimally control the loop forming elcu controller that can secure control performance and responsiveness within the design specification range.

In the present invention, the following values were obtained as the weighting matrix selection parameter of the loop forming Elcu controller which can satisfy the conditions of the following Table 1, which is the basic design specification of the thickness control system required in the continuous cold rolling mill consisting of five stands.

TABLE 1

The n and ρ is slightly different depending on the various rolling conditions, but is a range of values that can satisfy the design specifications of Table 1.

Once the weighting matrices N and R are determined, the optimal control input U is determined by obtaining feedback control gain G that minimizes J from equation (7) and substituting it into equation (3). Therefore, G, the control gain matrix of the loop forming Elcu control system, is determined as follows.

G = R ^-1 B ^T K (13)

In the above equation, K is a constant matrix that can be obtained by solving the following control logarithmic Riccati, a method of minimizing the price function in equation (7).

A ^T K + KA + Q-KBR ^-1 B ^T K = 0 (14)

As a result, the thickness control of the cold rolling using the loop forming Elcu control results in a problem that the optimization of the feedback control amount is determined depending on how appropriately the weighting matrixes Q and R included in the price function J of equation (7) are selected.

Meanwhile, mathematically modeled continuous cold rolling systems always contain modeling errors. If modeling errors are not taken into account in the design of the controller, stability as well as performance will not be satisfactory in practical systems. Therefore, stability and robustness against the modeling error of the designed controller must be tested before the practical application of the controller.

FIG. 4 (a) shows the loop forming Elcu control system of the present invention including the modeling error. Part (a) indicated by a dotted line means an initially designed Elcu control system, and part (b) represents an actual control system in consideration of modeling errors. The modeling error of the controller is denoted by E. The designed controller must meet the following conditions for stability and robustness.

σ _max [C ₁ (S)] <σ ^-1 _max [E ₁ (S)] (15)

That is, ① shown in Figure 4 (a) point, that is, a closed loop transfer function matrix of C ₁ (S) up characteristic value _{σ max [C 1 (S)} ] is the inverse of the maximum characteristic values of the modeling error of the cut in the plant input side Σ ⁻¹ _max [E ₁ (S)]. Here, the open loop transfer function matrix T (S) and the closed loop transfer function matrix C ₁ (S) cut at the point ① in FIG. 4 (a) are as follows.

T ₁ (S) = GΦ (S) B (16)

C ₁ (S) = T ₁ (S) (IT ₁ (S)) ^-1 (17)

In the above formula, Φ (S) is the characteristic of the plant and is expressed as Φ (S) = (SI-A). The stability-toughness verification condition of Equation (15) is shown in FIG. 4 (b). That is, the bandwidth W _b of the open-loop transfer function matrix T (S) of the designed controller must satisfy the following conditions by modeling error.

W _b <W _m (18)

Here, W _m represents a bandwidth limited by the modeling error considered in design and means a frequency when σ ⁻¹ _max [E ₁ (S)] is 0 dB.

For the control system using Q and R selected from Equation (8), when it is confirmed that the stability-toughness is satisfied by the method of Equation (15), the Elcu controller that satisfies the given design specification is completed.

EXAMPLE

The following is a computer simulation result to confirm the plate thickness control effect of the loop forming Elcu dispersion controller described so far. Computer simulation is a computerized calculation and analysis of various rolling phenomena during actual cold rolling, and it is a descriptive experiment that replaces demanding practical experiments such as stopping the production line for the experiment and fear of equipment accidents due to abnormal experimental conditions. This is a good alternative to save time and money.

The biggest factor in the occurrence of plate thickness deviation during cold rolling is the plate thickness deviation of the material to be rolled, that is, the plate thickness deviation existing in the hot rolled strap. In general, the longitudinal plate thickness variation of the rolled material is periodically changed with a certain size, in the present invention was formulated by the following sine wave function and used as a disturbance computer simulation.

H ₁ (t) = 30sin2πt (19)

Of equation (19) H ₁ means an amplitude, that is, a thickness deviation disturbance having a thickness deviation of ± 30 μm and a frequency of 1 kHz. For convenience, only one cycle of disturbance is simulated. And the thickness of the final stand exit plate thickness, which is the rolling phenomenon when the disturbance of equation (19) is applied to various thickness control methods change in h ₅ and rear tension The control performance was evaluated by comparing T _b5 .

The objects to be compared are the PI controller, which is a conventional distributed control system, a standard Elcu controller and a loop forming Elcu controller of the present invention. FIG. 5 (a) shows the thickness control results using the conventional PI controller. Although the thickness deviation of ± 30 µm initially decreased considerably to about ± 2 µm after the control, the rear tension is unstable to deviate significantly from the target value. Control characteristics are shown.

FIG. 5 (b) shows a thickness control result using a standard elcu controller, which shows much better control performance than the eye control in both thickness and tension, but still leaves unstable characteristics in the thickness control. In addition, it is inconvenient to use a trial-and-error method in determining the standard Elcu control gain G.

On the contrary, it can be seen that the loop forming elcu controller proposed in the present invention exhibits superior control characteristics than all other control methods in plate thickness control and tension control as shown in (c) of FIG. 5. In addition, since the method of organization is used in selecting the control gain, it has the advantage of saving time and ensuring sufficient stability and robustness.

Claims (4)

A method for controlling the thickness of a cold rolled steel sheet in a continuous cold rolling mill, wherein the process control is performed to control the sheet thickness by a multivariate control method using a roll gap and a roll speed at the same time. The method of claim 1, wherein the multivariate method uses a loop forming elcuum control technique to minimize a decrease in stability-toughness due to an uncertainty of a mathematical model. The cold rolled steel sheet according to claim 2, wherein an unknown number n and p are used to ensure stability and robustness against modeling error when selecting weighted columns Q and R used as design parameters of the loop forming Elcu controller. Thickness control method. 4. The thickness control of the cold rolled steel sheet according to claim 3, wherein when the weighting matrices Q and R are selected, the unknown n and p ranges are limited to n = 0.6 to 1 and p = 0.0002 to 0.0004, respectively. Way.