KR20150074948A - Multi input-multi output electromagnetic vibration control apparatus and method - Google Patents

Abstract

A multi-input and multi-output electromagnetic vibration control device according to an embodiment of the present invention includes multiple electromagnets applying a magnetic force in a direction intersectional to multi-input and multi-output strips for controlling the vibration of the strips; multiple gap sensors measuring the distance between the strips and corresponding electromagnets; a positive feedback control unit controlling the amount of currents inputted into the electromagnets according to distance information measured by the gap sensor; and a gain control unit calculating a control gain of the positive feedback control unit to satisfy stability conditions of a closed circuit system expressed with transfer functions of the strips and positive feedback control unit.

Description

TECHNICAL FIELD [0001] The present invention relates to a multi-input multi-output electromagnetic vibration control apparatus and a multi-input multi-

The present invention relates to a multi-input multi-output electromagnetic vibration control apparatus and method for a galvanized steel sheet, and more particularly to a vibration control apparatus and method for setting optimum gains for operating within a stable range in multi- ≪ / RTI >

Generally, a continuous galvanizing line (CGL) is provided with an electromagnetic vibration control device for suppressing vibration of a steel sheet. The vibration control device is intended to suppress vibration of a plated steel strip (strip) transferred between a plating bath roll and a cooling tower roll.

1 is a structural view of a general continuous hot dip galvanizing line.

As shown, the continuous hot-dip galvanizing line 100 facility includes a zinc pot 108, a plating bath roll 101, a safety roll 102 and a calibrating roll 103, 105, an air knife 104, and a vibration control device 106. [0033]

The continuous hot-dip galvanizing line facility is a process line facility for producing a plating strip. The most important facility is a plating bath 108, and there are three rolls in the plating bath 108 to coat the strip 105 with zinc And the curvature of the strip 105 can be controlled. An air knife 104 is provided at an upper portion in the strip traveling direction of the plating bath 108 to sweep zinc coated on the strip 105 to control the thickness of the zinc plating coating to be constant. A cooling tower roll (not shown) may be provided on the upper portion of the air knife 104 to cool the strip 105.

The air knife 104 serves to shear the zinc on both sides of the strip 105 and the strip 105 must pass through the center between both air knives 104 to ensure a uniform coating thickness. In addition, since the strip 105 freely oscillates between the plating bath roll 101 and the cooling tower roll (not shown), such a vibration is suppressed so that a uniform plating thickness of the strip 105 can be secured. Therefore, in the continuous hot-dip galvanizing line equipment, a vibration control device 106 for suppressing the vibration of the strip 105 is installed.

The vibration control device 106 may be an active vibration control device using an electromagnet and a sensor. As an active vibration control algorithm, a PID (proportional-integral-differential) control method is typically used. The PID control method uses a negative feedback control method for the amount of vibration of the strip 105. A problem with this control method is that the differential controller gain must be increased in order to reduce the vibration of the strip 105. In this case, a phenomenon called spill-over occurs. This spillover phenomenon is a phenomenon in which the strip 105 has multiple resonance frequencies from a low frequency to a high frequency, so that the amplification in the high frequency region is much increased in the differential control, and the vibration in the high frequency region becomes large.

The positive position feedback control method is a vibration control method that does not use differential control. It has a great advantage of attenuation in the high frequency region. However, when the instability region is reached when the gain is increased, 105 are directed to the electromagnet, which may cause a problem in stability rather than the negative feedback control method.

In the art, a vibration control apparatus and method for performing stable vibration control without a spillover phenomenon in a double feedback control for a strip having a multiple resonance frequency in multi-input-multiple output electromagnetic vibration control using a plurality of electromagnets and sensors Is required.

In order to solve the above problems, a first aspect of the present invention provides a multi-input multi-output electromagnetic vibration control apparatus. The multi-input multi-output electromagnetic vibration control apparatus includes a plurality of electromagnets for applying a magnetic force in a direction crossing a strip for vibration control of a multi-input multi-output strip, and a plurality of electromagnets for measuring a gap between the corresponding electromagnets and the strip A positive feedback control unit for controlling an amount of current input to the plurality of electromagnets in accordance with the distance information measured by the plurality of gap sensors; and a closed loop control unit, which is expressed by a transfer function of the strip and a transfer function of the positive feedback control unit, And a gain control unit for calculating a gain control of the positive feedback control unit so as to satisfy a stability condition in the system.

A second aspect of the present invention is a method for controlling a vibration of a multi-input multi-output strip, comprising a plurality of electromagnets for applying a magnetic force in a direction intersecting a strip, And a gain controller for calculating a control gain of the positive feedback control unit, wherein the positive feedback control unit controls an amount of current input to the plurality of electromagnets according to the distance information measured by the plurality of gap sensors, A multi-input multi-output electromagnetic vibration control method of an electromagnetic vibration control apparatus is provided. The multi-input multi-output electromagnetic vibration control method according to claim 1, wherein the gain control unit receives the electromagnetic force of the electromagnet and the vibration amount of the strip to derive a strip model that is a transfer function of the multi- Calculating a quantity of a current input to the electromagnet and a vibration amount of the strip to derive a positive feedback control part model which is a transfer function of the positive feedback control part; And calculating a control gain of the positive feedback control unit so as to satisfy a stability condition.

In addition, the solution of the above-mentioned problems does not list all the features of the present invention. The various features of the present invention and the advantages and effects thereof will be more fully understood by reference to the following specific embodiments.

In the multi-input-multi-output electromagnetic vibration control using a plurality of electromagnets and sensors, the optimum feedback of the feedback control unit for the strip having multiple resonance frequencies is calculated and set up so that the feedback control unit operates in a stable range A control apparatus and method can be provided.

1 is a structural view of a general continuous hot dip galvanizing line,
FIG. 2 is a block diagram showing a configuration of a multi-input multi-output electromagnetic vibration control apparatus according to an embodiment of the present invention;
FIG. 3 is a graph showing an increase in control gain until the stability is destroyed with respect to the stiffness matrix in the multi-input multi-output electromagnetic vibration control apparatus according to the embodiment of the present invention, and
4 is a flowchart illustrating a multi-input-multiple output electromagnetic vibration control method of a multi-input multi-output electromagnetic vibration control apparatus according to an embodiment of the present invention.

Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings. However, the embodiments of the present invention can be modified into various other forms, and the scope of the present invention is not limited to the embodiments described below. Further, the embodiments of the present invention are provided to more fully explain the present invention to those skilled in the art. The shape and size of elements in the drawings may be exaggerated for clarity.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a multi-input multi-output electromagnetic vibration control apparatus and method, particularly a vibration control apparatus and method for setting an optimum gain for operating within a stable range in multi-input-multiple output electromagnetic vibration control in a plating process Will be described.

2 is a block diagram showing the configuration of a multi-input-multiple output electromagnetic vibration control apparatus according to an embodiment of the present invention.

2, the multi-input multi-output electromagnetic vibration control apparatus 200 includes a plurality of electromagnets 210, a plurality of gap sensors 220, a feedback control unit 230, and a gain control unit 240 do. In the following description, five electromagnets 210 and five gap sensors 220 will be described as an example.

Each of the plurality of electromagnets 210 is constituted by an electromagnet pair and can apply a magnetic force in a direction intersecting the strip 250 for vibration control of the strip 250. Each of the electromagnets 210 may include two magnetic pads disposed at regular intervals on both sides of the strip 250 that travels during the plating process. The plurality of electromagnets 210 may generate Lorentz force according to the amount of current input from the feedback controller 230 to control the vibration of the strip 250 during operation.

Each of the plurality of gap sensors 220 may be constituted by a pair of gap sensors to measure an interval between the corresponding electromagnet 210 and the strip 250. The gap sensor pairs of the gap sensors 220 may be respectively disposed on the magnetic pads disposed at regular intervals on both sides of the strip 250 to measure the gap between the respective sides of the strip 250 and the respective magnetic pads . The distance information measured by the plurality of gap sensors 220 is both fed back to the feedback controller 230 and may be provided to the gain controller 240 to be used to obtain a gain for controlling the feedback controller 230 have.

The amount feedback control unit 230 may control an amount of current input to the plurality of electromagnets 210 according to the distance information measured by the plurality of gap sensors 220. The feedback control unit 230 initially controls the amount of current input to the plurality of electromagnets 210 according to the initially set target moving distance information and changes the distance between the strip 250 and the plurality of electromagnets 210 The amount of current input to the plurality of electromagnets 210 may be controlled by using the gain information calculated by the gain controller 240 and the distance information measured by the plurality of gap sensors 220. [

The gain control unit 240 controls the gain control unit 240 to satisfy the stability condition in the closed loop system represented by the strip model which is the transfer function of the strip 250 and the positive feedback control unit model which is the transfer function of the positive feedback control unit 230, The optimal control gain of the feedback control unit 230 can be calculated and set.

Hereinafter, a method of calculating and setting an optimum control gain of the feedback control unit 230 will be described in detail.

First, the gain control unit 240 receives the electromagnetic force of the electromagnet and the vibration amount of the strip, and derives a strip model that is a transfer function of the multiple input-multiple output strip 250 having multiple natural frequencies. The multi-input multi-output strip 250 having the multiple natural frequencies is modeled as a transfer function that receives the electromagnetic force U of the electromagnet as an input and outputs the vibration amount Y of the strip as shown in Equation (1) .

[Equation 1]

(k=0 ~ n-2)는 상기 전달함수의 영점의 계수,

(m = 0 ~ n-1)는 상기 전달함수의 극점의 계수, s는 라플라스 변수, n은 스트립 최대 공진 주파수의 차수이다. 여기서, i와 j는, 5개의 전자석(210)이 존재할 경우, 1~5의 값을 가질 수 있다.
In this case, G _ij (s) is the transfer function of the strip, Y _ij (s) is the vibration amount at the i-th position of the strip due to the electromagnet at the j-th position, U _j (s)

(k = 0 to n-2) is a coefficient of the zero point of the transfer function,

(m = 0 to n-1) is the coefficient of the pole of the transfer function, s is the Laplace parameter, and n is the order of the strip maximum resonance frequency. Here, i and j may have a value of 1 to 5 when five electromagnets 210 are present.

Equation (1) can be expressed by Equation (2) using only B _ij and A _{ij related} to the DC-gain according to the stability condition of the strip having multiple natural frequencies Can be expressed.

&Quot; (2) "

는 안정성 평가에 사용하기 위한 스트립 등가 전달함수, D_ij는 고유주파수별 감쇄계수이다.
here,

Is a strip equivalent transfer function for use in stability evaluation, and D _ij is the natural frequency-specific attenuation coefficient.

Equation (2) can be transformed into a time domain state variable equation as shown in Equation (3) below.

&Quot; (3) "

Here, K _{PPF , j} is the controller gain of the positive feedback controller, and p _j is the state variable of the filter of the positive feedback controller. y _i represents the vibration amount at the i-th position of the strip, and this represents the sum of the vibration amounts at the i-th position of the strip by the entire electromagnet.

Next, the gain control unit 240 inputs the amount of current input to the electromagnet and the amount of vibration of the strip, and derives a model of a positive feedback control unit, which is a transfer function of the positive feedback control unit 230. [ The positive feedback control unit 230 receives the vibration amount Y of the strip as input, multiplies the control gain K _{PPF , i} by a quadratic low-pass filter, and inputs it as an electromagnet Can be modeled as a transfer function with the amount of current U as an output.

&Quot; (4) "

는 양궤환 제어부의 필터 주파수, K_{PPF ,i}는 스트립의 i번째 위치에 대응하는 j번째 위치의 전자석에 대한 양궤환 제어부의 제어게인이다.
Where H _i (s) is the transfer function of the positive feedback control, U _i (s) is the amount of current input to the electromagnet corresponding to the ith position of the strip, Y _i (s) is the vibration amount at the i- D _{f , i} is the filter attenuation coefficient of the positive feedback control part,

Is the filter frequency of the feedback control unit, and K _{PPF , i} is the control gain of the positive feedback control unit for the electromagnet at the j-th position corresponding to the i-th position of the strip.

Equation (4) can be transformed into a time domain state variable equation as shown in Equation (5) below.

&Quot; (5) "

Next, the gain controller 240 calculates the optimal control gain of the positive feedback controller 230 so as to satisfy the stability condition in the closed circuit system in which the strip model and the positive feedback controller model are combined.

In order to apply the stability condition of the closed loop system combined with the strip model and the feedback controller model, the time domain state variable equation for the strip model (Equation 3) and the time domain state variable equation for the feedback controller model (5), the closed-loop state equations as shown in Equation (6) below can be derived.

&Quot; (6) "

Here, [N _k ] is a k * k matrix in which the k-th row has a value of 1 and all the remaining rows have a value of 0. This is an example in which i and j have values of 1 to 5.

The stability condition of the closed-loop state equation derived from Equation (6) is as follows. The coefficient matrix S multiplied by the state variable in Equation (6) is called a stiffness matrix. If the coefficient matrix is a positive definite, the entire closed loop system is stable. If such a stability condition is applied, the stability discrimination equation for Equation (6) can be derived as Equation (7).

&Quot; (7) "

Here, the matrix g is a DC gain matrix.

를 도입함으로써 해결될 수 있다. (K _{PPF , 1} , ..., K _{PPF, 5} ) in the stability determination equation of Equation (7), and it can be expressed as Equation (8) Decreasing control gain proportional constant

. ≪ / RTI >

&Quot; (8) "

를 1로 설정하면, 모든 전자석의 제어게인이 같은 값이 되며, 이에 따라 상기 <수학식 7>의 안정도 판별식은, 하기 <수학식 9>와 같이, 다입력-다출력의 차수에 해당하는 고차 다항식으로 간단하게 정리될 수 있다. Here, the control gain proportional constant

Is set to 1, the control gains of all the electromagnets become equal to each other. Accordingly, the stability discriminant of Equation (7) can be expressed as Equation (9) It can be simply summarized by a polynomial.

&Quot; (9) &quot;

와

및

에 의해 결정되는 상수이다.
Here, C _i is

Wow

And

Lt; / RTI &gt;

Therefore, the gain control unit 240 can determine the control gain K _{PPF , i} of the positive feedback control unit for each electromagnet by determining K by calculating Equation (9) and substituting it into Equation (8) have.

As a result, it can be seen that the control gain of the feedback controller 230 for the multi-input-multiple output system is simply determined by knowing the DC gain matrix of the strip. As described above, the gain control unit 240 according to the present embodiment can find out an optimal control gain that allows the both feedback control unit 230 to operate within a stable range.

As an example, in the case of a strip having a thickness of 0.8 mm, a width of 1200 mm, and a length of 2000 mm, to which a tension of 600 kgf is applied, the DC gain matrix of the strip is expressed as Equation (10) can do.

&Quot; (10) &quot;

를 1로 설정하면, 안정도 판별식은 하기 <수학식 11>과 같이 도출될 수 있다. The above Equation (10) is substituted into Equation (7), and the gain gain proportional constant

Is set to 1, the stability discriminant can be derived as Equation (11) below.

&Quot; (11) &quot;

When the above equation (11) is calculated, K = 2491.5, which is substituted into Equation (8), the control gain K _{PPF , i} of the positive feedback control unit for each electromagnet is given by Equation Can be determined.

&Quot; (12) &quot;

In order to verify the accuracy of the calculated value of Equation (11), if the control gain is increased until the stability of the stiffness matrix of Equation (6) is destroyed, as shown in FIG. 3, . Fig. 3 shows the results of controlling gains of 800kgf and 1300kgf as well as a tension of 600kgf.

The multi-input multi-output electromagnetic vibration control apparatus 200 according to the present embodiment derives a strip model first from the gain control unit 240 for a multi-input multi-output strip having multiple resonance frequencies, After calculating the model, the optimal feedback control is performed so that the feedback control unit 230 operates within the stable range through the step of determining the control gain for the feedback control unit 230 in the stability condition. Thus, the electromagnet 210 ) To control the vibration of the strip.

4 is a flowchart illustrating a multi-input-multiple output electromagnetic vibration control method of a multi-input multi-output electromagnetic vibration control apparatus according to an embodiment of the present invention.

Referring to FIG. 4, the gain control unit of the multi-input multi-output electromagnetic vibration control apparatus inputs the electromagnetic force of the electromagnet and the vibration amount of the strip in step 401 to derive a strip model which is a transfer function of the multi-input-multiple output strip.

Then, in step 403, the gain controller converts the strip model into a time domain state variable equation.

Then, in step 405, the gain controller inputs the amount of current input to the electromagnet and the amount of vibration of the strip to derive a model of a feedback controller, which is a transfer function of the both feedback controllers.

Then, in step 407, the gain controller converts the feedback controller model into a time domain state variable equation.

Then, in steps 409 through 413, the gain controller calculates an optimal control gain of the feedback controller to satisfy the stability condition in the closed loop system represented by the strip model and the positive feedback controller model.

In detail, in step 409, the gain controller combines the time domain state variable equation for the strip model and the time domain state variable equation for the positive feedback model to derive a closed loop state equation.

In step 411, the gain controller derives a stability discrimination expression that satisfies that the coefficient matrix multiplied by the state variable in the closed-loop state equations becomes positive definite.

Then, in step 413, the gain control unit sets the control gain proportional constant for determining the ratio of the control gains of the electromagnetic switches to 1, and determines the control gains of the both feedback control units for the respective electromagnets from the stability determination equation.

Thereafter, the gain control unit terminates the algorithm according to the present invention.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, It will be obvious to those of ordinary skill in the art.

210: electromagnet 220: gap sensor
230: positive feedback control unit 240: gain control unit
250: Strip

Claims (6)

A plurality of electromagnets for applying a magnetic force in a direction crossing the strip for vibration control of the multi-input multi-output strip,
A plurality of gap sensors for measuring an interval between the corresponding electromagnets and the strip,
A positive feedback control unit for controlling an amount of current input to the plurality of electromagnets according to distance information measured by the plurality of gap sensors;
And a gain control unit for calculating a gain of the positive feedback control unit so as to satisfy a stability condition in a closed circuit system represented by a transfer function of the strip and a transfer function of a positive feedback control unit. Device.
The apparatus according to claim 1,
The electromagnetic force of the electromagnet and the amount of vibration of the strip are inputted to derive a strip model which is a transfer function of the multi-input-multiple output strip,
Transforming the strip model into a time domain state variable equation,
An amount of current input to the electromagnet and a vibration amount of the strip are input to derive a positive feedback control unit model which is a transfer function of the positive feedback control unit,
Converting the model of the feedback controller into a time domain state variable equation,
A closed-loop state equation is derived by combining a time-domain state variable equation for the strip model and a time-domain state variable equation for the positive feedback model,
Deriving a stability discriminant satisfying that a coefficient matrix multiplied by a state variable in the closed-loop state equations becomes a positive definite,
Wherein the control gain of each of the electromagnets is determined from the stability discrimination formula by setting the control gain proportional constant for determining the ratio of the control gains of the respective electromagnets to 1, Device.
3. The method of claim 2,
Wherein the multi-input multiple output strip is modeled as a transfer function that receives the electromagnetic force U of the electromagnet as an input and outputs the vibration amount Y of the strip as follows: Device.

In this case, G _ij (s) is the transfer function of the strip, Y _ij (s) is the vibration amount at the i-th position of the strip due to the electromagnet at the j-th position, U _j (s)

(k = 0 to n-2) is a coefficient of the zero point of the transfer function,

(m = 0 to n-1) is the coefficient of the pole of the transfer function, s is the Laplace parameter, and n is the difference of the maximum resonance frequency of the strip.
The method of claim 3,
The positive feedback control unit receives the amount of vibration Y of the strip as input, multiplies the control gain K _{PPF , i} by a quadratic low-pass filter, and outputs the amount of current U input to the electromagnet as And the output is modeled as a transfer function.

Where H _i (s) is the transfer function of the positive feedback control, U _i (s) is the amount of current input to the electromagnet corresponding to the ith position of the strip, Y _i (s) is the vibration amount at the i- D _{f , i} is the filter attenuation coefficient of the positive feedback control part,

Is the filter frequency of the feedback control unit, and K _{PPF , i} is the control gain of the positive feedback control unit for the electromagnet at the j-th position corresponding to the i-th position of the strip.
5. The method of claim 4,
Wherein the stability determination equation is expressed based on a product of a control gain K _{PPF , i} of a positive feedback control unit and a DC gain matrix.
A plurality of electromagnets for applying a magnetic force in a direction crossing the strip for vibration control of a multi-input multi-output strip, a plurality of gap sensors for measuring a gap between the corresponding electromagnets and the strip, A multi-input-multiple output electromagnetic vibration control apparatus comprising a positive feedback control unit for controlling an amount of current input to the plurality of electromagnets according to measured distance information, and a gain control unit for calculating a gain control of the positive feedback control unit, A multi-output electromagnetic vibration control method,
Inputting an electromagnetic force of the electromagnet and a vibration amount of the strip to derive a strip model which is a transfer function of the multi-input multi-output strip;
Calculating a quantity of a current input to the electromagnet and a vibration amount of the strip to derive a model of a feedback controller as a transfer function of the positive feedback controller;
And calculating a control gain of the positive feedback control unit so as to satisfy a stability condition in a closed loop system represented by the strip model and the positive feedback control unit model.

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