JPH05338840A - Controlling method for magnetically levitating system including magnetic material - Google Patents

Abstract

PURPOSE:To provide a magnetically levitating system which is stable with the effects of the magnetic saturation phenomenon of magnetic material on the magnetically levitating system taken into account by introducing change in the relative permeability of the magnetic material along the fieldrelative permeability curve of the magnetic material into an equation expressing the magnetically levitating system. CONSTITUTION:A magnetically levitating system attracts a steel plate 2 using an electromagnet 1 to carry the steel plate 2. A coil terminal voltage applied to the electromagnet 1 from a power circuit 5 is subjected to feedback control by comparison of set values of plate thickness, gap and current, all of which are input to a control circuit 6, with actual values of plate thickness, gap and current from a gap sensor 7 and a current sensor 8. In that case, field-relative permeability curves are formed as to the iron core of the electromagnet 1 and the steel plate attracted, and then an attracting force and inductance at a point of equilibrium, and their rates of change are calculated using the curves and an equation expressing the magnetically levitating system, and an equation of state is formed using them. The optimal regulator of the modern control theory is applied thereto.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a magnetic levitation system control method including a magnetic material which can be suitably applied to the design of a control system in a magnetic levitation transfer technique for magnetic materials such as steel plates.

[0002]

2. Description of the Related Art An attraction type magnetic levitation system of a tertiary system one point support model assuming that a steel plate 2 is attracted and conveyed by an electromagnet 1 as shown in the schematic view of FIG. 1 is expressed by the following equation. J · d ² / dt ² · θ = mgl ₀ + ΔN−f _m l ₀ e = R · i + d / dt · (L (x) · i) f _m = α (i / x) L = L _a + L _b / x where J: moment of inertia around the fulcrum (= m _e l ₀
²⁾ theta: angular displacement mg around fulcrum gravitational l ₀ acting on the steel sheet: Distance of the fulcrum and the suction point .DELTA.N: disturbance moment f _m: attraction acting on the steel sheet e: coil terminal voltage R: galvanic coil resistance i: excitation current L (x): system inductance x: gap size _{^{α = μ 0 n 2 S 1}} /2 L a: leakage inductance ^{_{L b = μ 0 n 2 S}} 1/2 μ 0: permeability of vacuum n: the number of turns of the coil S ₁ : the cross-sectional area of the iron core.

Since the above equation is a non-linear equation, the following equation is established by introducing minute displacements Δx and Δi from the equilibrium point and linearizing the equations. _{^{m e · d 2 / dt 2}} · Δx = Δf ex -Δf m Δe = RΔi + d / dt {L 0 Δi- (L 0 - L a) γΔx} Δf m = β (Δi-γΔx) Δe = -Ku However , m _e: inertia equivalent mass L _0: x = x ₀ system inductance _{γ = i 0 / x 0 β} = 2αγ / x when the ₀ i _0: current when x = x ₀ u: input of the control system K: The gain of the control system.

In the above equation, the state variables are [Δx, Δx ',
Δi] gives the following equation of state:

[0005]

[Equation 1]

However, ξ = β / m _e , and Δx ′ represents the first-order derivative of Δx with respect to time.

By applying an optimum regulator, which is a stabilizing method in modern control theory, to this state equation to determine the feedback gain k, the state variable can be controlled so as to approach the equilibrium point. ..

[0008]

However, in the above-mentioned method, the magnetic material is irrespective of the exciting current of the coil, the thickness of the magnetic material to be attracted, or the size of the gap between the coil and the magnetic material. It is assumed that the relative permeability of is constant. Therefore, for example, when the magnetic saturation phenomenon occurs due to the change of the exciting current of the coil and the relative permeability of the magnetic material changes, the input u determined by the above-described method causes the state variable to approach the equilibrium point. As a result, a stable magnetic levitation system could not be realized.

In view of such conventional inconveniences, an object of the present invention includes a magnetic material capable of realizing a stable magnetic levitation system in consideration of the influence of the magnetic saturation phenomenon of the magnetic material on the magnetic levitation system. It is to provide a control method of a magnetic levitation system.

[0010]

Such an object is to provide a magnetic field for each of the iron core of the electromagnet and the steel plate to be attracted.
Create a relative permeability curve formula, find the attraction force at the equilibrium point, the inductance, and the rate of change of the attraction force and the inductance by using this magnetic field-relative permeability curve formula and the equation representing the magnetic levitation system, and calculate them. To create an equation of state using
This is achieved by applying the optimal regulator in modern control theory.

[0011]

According to the present invention, the control is performed in consideration of the magnetic saturation characteristics of the magnetic material. Therefore, it is possible to stably control the magnetic levitation system when a magnetic saturation phenomenon occurs, which cannot be stably levitated by the conventional control method.

[0012]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described in detail below with reference to the embodiments shown in the accompanying drawings.

In FIG. 1, the coil terminal voltage e applied from the power supply circuit 5 to the electromagnet 1 is the plate thickness value, the gap, and the current set value given to the control circuit 6, and the actual gap from the gap sensor 7 is used. And feedback control is performed by comparing with the actual current from the current sensor 8.

An equation representing the magnetic levitation system in consideration of magnetic saturation is expressed by the following equation. J · d ² / dt ² · θ = mgl ₀ + ΔN−f _m l ₀ e = R · i + d / dt (L (x, i, d) · i) f _m = (n · i) ² / μ ₀ S _x · (1 / R _m ² ) · R _l ² / (R _x + R _m1 + R _l ) ² L = (n ² / μ ₀ ) · (1 / R _m ² ) · {l ₁ / μ _r1 S ₁ + (L ₃ / S ₃ ) · (R _x + R _m2 ) ² / (R _x + R _m1 + R _l ) ² + (2x / S _x ) · R _l ² / (R _x + R _m1 + R _l ) ² + (l ₂ / Μ _r2 S ₂ ) ・ R _l ² / (R _x + R _m1 + R _l ) ² } where μ _r1 : the relative permeability of the iron core μ _r2 : the relative permeability of the steel sheet R _m1 : the magnetic resistance of the iron core (= l ₁ / (Μ _r1 μ
₀ S ₁ )) R _m2 : Magnetic resistance of steel plate (= l ₂ / (μ _r2 μ
₀ S ₂ )) R _x : Magnetic resistance of void (= 2x / (μ
₀ S _x )) R _l : Magnetic resistance to leakage flux (= l ₃ /
(Μ ₀ S ₃ )) R _m : combined resistance of magnetic path (= R _m1 + R _l (R _x +
R _m2 ) / (R _x + R _m2 + R _l )) S ₁ : Cross-sectional area of iron core S ₂ : Cross-sectional area of steel plate S _x : Equivalent cross-sectional area of air gap S ₃ : Equivalent cross-sectional area for leakage flux.

A magnetic field-relative permeability curve of a magnetic material in consideration of the magnetic saturation phenomenon is expressed by the following equation. μ _r = (aH + b) / (cH ² + d) + e where μ _r : relative permeability H: magnetic field (A / m) a, b, c, d, e: actual coefficient determined by material (obtained from experiment) is there.

In the equation representing the magnetic field-relative permeability curve of a magnetic material, if the number of terms in the equation is small, the curve is controlled by
If it cannot be expressed with sufficient accuracy, and if the number of terms in the equation is increased, the accuracy of the curve can be increased, but the number of actual coefficients determined by the material increases, so the procedure for obtaining the curve equation becomes complicated. Become. In view of these points, the above formula is the most practical one.

In order to introduce the equation representing the magnetic field-relative permeability curve into the equation of the magnetic levitation system, the relative permeability of the iron core (μ _r1 ) and the relative permeability of the steel plate (μ _r2 ) are _calculated as follows. The simultaneous equations in the magnetic circuit of the system are solved and obtained in advance. n · i = R _m1 μ _r1 (H ₁ ) μ ₀ S ₁ H ₁ + R _l {μ _r1 (H ₁ ) μ ₀ S ₁ H ₁ −μ _{r 2} (H ₂ ) μ ₀ S ₂ H ₂ } n · i = R _m1 μ _r1 (H ₁ ) μ ₀ S ₁ H ₁ + (R _x + R _m2 ) μ _{r 2} (H ₂ ) μ ₀ S ₂ H ₂ where H ₁ : magnetic field (A / m) H _{2 in the} iron core: It is the magnetic field (A / m) in the steel plate. Further, a linearized equation is derived using the differential coefficient at the equilibrium point x _{0 given} below.

[0018]

[Equation 2]

Then, the following equation is obtained.

[0020]

[Equation 3]

In the above equation, the state variables are [Δx, Δx ',
Δi] gives the following equation of state:

[0022]

[Equation 4]

Where L ₀ is the inductance at the equilibrium point.

Next, in the embodiment shown in FIG. 1, each condition is set as follows, and an actual simulation is performed. In FIG. 1, reference numeral 3 indicates a coil and reference numeral 4 indicates an iron core. Magnetic path length of iron core 4: l ₁ = 130 mm Magnetic path length of steel plate 2: l ₂ = 56 mm Width of coil 3: l ₃ = 40 mm Height of coil 3: T = 30 mm Length of iron core 4: l _z = 300 mm Width of iron core 4: w = 15 mm Weight of steel plate 2: m = 2 kg Weight of steel plate 2: d ₀ = 1 mm Equilibrium point of steel plate 2: x ₀ = 5 mm Equilibrium point of exciting current: i ₀ = 6 A of coil 3 Number of turns: n = 300

As a magnetic material, ordinary steel (C = 0.16)
%), The magnetic field-relative permeability curve is given by the following equation. μ _r = {180 / (1.508 × 10 ⁻⁴ H ² +12.57)} + 1

FIG. 2 shows a graph in which measured values are plotted on the magnetic field-relative permeability curve expressed by the above equation. The difference between the two is extremely small, and the experimental values are in good agreement with the theoretical values. I understand.

Next, a control system considering magnetic saturation is designed from the magnetic field-relative permeability curve and the equation representing the magnetic levitation system. Control system design methods include classical control theory method, pole placement method, fuzzy theory method, modern control theory method, etc. Not established. The method based on fuzzy theory has a drawback that the design procedure is complicated and not clear, and is not suitable when the model of the object to be controlled, such as a magnetic levitation system, has no ambiguity. Therefore, the design procedure of the control system is established, and the design is performed using modern control theory whose stability is guaranteed.

When the equation of state considering magnetic saturation is derived from the equation (1) using the equation representing the magnetic field-relative permeability curve and the magnetic levitation system, the following equation is obtained.

[0029]

[Equation 5]

However, the gain of the control system is K = 1.

Next, modern control theory is applied to the equation (2) to calculate the optimum feedback gain k = [k ₁ , k ₂ , k ₃ ] defined by the following equation.

[0032]

[Equation 6]

At this time, how to select the evaluation function J becomes a problem, but here,

[0034]

[Equation 7]

Regarding

[0036]

[Equation 8]

Then, the optimum feedback gain [k
₁ , k ₂ , k ₃ ] was obtained.

As a result, k ₁ = 7.002, k ₂ = 5.3786, k ₃ = −0.
5235 was obtained.

The values of these feedback gains were substituted into the above equation (3), and the time response when feedback was applied to the equation (2) was simulated. The result is shown in FIG. The horizontal axis represents time t, and the vertical axis represents the displacement Δx from the equilibrium point. If the initial value of Δx is 1 mm,
It can be seen that it takes about 5 seconds to settle.

Next, the case of the conventional method that does not consider magnetic saturation will be simulated. An equation derived by the conventional method that does not consider magnetic saturation is given by the following equation.

[0041]

[Equation 9]

Here, the evaluation function J is expressed by the above equation (4).
When selected in the same manner as the equation (6), the feedback gains [k ₁ ', k ₂ ', k ₃ '] obtained from the equation (7) are k ₁ ' = 5.8365, k ₂ '= 1.5471. , K ₃ '=
It becomes -1.1338.

The feedback gains [k ₁ ', k ₂ ', k ₃ '] set without considering the magnetic saturation are substituted into the above equation (3) to form a closed loop system for the equation (2). The result of the simulation is shown in FIG. this is,
This is equivalent to applying the feedback gain derived from the model without magnetic saturation to the model with magnetic saturation.

Compared to FIG. 3, the settling time is long and the behavior is oscillatory, and the simulation result of FIG. 3 is superior.

To summarize the process of the present invention, as shown in FIG. 5, the actual coefficient of the magnetic field-relative permeability curve is calculated by using the measured values of the magnetic field and the relative permeability for each of the iron core and the steel sheet, for example, the least squares method. To determine a magnetic field-relative permeability curve formula (step 1).

Next, the displacement x at the equilibrium point of the magnetic levitation system is input (step 2).

Next, the attraction force and the inductance at the equilibrium point are obtained using the magnetic field-relative permeability curve equation and the equation representing the magnetic levitation system (step 3).

Next, the amount of displacement Δx from the equilibrium point is input (step 4).

Next, the attraction force and the inductance when displaced from the equilibrium point are obtained using the magnetic field-relative permeability curve equation and the equation representing the magnetic levitation system (step 5).

By creating an equation of state using the attraction force and inductance at the equilibrium point and the attraction force and inductance when displaced from the equilibrium point, and applying the optimum regulator in modern control theory to it, feedback is obtained. The gain k is determined (step 6).

As a result, the value of the displacement amount Δx can be settled to 0 stably and quickly.

[0052]

As described above, according to the present invention, a control system for stably levitating a magnetic levitation system when a magnetic saturation phenomenon occurs, which cannot be stably levitated by the conventional control method, is designed. can do.

[Brief description of drawings]

FIG. 1 is a model diagram of a magnetic levitation system.

FIG. 2 is a comparative graph of an approximate expression of a magnetic field-relative permeability curve and measured values.

FIG. 3 is a simulation result using a feedback gain derived in consideration of magnetic saturation.

FIG. 4 is a simulation result using a feedback gain derived without considering magnetic saturation.

FIG. 5 is a flowchart of a control method according to the present invention.

[Explanation of symbols]

 1 Electromagnet 2 Steel Plate 3 Coil 4 Iron Core 5 Power Supply Circuit 6 Control Circuit 7 Gap Sensor 8 Current Sensor

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Kenji Umezu 20-1 Shintomi, Futtsu City Nippon Steel Co., Ltd. Technical Development Division (72) Inventor Hideo Saeki 1st Nishinosu, Oita-shi Nippon Steel Co., Ltd. Inside Oita Works (72) Inventor Hiroshi Otobe 1 Nishinozu, Oita-shi, Oita Works Inside Nippon Steel Co., Ltd.

Claims (2)

[Claims] 1. A method of controlling a magnetic levitation system including a magnetic material, wherein the magnetic levitation system indicates that the relative permeability of the magnetic material changes along a magnetic field-relative permeability curve of the magnetic material. A method for controlling a magnetic levitation system including a magnetic material, characterized in that the magnetic levitation system is controlled by introducing it into an equation. 2. The method for controlling a magnetic levitation system including a magnetic material according to claim 1, further comprising the step of applying an optimum regulator based on modern control theory to determine a feedback gain.