JP2835942B2 - Magnetic bearing control device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a control device for a magnetic bearing, and more particularly, to a sliding mode control theory which is a representative of a nonlinear robust control theory.
e Control Theory), and a control device for a magnetic bearing related to a so-called displacement sensor-less system in which the displacement of a rotating body to be controlled is not directly detected by a displacement sensor.

[0002]

2. Description of the Related Art Heretofore, the following systems have been known as this type of magnetic bearing control system. (1) A method in which only the current flowing through the coil of the electromagnet forming the magnetic bearing is observed, and the displacement of the rotor (rotor) is estimated based on the state estimation theory based on modern control theory to control the rotor to a target position. (2) A method based on modulation of a PWM carrier. (3) A method for estimating the displacement of the rotating body from the magnetic flux feedback of the Hall element and the current.

[0003]

However, the above-described system has the following problems. First, the state estimation theory does not consider disturbance and does not consider uncertainty, so that high-speed rotation and load could not be applied practically. In addition, the PWM method handles a high frequency of several tens KHz, and thus has a problem in realizing a circuit. further,
When a hall element is used, the production cost increases and the installation place is restricted, and therefore, it cannot be said that the sensor is sensorless. Furthermore, the emergence of a control device for a magnetic bearing without a displacement sensor capable of improving robust performance against parameter fluctuation and robustness against non-linear characteristics has been desired.

Accordingly, an object of the present invention is to provide a magnetic bearing control device capable of improving suppression of disturbances such as unbalanced disturbances, improving robustness against parameter fluctuations, and improving robustness against nonlinear characteristics. Is to do.

[0005]

According to the present invention, an electromagnet for magnetically supporting a rotating body, electromagnet driving means for driving the electromagnet, and current detection for detecting a current flowing through a coil of the electromagnet are provided. Means for estimating a displacement of the rotating body at a position where the electromagnet is installed and a displacement of an arbitrary position of the rotating body based on an input of the electromagnet driving means and a detection current of the current detecting means.
Structure system, variable structure system) Observer, comparison means for comparing the displacement of the rotating body at the position of the electromagnet estimated by the VSS observer with a reference value to determine a deviation between the two, and the comparison means Based on the deviation and the displacement of an arbitrary position of the rotating body estimated by the VSS observer, a predetermined linear gain and a non-linear gain are obtained as signals for adjusting the electromagnet, and a VSC (Variable St) is obtained by adding the two.
The present invention achieves the above object by supplying an output signal of the VSC controller to the electromagnet driving means.

According to the second aspect of the present invention, an electromagnet which magnetically supports the rotating body, electromagnet driving means for driving the electromagnet, current detecting means for detecting a current flowing through a coil of the electromagnet, and the electromagnet driving Based on the input of the means and the detected current of the current detecting means, the displacement of the rotating body at the installation position of the electromagnet, the displacement of an arbitrary position of the rotating body, and the disturbance acting on the rotating body, respectively. V to be estimated
SS (Variable Structure System)
em) a disturbance type observer, and coefficient means for multiplying the estimated disturbance of the VSS disturbance type observer by a predetermined coefficient;
Comparing means for comparing the displacement of the rotating body at the installation position of the electromagnet estimated by the VSS disturbance type observer with a reference value to obtain a deviation between the two; and a deviation obtained by the comparison means and the VSS disturbance type observer. A VSC (Variable Struct) that obtains a predetermined linear gain and a non-linear gain as a signal for adjusting the electromagnet based on the estimated displacement of an arbitrary position of the rotating body and adds both of them.
cure control) and this VS
An adding means for adding a signal obtained by the C controller and an output signal from the coefficient means is provided, and an output signal of the adding means is supplied to the electromagnet driving means to achieve the object.

[0007]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of the present invention will be described below in detail with reference to FIGS. In addition,
In this specification, when expressing a state vector or the like, a dot is generally attached to a character, and a symbol "" is used instead of the dot. For example, the notation " _xf dot" is referred to as " _xf ". It shall be expressed as follows. Also,
When placing a bar on a character, use the symbol "'" instead of this bar to replace the notation x _d bar with' x _d '.
It shall be expressed as follows. Further, as examples of symbols to indicate that an estimated value, typically "using the estimated values of x _d instead of hat symbols used""" as "expressed as x _d" I do. In the description of the mathematical formulas, the symbol of the first derivative used to express the equation of motion or the like is expressed as "q" using "'", and the symbol of the second derivative is expressed as "". Is expressed as q ″. The expression in the drawing is expressed as
Unless otherwise specified, a general display method is used. FIG. 1 is a block diagram of a control system of a control device for a magnetic bearing according to a first embodiment of the present invention. FIG. 2 shows a schematic configuration of the magnetic bearing. The control device according to the first embodiment constitutes a servo-type sliding mode control system using sliding mode control theory as a representative of nonlinear robust control.

As shown in FIG. 2, the control target of this control system is a rotating body 1 magnetically supported by electromagnets 2 and 3 forming a magnetic bearing. In order to model this rotating body 1 as an elastic rotor, n (13 in this case) are set in the axial direction.
And electromagnets 2 and 3 are placed at the division positions "5" and "11".
Is arranged. In this magnetic bearing, no displacement sensor for detecting the radial displacement of the rotating body 1 is particularly arranged, and the radial displacement of the rotating body 1 is applied to each coil i of the electromagnets 2 and 3 as described later. It is estimated using the flowing current. This control system, as shown in FIGS.
SS (Variable Structure Sys)
tem) Observer 21, comparison unit 22, integration unit 23, addition unit 24, VSC (Variable Structure)
re Control: Variable structure control) Controller 2
5, an adder 26, an amplifier 27, and electromagnets 2 and 3.

[0011] The VSS observer 21 determines the electromagnets 2 and 3 that cannot be directly observed based on the output signal u from the VSC controller 25 and the current i flowing through the coils of the electromagnets 2 and 3.
The mode displacement and the speed in the radial direction of the rotating body 1 at the installation positions “5” and “11” are estimated by a predetermined procedure, and the dividing positions “1” to “4” of the rotating body 1
Each mode displacement and its speed in “6” to “10”, “12”, and “13” are estimated by a predetermined procedure, and the estimated value is set to “x ₂ ” (see FIGS. 1 and 2). Comparison section 22
Sets the estimated value “x ₁ ” of the displacement of the rotating body 1 at the installation positions “5” and “11” of the electromagnets 2 and 3 estimated by the VSS observer 21 as a target set in advance corresponding to the estimated value. The value R is compared with the value R to determine each deviation. The integrator 23 integrates each deviation obtained by the comparator 22 and outputs the result to the adder 24. The addition unit 24 calculates the integrated deviations output from the integration unit 23 and the estimated values “x” of the respective mode displacements and speeds at the division positions “1” to “13” of the rotating body 1 estimated by the VSS observer 21. Addition to ₂ ".

The VSC controller 25 includes a linear processing unit 2
5A, a non-linear processing unit 25B, and an adding unit 25C. The linear processing unit 25A gives a predetermined linear (proportional) gain to the addition result of the adder 24, and the nonlinear processing unit 25B gives a predetermined nonlinear ( (Not proportional) gain. The adding unit 25C includes a linear processing unit 25A.
Is added to the value ul linearly processed by the above and the value unl nonlinearly processed by the non-linear processing unit 25B. The adding unit 26 adds the disturbance E to the addition result of the adding unit 25C. Disturbance E
Is caused by a change in driving of the electromagnets 2 and 3 and the like.
The amplifier 27 drives the electromagnets 2 and 3 according to a signal from the adder 26.

Next, the operation of the first embodiment configured as described above will be described. Now, when the current i flowing through the coils of the electromagnets 2 and 3 and the output signal u from the VSC controller 25 are input to the VSS observer 21,
The VSS observer 21 determines, based on the current i and the signal u as a control input, the mode displacement and the velocity of the rotating body 1 in the radial direction at the installation positions “5” and “11” of the electromagnets 2 and 3 which cannot be directly observed. In addition to the estimation, the dividing positions of the rotating body 1 are “1” to “4”, and “6” are “1”.
The mode displacements and their velocities at “0”, “12”, and “13” are estimated, and the estimated value is set to “x ₂ ” (see FIGS. 1 and 2). The comparison unit 22 sets in advance the estimated value “x ₁ ” of the displacement of the rotating body 1 at the installation positions “5” and “11” of the electromagnets 2 and 3 estimated by the VSS observer 21 in accordance with the estimated values. Compared to the target value R
Obtain each deviation. These deviations are input to the integration unit 23 and integrated, and then supplied to the addition unit 24. On the other hand, the estimated value “x ₂ ” of each mode displacement and its speed at the division positions “1” to “13” of the rotating body 1 estimated by the VSS observer 21 is supplied to the addition unit 24.

The adder 24 adds each of the integrated deviations output from the integrator 23 and the estimated value “x ₂ ” from the VSS observer 24. The addition result of the addition unit 24 is supplied to the linear processing unit 25A and the non-linear processing unit 25B of the VSC controller 25, respectively. The linear processing unit 25A of the VSC controller 25 gives a predetermined linear gain to the addition result of the adder 24, and the nonlinear processing unit 25B provides a predetermined nonlinear gain to the addition result. give. Thus, the value u linearly processed by the linear processing unit 25A
_l and the value u _nl subjected to the non-linear processing in the non-linear processing unit 25B are added in the adding unit 25C.

The output of the adder 25C is supplied to the adder 26 of the next stage.
, Where the disturbance E is added and the amplifier 27
Supplied to The amplifier 27 drives the electromagnets 2 and 3 according to a signal from the adding unit 26. Thereby, the rotating body 1 to be controlled is controlled so as to come to the center of the magnetic bearing which is the target position.

The specific structure of the VSS observer 21 is shown in a block diagram as shown in FIG. This V
Since the basic principle of the SS observer 21 is generally known, a detailed description thereof will be omitted.

Next, an outline of a design procedure of the control device according to the first embodiment will be described below. (1) Modeling of Controlled Object and Reduction of Its Dimension This is an operation of treating the rotating body 1 as an elastic rotor and deriving a state equation and an output equation under predetermined conditions. It should be noted that the construction of a reduced-order model is considered from the standpoint of stabilizing two rigid modes and controlling the vibration of a lower-order elastic bending mode. (2) Design of VSS Observer The control system of this magnetic bearing is an output feedback system for estimating the radial displacement of the rotating body 1 without using a displacement sensor. Therefore, the design is necessary for estimating an unobservable state quantity (such as the displacement of the rotating body 1 and its speed) of the rotating body 1 to be controlled. (3) Design of Servo System Hyperplane In the sliding mode control applied to the present invention, switching of a feedback gain or switching of a control input is performed on a surface called a hyperplane (switching surface) designed in a state space. This is a control system that obtains ideal control characteristics by restricting the state to a hyperplane. Therefore, the design of the hyperplane is important.

(4) Design of VSC Controller The sliding mode control system (variable structure control system) can be regarded as a closed loop system having an adaptive variable gain. In other words, a control input consisting of an adaptive variable gain can be considered to consist of two control inputs. That is, it is composed of a conventional linear control input and a non-linear control input with a newly added switching specific to the sliding mode control. Due to this non-linear control input, the closed loop will be adaptive and robust. With this non-linear control input, a mode can be realized in which the state reaches the hyperplane in the shortest time, or the state is constrained on the hyperplane and slides to the origin. Therefore, the design of the VSC controller requires that non-linear inputs be determined that do not overshoot the hyperplane.

(5) Generation of control algorithm and DS
Implementation on P Since the VSS observer and VSC controller designed as described above are realized by a DSP (Digital Signal Processor), a control algorithm is created. (6) Execution of Control As will be described later, control is executed by being embodied in a control device as shown in FIG.

Next, a specific configuration of the control device designed in such a procedure will be described with reference to FIG.
This control device is a five-axis control type magnetic bearing, in which a rotating body 1 has radial bearings 41, 4 on both sides of a motor (not shown).
2 and a thrust bearing 43 at the left end of the rotating body 1. The radial bearings 41 and 42 are controlled in two perpendicular directions, and the thrust bearing 43 is controlled only in the axial direction. The radial bearings 41 and 42 are formed by electromagnets 41A and 42A.

Further, this control device is provided with the VS in FIG.
S observer 21, comparison unit 22, integration unit 23, addition unit 2
4. The function of the VSC controller 25 is realized by a DSP (digital signal processor) 44.
The DSP 44 is configured to perform high-speed data processing with the host computer 45. An A / D converter 46 is connected to an input side of the DSP 44, and a D / A converter 47 is connected to an output side of the DSP 44. DA
The output of the converter 47 and the output of the bias current supply circuit 48 are supplied to a power amplifier 49, and the power amplifier 49 is configured to drive the electromagnets 41A, 42A of the radial bearings 41, 42. Also, the electromagnets 41A and 42A
Is configured to be supplied to the AD converter 46. According to such a configuration, after the current i flowing through each coil of the electromagnets 41A and 42A is supplied to the A / D converter 46, it is A / D converted and the DSP 4
4, the DSP 44 obtains a control input by a predetermined calculation. The obtained control input u is DA-converted by the DA converter 47 and supplied to the power amplifier 49, which drives the electromagnets 41A, 42A constituting the radial bearings 41, 42.

Next, a control device for a magnetic bearing according to a second embodiment of the present invention will be described. This control device, as shown in FIG.
An SS disturbance type observer 31 is provided, and a coefficient unit 32 for generating a signal for removing an influence of a disturbance F to be controlled (a load variation of the rotating body 1 or the like) by a disturbance (“F”) estimated by the VSS disturbance type observer 31. And the VSC controller 33 has a function of creating a signal for removing the influence of the disturbance E. Note that the other configuration is the same as that of the first embodiment, and thus the same reference numerals are given and the detailed description thereof is omitted.

The VSS disturbance type observer 31 sets the positions “5” and “11” of the electromagnets 2 and 3 that cannot be directly observed based on the output signal u from the VSC controller 33 and the current i flowing through each coil of the electromagnets 2 and 3. Of rotating body 1
The mode displacement and the velocity in the radial direction of the rotating body 1 are estimated by a predetermined procedure, and each mode at the divided positions “1” to “4”, “6” to “10”, “12”, and “13” of the rotating body 1 is The displacement and its speed are estimated by a predetermined procedure.
Further, the VSS disturbance observer 31 estimates the disturbance in a predetermined procedure based on the signal u and the current i. Then, the estimated value of the estimated displacement or velocity is defined as “x ₂ ”,
The estimated disturbance is “F”.

The coefficient section 32 includes a VSS disturbance observer 3
The estimated disturbance is multiplied by a predetermined coefficient in order to generate a signal for eliminating the influence of the disturbance F of the control object by the estimated disturbance "F" of No. 1. The comparison unit 22 includes the VSS observer 21
The estimated value “x ₁ ” of the displacement and speed of the rotating body 1 at the installation positions “5” and “11” of the electromagnets 2 and 3 estimated by
The respective deviations are obtained by comparing with a target value R set in advance corresponding to the estimated value. These deviations are input to the integration unit 23 and integrated, and then supplied to the addition unit 24. The VSC controller 33 includes a linear processing unit 33
A, a nonlinear processing unit 33B, an adding unit 33C, and an adding unit 33D. The linear processing unit 33A includes the adding unit 2
In addition to giving a predetermined linear gain to the addition result of No. 4, the nonlinear processing unit 33B gives a predetermined nonlinear gain to the addition result. The adding unit 33C adds the value u _l that has been linearly processed by the linear processing unit 33A and the value u _nl that has been non-linearly processed by the non-linear processing unit 33B. The addition unit 33D adds the output of the addition unit 33C and the output of the coefficient unit 32, and outputs the addition result.

Next, the operation of the second embodiment configured as described above will be described. Now, when the current i flowing through the coils of the electromagnets 2 and 3 and the output signal u from the VSC controller 33 are input to the VSS observer 31,
The VSS observer 31 determines the mode displacement and the velocity of the rotating body 1 in the radial direction at the installation positions “5” and “11” of the electromagnets 2 and 3 which cannot be directly observed based on the current i and the signal u which is the control input. In addition to the estimation, the dividing positions of the rotating body 1 are “1” to “4”, and “6” are “1”.
Estimate each mode displacement and its speed at "0", "12", and "13". In addition, the VSS disturbance observer 31
Estimates the disturbance by a predetermined procedure based on the signal u and the current i. The estimated value of the estimated displacement or velocity is set to “x ₂ ”, and the estimated disturbance is set to “F”.

When the estimated value “x ₁ ” of the displacement and speed of the rotating body 1 at the installation positions “5” and “11” of the electromagnets 2 and 3 estimated by the VSS observer 31 is supplied to the comparing unit 22, The unit 22 compares each of the deviations with a target value R set in advance corresponding to the estimated value. These deviations are input to the integration unit 23 and integrated, and then supplied to the addition unit 24. Further, from the division position “1” of the rotating body 1 estimated by the VSS observer 31 to “1”
The estimated value “x ₂ ” of each displacement and its speed in “3” is supplied to the adding unit 24.

The adder 24 adds the integrated deviations output from the integrator 23 and the estimated value “x ₂ ” from the VSS observer 24. The addition result of the addition unit 24 is supplied to the linear processing unit 25A and the non-linear processing unit 25B of the VSC controller 25, respectively. The linear processing unit 33A of the VSC controller 33 gives a predetermined linear gain to the addition result of the addition unit 24, and the nonlinear processing unit 33B provides a predetermined nonlinear gain to the addition result. give. Thus, the value u linearly processed by the linear processing unit 33A
_l and the value u _nl subjected to the non-linear processing in the non-linear processing unit 33B are added in the adding unit 33C.

On the other hand, based on the disturbance "F" estimated by the VSS disturbance type observer 31, a coefficient unit 32 generates a signal for removing the influence of the disturbance F of the control object by a predetermined coefficient. Multiply. The output of the coefficient unit 32 and the output of the adding unit 33C are supplied to an adding unit 33D, where the two are added. The output of the adder 33D is
The control input u to be controlled is supplied to the amplifier 27 via the adder 26. The amplifier 27 drives the electromagnets 2 and 3 according to a signal from the adding unit 26. This allows
The rotating body 1 to be controlled is controlled so as to come to the center of the magnetic bearing at the target position.

Next, the design procedure of the second embodiment will be described, which is basically the same as the design procedure of the first embodiment. Therefore, the design procedure is as follows (1)
To (6). Among them, (1) modeling of a control target and reduction of the dimension thereof, (2) design of a VSS disturbance observer, and (4) design of a VSC controller will be described in detail as follows. (1) Modeling of controlled object and reduction of its dimension (2) Design of VSS disturbance observer (3) Design of servo system hyperplane (4) Design of VSC controller (5) Generation of control algorithm and implementation on DSP ( 6) Execution of control

Next, the modeling of the controlled object and the design for reducing the dimension thereof will be described in detail below. The rotor of the magnetic bearing spindle applied to the second embodiment has a complicated shape in fact, and has an infinite vibration mode since it is a continuum, so that modeling is difficult. .
Here, only the X direction is handled for simplicity. The elastic rotor as a continuum is simplified as shown in FIG. 6 and the whole span length is divided into 12 elements for different axes and concentrated on 13 disks in order to apply the finite element method. Loading mass.

(A) Modeling of Elastic Rotor Referring to FIG. 6, the equation of motion in the free-free elastic rotor is represented by the following equation. Mq ″ + Kq ′ = 0 (1) where q = [x ₁ , θ ₁ , x ₂ , θ ₂ ,... X ₁₃ ,
θ ₁₃ ] ^T. X _j , θ _j (j = 1,..., 13)
Represents the displacement and angle of the mass of each rotor. In particular, x ₅ and x ₁₁ shows the location of the electromagnet, as shown in Figure 6. M∈R ^{26 * 26} is the inertia matrix, K 、 R
^{26 * 26} is a rigidity matrix, and the symbol “*” is a substitute for the symbol “x” indicating multiplication. The same applies to the following, and the same applies to the drawings.

Strictly speaking, the attractive force of the electromagnetic force is a complicated expression.
However, the following simplified expression is sufficient for practical use. P '= A / μ₀ ・ B^Two = A / μ₀ [N (i₀ + I) / (1 / μ + 2 (x₀ + X) / μ₀)] ^Two ... (2) where P ': suction force, μ₀ : Magnetic permeability, A: facing area,
N: number of coil turns, x₀: Gap length, i₀: Steady current
You. Equation (2) is tailored with respect to i and x, and i₀≫i,
x₀ Extracting only the linear term under the assumption of ≫x,
The force is: P '₁ ≒ p₀ + K_xx−k_ii ...
・ (3) where p₀ = Μ₀ AN^Two i₀ ^Two / 4x₀ ^Two , K_x= 2
p₀ / X₀ , K_i= 2p₀ / I₀ It is. Where p₀ 
Is the steady suction force. On the other hand, suction of electromagnetic force placed opposite
The force is: P '_Two ≒ p₀ -K_xx + k_ii ... (4)

Generally, this linearization is often realized by a pair of facing electromagnets, in which case the attractive force of the electromagnets is given by: P = P ′ ₁ −P ′ ₂ = 2 k _× x−2 k _i i (5) In the case of the model of FIG. 6, the elastic rotor of Expression (1) is obtained by Expression (5).
Is controlled and constrained by the attraction force, the following equation is obtained. Mq ″ + Kq = Fp + D (6) where F, P, P ₅ , and P ₁₁ are as shown in FIG. 9A, where F is a matrix indicating the installation location of the electromagnet. , D∈R ^{26 * 1} represents the unbalance force and other disturbance / load forces.If the equation (6) is rearranged into a bias suction force and a control suction force, the following equation is obtained: Mq ″ + Cq ′ + K ₀ q = F ₀ i + D (7) where i, K ₀ , F ₀ , and _Ki are as shown in FIG. 9B.

Now, applying the method of modal analysis and using the normalized mode matrix Ψ∈R ^{26 * 26} , q = Ψξ (8), the equation (7) becomes The following equation is obtained from the displacement vector ξ∈R ^{26 * 1} in the system. ^{ξ "+ Λξ '+ Ω 2} ξ = f 0 i + d' ··· (9) ^{However, I = Ψ T MΨ, Ω} 2 = Ψ T K 0 Ψ, Λ = 2ξΩ
= Ψ ^T CΨ, is _{^{f 0 = Ψ T F 0,}} d '= Ψ T D = Πd.

(B) Modeling of Actuator Between the input voltage to the magnetic bearing electromagnet coil and the coil current
Assumes that inductance is independent of frequency and gap.
In general, the following equation holds. V '₁ = (D / dt) · (L₁(i₀ + I)) + R (i₀ + I) + e (10) where V ′₁ : Coil input voltage, L₁ : Coil in
Ductance, R: Coil resistance, i: Coil current, e: Outside
It is a rebellion. The inductance of the coil is given by the following equation. L₁ = N^Two A ((l₀ / μ) +2 (x₀ + X) / μ₀ )^-1≒ μ₀ N^Two A / 2 (x₀ + X) (11) Accordingly, the first term on the right side of Expression (10) is as follows. (D / dt) (L₁(i₀ + I)) = (∂ / ∂L₁ ) (L₁ (I₀ + I)) dL ₁ / Dt + (∂ / ∂ (i₀ + I)) (L₁ (I₀ + I)) · di / dt ≒ −μ₀ N^Two A / 2 (x₀ + X)^Two ・ (I₀ + I) ν + L₁ Di / dt (12) where ν = dx / dt.

As a result, equation (10) becomes the following equation. V ′ ₁ ≒ −μ ₀ N ² A / 2 (x ₀ + x) · (i ₀ + i) ν + L ₁ · di / dt + R (i ₀ + i) + e (13) i ₀ {i, x ₀ } Assuming x, equation (13) becomes as follows. _{V '1 ≒ -k v ν +} L 1 · di / dt + R (i 0 + i) + e ·· (14a) _{where, k v = (μ 0 N} 2 A / 2x 0 2) i is _0.

On the other hand, the following equation is established for the electromagnet placed opposite. V ′ ₂ ≒ k _v ν−L ₂ · di / dt + R (i ₀ −i) −e (14b) where L ₂ ≒ μ ₀ N ² A / 2 (x ₀ −x). As a result, the voltage of the pair of opposing electromagnetic forces is: V = V ′ ₁ −V ′ ₂ ≒ −2k _v ν + (L ₁ + L ₂ ) ・ di / dt + 2Ri + 2e ≒ −2k _v ν + 2L · di / dt + 2Ri + 2e (15) where L ₁ ≒ L ₂ ≒ L ≒ μ ₀ N ² A / 2 × ₀ .

(C) Modeling of magnetic bearing From equations (9) and (15), the state equation of the magnetic bearing is as follows. "X _f" = A at _{f x f + B f u +} D f ··· (16a) _{where, x f, u, A f} , B f, D f, E 1, E i, E
_u and E are as shown in FIG. The output equation of the sensorless magnetic bearing device is as follows. _{y = C f x f = [} i 5 i 11] T ··· (16b) where, C _f is that shown in FIG. 11 (A).

An elastic rotor free of both ends generally has countless vibration modes. Since the elastic rotor / magnetic bearing system is inherently unstable, it is necessary to first perform stabilization control.
In this case, strictly speaking, the unstable mode is only two rigid modes, parallel and conical, and the elastic mode is an inherently stable mode, although the damping property is poor. Therefore, when creating a reduced-order model, it is necessary to consider the stabilization of the two rigid modes and the order of the elastic mode to be damped. The reduced-order model is created by discarding higher-order vibration modes in the mode coordinate system. Here, if the state equation of the reduced-order model including up to the r-th mode is described, the equation (16) becomes the following equation. "X _r" = A _r x _r + at _{B r u + D r ···· (} 17a) y = C r x r = [i 5 i 11] T ··· (17b) where, x _r, A _r, B _r , C _r , and D _r are as shown in FIG.

Next, a method of designing a VSS disturbance observer using the reduced-order model obtained above will be described. The above mechanical analysis of the plant is based on the assumption that all system state variables are known. However, in this system, only the currents of the two electromagnets (actuators) can be directly measured, so the state observer must use system state estimation. Furthermore,
It is difficult to measure the unbalanced disturbance D _{f1 in} Expression (15). In order to directly correct this unbalanced disturbance, disturbance estimation must be used to generate a disturbance signal. The discrete-time VSS observer is described in this section as estimating the state vector of the system and the unbalanced disturbance simultaneously. In this magnetic bearing device, the sinusoidal force acting on the rotor generally causes unbalanced vibration that does not satisfy the matching state. Therefore, here, an unbalanced force (disturbance w ₁ ) is considered as follows. w ₁ = asinω ₀ t (21) If this unbalanced force is regarded as a state quantity, the state equation is as follows when the state vector is (w). “W” = A _W w (22a) d = Lw (22b) Here, w, A _W , and L are as shown in FIG.

Next, an enlargement system is created from equations (21) and (22). The state equation and output equation of the expanded system are as follows. In "x _{d" = A d x d + B d} u + D d ··· (23a) y d = C d x d ··· (23b) _{where, x d, A d, B} d, C d, D d is , As shown in FIG. Also, A _r , B _r , C _r ,
_Dr is as shown in the above equation (17). Equation (2
The equivalent discrete time system of 3) is as follows. x _d (k + 1) = Φ _d x _d (k) + Γ _d1 u (k) + Γ _d2 (k) (24a) y _d = C _d x _d (k) (24b) where Φ _d , Γ _d1, gamma _d2 is as shown in FIG. 12 (C).

The following assumption is made for a disturbance satisfying the matching condition. Γ _d2 (k) = Γ _d1 h (k) (25) Here, {h (k)} ≦ η, η> 0, and h (k) is the maximum estimated value of the disturbance. Since (C _d , Φ _d ) is observable, there exists a certain matrix G _O. That is, Φ _O = Φ _d −G _O C _d (26) where G _O = (R + C _d PC _d ^T ) ⁻¹ C _d PΦ _d ^T (27) This is the solution of the Riccati equation. ^{_{Φ d PΦ d T -Φ d PC}} d T (R + C d PC d T) -1 C d T P T Φ d T + Q = P ··· (28) provided that Q ≧ 0, R> 0.

From the following, it is assumed that the positive definite symmetric matrices Q ₁ and F ₁ with respect to the equation (24) exist, and the following equation is assumed. F ₁ C _d = Γ _d1 ^T P ₁ (29) where P ₁ is the only positive symmetric solution of the following Lyapunov equation. Φ _O ^T P ₁ Φ _O + Q ₁ = P ₁ , Q ₁ ≧ 0 (30) In this case, since the number of inputs and outputs of the system of equation (24) is the same, it is necessary to obtain F ₁ = I _2. Can be. The error from the output of the observer to the state of the system is given by the following equation. 'x _d ' (k) = “x _d ” (k) −x _d (k) (31)

At this time, the VSS disturbance observer having improved robustness is expressed by the following equation. _{"X d" (k + 1} ) = Φ O "x d" (k) + G 0 'y d' also _{(k) + M (y d} (k)) + Γ d1 u (k) ··· (32), (32 )), M (y _d (k)), x _d , and y _d (k) of the third term on the right side are as shown in (D) of FIG. Here, ρ is determined as follows, and γ>
0 is a positive number. The effect of gamma results in a compromise between true sliding conditions and motion near hyperplane intersection. Equations (24), (25), (3
When 2) is combined, the error between the output of the observer and the state follows the following equation. “X _d ” (k + 1) = Φ _O “x _d ” (k) + M (′ y _d ′ (k)) − Γ _d1 h (k) (32A) If ρ is selected according to ρ ≧ η, an error occurs. Can be reduced exponentially. (3)
FIG. 7 shows the equation (2) in a block diagram.

Next, the discrete time sliding mode controller is designed using the state quantity and the disturbance estimated by the VSS disturbance observer designed as described above.
The procedure will be described. Here, it is necessary to design a type 1 servo system, and the integral value z of the difference between the target value and the amount of observation is required.
(Vector quantity) is given by the following equation as a new state variable. z = r- "x" ··· ( 33) _{where, r = [r 5 r 11} ] T, "x" = [ "x 5""x
₁₁ "is a ^T. Incidentally, r is a target value input. Enlargement state equation derived from this and the original dimension reduction of motion equation (Equation (17)) and the following equation." X _{i "= A i x i + B i} u + D i + Gr ··· (34a) y = C i x i = [i 5 i 11] T ··· (34b) _{where, x i, z, r,} A i, B _i , D _i , G, E ₂ ,
C _i is as shown in FIG.

From equation (34), the equivalent discrete-time system is as follows. _{x i (k + 1) =} Φx i (k) + Γ 1 u (k) + Γ 2 r (k) + Ξ 1 (k) + Ξ 2 (k) ··· (35a) y (k) = C i x i (k (35b) Here, Φ, Γ ₁ , Γ ₂ , and u (t) are represented by (B) in FIG.
As shown in FIG. Further, the disturbance in the equation (34) is as shown in FIG. Here, Ξ ₂ (k) = D _i2 (k) = Γ ₁ h (k) (36A) Ξ ₁ (k) = D _i1 (k).

The switching function σ (k) is defined as follows. σ (k) = Sx _i (k) (37) S is designed to stabilize the state of the system of equation (35) on the hyperplane of the state space satisfying σ (k) = 0. . First, at a sample time on this hyperplane, when Sx _i (k) reaches a hyperplane having a constant value,
Let's try to find an equivalent input that keeps the state on the hyperplane at successive sample times. When σ (k) = Sx _i (k), σ (k) = σ (k + 1) for k> k _1.
The equivalent input that satisfies (38) is as follows. u _eq (k) = − (SΓ) ⁻¹ [S (Φ−I) x _i (k) + SΓ ₂ r (k)] − h (k) (39) where Ξ ₁ (k) Is as shown in FIG.

It is assumed that the matrix (SΓ ₁ ) ^-1 is a regular matrix. At this time, the equation of motion of the system is given as follows. x _i (k + 1) = [Φ−Γ ₁ (SΓ ₁ ) ⁻¹ S (Φ−I)] x _i (k) + [I−Γ ₁ (SΓ ₁ ) ⁻¹ S] Γ ₂ r (k) · ·· (40a) σ (k) = Sx it (k) = 0 ··· (40b) therefrom, switching matrix S is should be chosen so the system becomes stable. Here, a method utilizing the zero point of the system is used for this design method. Here, the system Φ specifying the stability is expressed by the following equation. Φ _e = Φ + eI, e ≧ 0 (41) Further, S is obtained by the following equation. _{^{S T = (R 2 + Γ}} 1 T PΓ 1) -1 Γ 1 T PΦ e ··· (42) However, P is a solution of the following Rikatti equation. P−Φ _e ^T PΦ _e + Φ _e ^T PΓ ₁ (R ₂ + Γ ₁ ^T PΓ ₁ ) ⁻¹ Γ ₁ ^T PΦ _e −Q ₂ = 0... (43) where Q ₂ ≧ 0, R ₂ > 0.

After designing the hyperplane, the next important thing is to guarantee the existence of the sliding mode. VSS
Can be considered as a closed loop system with a variable feedback gain. Now, consider the Lyapunov function as follows. V (t) = 0 · 5σ (t) ² (44) Equation (44) is discretized, and its derivative is given by the following equation. V (k + 1) = σ (k) ^T (σ (k + 1) −σ (k)) / Δ (45)

On the other hand, the following new Lyapunov function is provided. V (k + 1) = - σ (k) T G 1 σ (k) ··· (46) _{wherein, G 1 = diag [g 1} , ···, g m], g 1>
0, (i = 1,..., M). Equations (45), (4
From 6), the following equation is obtained. σ (k) ^T [G ₁ σ (k) + (σ (k + 1) −σ (k)) / Δ] = 0 (47) As a result, the following equation is obtained. σ (k + 1) −σ (k) =
−ΔG ₁ σ (k) = − Jσ (k) (48) where J = diag [Δg ₁ ,..., Δg _m ] = diag [j
₁ ,..., J _m ], 0 <j _i <1 (i = 1,.
m).

On the other hand, from equations (37) and (35), the following equation is obtained. σ (k + 1) -σ ( k) = Sx i (k + 1) -Sx i (k) = SΦx i (k) + SΓ 1 u (k) + SΞ 2 (k) + SΓ 2 r (k) -Sx i (k) (49) When the equation (49) is substituted into the equation (48), the following equation is obtained. _{-Jσ (k) = SΦx i (} k) + SΓ 1 u (k) + SΞ 2 (k) + SΓ 2 r (k) -Sx i (k) ··· (50) equation (36A) by equation (50) , The following control law can be obtained. u (k) = - (SΓ 1) -1 [S (Φ-I) x i (k) + SΓ 2 r (k)] - h (k) - (SΓ 1) -1 JSx i (k) ·· (51) Comparing Equations 50 and 39 gives Equation 46 below. _{u (k) = u eq (} k) - (SΓ 1) -1 JSx i (k) ··· (52)

The actual value of the undefined matching component h (k) in equation (50) is generally unknown, but is indicated by a known range (bounds). To simplify the notation, it is assumed that the range of h (k) is obtained from the following equation (53). H _min ≤ h (k) ≤ H _max (53) If the selection is made as in equation (54), it is clear that the assumption in equation (25) is a special case of equation (53). It is. H _max = −H _min = η · Define H ₁ = H _min + H _max / 2, H ₂ = H _min −H _max / 2 (54) The component h (k) is expressed as follows. . h (k) = H ₁ + H ₂ sgn (σ (k)) (5)
5) Equation (55) By substituting equation (51), the final control law is expressed as follows. _{u (k) = u 1 (} k) + u 2 (k) ··· (56) _{where, u 1 (k) = -} (SΓ 1) -1 [S (Φ-I) x
_{i (k) + SΓ 2 r} (k)] - H 1 -H 2 sgn (σ
(K)) (SΓ ₁₎ is ^-1 JSx _i (k), u
₂ (k) = - a ^{_{(SΓ 1) -1 SΞ 1 (}} k).

A closed loop system including the device, the discrete time VSS disturbance observer, and the discrete time sliding mode controller obtains a stable eigenvalue within the unit circle. FIG. 8 is an overall block diagram of a proposed sliding mode control system based on the VSS observer.

The control device designed by such a procedure is as follows.
As in the case of the first embodiment, it can be realized by the control device of FIG. However, the functions of the VSS disturbance observer 31 and the VSC controller 33 shown in FIG.
VSS observer 21 and VSC controller 25 shown in
Is different from the VSS disturbance observer 31 or VSC
DS by program that satisfies the function of controller 33
It is necessary to operate a P (digital signal processor) 44.

Next, FIGS. 14 and 15 show simulation results of the response to the impulse disturbance under the same conditions in the case of the VSS observer according to the present invention and the conventional linear observer. 14A and 14B show the results of the VSS observer. FIG. 14A shows the relationship between time (Time) and displacement (Displacement), and FIG. 14B shows the relationship between time and current (Current).
FIG. 15 shows the result of a conventional linear observer. As is clear from the figure, in the case of the sliding mode control using the VSS observer according to the present invention, the disturbance attenuates in a short time with time and converges to zero. In the case of the sliding mode control using the VSS observer, the amplitude with respect to the disturbance can be reduced to about 1/100 as compared with the conventional linear observer.

According to the above-described embodiment, the following effects can be obtained. (1) The control performance against the unbalance force is improved as compared with the related art. (2) Robust performance against parameter fluctuation is improved. (3) Robust against nonlinear characteristics. (4) When implemented by digital control, implementation is easy. (5) Nominal control characteristics (nominal performance) for the same control input are superior to the prior art.

[0055]

As described above, according to the first aspect of the present invention, the VSS mode is established using the sliding mode control theory.
The observer estimates the displacement of the rotating body that cannot be directly observed from the current flowing through the coil of the electromagnet and the control input, and based on the estimated displacement, the VSC controller provides a predetermined linear gain and nonlinear signal as a signal for adjusting the electromagnet. The two gains are added together to obtain a specific gain, and the added signal is used as a control input. According to the second aspect of the present invention, based on the sliding mode control theory, the VSS disturbance type observer uses the current flowing through the coil of the electromagnet and the control input to displace the rotating body that cannot be directly observed, and to disturb the rotating body. Is estimated. Then, while multiplying the estimated disturbance by a predetermined coefficient, based on the estimated displacement,
The VSC controller obtains a predetermined linear gain and a non-linear gain as a signal for adjusting the electromagnet, adds both of them, and adds this added signal to the estimated disturbance multiplied by the above coefficient, and The addition signal is used as a control input.

Therefore, according to the first and second aspects of the present invention, the following effects can be obtained. (1) The whirling motion can be suppressed with respect to the unbalanced disturbance, and it can be said that it is strong against the unbalanced disturbance. (2) Robust performance against parameter fluctuation is excellent, for example, following a target position with high accuracy. (3) Robust to nonlinear characteristics.

[Brief description of the drawings]

FIG. 1 is a block diagram of a control device for a magnetic bearing according to a first embodiment of the present invention.

FIG. 2 is a view showing a schematic configuration of the magnetic bearing.

FIG. 3 is a block diagram illustrating a configuration of a VSS observer illustrated in FIG. 1;

FIG. 4 is a configuration diagram showing a specific configuration of a control device for a magnetic bearing according to the first embodiment.

FIG. 5 is a block diagram of a control device for a magnetic bearing according to a second embodiment of the present invention.

FIG. 6 is a diagram showing a model of a magnetic bearing spindle.

FIG. 7 is a block diagram illustrating a configuration of a VSS disturbance observer illustrated in FIG. 5;

FIG. 8 is a block diagram of a sliding mode control system obtained by a design procedure of a discrete time sliding mode controller.

FIG. 9 is a diagram depicting mathematical formulas and the like necessary for explaining the design procedure.

FIG. 10 is a diagram illustrating mathematical formulas and the like necessary for explaining the design procedure.

FIG. 11 is a diagram illustrating mathematical formulas and the like necessary for explaining the design procedure.

FIG. 12 is a diagram illustrating mathematical formulas and the like necessary for explaining the design procedure.

FIG. 13 is a diagram illustrating mathematical formulas and the like necessary for explaining the design procedure.

FIG. 14 is a diagram illustrating a simulation result of the response of the VSS observer to an impulse disturbance according to the present invention.

FIG. 15 is a diagram showing the result of a simulation of the response of a conventional linear observer to an impulse disturbance.

[Explanation of symbols]

 Reference Signs List 1 rotating body (rotor) 2, 3 electromagnet 21 VSS observer 22 comparing unit 23 integrating unit 24 adding unit 25, 33 VSC controller 25A, 33A linear processing unit 25B, 33B nonlinear processing unit 25C, 33C, 33D adding unit 26 adding unit 27 Amplifier 31 VSS disturbance type observer 32 Coefficient part 41, 42 Radial bearing 41A, 42A Electromagnet 43 Thrust bearing 43 44 DSP (digital signal processor) 45 Host computer 46 A / D converter 47 D / A converter 48 Bias current supply circuit 49 Power Amplifier

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int.Cl. ⁶ , DB name) F16C 32/04 G05B 13/00

Claims (2)

(57) [Claims] 1. An electromagnet that magnetically supports a rotating body, an electromagnet driving unit that drives the electromagnet, a current detection unit that detects a current flowing through a coil of the electromagnet, an input of the electromagnet driving unit, and the current VSS for estimating a displacement of the rotating body at an installation position of the electromagnet and a displacement of an arbitrary position of the rotating body based on a detection current of a detection unit.
(Variable Structure System
m, a variable structure system) an observer, a comparison means for comparing the displacement of the rotating body at the installation position of the electromagnet estimated by the VSS observer with a reference value to obtain a deviation between the two, and a deviation obtained by the comparison means And a VSC (Vari) for obtaining a predetermined linear gain and a non-linear gain as a signal for adjusting the electromagnet based on the displacement of an arbitrary position of the rotating body estimated by the VSS observer, and adding the two.
and a controller for controlling the magnetic bearing, wherein an output signal of the VSC controller is supplied to the electromagnet driving means. 2. An electromagnet for magnetically supporting a rotating body, electromagnet driving means for driving the electromagnet, current detection means for detecting a current flowing through a coil of the electromagnet, an input of the electromagnet driving means and the current A VSS (Varia) for estimating a displacement of the rotating body at the installation position of the electromagnet, a displacement of an arbitrary position of the rotating body, and a disturbance acting on the rotating body, based on a detection current of the detecting means.
ble Structure System) a disturbance type observer, a coefficient means for multiplying the estimated disturbance of the VSS disturbance type observer by a predetermined coefficient, and a displacement of the rotating body at the estimated position of the electromagnet estimated by the VSS disturbance type observer, Comparing means for obtaining a deviation between the two by comparing with a reference value; based on the deviation obtained by the comparing means and the displacement of an arbitrary position of the rotating body estimated by the VSS disturbance observer,
As a signal for adjusting the electromagnet, a predetermined linear gain and a non-linear gain are obtained, and VSC (V
ARRIABLESTRUCTURE CONTROL)
A controller, and adding means for adding a signal obtained by the VSC controller and an output signal from the coefficient means, wherein an output signal of the adding means is supplied to the electromagnet driving means. Control device for magnetic bearings.