JP2005020800A - Method for controlling axial deflection of rotor and flywheel device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce the energy loss of a rotor under an axial deflection control and to enable a power storage for a long time to be made by raising the storage efficiency of the power by reducing the energy loss of the rotor under the axial deflection control in a flywheel device. <P>SOLUTION: A method for controlling the axial deflection of the rotor includes conducting of a motor operated control and the power generation control of the rotor by the current control of the same winding, and radial direction controlling of a rotary shaft by controlling a current value flowing to each winding by this current control. According to this bearing control, the bearing control can be performed by using current required for the motor operation or the power generation, the current used only for the bearing control can be dispensed, and the energy loss of the rotor in association with the bearing control can be reduced. Further, since this axial deflection control is performed without contact with the rotor, the energy loss due to a friction can be abolished as well. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

【００５１】
ただし、Ωｚはロータのｚ軸まわりの回転角速度であり、ｉｕｙ，ｉｌｙはｙ方向の巻線に流れる電流であり、ｉｕｘ，ｉｌｘはｘ方向の巻線に流れる電流であり、θｘ，θｙはそれぞれｘ軸，ｙ軸のまわりの回転角であり、ｋ_１，ｋ_２は定数である。
【００５２】
この式において、左辺の第２項はジャイロ効果によるものであり、ｙ軸まわりの運動にｘ軸まわりの運動が干渉し、ｘ軸まわりの運動にｙ軸まわりの運動が干渉している。
【００５３】
この式（１），（２）の運動方程式を状態方程式に直すと、
ｄｘ（ｔ）／ｄｘ＝Ａｘ（ｔ）＋Ｂｕ（ｔ） …（３）
となる。なお、上記式において、ｘ（ｔ），Ａ，Ｂ，ｕ（ｔ）は、それぞれ以下の数２で示される行列式である。
【数２】

【００５４】
また、ｕ_１，ｕ_２、ａは、それぞれ以下の式（６），（７），（８）で表される。
ｕ_１＝Δｉ_{ｙ １}−Δｉ_{ｙ ２} …（６）
ｕ_２＝Δｉ_{ｘ １}−Δｉ_{ｘ ２} …（７）
ａ＝２ｋ_２ｌ^２／Ｉｘｙ，ｂ＝ｋ_１ｌ／Ｉｘｙ，ｃ＝Ｉｚ／Ｉｘｙ …（８）
【００５５】
また、ｋ_１，ｋ_２は半径方向（軸方向）の電磁石の特性から定まる定数であり、以下の式（９），（１０）で表される。
ｋ_１＝Ｓ・Ｂ_ｒ・Ｎ／ｘ …（９）
ｋ_２＝４Ｆ_０／ｘ・ｋ_ｆ …（１０）
ただし、Ｓは磁極の総有効面積、Ｂ_ｒはモータ（例えば、ＰＭ（パルスモータ））の残留磁束密度、ｋ_ｆは吸引力の補正係数、Ｆ_０は定常吸引力、ｘは定常ギャップである。
【００５６】
この状態方程式を元に、状態フィードバックによる最適制御を用いて安定した制御系を求める。
【００５７】
状態フィードバックにおいて、制御入力を
ｕ（ｔ）＝−Ｆｘ（ｔ） …（１１）
とし、安定した系を評価関数を用いた最適制御法により求める。なお、ｕ（ｔ），Ｆ，ｘ（ｔ）はそれぞれ行列式で表される。
【００５８】
ここで、

とすると、制御系の最適制御入力ｕ_１，ｕ_２は、以下の数３で示される式（１５），（１６）で表される。
【数３】

【００５９】
図６は、この状態フィードバックを用いた制御系のブロック図である。なお、図６では、ｕ_１をｘ方向の電流ｕ_ｘとし、ｕ_２を_ｙ方向の電流ｕ_ｙとしている。
【００６０】
この制御系により、ｘ軸の出力からｘ軸の入力、ｙ軸の出力からｙ軸の入力へフィードバックされる通常のＰＤフィードバックに加え、ｘ軸の出力からｙ軸の入力、ｙ軸の出力からｘ軸の入力へのフィードバック、すなわち逆対称交差結合（クロスフィードバック）が行われ、このクロスフィードバックにより、ジャイロ効果によるｘ，ｙ軸の相互干渉に対する制御を行うことができる。
【００６１】
上記の制御系のシミュレーション例について、図７〜図９を用いて説明する。ここでは、シミュレーション条件として、Ｋ_ｐ＝１×１０^−７とし、回転体が回転数Ωで定速回転を行っている定常状態において、ｔ＝０において、Δｄθ_ｘ／ｄｔ＝１［ｒａｄ／ｓｅｃ］にパルス状外乱を与えている。
【００６２】
図７〜図９は、制御軸のｘ，ｙ座標の応答を示している。
【００６３】
図７（ａ）は、Ω＝６００［ｒａｄ／ｓｅｃ］で回転させたときのｘ，ｙ座標の応答を示している。この場合には、外乱によりｘ軸方向にずれが生じ、それに伴いジャイロ効果によりｙ軸方向にもずれが生じているが、制御により約０．０３［ｓｅｃ］で収束し、振動数も少なく抑えられる。
【００６４】
図７（ｂ）は、図７（ａ）のシミュレーション結果をｘ，ｙ面にプロットしたものであり、高速回転時においても歳差運動による回転が１回転半程度に抑えられる。
【００６５】
図８（ａ）は、実際の回転数に近いΩ＝１００［ｒａｄ／ｓｅｃ］における軸の応答を示している。図７（ａ）に示したΩ＝６００［ｒａｄ／ｓｅｃ］の場合と比較して、振動数が増え、収束時間も約２．５［ｓｅｃ］と長くなっている。図８（ｂ）は、図８（ａ）のシミュレーション結果をｘ，ｙ面にプロットしたものであり、歳差運動の抑制が不十分となっている。
【００６６】
ここで、低速回転時における応答を向上させるために、前記式（１５），（１６）のクロスフィードバック要素の比例項に微分項を加えることにより、制御系の最適制御入力ｕ_１，ｕ_２は、以下の数４で示される式（１７），（１８）で表される。
【数４】

【００６７】
図９は、クロスフィードバック要素に微分項を加えた最適制御入力ｕ_１，ｕ_２を用いて、Ω＝１００［ｒａｄ／ｓｅｃ］、Ｋ_ｐ＝１×１０^−７、Ｋ_ｃｄ＝７．０×１０^−５としたときの軸の応答を示している。
【００６８】
この制御系によれば、収束時間は０．０３［ｓｅｃ］となり、歳差運動による回転が１回転程度となり、微分項を追加することにより応答を大幅に改善することができる。
【００６９】
次に、図１０〜図１３を用いて軸ぶれ制御のシミュレーション例を説明する。ここで、ステータを、巻線が３相４極、コイル数を６つで毎相毎極のスロット数を４とし、１スロットの直列巻線回数を６０回とし、ポールピッチを５６．８３４［ｍｍ］とする。また、ステータの外径を１１１．０［ｍｍ］、巻線部分の外径を９９．５［ｍｍ］、内径を７２．４［ｍｍ］とする。なお、ステータのその他の定数、及びロータの定数、その他仕様は表１に示している。
【表１】

【００７０】
前記式（１５）〜（１８）で表された最適制御入力ｕ_１，ｕ_２は、それぞれ所定方向（例えば、ｘ方向及びｙ方向）の電流であるため、これを各コイルの電流に変換すると以下の式（１９）〜（２４）で表される。
ｉ_ｕ１＝ｕ_１／ｃｏｓ（π／１２）−ｕ_２／ｃｏｓ（５π／１２） …（１９）
ｉ_ｖ１＝ｕ_１／ｃｏｓ（π／４）＋ｕ_２／ｃｏｓ（５π／４） …（２０）
ｉ_ｗ１＝−ｕ_１／ｃｏｓ（５π／１２）−ｕ_２／ｃｏｓ（５π／１２）…（２１）
ｉ_{ｕ ２}＝−ｕ_１／ｃｏｓ（５π／１２）＋ｕ_２／ｃｏｓ（５π／１２）…（２２）
ｉ_ｖ２＝−ｕ_１／ｃｏｓ（π／４）−ｕ_２／ｃｏｓ（５π／４） …（２３）
ｉ_ｗ２＝ｕ_１／ｃｏｓ（５π／１２）＋ｕ_２／ｃｏｓ（π／１２） …（２４）
【００７１】
上記のフィードバック制御によるシミュレーション例について、図１０〜図１３を用いて説明する。
【００７２】
図１０は、シミュレーション条件として、定常状態で回転体が定速回転している状態において、外乱をｔ＝０．４［ｓｅｃ］でｘ＝［ｍｍ］を与え、制御定数はＫ_ｐ＝５００、Ｋ_ｃｄ＝５としたときの軸の応答を示している。図１１（ａ）、（ｂ）は、このときの上記式で求められる各コイルの電流を示している。
【００７３】
また、図１２（ａ）は電磁石の吸引力の応答を示し、図１２（ｂ）は推力の応答を示している。図１２（ａ）はｘ軸方向とｙ軸方向におけるそれぞれの吸引力の差であり、図１２（ｂ）はこれらのコイルにより発生する推力の和である。
【００７４】
また、図１３はギャップ中の磁束密度を示し、図１３（ａ）はｔ＝０．４０００２［ｓｅｃ］のときであって制御開始時の状態を示し、図１３（ｂ）はｔ＝０．５［ｓｅｃ］のときであって回転体の姿勢が安定した時の状態を示している。
【００７５】
なお、横軸ｘ′は動的座標であり、刻み幅は２ｅ−５［ｓｅｃ］である。
【００７６】
このフィードバック制御によるシミュレーション例によれば、外乱が生じてから０．０８［ｓｅｃ］ほどで姿勢を制御することができる。
【００７７】
なお、制御定数はＫ_ｐ＝５００、Ｋ_ｃｄ＝５としているが、Ｋ_ｐは５０〜２０００ほどの範囲で、またＫ_ｃｄは１〜１０の範囲で制御することができる。
【００７８】
【発明の効果】
以上説明したように、本発明によれば、軸ぶれ制御において回転体のエネルギー損失を小さくすることができる。また、フライホイール装置において、軸ぶれ制御における回転体のエネルギー損失を小さくして、電力の貯蔵効率を高め、長時間の電力貯蔵を可能とすることができる。
【図面の簡単な説明】
【図１】本発明の回転体の軸ぶれ制御方法を適用するフライホイール装置の一構成例を説明するための図である。
【図２】軸ぶれ及び軸ぶれ制御を説明するための図である。
【図３】電力変換手段の一構成例を説明するための図である。
【図４】軸ぶれ制御における巻線への電流供給を説明するための図である。
【図５】本発明の電力変換手段が供給する電流の各相の位相関係と電流値の大きさとの関係を示す図である。
【図６】状態フィードバックを用いた制御系のブロック図である。
【図７】制御軸のｘ，ｙ座標の高速時の応答のシミュレーション例を示す図である。
【図８】制御軸のｘ，ｙ座標の低速時の応答のシミュレーション例を示す図である。
【図９】制御軸のｘ，ｙ座標の低速時において微分項を加えた応答のシミュレーション例を示す図である。
【図１０】軸ぶれ制御のシミュレーション例の軸応答を示す図である。
【図１１】軸ぶれ制御のシミュレーション例の電流応答を示す図である。
【図１２】軸ぶれ制御のシミュレーション例の吸引力、推力の応答を示す図である。
【図１３】軸ぶれ制御のシミュレーション例のギャップ中の磁束密度を示す図である。
【図１４】従来の超伝導軸受けを備えるフライホイール装置の構成を説明するための概略断面図である。
【符号の説明】
１…フライホイール装置
２…回転軸
３…発電電動機
３Ａ…ロータ
３Ｂ…ステータ
３ａ…回転体
３ｂ…磁石
３ｃ…フレーム
３ｄ…巻線
３ｅ…ギャップ
４…フライホイール
５…超伝導軸受け
５ａ…ＨＴＳバルク
５ｂ，５ｃ…磁石
６，６ｘ，６ｙ…偏位センサ
７…電力変換手段
７ａ〜７ｃ，７ａ′〜７ｃ′…インバータ
８…制御手段[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a shaft shake control method and a flywheel device to which the shaft shake control method is applied.
[0002]
[Prior art]
In the field of power systems, the power disparity between day and night and specific time zones is widening due to the increase in power demand and changes in the form of power demand. There is a need to develop and introduce a power storage device that distributes and distributes power distribution substations close to power demand areas for effective daily load leveling.
[0003]
Various types of power storage devices are known, and one of them is a high-temperature superconducting flywheel device.
[0004]
The flywheel device stores electric power as rotational energy of the flywheel during a time period with a low electric power demand such as midnight, and takes it out as electric energy at the peak of electric power demand. The flywheel has features such as being able to quickly respond to load fluctuations, high storage energy density, and low environmental pollution.
[0005]
A conventional flywheel for power storage includes a rotating body, a generator motor, a power converter, and the like. The flywheel uses the inertia of an object to convert electric power into rotational energy and store it. In order to increase the stored energy, it is necessary to rotate an object having a large moment of inertia at high speed. Since the rotational energy accumulated in the flywheel is reduced by the rotational loss of the bearing, it is required to reduce the rotational loss of the bearing.
[0006]
For this purpose, there has been proposed one that supports the rotating shaft of a flywheel with a superconducting bearing. FIG. 14 is a schematic cross-sectional view for explaining the configuration of a flywheel device having a conventional superconducting bearing.
[0007]
In FIG. 14, a flywheel device 11 has a flywheel 14 attached to a rotary shaft 12, and energy is accumulated and extracted from the flywheel 14 by a generator motor 13. A superconducting bearing 15 is provided at the lower part of the rotating shaft 12, and the magnetic repulsive force and pinning force between the permanent magnets 15 b and 15 c attached on the rotating shaft 12 side and the superconducting bulk body 15 a provided on the stationary side are provided. The thrust load of the rotating body is supported in a non-contact manner.
[0008]
Superconducting bearings can support a large load without contact without contact, but there is a problem that the radial stiffness and damping constant are small and it is difficult to control the shaft runout only with this superconducting bearing. . This axial vibration has a problem that the resonance point is lowered and the dangerous rotational speed is lowered, and the vibration amplitude is increased at the resonance point. In addition, there is a problem that sufficient support cannot be provided for the unbalanced suction force generated in the radial direction due to the eccentricity of the rotor of the generator motor.
[0009]
In order to solve such problems, a configuration of a flywheel device in which a non-superconducting active bearing supporting a radial load in addition to a superconducting bearing supporting a thrust load is provided on the upper portion of the rotating shaft has been proposed. ing. A bearing 16 in FIG. 16 is an example of this active bearing. The above problem and configuration are disclosed in, for example, Patent Document 1.
[0010]
[Patent Document 1]
JP-A-5-248437
[0011]
[Problems to be solved by the invention]
In order to prevent shaft runout, in addition to the superconducting bearing that supports the thrust load, the configuration in which the bearing that supports the radial load is provided above the rotating shaft has a problem that the loss increases. For example, when a mechanical bearing is provided as a bearing for supporting a radial load, there is a problem of energy loss due to friction, and when a non-superconducting active bearing is provided, the active bearing is driven. Therefore, since external power is required, there is a problem that the storage efficiency of power decreases when viewed from the power system.
[0012]
Therefore, there is a problem that the energy loss of the rotating body is large in the conventional method of controlling shaft runout, and the energy storage efficiency is low because the energy loss is large in the flywheel device, and the power cannot be stored for a long time. There is a problem.
[0013]
Accordingly, the present invention aims to solve the above-described conventional problems and reduce the energy loss of the rotating body in the shaft shake control. Further, in the flywheel device, the energy loss of the rotating body in the shaft shake control is reduced. Thus, it is an object to increase power storage efficiency and enable long-time power storage.
[0014]
[Means for Solving the Problems]
The present invention uses a generator motor as a magnetically controlled bearing, thereby supporting the rotating body in a non-contact manner and reducing power loss associated with shaft shake control of the rotating body.
[0015]
The aspect of the present invention can be an aspect of a method of controlling the axial shake of a rotating body and an aspect of a flywheel device in which the method of controlling the axial shake is applied to a rotating body including a flywheel.
[0016]
According to the rotating body shake control method of the present invention, in the rotating shake control of the rotating body, electric control and power generation control of the rotating body are performed by current control of the same winding. By controlling, the radial direction of the rotating shaft is controlled. According to this bearing control, by controlling the current value flowing through each winding in electric control and power generation control, bearing control can be performed using the current required for electric or power generation, and it is used only for bearing control. An electric current can be made unnecessary, and the energy loss of the rotary body accompanying bearing control can be reduced. Further, since this shaft shake control is non-contact with the rotating body, energy loss due to friction can be eliminated.
[0017]
A flywheel device to which this shaft shake control method is applied is a flywheel device having a flywheel and a generator motor on a rotating shaft, and includes a current control means for controlling the current of the generator motor. The means controls the radial direction of the rotating shaft by controlling the current flowing through the windings of the generator motor and adjusting the electromagnetic force generated by the generator motor.
[0018]
The current control is performed by controlling the current value of the in-phase current that flows through the pair of windings arranged to face the rotating body. As a result, an electromagnetic force having a magnitude corresponding to the current value of the current supplied to each winding is generated from the two windings arranged opposite to each other, and a suction force having a magnitude based on the difference in the current value with respect to the rotating body. Alternatively, a repulsive force acts, thereby controlling the shaft shake of the rotating body. The current control means of the flywheel device controls the shake of the rotating shaft including the flywheel by controlling the current value of the in-phase current that flows through the pair of windings arranged opposite to each other provided in the generator motor.
[0019]
In the current value control, the current value that flows through the winding pair is obtained from the deviation from the rotation center axis of the rotating body by the optimum control by the state feedback that feeds back the deviation to the supply current. The deviation can be an axial deflection angle of a bi-directional axis orthogonal to the axial direction of the rotating body, and the axial deflection angle can be obtained by a displacement from the rotation center axis of the rotating body.
[0020]
Optimal control includes PD feedback that feeds back between the coaxial axes in two-way axes, and cross feedback that feeds back between different axes (inverse symmetric cross coupling). By including cross feedback, each axis due to the gyro effect of the rotating body Mutual interference between the two can be controlled.
[0021]
The current control means included in the flywheel device has the function of performing the current control, so that the method of controlling the shaft shake of the rotating body of the present invention can be applied.
[0022]
In shaft runout control, it is possible to reduce power loss due to friction in the bearing shaft and power loss due to external power for driving the magnetic bearing, so the power storage efficiency of the flywheel device can be increased, Maintenance management such as replenishment of lubricant and countermeasures against friction is not required, and power can be stored for a long time.
[0023]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The configuration of the shaft shake control and current control of the rotating body of the present invention will be described with reference to FIGS. 1 to 5, the control system of the present invention will be described with reference to FIG. 6, and the control system will be described with reference to FIGS. A simulation example of shaft shake control will be described with reference to FIGS.
[0024]
First, an example of the configuration of a flywheel device to which the shaft shake control method of a rotating body of the present invention is applied will be described with reference to FIG.
[0025]
In FIG. 1, a flywheel device 1 has a flywheel 4 attached to a rotating shaft 2, and energy is accumulated and extracted from the flywheel 4 by a generator motor 3.
[0026]
A superconducting bearing 5 using a superconducting bulk bearing is provided below the rotating shaft 2, and permanent magnets 5b and 5c attached to the rotating shaft 2 side and a superconducting bulk body (HTS bulk) 5a provided on the stationary side. The thrust load of the rotating body is supported in a non-contact manner by the magnetic repulsive force and the pinning force between them.
[0027]
Since the permanent magnets 5b and 5c generate a uniform magnetic field, the magnetic field received by the stationary superconducting bulk body (HTS bulk) 5a is constant even when the permanent magnets 5b and 5c are rotating. is there. Here, if the distance between the permanent magnets 5b and 5c and the superconducting bulk body 5a is to change, the magnetic field received by the superconducting bulk body 5a tends to change, and the force in the direction that prevents this magnetic field change is affected by the permanent magnet 5b. , 5c, and tries to keep the vertical position of the flywheel 4 constant. Thereby, the superconducting bearing 5 can support the thrust load in a non-contact manner.
[0028]
The generator motor 3 includes a rotor 3A that is attached to the rotary shaft 2 and is rotatably supported, and a fixed stator 3B. Energy is stored by operating the generator motor 3 as a motor, and the generator motor 3 is driven by the power supplied via the power converter 7 to rotate the flywheel 4 to store electric energy in the form of rotational energy. To do. On the other hand, the energy is stored by operating the generator motor 3 as a generator, and the generator motor 3 is generated by the rotational movement of the flywheel 4, and the rotational energy stored in the flywheel 4 is converted into electric power in the form of electric energy. Take out via the converter 7.
[0029]
The rotor 3A includes a central rotating body 3a formed of, for example, aluminum, and a magnet 3b disposed on the outer periphery of the rotating body 3a. The rotating body 3a is attached to the rotary shaft 2. For the magnet 3b, Nb—Fe—B magnets are alternately arranged, for example, N, S, N, S. The stator 3B is a normal conductive magnet that generates thrust and attractive force, and includes a frame 3c and a winding 3d. A gap 3e is formed between the outer peripheral surface of the magnet 3b of the rotor 3A and the inner peripheral surface of the winding 3d of the stator 3B, and the rotor 3A is rotatable within the stator 3B.
[0030]
When a 4-pole generator motor is configured, the number of windings of the stator 3B is set to 6, and the current supplied to each winding is controlled. Moreover, the magnet 3b of the rotor 3A arranges four magnets alternately every 90 degrees.
[0031]
A displacement sensor 6 that detects the displacement of the rotation shaft 2 is provided at an upper position of the rotation shaft 2. The displacement sensor 6 can be, for example, two sensors 6x and 6y that detect a displacement in a biaxial direction orthogonal to the axial direction of the rotating shaft 2. As the displacement sensor 6, for example, a gap sensor that detects a gap with the rotating shaft 2 can be used.
[0032]
The power conversion means 7 performs electric control and power generation control of the generator motor 3 and performs shaft shake control.
[0033]
Electric control and power generation control of the generator motor 3 are the same as those performed by a normal generator motor. In the electric control, the rotor 3A is rotated by electric power supplied from an external power source, and rotational energy is accumulated in the flywheel 4. . On the other hand, in the power generation control, power is generated by the rotation of the rotor 3A, and the rotational energy stored in the flywheel 4 is extracted outside in the form of electric energy. The power conversion means 7 performs switching between the electric control and the power generation control.
[0034]
The power conversion means 7 performs shaft shake control simultaneously with the electric control and power generation control. The axial shake control is control for compensating for the deviation of the rotation axis from the rotation center axis. FIG. 2 is a diagram for explaining shaft shake and shaft shake control.
[0035]
In FIG. 2, the rotation axis 2a indicated by a solid line indicates a case where the rotation axis is on the rotation center axis, and the rotation axis 2b indicated by a broken line indicates a case where the rotation axis 2b is displaced from the rotation center axis. In the shaft shake control, the position-shifted rotating shaft 2b is position-controlled to the rotating shaft 2a on the rotation center axis to compensate for the deviation. The deviation of the rotation shaft 2b from the rotation center axis can be obtained by, for example, the displacement sensors 6x and 6y. For example, when a gap sensor is used as the displacement sensor 6, the gap sensor detects distances Δx and Δy from the outer peripheral surface of the rotating shaft 2b. The displacement sensor 6 is not limited to this gap sensor, and other sensors can be used.
[0036]
The control means 8 obtains the control amount of the power conversion means 7 based on the displacement amount detected by the displacement sensor 6 and outputs a control signal. The power conversion means 7 controls the amount of current flowing through the winding 3d of the stator 3B based on the control signal input from the control means 8.
[0037]
FIG. 3 is a diagram for explaining a configuration example of the power conversion means, and FIG. 4 is a diagram for explaining current supply to the windings in the shaft shake control.
[0038]
In FIG. 3, the power conversion means 7 is composed of a plurality of inverters. Here, an example in which the generator motor includes six windings and is driven by a three-phase current will be described.
[0039]
Power conversion means 7 and two inverters 7 for each phase are provided, and by performing orthogonal transformation between external AC (AC) and generator motor DC (DC), electric control or power generation control In addition, shaft shake control is performed by controlling the current value in each same phase.
[0040]
The inverter 7 includes inverters 7a and 7a 'that control the A phase and A' phase of the same phase, inverters 7b and 7b 'that control the B phase and B' phase of the same phase, and inverters that control the C phase and C 'phase of the same phase. 7c, 7c ', a total of six inverters, and the inverters controlling the same phase (inverters 7a and 7a', inverters 7b and 7b ', and inverters 7c and 7c') have different current values in the same phase. Current is passed through the windings arranged opposite to each other with the rotating shaft 2 interposed therebetween. As a result, the magnetic force generated by the winding applies an attractive force or a repulsive force to the rotating shaft 2 and applies a force to the rotating shaft 2 on the side opposite to the shaft shake in the direction connecting the windings arranged opposite to each other. , Shake control is performed.
[0041]
In FIG. 4, six windings are arranged around the rotating shaft 2 at intervals of 60 degrees, and the shaft shake control is performed with the windings arranged at a position of 180 degrees across the rotating shaft 2 as one set. In FIG. 4, winding 3d-A and winding 3d-A ', winding 3d-B and winding 3d-B', winding 3d-C and winding 3d-C 'sandwich the rotating shaft 2, respectively. An inverter 7 that is arranged at a position of 180 degrees and flows current of the same phase is connected to each winding. For example, the winding 3d-A and the winding 3d-A ′ are connected to the inverter 7a ′ that supplies the A′-phase current in the same phase as the inverter 7a that supplies the A-phase current. B and winding 3d-B 'are connected to inverter 7b' for supplying B'-phase current in phase with inverter 7b for supplying B-phase current, respectively, and winding 3d-C and winding 3d-B 'are connected to winding 3d-B'. 3d-C ′ is connected to an inverter 7c ′ that supplies a C′-phase current in phase with an inverter 7c that supplies a C-phase current.
[0042]
Among them, the windings 3d-A and 3d-A 'are supplied with currents having the same phase and different current values from the inverters 7a and 7a', and the magnitudes of the supplied current values are set. The rotary shaft 2 is controlled to move on the line connecting the winding 3d-A and the winding 3d-A ′ by the suction force or repulsive force generated accordingly. Shake-out control is performed by similarly controlling the winding 3d-B and winding 3d-B 'and the winding 3d-C and winding 3d-C'.
[0043]
In the above example, the windings for passing the current of the same phase are arranged opposite to each other at 180 degrees with the rotating body interposed therebetween. However, this winding arrangement is not limited to this, and other angular arrangements may be used. You can also This case can be dealt with by controlling the magnitude of the current flowing in each phase so that the components in each direction of the magnetic force generated by each arrangement are eliminated.
[0044]
This shaft shake control can be performed by controlling the current flowing through each winding during the power generation operation or the electric operation, and no current for shaft shake control is required other than the current required for power generation or electric drive.
[0045]
The power conversion means 7 also controls shaft shake by causing a predetermined current to flow in the windings while storing energy by freely rotating the flywheel in addition to control of electric control and power generation control. It can be performed.
[0046]
FIG. 5 shows the relationship between the phase relationship of each phase (A phase, A ′ phase, B phase, B ′ phase, C phase, C ′ phase) and the magnitude of the current value. FIG. 5A shows the relationship between the A-phase current (indicated by a solid line) and the A′-phase (indicated by a broken line). The A-phase current and the A′-phase current have the same phase and different current values. Similarly, FIG. 5B shows the relationship between the B-phase current (shown by a solid line) and the B′-phase (shown by a broken line), and FIG. 5C shows the C-phase current (shown by a solid line). The relationship of the electric current of C 'phase (it shows with a broken line) is shown. The magnitude of this current value depends on the direction of the shaft shake of the rotating shaft 2 and the degree of shaft shake. Therefore, the relationship between the magnitudes of the current values shown in FIG.
[0047]
Next, the control system of the present invention will be described with reference to FIGS.
[0048]
In one-dimensional levitation control in which the rotation direction of the rotor is limited to around the x axis (and around the z axis), it is known that levitation control can be stably performed by PID control. However, in the two-dimensional levitation control that can freely rotate all around the x, y, and z axes, PID control that controls rotation around the x axis and PID control that controls rotation around the y axis are simply performed. In combination, stable control cannot be performed. This is because mutual interference occurs in the rotational movement around the x and y axes due to the gyro effect.
[0049]
Therefore, in the present invention, control is performed in consideration of mutual interference between rotational motions about the x and y axes due to the gyro effect by using optimal control based on state feedback.
[0050]
Here, for a four-pole model in which four linear synchronous motors (LMS) are arranged around the rotor, the equations of motion about the x and y axes are expressed by equations (1) and (2) shown in equation (1).
[Expression 1]

[0051]
Where Ωz is the rotational angular velocity around the z-axis of the rotor, iuy, ily are currents flowing in the y-direction winding, iux, ilx are currents flowing in the x-direction winding, and θx, θy are respectively the rotation angle around the x and y axes, k₁, K₂Is a constant.
[0052]
In this equation, the second term on the left side is due to the gyro effect, and the movement around the x axis interferes with the movement around the y axis, and the movement around the y axis interferes with the movement around the x axis.
[0053]
When the equations of motion of these equations (1) and (2) are converted into the state equations,
dx (t) / dx = Ax (t) + Bu (t) (3)
It becomes. In the above formula, x (t), A, B, and u (t) are determinants represented by the following Equation 2, respectively.
[Expression 2]

[0054]
U₁, U₂, A are represented by the following equations (6), (7), (8), respectively.
u₁= Δi_{y 1}-Δi_{y 2}                                    (6)
u₂= Δi_{x 1}-Δi_{x 2}                                    ... (7)
a = 2k₂l²/ Ixy, b = k₁l / Ixy, c = Iz / Ixy (8)
[0055]
And k₁, K₂Is a constant determined from the characteristics of the electromagnet in the radial direction (axial direction) and is expressed by the following equations (9) and (10).
k₁= SB_r・ N / x (9)
k₂= 4F₀/ X ・ k_f                                    (10)
Where S is the total effective area of the magnetic poles and B_rIs the residual magnetic flux density of the motor (for example, PM (pulse motor)), k_fIs the correction coefficient for suction force, F₀Is a steady suction force and x is a steady gap.
[0056]
Based on this state equation, a stable control system is obtained using optimal control based on state feedback.
[0057]
In state feedback, control input
u (t) = − Fx (t) (11)
A stable system is obtained by an optimal control method using an evaluation function. U (t), F, and x (t) are each represented by a determinant.
[0058]
here,

Then, the optimal control input u of the control system₁, U₂Is expressed by the following equations (15) and (16).
[Equation 3]

[0059]
FIG. 6 is a block diagram of a control system using this state feedback. In FIG. 6, u₁X current u_xAnd u₂The_yDirectional current u_yIt is said.
[0060]
With this control system, in addition to the normal PD feedback fed back from the x-axis output to the x-axis input and from the y-axis output to the y-axis input, from the x-axis output to the y-axis input and from the y-axis output Feedback to the input of the x axis, that is, reverse symmetric cross coupling (cross feedback) is performed, and the cross feedback can control the mutual interference of the x and y axes due to the gyro effect.
[0061]
A simulation example of the above control system will be described with reference to FIGS. Here, as simulation conditions, K_p= 1 x 10^-7In a steady state where the rotating body is rotating at a constant speed Ω, Δdθ at t = 0_xA pulsed disturbance is applied to / dt = 1 [rad / sec].
[0062]
7 to 9 show the responses of the x and y coordinates of the control axis.
[0063]
FIG. 7A shows the response of the x and y coordinates when rotating at Ω = 600 [rad / sec]. In this case, a shift occurs in the x-axis direction due to disturbance, and a shift also occurs in the y-axis direction due to the gyro effect. However, the control converges in about 0.03 [sec], and the frequency is suppressed to a low level. It is done.
[0064]
FIG. 7B is a plot of the simulation results of FIG. 7A on the x and y planes, and rotation due to precession is suppressed to about one and a half rotations even at high speed rotation.
[0065]
FIG. 8A shows the shaft response at Ω = 100 [rad / sec] close to the actual rotational speed. Compared to the case of Ω = 600 [rad / sec] shown in FIG. 7A, the frequency is increased and the convergence time is also increased to about 2.5 [sec]. FIG. 8B is a plot of the simulation results of FIG. 8A on the x and y planes, and the suppression of precession is insufficient.
[0066]
Here, in order to improve the response at the time of low-speed rotation, an optimum control input u of the control system is obtained by adding a derivative term to the proportional term of the cross feedback element of the above equations (15) and (16).₁, U₂Is expressed by equations (17) and (18) expressed by the following equation (4).
[Expression 4]

[0067]
FIG. 9 shows an optimal control input u with a differential term added to the cross feedback element.₁, U₂, Ω = 100 [rad / sec], K_p= 1 x 10^-7, K_cd= 7.0 × 10^-5The response of the axis is shown.
[0068]
According to this control system, the convergence time is 0.03 [sec], the rotation due to precession is about one rotation, and the response can be greatly improved by adding a differential term.
[0069]
Next, a simulation example of shaft shake control will be described with reference to FIGS. Here, the stator has three phases and four poles, the number of coils is six, the number of slots per pole is four, the number of series windings of one slot is 60, and the pole pitch is 56.834 [ mm]. Further, the outer diameter of the stator is 111.0 [mm], the outer diameter of the winding portion is 99.5 [mm], and the inner diameter is 72.4 [mm]. Table 1 shows other stator constants, rotor constants, and other specifications.
[Table 1]

[0070]
Optimal control input u expressed by the equations (15) to (18)₁, U₂Are currents in predetermined directions (for example, the x direction and the y direction), and are converted into currents of the respective coils, and are expressed by the following equations (19) to (24).
i_u1= U₁/ Cos (π / 12) -u₂/ Cos (5π / 12) (19)
i_v1= U₁/ Cos (π / 4) + u₂/ Cos (5π / 4) (20)
i_w1= -U₁/ Cos (5π / 12) -u₂/ Cos (5π / 12) (21)
i_{u 2}= -U₁/ Cos (5π / 12) + u₂/ Cos (5π / 12) (22)
i_v2= -U₁/ Cos (π / 4) -u₂/ Cos (5π / 4) (23)
i_w2= U₁/ Cos (5π / 12) + u₂/ Cos (π / 12) (24)
[0071]
A simulation example based on the feedback control will be described with reference to FIGS.
[0072]
FIG. 10 shows a simulation condition in which the disturbance is given by t = 0.4 [sec] and x = [mm] in a steady state where the rotating body is rotating at a constant speed, and the control constant is K_p= 500, K_cdThe axis response is shown when = 5. FIGS. 11A and 11B show the current of each coil obtained by the above formula at this time.
[0073]
FIG. 12A shows the response of the attractive force of the electromagnet, and FIG. 12B shows the response of the thrust. FIG. 12A shows the difference between the suction forces in the x-axis direction and the y-axis direction, and FIG. 12B shows the sum of the thrusts generated by these coils.
[0074]
FIG. 13 shows the magnetic flux density in the gap, FIG. 13 (a) shows the state at the start of control when t = 0.0002 [sec], and FIG. 13 (b) shows t = 0. It shows a state when the posture of the rotating body is stable at 5 [sec].
[0075]
The horizontal axis x ′ is dynamic coordinates, and the step size is 2e−5 [sec].
[0076]
According to the simulation example by the feedback control, the posture can be controlled about 0.08 [sec] after the disturbance occurs.
[0077]
The control constant is K_p= 500, K_cd= 5, but K_pIs in the range of 50-2000, and K_cdCan be controlled in the range of 1-10.
[0078]
【The invention's effect】
As described above, according to the present invention, it is possible to reduce the energy loss of the rotating body in the shaft shake control. Further, in the flywheel device, it is possible to reduce the energy loss of the rotating body in the shaft shake control, increase the power storage efficiency, and enable long-term power storage.
[Brief description of the drawings]
FIG. 1 is a diagram for explaining a configuration example of a flywheel apparatus to which a rotating body shake control method of a rotating body according to the present invention is applied.
FIG. 2 is a diagram for explaining shaft shake and shaft shake control;
FIG. 3 is a diagram for explaining a configuration example of power conversion means.
FIG. 4 is a diagram for explaining current supply to a winding in shaft shake control.
FIG. 5 is a diagram showing the relationship between the phase relationship of each phase of the current supplied by the power conversion means of the present invention and the magnitude of the current value.
FIG. 6 is a block diagram of a control system using state feedback.
FIG. 7 is a diagram showing a simulation example of a response at high speed of x and y coordinates of a control axis.
FIG. 8 is a diagram showing a simulation example of a response at a low speed of the x and y coordinates of the control axis.
FIG. 9 is a diagram showing a simulation example of a response with a differential term added when the x and y coordinates of the control axis are low.
FIG. 10 is a diagram illustrating an axial response of a simulation example of shaft shake control.
FIG. 11 is a diagram illustrating a current response of a simulation example of shaft shake control.
FIG. 12 is a diagram showing a response of suction force and thrust in a simulation example of shaft shake control.
FIG. 13 is a diagram illustrating magnetic flux density in a gap in a simulation example of shaft shake control.
FIG. 14 is a schematic cross-sectional view for explaining the configuration of a flywheel device having a conventional superconducting bearing.
[Explanation of symbols]
1 ... Flywheel device
2 ... Rotation axis
3 ... Generator motor
3A ... Rotor
3B ... Stator
3a ... Rotating body
3b ... Magnet
3c ... Frame
3d ... Winding
3e ... Gap
4 ... Flywheel
5. Superconducting bearing
5a ... HTS bulk
5b, 5c ... Magnet
6, 6x, 6y ... Deviation sensor
7. Power conversion means
7a-7c, 7a'-7c '... inverter
8. Control means

Claims (12)

In the shaft runout control of a rotating body,
The electric control and power generation control of the rotating body is performed by current control of the same winding, and the radial direction control of the rotating shaft is performed by controlling the current value flowing through each winding by the current control. Body shake control method. 2. The method according to claim 1, wherein the current control is a current value control of an in-phase current that flows in a pair of windings arranged to face the rotating body. 3. The current value control is characterized in that a current value to be passed through a winding pair is obtained from deviation from a rotation center axis of a rotating body by optimal control by state feedback that feeds deviation to a supply current. A method for controlling shaft shake of a rotating body according to claim 1. The method according to claim 3, wherein the displacement is a shaft deflection angle of a bi-directional axis orthogonal to the axial direction of the rotating body. The method according to claim 4, wherein the shaft deflection angle is obtained by displacement from a rotation center axis of the rotating body. 6. The optimal control includes PD feedback that feeds back between the coaxial axes in the bi-directional axis, and cross feedback that feeds back between different axes (inverse symmetric cross coupling). A method for controlling shaft shake of a rotating body according to claim 1. In a flywheel device provided with a flywheel and a generator motor on a rotating shaft,
Comprising current control means for controlling the current of the generator motor;
The flywheel device characterized in that the current control means controls the current flowing through the generator motor and controls the radial direction of the rotating shaft by adjusting the electromagnetic force generated by the generator motor. The flywheel device according to claim 7, wherein the current control unit controls a current value of an in-phase current that flows through a pair of windings arranged opposite to each other provided in the generator motor. The current value control means obtains a current value to be passed through the winding pair from the deviation from the rotation center axis of the rotating body by optimal control by state feedback for feeding back the deviation to the supply current. 9. The flywheel device according to 8. 10. The flywheel device according to claim 9, wherein the current control unit uses the displacement as an axial deflection angle of a bi-directional axis orthogonal to the axial direction of the rotating body. The flywheel device according to claim 10, wherein the current control unit obtains the shaft deflection angle from a displacement from a rotation center axis of a rotating body. The optimal control performed by the current control means includes PD feedback that feeds back between the coaxial axes in the bi-directional axis, and cross feedback that feeds back between different axes (inverse symmetric cross coupling). The flywheel apparatus in any one of thru | or 11.

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