JP4032845B2 - Control device for synchronous motor - Google Patents

Description

【００１４】
（１）式のモータモデルを用いることにより、端子電圧と電流情報から磁束を推定する適応磁束オブザーバを構成することができ（２）式となる。
【００１５】
【数２】

【００１６】
ここで、ｉ₁：電流推定値、λ₁：磁束推定値、ω₁：速度推定値、ｇ₁，ｇ₂，ｇ₃，ｇ₄：オブザーバゲインである。
【００１７】
速度の適応同定部分は電流誤差と磁束から速度を演算する（３）式を使用している。
【００１８】
【数３】

【００１９】
ここで、Ｋωｉ：速度適応の積分ゲインである。
【００２０】
この磁束オブザーバと速度適応同定部分をブロック図で表現したものが図２で、（３）式の適応同定部分の演算はベクトルの内積「記号・で表現」を使用している。
【００２１】
〈２〉誘起起電力オブザーバへの展開
図３は起電力オブザーバの伝達関数を示したものである。図３の磁束オブザーバは、電流誤差のフィードバックや電機子側と界磁側との干渉項があるため、このままでは物理的な意味が分かりにくい。そこで、界磁側のブロックが簡素であることに着目して、図３の手順で伝達関数のブロック図を展開すると、最終的には起電力を推定する伝達関数に変換することができる。
【００２２】
まず図３（ａ）で、各積分項にかかっているマイナーフィードバックを伝達関数としてまとめておき、次の（ｂ）図でＬ（ｇ₁Ｉ＋ｇ₂Ｊ）ブロックの加算先を移動してマイナーループの形に変換する。さらに１／（Ｌｓ＋Ｒ）Ｉの項をループ内部に移動すると図３（ｃ）のブロック図となり、入力部は電圧ｖから電流入力の（Ｌｓ＋Ｒ）Ｉの一次進み項を減算する形式に変形できる。これは、永久磁石の磁束による速度起電力成分ｅを演算していることに相当する。
【００２３】
また、フィードバックループ内部は、Ｇ（ｓ）の補償部と回転ベクトル発信器１／ｓＩ＋ωＪで構成された形になる。丁度オブザーバゲインｇ₁〜ｇ₄がこのＧ（ｓ）に集中しており、オブザーバの設計とはこの補償部をどのような特性に設計するかという問題として表現することもてきる。
【００２４】
さらに、フィードバックループをまとめて図３（ｄ）のＨ（ｓ）のような起電力に対する伝達関数の形態に変換することもできるが、４次式となるため、この式のままでは解析的に解くことは難しい。
【００２５】
そこで、図３（ｃ）の要素ブロックを利用して図２の全体ブロック図を再度表現すると図４のようになる。この結果、速度の適応同定機構を有する磁束オブザーバは、速度起電力ｅの演算部１１，補償フィルタ部Ｇ（ｓ）１２，回転ベクトル発信器部１３及び速度適応同定部１４の４つのブロックで構成された起電力オブザーバと等価になることが分かる。
ここで、補償部Ｇ（ｓ）は分母のみｓ項が存在することから一種の帯域フィルタ特性が含まれているものとみなし、（５）式の補償フィルタＦ_G（ｓ）と補償ゲイン｛Ｇ₁Ｉ＋Ｇ₂Ｊ｝に分離した（４）として扱うことにする。
【００２６】
【数４】

【００２７】
ここに、Ｇ₁＝−ω₁ｇ₄／Ｌ，Ｇ₂＝ω₁ｇ₃／Ｌ
【００２８】
【数５】

【００２９】
図４では、起電力成分ｅと推定値ｅ₁の誤差△ｅにＦ_G（ｓ）の補償フィルタを通して△ｅ’の信号を出力している。一般的に微分を演算する場合には高域遮断フィルタをかけることが行われているが、Ｆ_G（ｓ）がこの帯域制限フィルタに相当しているものと考えられる。
このＦ_G（ｓ）は、磁束オブザーバと速度の適応同定の両方に共通にかかっているが、これに対してゲイン｛Ｇ₁Ｉ＋Ｇ₂Ｊ｝は磁束オブザーバの積分項（回転ベクトル発信器）のみに、積分ゲインＫωｉは適応同定側のみにかかっている。このことから、｛Ｇ₁Ｉ＋Ｇ₂Ｊ｝とＫωｉが相互に関係しながらオブザーバの特性を支配していることが分かる。
また、図４の適応同定の部分は、内積の各入力成分にＪと１／Ｊが存在しているため、これらをキャンセルさせて表現している。これによって、適応同定は起電力の振幅を一致させるように動作していることも明確になってくる。
【００３０】
なお、図４は図２と等価であるため紛らわしいが、実際に製品として実装する場合には微分演算が不要な図２のブロックの方が有利である。図４は、物理的な意味を調べるためのブロック図である。
【００３１】
〈３〉フィルタ特性としてのゲイン設計指針
前項で明かにした磁束オブザーバの各ブロックの機能をもとにしてゲインの設計について検討する。
【００３２】
（ａ）起電力オブザーバの簡易伝達関数
図３（ｄ）のように全体の伝達関数Ｈ（ｓ）は４次式となっているので、まずこれを２次式に近似する。帯域フィルタＦ_G（ｓ）の通過帯域幅を十分に広く設定すれば、Ｇ（ｓ）ブロックは｛Ｇ₁Ｉ＋Ｇ₂Ｊ｝の固定ゲインに近似することができる。こうすると、図３（ｄ）のオブザーバ全体の伝達関数Ｈ（ｓ）は、（６）式のように２次式に近似することができる。
また、この全体の伝達関数Ｈ（ｓ）も、Ｇ（ｓ）と同様に（７）式のようなオブザーバの動作をする帯域フィルタＦ_H（ｓ）と固定ゲイン｛Ｇ₁Ｉ＋Ｇ₂Ｊ｝に分離して表現することができる。
【００３３】
【数６】

【００３４】
【数７】

【００３５】
（ｂ）フィルタ特性としてのゲイン設計指針
（７）式のＦ_H（ｓ）にはＪ項が含まれているため特性が分かりにくい。そこで、まずこのフィルタの特性について補足説明しておく。
固定座標上では（８）式で表現される伝達関数を例にとり、これをｂ₀の周波数で回転する座標に変換すると（９）式のＦ₀ ^e（ｓ）になる。
【００３６】
【数８】

【００３７】
【数９】

【００３８】
回転座標のＦ₀ ^e（ｓ）は、帯域幅がａ₀の一次低域通過フィルタが各軸独立に構成されているものであり、これを固定座標上からみたＦ₀（ｓ）は、図５のように帯域幅がａ₀で中心周波数をｂ₀だれ移動させた一次低域通過フィルタ特性として動作することが分かる。
このことから、（７）式のフィルタＦ_H（ｓ）も帯域幅と中心周波数で表現でき、これを利用するとオブザーバの動作する帯域が明確になってくる。
【００３９】
しかし二次式に近似しても、速度適応同定部の積分ゲインＫｗｉが非線形に関係してくるため、適応系を含んだ全体系は解析的に解くことができない。そこで、ゲインの組み合わせを変化させてシミュレーションを行って安定条件を調査したところ、次のような２つの設計指針を得ることができた。
【００４０】
（ア）（Ｒ／Ｌ−ｇ₁）を図６のＦ_G（ｓ）特性のように最高運転周波数以上に設定する。また、ｇ₂＝０とおき、フィルタの中心周波数は移動させない。
【００４１】
（イ）Ｇ₁＝Ｇ₂とおき、Ｇ₁はオブザーバとして必要な応答性に基づいて、動作帯域幅に相当する値を設定する。さらに、（４）式の関係を利用して最終的な設定ゲインｇ₃とｇ₄を設定する。そして、残った速度適応同定部の積分ゲインＫｗｉは調整要素とし、実験などによって最適値に調整する。
【００４２】
以上をまとめると、最高運転周波数をωｍａｘ、オブザーバの応答周波数帯域をω_Hとすると、（１０）式の関係を成立させればよいことになる。
【００４３】
【数１０】

【００４４】
ここで、ゲイン設定法について定性的な意味について述べる。
前記設計指針（イ）項においてゲインをＧ₁＝Ｇ₂の条件に設定することは、図６で示されるように、磁束オブザーバのフィルタ特性Ｆ_H（ｓ）について帯域幅とω₁から中心周波数の移動量を等しくすることになる。つまり、オブザーバの動作帯域Ｆ_H（ｓ）は、運転周波数を中心とする側帯波成分のうち片側のみを通過させることに相当している。
もしも運転周波数のままで起電力誤差△ｅの振幅成分のみが発生した場合には、正相分と逆相分に分離した片側のみを通過させるために、推定磁束の振幅成分の変動は少なくなり、主に位相成分を変化させる効果が生じる。
【００４５】
また、推定起電力ｅ₁に対して直交成分だけの起電力誤差△ｅが発生した場合、本来は同相成分が存在しないため速度の適応同定は動作しない。
しかし、Ｇ₁＝Ｇ₂に設定すると補償ゲイン｛Ｇ₁Ｉ＋Ｇ₂Ｊ｝によって誤差ベクトルを４５゜回転させた方向に磁束オブザーバの推定磁束ベクトルは移動する。
そうすると、推定磁束側の振幅が変化したことにより、起電力誤差△ｅの振幅誤差が発生して間接的に速度の適応同定も動作できるようになる。
このように、磁束オブザーバ単体と速度適応同定とに相互作用が存在するので、適切に磁束と速度を応答させるようなゲインにＫｗｉを調節すればよい。
【００４６】
次に、設計指針（ア）項における（Ｒ／Ｌ−ｇ₁）であるが、これは微分演算の高域制限フィルタの周波数帯域幅に相当しており、あまり高くしすぎると微分演算で生じる高域側のノイズが増幅されてしまい、低すぎると基本周波数成分まで遮断してしまう。
また、ｇ₂はこの低域フィルタの中心周波数に相当しており、オブザーバとして必要な帯域を通過させればよい。そこで、図６のようにｇ₂＝０とおいて中心周波数は移動させないことにして、（Ｒ／Ｌ−ｇ₁）を運転周波数よりも少し大きく、かつ必要最低限の帯域に設定することとする。
【００４７】
以上より判明したオブザーバ特性より、（１０）式のようにゲインを設定することはオブザーバの動作帯域を図６のように設定することに相当している。
この（１０）式に基づいて設計した適応磁束オブザーバゲインを、図１で示す位置推定演算部６内の適応磁束オブザーバに適用してシミュレーションを実施した結果、応答が速く、且つ、振動の少ない磁束推定結果が得られることが確認できた。
このことにより、運転周波数が２００Ｈｚを越える周波数帯域でも安定にＰＭモータのセンサレス制御の適用が可能となる。
また、本来は５個のゲインが存在するため設定ゲインは多くの組み合わせがあり、安定なゲインを調整によって見つけようとするとかなり多くの試行が必要となるが、この実施形態に基づくゲイン決定法を適用することにより、最終的には速度の適応部の積分ゲインを調整するだけでよいので簡単に調整することが出来る。
【００４８】
なお、上記説明においては、磁束オブザーバと適応磁束オブザーバとの表現を使用している。
磁束オブザーバは、ＰＭモータの端子電圧と端子電流から永久磁石の磁束を推定する部分を指している。
また、適応磁束オブザーバの表現については次の理由による。
磁束オブザーバには速度（周波数）情報ω₁が必要であるため、この速度（周波数）を推定する機能も追加する。追加された速度推定の方式は直接演算するものではなく、磁束オブザーバの内部誤差が零となるように動作している。つまり自分自身のブロック内では閉じておらず、他のブロックを参照することにより推定ができるため、速度の”推定”とは呼ばず速度の”適応”として表現している。
【００４９】
【実施形態２】
実施形態１においては、オブザーバゲインの設定方法としてＦ_G（ｓ）のフィルタ帯域が図６の破線のような帯域となるように設定した。
実際には、図６の実線と塗りつぶしで示したＦ_H（ｓ）の帯域を含んでいればよく、帯域幅を狭くとり、その代わりに中心周波数を運転周波数に比例して移動させてもよい。そうすると、図６に相当するオブザーバの動作帯域は図７のようになる。
【００５０】
以上をまとめると、運転周波数をω₁，オブザーバの応答周波数帯域をω_Hとすると、（１１）式の関係を成立させればよいことになる。
【００５１】
【数１１】

【００５２】
（１１）式ては、ｇ₂≠０であるので、演算を省略できないために演算量は増えるが、実施形態１と同様に応答が速く、且つ、振動の少ない磁束推定結果が得られる。
【００５３】
【実施形態３】
図２で示す磁束オブザーバは、固定座標系上に構成している。しかし、推定する磁束は正弦波状に変化するので、ディジタル演算器を利用して離散値系で実現する場合には、離散近似による誤差が発生する。
この離散近似の誤差を抑制するためには、高次の積分近似演算を適用する必要がある。
【００５４】
しかし、高次の積分近似演算は演算量が多くなる欠点がある。そこで、回転子の演算部分のみを回転座標上で構成すると、離散近似誤差を抑制することができる。この回転子部分を回転座標上に構成した磁束オブザーバが図８である。
図８では、速度の適応出力である速度推定ω₁を積分して位相θ₁ωを演算し、これを基準とする回転座標変換を回転子の演算部の入出力に挿入している。
速度の適応同定部分は、図２のような固定座標上でも図８のような回転座標上でも特性は同じであるが、図８では回転座標上で構成した例を示している。
【００５５】
この実施形態においては、多極機のように運転周波数が高くなり、ディジタル演算のための信号のサンプリング周波数が運転周波数よりも十分に高いという近似が成立しなくなり、離散近似誤差の影響が無視できなくなる場合においても、回転子部分を回転座標系で構成したことにより、離散近似の誤差を抑制することができ、運転周波数の上限をさらに高くすることがてきる。
【００５６】
【発明の効果】
以上のとおり、本発明によるオブザーバゲインを使用することにより、運転周波数をより高い領域にまで、応答を速く、且つ、振動の少ない磁束推定結果を得ることができる。
【図面の簡単な説明】
【図１】本発明の実施形態を示す位置センサレス制御系の構成図。
【図２】適応磁束オブザーバのブロック図。
【図３】起電力オブザーバの伝達関数のブロック図。
【図４】起電力オブザーバのブロック図。
【図５】説明のための低域通過フィルタ特性図
【図６】説明のための起電力オブザーバの周波数帯域図。
【図７】説明のための起電力オブザーバの周波数帯域図。
【図８】適応磁束オブザーバのブロック図。
【符号の説明】
１…同期電動機
２…電流検出器
３…可変速制御部
４…回転座標変換部
５…逆回転座標変換部
６…位置推定演算部
７…位相演算部
８…速度検出部
９…速度制御部
１０…電流制御部[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a sensorless control device for a synchronous motor (hereinafter referred to as a PM motor) having a permanent magnet as a field, and particularly to gain setting for the same-dimensional magnetic flux observer.
[0002]
[Prior art]
The PM motor does not require a secondary circuit as compared with the induction machine, and therefore has a merit such that the rotor is small and has low inertia, and there is no loss of copper in the secondary circuit, so that the loss is small.
When this PM motor is driven by a variable speed control device such as an inverter, the position of the magnetic pole needs to be detected by a position sensor or the like. However, since this position sensor has a built-in semiconductor element and optical element, it has low environmental resistance and is likely to fail. For this reason, a position sensorless control method is required and proposed for industrial equipment applications.
[0003]
As a position sensorless system, there is a method of using a speed electromotive force generated by a magnetic flux of a permanent magnet when the rotor rotates. This is a method of estimating the phase of the magnetic pole by detecting this speed electromotive force because it always occurs in the direction orthogonal to the magnetic flux axis at an electrical angle.
However, since there is actually a voltage drop component due to the impedance of the motor winding, the voltage drop component due to this impedance must be subtracted from the motor terminal voltage.
[0004]
Here, since various methods exist in the part which estimates magnetic flux or its speed electromotive force from a terminal voltage and a terminal current, many methods also exist in the position sensorless control system of PM motor.
Among them, there are those described in “Position sensorless control of brushless DC motor by adaptive observer”, IEICE Transactions D, Vol. 113, No. 5, 579-586 (1993).
[0005]
[Problems to be solved by the invention]
In the above document, a gain design formula of the magnetic flux observer is shown. This design formula is obtained by arranging the observer poles k times the pole of the motor confidence. However, when a simulation based on this design formula was simulated, it was found that the operation frequency becomes unstable when the operating frequency exceeds about 200 Hz.
In order to enable more stable operation of the PM motor, it is required to set an observer gain that can obtain a magnetic flux estimation result that has a quick response and little vibration.
[0006]
The present invention has been made in view of such a point, and an object thereof is to provide an apparatus in which a more effective observer gain is set.
[0007]
[Means for Solving the Problems]
In the first aspect of the present invention, a difference signal between a speed command and a speed estimate is input to a speed control unit, a torque current command is calculated, and then converted into a voltage command by the current control unit. Is a control device for controlling a synchronous motor using a permanent magnet as a field source by the variable speed control unit, and inputting the current and voltage of the synchronous motor to obtain a magnetic flux vector. An estimation phase signal is obtained by the phase calculation unit from the calculation unit to be estimated and the two-axis components of the magnetic flux estimation output by the position estimation calculation unit, and the current detected based on the estimated phase is input to the rotary coordinate conversion unit. In what is configured to convert to a reverse current coordinate conversion in the reverse rotation coordinate conversion unit by this two-axis current and the voltage command ,
A fixed coordinate system having a one-dimensional magnetic flux observer for estimating a magnetic flux component from the terminal current and voltage command of the synchronous motor in the position estimation calculating unit, and a speed adapting unit for calculating the magnetic flux observer from the current error and the magnetic flux And the gain of the magnetic flux observer is set by the relationship of the following equation.
(R / L-g ₁ ) ≧ ωmax
g ₂ = 0
g ₃ = sign (ω ₁ ) · g ₄
g ₄ = −L · ω _H / | ω ₁ |
Where R: resistance, L: inductance, g _{1 to} g ₄ : observer gain, ω: speed, ω ₁ : estimated speed value, ω _H : response frequency band of the observer.
[0008]
The second aspect of the present invention is characterized in that the gain of the magnetic flux observer is set by the relationship of the following equation.
(R / L-g ₁ )> ω _H
g ₂ = ω ₁
g ₃ = sign (ω ₁ ) · g ₄
g ₄ = −L · ω _H / | ω ₁ |
According to a third aspect of the present invention, the phase is obtained by integrating the output speed of the speed adaptation section, and the rotor portion of the magnetic flux observer is calculated on the rotational coordinates synchronized with the phase. .
[0009]
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 is a block diagram showing an embodiment of the present invention, in which 1 is a PM motor, 2 is a current detector for detecting a current flowing in the PM motor 1, 3 is a variable speed control unit, and an inverter is used here. . Reference numeral 4 denotes a rotating coordinate conversion unit. The conversion unit 4 receives the current signal detected by the current detector 3 and the phase estimation signal θ ₁ and converts it into a biaxial current of d and q. In the following, in order to distinguish between actual machine variables and estimated variables, estimated variables are expressed by adding the suffix “ ₁ ” to the symbol. Reference numeral 5 is a reverse rotation coordinate conversion unit, and 6 is a position estimation calculation unit that estimates the position of the vector. The calculation unit executes the magnetic flux estimation by inputting the voltage v and the current i. This calculation unit is used for the adaptive magnetic flux observer shown in FIG. It has a block configuration. Although a voltage detection signal and a current detection signal are input to the magnetic flux observer in the position estimation calculation unit 6, a voltage command is used instead of voltage detection in FIG.
[0010]
Reference numeral 7 denotes a phase calculation unit which calculates a phase from the biaxial components of the magnetic flux estimation output λ ₁ estimated by the position estimation calculation unit 6 to obtain an estimated phase θ _1. The estimated phase signal θ ₁ is transmitted to the rotating coordinate conversion unit 4. In addition to being output, it is sent to the speed calculation unit 8 and differentiated to obtain a speed detection signal ωr ₁ . The detected speed signal ωr ₁ is added to the opposite polarity to the speed command ωr, and the deviation signal is output to the speed control unit 9 to obtain a torque / current command. This torque command is added to the current signal from the rotation coordinate conversion unit 4 and is given to the current control unit 10 as a q-axis current command.
[0011]
The current control unit is composed of a rotating coordinate system that rotates in synchronization with the estimated magnetic flux θ _1, and is converted from a detected current i of the fixed coordinate system to a current on the rotating coordinate by applying the rotating coordinate conversion unit 4. . The voltage command that is the output of the current control unit 10 is returned to the value of the fixed coordinate system via the reverse rotation coordinate conversion unit 5 and applied to the variable speed control unit 3 as a PWM signal.
[0012]
Embodiment 1
<1> PM motor voltage-current equation and adaptive magnetic flux observer The state equation of PM motor is a relatively simple equation because the field is a fixed magnetic flux source called a permanent magnet, and fixed coordinates (based on the armature winding) When expressed in terms of (α, β coordinates), equation (1) is obtained. Here, the expression is simply expressed using a vector quantity as a variable. However, since each variable includes a biaxial component of αβ, the equation is actually a 4 × 4 equation. In this embodiment, the motor of Ld = Lq without saliency is targeted.
[0013]
[Expression 1]

[0014]
By using the motor model of equation (1), an adaptive magnetic flux observer that estimates magnetic flux from terminal voltage and current information can be configured, and equation (2) is obtained.
[0015]
[Expression 2]

[0016]
Here, i _{1 is an} estimated current value, λ _{1 is an} estimated magnetic flux value, ω _{1 is an} estimated speed value, and g ₁ , g ₂ , g ₃ , and g _{4 are} observer gains.
[0017]
The speed adaptive identification part uses equation (3) for calculating the speed from the current error and the magnetic flux.
[0018]
[Equation 3]

[0019]
Here, Kωi is an integral gain for speed adaptation.
[0020]
FIG. 2 is a block diagram showing the magnetic flux observer and the speed adaptive identification part, and the calculation of the adaptive identification part of the equation (3) uses an inner product “representation by symbol / symbol”.
[0021]
<2> Development to induced electromotive force observer FIG. 3 shows a transfer function of the electromotive force observer. The magnetic flux observer in FIG. 3 has a current error feedback and an interference term between the armature side and the field side. Therefore, focusing on the fact that the block on the field side is simple, if the block diagram of the transfer function is developed by the procedure of FIG. 3, it can be finally converted into a transfer function for estimating the electromotive force.
[0022]
First, in FIG. 3A, the minor feedback applied to each integral term is summarized as a transfer function, and in the next diagram (b), the addition destination of the L (g ₁ I + g ₂ J) block is moved to move the minor loop. Convert to the form of Further, when the term 1 / (Ls + R) I is moved inside the loop, the block diagram of FIG. 3C is obtained, and the input unit can be transformed into a form in which the primary advance term of (Ls + R) I of the current input is subtracted from the voltage v. This is equivalent to calculating the speed electromotive force component e due to the magnetic flux of the permanent magnet.
[0023]
In addition, the inside of the feedback loop is configured by a G (s) compensation unit and a rotation vector transmitter 1 / sI + ωJ. Observer gains g _{1 to} g ₄ are concentrated on this G (s), and the observer design can also be expressed as a problem of the characteristics of the compensation unit.
[0024]
Furthermore, the feedback loop can be collectively converted into a transfer function with respect to the electromotive force such as H (s) in FIG. 3 (d). It is difficult to solve.
[0025]
Therefore, if the whole block diagram of FIG. 2 is expressed again using the element block of FIG. 3C, it is as shown in FIG. As a result, the magnetic flux observer having the speed adaptive identification mechanism is configured by four blocks of the speed electromotive force e calculation unit 11, the compensation filter unit G (s) 12, the rotation vector transmitter unit 13, and the speed adaptive identification unit 14. It can be seen that this is equivalent to the generated electromotive force observer.
Here, since the compensation unit G (s) has an s term only in the denominator, it is considered that a kind of band filter characteristic is included, and the compensation filter F _G (s) and the compensation gain {G _{1 (} I + G ₂ J) is treated as (4).
[0026]
[Expression 4]

[0027]
Here, G ₁ = −ω ₁ g ₄ / L, G ₂ = ω ₁ g ₃ / L
[0028]
[Equation 5]

[0029]
In FIG. 4, a signal of Δe ′ is output through the compensation filter of F _G (s) to the error Δe between the electromotive force component e and the estimated value e ₁ . In general, when a derivative is calculated, a high-frequency cutoff filter is applied. It is considered that F _G (s) corresponds to this band-limiting filter.
This F _G (s) is commonly applied to both the magnetic flux observer and the adaptive identification of the speed, whereas the gain {G ₁ I + G ₂ J} is only the integral term (rotation vector oscillator) of the magnetic flux observer. In addition, the integral gain Kωi depends only on the adaptive identification side. From this, it can be seen that {G ₁ I + G ₂ J} and Kωi dominate the characteristics of the observer while being related to each other.
Also, the adaptive identification portion of FIG. 4 is expressed by canceling J and 1 / J since each input component of the inner product exists. This also makes it clear that adaptive identification operates to match the amplitudes of electromotive forces.
[0030]
Although FIG. 4 is confusing because it is equivalent to FIG. 2, the block of FIG. 2 that does not require differential operation is more advantageous when actually mounted as a product. FIG. 4 is a block diagram for examining the physical meaning.
[0031]
<3> Gain design guidelines as filter characteristics The gain design will be examined based on the function of each block of the magnetic flux observer as clarified in the previous section.
[0032]
(A) Simplified transfer function of electromotive force observer As shown in FIG. 3 (d), the entire transfer function H (s) is a quartic equation, so this is first approximated to a quadratic equation. If the pass bandwidth of the band filter F _G (s) is set sufficiently wide, the G (s) block can be approximated to a fixed gain of {G ₁ I + G ₂ J}. In this way, the transfer function H (s) of the entire observer in FIG. 3D can be approximated to a quadratic expression as shown in Expression (6).
In addition, the entire transfer function H (s) is also applied to a band filter F _H (s) that operates as an observer as in the equation (7) and a fixed gain {G ₁ I + G ₂ J} as in G (s). It can be expressed separately.
[0033]
[Formula 6]

[0034]
[Expression 7]

[0035]
(B) Gain design guidelines as filter characteristics F _H (s) in equation (7) includes the J term, and the characteristics are difficult to understand. First, a supplementary explanation will be given of the characteristics of this filter.
On the fixed coordinates, the transfer function expressed by the equation (8) is taken as an example, and when this is converted into coordinates rotating at the frequency of b ₀ , F ₀ ^e (s) in the equation (9) is obtained.
[0036]
[Equation 8]

[0037]
[Equation 9]

[0038]
The rotation coordinate F ₀ ^e (s) is a configuration in which a first-order low-pass filter having a bandwidth a ₀ is configured independently for each axis, and F ₀ (s) viewed from a fixed coordinate is shown in FIG. As can be seen from FIG. 5, the filter operates as a first-order low-pass filter characteristic in which the bandwidth is a ₀ and the center frequency is shifted by b ₀ .
From this, the filter F _H (s) in the expression (7) can also be expressed by the bandwidth and the center frequency, and when this is used, the band in which the observer operates becomes clear.
[0039]
However, even if approximated by a quadratic expression, the integral gain Kwi of the speed adaptive identification unit is nonlinearly related, so the entire system including the adaptive system cannot be solved analytically. Therefore, when the stability condition was investigated by performing a simulation by changing the combination of gains, the following two design guidelines could be obtained.
[0040]
(A) Set (R / L-g ₁ ) to be equal to or higher than the maximum operating frequency as shown by the F _G (s) characteristic in FIG. Further, g ₂ = 0 is set, and the center frequency of the filter is not moved.
[0041]
(A) G ₁ = G ₂ , and G ₁ is set to a value corresponding to the operating bandwidth based on the response required as an observer. Further, the final set gains g ₃ and g ₄ are set using the relationship of the expression (4). Then, the remaining integral gain Kwi of the speed adaptive identification unit is used as an adjustment factor, and is adjusted to an optimum value through experiments or the like.
[0042]
In summary, assuming that the maximum operating frequency is ωmax and the response frequency band of the observer is ω _H , the relationship of equation (10) may be satisfied.
[0043]
[Expression 10]

[0044]
Here, the qualitative meaning of the gain setting method will be described.
Setting the gain to the condition of G ₁ = G _{2 in} the design guideline (A) term means that the center frequency is determined from the bandwidth and ω ₁ for the filter characteristic F _H (s) of the magnetic flux observer as shown in FIG. Will be equalized. That is, the operating band F _H (s) of the observer corresponds to passing only one side of the sideband component centered on the operating frequency.
If only the amplitude component of the electromotive force error Δe occurs at the operating frequency, only one side separated into the positive phase component and the reverse phase component is allowed to pass, so the fluctuation of the amplitude component of the estimated magnetic flux is reduced. The effect of changing the phase component mainly occurs.
[0045]
Further, when an electromotive force error Δe having only a quadrature component occurs with respect to the estimated electromotive force e ₁ , adaptive identification of the speed does not operate because an in-phase component originally does not exist.
However, when G ₁ = G ₂ is set, the estimated magnetic flux vector of the magnetic flux observer moves in the direction in which the error vector is rotated 45 ° by the compensation gain {G ₁ I + G ₂ J}.
Then, since the amplitude on the estimated magnetic flux side is changed, an amplitude error of the electromotive force error Δe is generated, and the adaptive identification of the speed can be operated indirectly.
As described above, since there is an interaction between the magnetic flux observer and the speed adaptive identification, Kwi may be adjusted to a gain that makes the magnetic flux and the speed respond appropriately.
[0046]
Next, (R / L-g ₁ ) in the design guideline (a) corresponds to the frequency bandwidth of the high-frequency limiting filter for differential operation. If it is too high, it will be generated by differential operation. Noise on the high frequency side is amplified, and if it is too low, the fundamental frequency component is blocked.
Further, g ₂ corresponds to the center frequency of this low-pass filter, and it is sufficient to pass a band necessary as an observer. Therefore, as shown in FIG. 6, the center frequency is not moved with g ₂ = 0, and (R / L−g ₁ ) is set to a slightly higher band than the operating frequency. .
[0047]
From the observer characteristics found out above, setting the gain as shown in equation (10) corresponds to setting the operating band of the observer as shown in FIG.
As a result of performing simulation by applying the adaptive magnetic flux observer gain designed based on the equation (10) to the adaptive magnetic flux observer in the position estimation calculation unit 6 shown in FIG. 1, the magnetic flux is fast in response and has little vibration. It was confirmed that an estimation result was obtained.
This makes it possible to stably apply sensorless control of the PM motor even in a frequency band where the operating frequency exceeds 200 Hz.
In addition, since there are originally five gains, there are many combinations of the set gains, and when trying to find a stable gain by adjustment, a considerable number of trials are necessary. By applying it, it is only necessary to finally adjust the integral gain of the speed adaptation unit, so that it can be easily adjusted.
[0048]
In the above description, expressions of magnetic flux observer and adaptive magnetic flux observer are used.
The magnetic flux observer refers to a portion that estimates the magnetic flux of the permanent magnet from the terminal voltage and terminal current of the PM motor.
The expression of the adaptive magnetic flux observer is as follows.
Since the magnetic flux observer requires speed (frequency) information ω ₁ , a function for estimating the speed (frequency) is also added. The added speed estimation method does not directly calculate, but operates so that the internal error of the magnetic flux observer becomes zero. In other words, it is not closed in its own block, and can be estimated by referring to other blocks, so it is not called “estimation” of speed but is expressed as “adaptation” of speed.
[0049]
Embodiment 2
In the first embodiment, as a method for setting the observer gain, the filter band of F _G (s) is set to be a band as shown by a broken line in FIG.
Actually, it suffices to include the F _H (s) band indicated by the solid line and the solid line in FIG. 6, and the bandwidth may be narrowed, and instead the center frequency may be moved in proportion to the operating frequency. . Then, the operation band of the observer corresponding to FIG. 6 is as shown in FIG.
[0050]
In summary, assuming that the operating frequency is ω ₁ and the response frequency band of the observer is ω _H , the relationship of equation (11) may be satisfied.
[0051]
## EQU11 ##

[0052]
In Expression (11), since g ₂ ≠ 0, the calculation amount cannot be omitted and the amount of calculation increases. However, as in the first embodiment, a fast response and a magnetic flux estimation result with little vibration can be obtained.
[0053]
Embodiment 3
The magnetic flux observer shown in FIG. 2 is configured on a fixed coordinate system. However, since the estimated magnetic flux changes in a sine wave shape, an error due to discrete approximation occurs when it is realized as a discrete value system using a digital arithmetic unit.
In order to suppress the error of the discrete approximation, it is necessary to apply a higher-order integral approximation calculation.
[0054]
However, the high-order integral approximation calculation has a drawback that the amount of calculation increases. Therefore, if only the calculation part of the rotor is configured on the rotation coordinates, the discrete approximation error can be suppressed. FIG. 8 shows a magnetic flux observer in which the rotor portion is configured on the rotation coordinates.
In Figure 8, and calculates the phase theta ₁ omega by integrating the estimated speed omega ₁ is an adaptive output of the velocity, and the rotational coordinate transformation relative to the this is inserted into input and output of the arithmetic unit of the rotor.
The adaptive identification portion of the speed has the same characteristics on the fixed coordinate as shown in FIG. 2 and the rotated coordinate as shown in FIG. 8, but FIG. 8 shows an example configured on the rotary coordinate.
[0055]
In this embodiment, the operation frequency becomes high like a multi-pole machine, and the approximation that the sampling frequency of the signal for digital calculation is sufficiently higher than the operation frequency is not established, and the influence of the discrete approximation error can be ignored. Even in the case of disappearance, by configuring the rotor portion in the rotating coordinate system, errors in discrete approximation can be suppressed, and the upper limit of the operating frequency can be further increased.
[0056]
【The invention's effect】
As described above, by using the observer gain according to the present invention, it is possible to obtain a magnetic flux estimation result with a quick response and a small vibration even in a higher operating frequency range.
[Brief description of the drawings]
FIG. 1 is a configuration diagram of a position sensorless control system showing an embodiment of the present invention.
FIG. 2 is a block diagram of an adaptive magnetic flux observer.
FIG. 3 is a block diagram of a transfer function of an electromotive force observer.
FIG. 4 is a block diagram of an electromotive force observer.
FIG. 5 is a low-pass filter characteristic diagram for explanation. FIG. 6 is a frequency band diagram of an electromotive force observer for explanation.
FIG. 7 is a frequency band diagram of an electromotive force observer for explanation.
FIG. 8 is a block diagram of an adaptive magnetic flux observer.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Synchronous motor 2 ... Current detector 3 ... Variable speed control part 4 ... Rotation coordinate conversion part 5 ... Reverse rotation coordinate conversion part 6 ... Position estimation calculation part 7 ... Phase calculation part 8 ... Speed detection part 9 ... Speed control part 10 ... Current controller

Claims (3)

The difference signal between the speed command and the speed estimate is input to the speed control unit, the torque current command is calculated, then converted to a voltage command by the current control unit, and this voltage command is variable speed controlled via the reverse rotation coordinate conversion unit. A control device for controlling the synchronous motor using a permanent magnet as a field source by the variable speed control unit, and calculating a magnetic flux vector by inputting the current and voltage of the synchronous motor, The phase calculation unit obtains an estimated phase signal from the biaxial component of the magnetic flux estimation output by the position estimation calculation unit, and the current detected based on this estimated phase is input to the rotating coordinate conversion unit to convert it into a biaxial current. In the reverse rotation coordinate conversion unit in the reverse rotation coordinate conversion unit by the biaxial current and the voltage command ,
A fixed coordinate system having a one-dimensional magnetic flux observer for estimating a magnetic flux component from the terminal current and voltage command of the synchronous motor in the position estimation calculating unit, and a speed adapting unit for calculating the magnetic flux observer from the current error and the magnetic flux And a control device for the synchronous motor, wherein the gain of the magnetic flux observer is set according to the relationship of the following equation.
(R / L-g ₁ ) ≧ ωmax
g ₂ = 0
g ₃ = sign (ω ₁ ) · g ₄
g ₄ = −L · ω _H / | ω ₁ |
Where R: resistance, L: inductance, g _{1 to} g ₄ : observer gain, ω: speed, ω ₁ : estimated speed value, ω _H : response frequency band of the observer. 2. The synchronous motor control device according to claim 1, wherein the gain of the magnetic flux observer is set by the relationship of the following equation.
(R / L-g ₁ )> ω _H
g ₂ = ω ₁
g ₃ = sign (ω ₁ ) · g ₄
g ₄ = −L · ω _H / | ω ₁ |   The synchronous motor according to claim 1 or 2, wherein a phase is obtained by integrating the output speed of the speed adaptation unit, and a rotor part of a magnetic flux observer is calculated on a rotation coordinate synchronized with the phase. Control device.

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