JPH0347073B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a vector calculation circuit for a drive control device for an induction motor using vector control. Since industrial robots and machining centers are actually responsible for transportation, processing, and assembly in FMS, servos play a large role as a means of moving tools and workpieces accurately and at high speed.
Moreover, advanced control technology is desired. Servo systems must control torque to control the position and speed of the motor.
When using an induction motor (hereinafter abbreviated as IM) in a servo system, the output torque of the IM depends on the voltage of the power supply,
Since there is no direct proportional relationship between current, frequency, etc., the current or voltage applied to the stator winding of the IM is controlled in order to generate the desired torque in the IM. That is ^, in a general servo system, as shown in FIG. is required.
The position error θe is multiplied by the position loop gain Gp in the position control element circuit 3 and converted into a speed command value ω ^* . Here, the speed error ωe is determined from the difference between the speed feedback value ωr obtained by subtracting the position feedback value θ by a difference circuit 4 and the speed command value ω ^* . The speed error ωe is multiplied by the speed loop gain Gs in the speed control element circuit 5 and converted into a torque command value T ^* , and then provided to the vector calculation circuit 6. The vector calculation circuit 6 determines a stator current command value i ^* _S or a stator voltage command value V ^* _S based on the torque command value T ^* . The stator current command value i ^* _S or stator voltage command value V ^* _S thus obtained is converted into an analog quantity by a D/A converter (not shown), and then the power amplifier circuit 7
After the power is amplified by the IM, it is applied to the stator winding of the IM. Therefore, we will discuss the current control method and voltage control method of conventional IM. Here, 2-phase 4-pole squirrel cage type
I will explain via IM. Now, the current and voltage of the stator and rotor windings in the stationary coordinate system are expressed by the following vectors (second
(see figure). i=is ir, is=ids idr, ir=iqr ids (1a, b, c) V=Vs Vr, Vs=vds vqs, Vr=vdr vqr≡0(2a,b,c) The current-voltage equation of IM is It is expressed by the following formula. V=Fi...(3) Here, Rs and Rr are the resistances of the stator and rotor windings, Ls, Lr, and Lm are the self-inductance and mutual inductance of the stator and rotor windings, and ωr
is the angular velocity of the rotor, P is the time differential operator d/dt E=1 0 0 1, J=0 −1 1 0. The following relationship holds between the magnetic fluxes φs and φr interlinking with the stator and rotor windings and the current i. Φ＝Li ……(5) Here, Φ＝Φs φr

[Formula]. Now, if we think about the output torque, IM
The power p consumed in is expressed as p=itV=itFi (6) using equation (3). Here, t means transposition. At this time, matrix F is decomposed as follows. F=R+PL+ωrG...(7) Here,

【formula】

[Formula] is. When formula (7) is substituted into formula (6) and expanded, p=i ^t Ri+i ^t PLi+i ^t ωrGi (8). The first term on the right side of equation (8) represents active power, and the second term represents reactive power. The third term means mechanical output, and when divided by the angular velocity ωr of the rotor, it becomes equal to the output torque T. T=i ^t Gi ……(9) Here, the torque T is maximum due to the rotor current
This is when ir and rotor magnetic flux Φr are orthogonal (see Figure 3). Therefore, the maximum torque T is expressed by the cross product of ir and Φr as follows. T=i ^t _r JΦr ...(10) Therefore, by considering the relationship of equation (10) to equation (9), the condition for the maximum output torque T is the following theorem 1.
Represented by Theorem 1 The condition for the maximum output torque T is that the rotor current ir and the rotor magnetic flux Φr are orthogonal. That is, i ^t _r Φr=0 (11). Here, equation (11) means that the inner product of ir and Φr becomes zero. Generally, both ends of the rotor winding of a squirrel cage IM are short-circuited, so vr=0 at all times. Therefore, Eq.
Substituting the relationship in equation (5) into the third and fourth row components of (3),
Solving is and ir using Φr leads to the following equation. is=l/Lm {(1+Lr/RrP)E +Lr/RrωrJ}Φr...(12a) ir=-1/Rr(PE+ωrJ)Φr...(12b) Expression (12a) is converted into conditional expression (11) of Theorem 1 By substituting into the left side of and eliminating ir, the following equation is derived. i ^t _r Φr=−(1/2Rr)P|Φr| ² Therefore, the following theorem holds true. Theorem 2 The necessary and sufficient condition for rotor current ir and rotor magnetic flux Φr to be orthogonal is the absolute value of rotor magnetic flux |
Φr| becomes constant with respect to time. i ^t _r Φr=0P|Φr|=0 According to Theorem 2, the rotor magnetic speed Φr that satisfies the condition of Theorem 1 is defined by the following equation (see FIG. 4). Φr=CφΦ ₀ (13) Here, Cφ=cos sin −sin cos, Φ ₀ = Φ ₀ 0 Φ ₀ = (constant), and d/dt=ω. That is,
Φr has an absolute value of Φ ₀ and is represented by a vector rotating at an angular velocity ω. <Current control method> Substitute equation (13) for the rotor magnetic flux that satisfies the condition for maximum torque into equation (12a) to find the stator current command value i ^* _S. i ^* _S = Cφ [1/Lm {E −Lr/Rr (ω−ωr)}] Φ ₀ ... (14) Here, the difference between the angular velocity ω of the rotor magnetic flux and the angular velocity ωr of the rotor is the slip angular velocity ωs It is a quantity called. ωs=ω−ωr, ω=ωs+ωr (15) Therefore, the angle of the rotor magnetic flux is expressed by the following equation. =∫(ωs+ωr)dt...(16) Also, by substituting equations (12b) and (13) into equation (10), ωs
By solving for ωs, the relationship between ωs and torque T can be derived. ωs=Rr/Φ _2/0 T (17) Since the absolute value Φ ₀ of the rotor magnetic flux is constant according to Theorem 2, a proportional relationship is established between T and ωs.
Therefore, in an actual system, the difference between the frequency of the stator current and the rotational speed of the rotor, that is, the slip speed, is proportional to the output torque, so this method is also called slip frequency control. Here, if we set the field current I ₀ and torque current I ₂ as I ₀ = Φ ₀ /Lm, I ₂ = Lr / LmT / Φ ₀ ... (18a, b), then i ^* _S is calculated by the formula (14 ), it is expressed as follows. i ^* _S = CφI ₀ I ₂ ... (19) This is a formula that gives the stator current command value i ^* _S required by formula (19). The field current I ₀ represents the stator current required to generate the rotor flux, and the torque current I ₂
represents the stator current required to obtain the output torque T. Therefore, equation (19) makes it possible to independently control the IM field and torque. Incidentally, the stator current command value i ^* _S can be determined by the circuits shown in FIGS. 5 to 8. In other words, the torque command value is applied to the circuit shown in Fig. 5.
Inputting T ^* and the absolute value Φ ₀ of the rotor magnetic flux Φr, we get
Field current I ₀ and torque current I ₂ are determined based on the above equations (18a, b). Furthermore, when the torque command value T ^* and the absolute value Φ ₀ of the rotor magnetic flux are input to the circuit shown in FIG. 6, the slip angular velocity ωs is determined based on the above equation (17). Further, when the slip angular velocity ωs and the rotor angle θ are input to the circuit shown in FIG. 7, the angle and angular velocity ω of the rotor magnetic flux Φr are determined based on the equation (16). From the above, when the angle of the rotor magnetic flux Φr, the field current I ₀ and the current I ₂ are input to the circuit of FIG. 8, the stator current command value i ^* _S is determined based on the above equation (19). Therefore, the vector calculation circuit 6 based on the conventional current control method has a circuit configuration as shown in FIG. In the figure, blocks C ₅ , C ₆ , C ₇ , and C ₈ are the circuits shown in FIGS. 5, 6, 7, and 8, respectively. The determined stator current command value i ^* is output. However, such a current control method has the following problems when used for spindle control. Generally, a spindle must maintain high rotation accuracy with low ripple over a wide range of rotations, from low speeds of several tens of rpm to high speeds of up to 4000 rpm. At the same time, output torque and output power are desired to be as large as possible.If the input voltage is constant, the output torque will attenuate in proportion to the square of the frequency, and the output power will attenuate in proportion to the first power. do. Furthermore, since the reactance of the IM increases in proportion to the frequency, current control will no longer be able to obtain the voltage necessary to produce the desired output power in the high-speed rotation range. Therefore, in order to generate the maximum power of the motor's ability in the high-speed rotation range, a voltage control method is required. <Voltage control method> The stator voltage Vs is expressed as Vs=(Rs+LsP)is, LmPir (20) from the first and second row components of equation (3). The desired stator voltage command value V ^* _S can be obtained by eliminating is and ir from equation (20) and expressing Vs by Φr. That is, by substituting equation (5) into equation (20) and eliminating ir, we get Vs=Rsis+PΦs (21). Here, it is assumed that there is no leakage flux. Based on this assumption, we set Φs = Φr and substitute equation (12a),
By eliminating is, substituting equation (11), and considering the conditions of theorems 1 and 2, the voltage command value V ^* _S to be obtained is expressed by the following equation. V ^* _S =Cφ{Rs/LmE−(ω+Rs/Lm Lr/φ _2/0 T)}φ ₀ (22) This is expressed as I ₀ and I ₂ using equations (18a, b). V ^* _S = CφRs Lmω 0 RsI ₀ I ₂ ... (23) This is an equation that gives the stator voltage command value V ^* _S that is determined by equation (23). By the way, the stator voltage command value V ^* _S is shown in Fig. 5,
This can be determined using the circuits shown in FIGS. 6, 7, 9, and 10. That is, the ninth
When the field current I ₀ and torque current I ₂ obtained using the circuit shown in Fig. 5 and the rotor magnetic flux angular velocity ω obtained using the circuit shown in Figs. 6 and 7 are input into the circuit shown in the figure, the stator voltage The amplitudes Vα and Vβ of the command values are found. When the amplitudes Vα and Vβ of the stator voltage command value and the angle of the rotor magnetic flux Φr determined by the circuits of FIGS. 6 and 7 are input to the circuit of FIG. The stator voltage command value V ^* _S is obtained. Therefore, the vector calculation circuit 6 based on the conventional voltage control method has a circuit configuration as shown in FIG. In the figure, blocks C ₅ , C ₆ , C ₇ , C ₉ ,
C ₁₀ is shown in the above-mentioned figures 5, 6, and 7, respectively.
These are the circuits shown in FIGS. 9 and 10, and the stator voltage command value V ^* _S determined by each of these vector calculation circuits 6 is outputted. However, such a voltage control method assumes that the field is constant, but since the field is not constant in the spindle due to "field weakening", the above assumption is not satisfied, and this condition is currently ignored. The reality is that it is. Furthermore, since the above equation (23) was derived assuming that there is no leakage magnetic flux, there is a drawback that highly accurate control cannot be expected. SUMMARY OF THE INVENTION An object of the present invention is to provide a vector calculation circuit for a drive control device for an induction motor that enables highly accurate control in a voltage control system. Therefore, in the first aspect of the present invention, the resistances of the stator and rotor windings of the induction motor are Rs, Rr,
As a vector calculation circuit for a drive control device for an induction motor in which the self-inductance and mutual inductance of the stator and rotor windings are Ls, Lr, and Lm, from the input of the absolute value of the rotor magnetic flux Φ ₀ and the torque command value T ^* , the formula I ₀ = Φ ₀ /Lm, I ₂ = Lr / Lm・T ^* / Φ ₀ , and a first circuit that calculates field current I ₀ and torque current I ₂ , and calculates the absolute value of rotor magnetic flux Φ ₀ and torque. A second circuit calculates the formula ωs=Rr/Φ ₀ T ^* from the input of the command value T ^* and outputs the slip angular velocity ωs, and calculates the rotor angle θ and the slip angular velocity ωs output from the second circuit. It is equipped with a third circuit that calculates the formula ψ=∫(ωs+ωr)dt from the input, where ωs=ω−ωr, ω=ωs−ωr, and outputs the angular velocity ω of the rotor magnetic flux and the angle ψ of the rotor magnetic flux, and outputs the torque command. When the value T ^* is input, the formula Vs ^* = CφRs − (LsLr−Lm ² )
ω/Lr Lsω+(LsLr−Lm ² )P(ωs)/Rr RsI ₀ I ₂ However, P is a time differential operator, Cφ=cosψ sinψ − sinψ cosψ is calculated to find the value of V ^* _S , and the stator A vector calculation circuit is configured to output a voltage command value V ^* _S to be applied to the winding, and this is intended to perform voltage control that takes leakage magnetic flux into consideration. Further, the second invention of the present invention is a vector calculation circuit of a drive control device for an induction motor, and calculates the formula ωs=Rr/Φ ₀ T ^* from the input of the absolute value Φ ₀ of the rotor magnetic flux and the torque command value T ^* . Then, from the input of the second circuit that outputs the slip angular velocity ωs, the rotor angle θ, and the slip angular velocity ωs output from the second circuit, the formula ψ=∫(ωs+ωr)dt where ωs=ω−ωr, ω = ωs−ωr and a third circuit that outputs the angular velocity ω of the rotor magnetic flux and the angle ψ of the rotor magnetic flux, the time differential operator is P, and Cφ=cosψ sinψ −sinψ cosψ X=LrLs− Lm ² /LmRr A=X・Cφ, B={(A+LrRs+LsRr/LmRr) E−2ωAJ}Cφ C=−AP(ωs)JCφ−ωrωsACφ −LrRs/LmRrωsJCφ+(Rs/LmE −Ls/LmωJ)Cφ E=1 When 0 0 1 J = 0 - 1 1 0, calculate the value of V ^{* S by calculating the formula V *} _S ⁼ _AP ² (Φ ₀ ) + BP (Φ ₀ ) + C and add it to the stator winding. Construct a vector calculation circuit that outputs the voltage command value V ^* _S , thereby setting P, and Cφ=cosψ sinψ −sinψ cosψ X=LrLs−Lm ² /LmRr A=X・Cφ B={(A+LrRs+LsRr/LmRr) E−2ωAJ}Cφ C=−AP(ωs)JCφ−ωrωsACφ −LrRs/LmRrωsJCφ+(Rs/LmE −Ls/LmωJ)Cφ When E=1 0 0 1 J=0 −1 1 0, the stator winding The applied voltage command value V ^* _S is expressed as Vs ^* = CφRs − (LsLr − Lm ² ) ω
/Lr Lsω+(LsLr−Lm ² )P(ωs)/Rr RsI ₀ I ₂ Voltage control is performed in consideration of field changes to achieve the above object. Therefore, the voltage control method of the present invention will be theoretically analyzed. Here, first, the stator voltage command value V ^* _S in consideration of leakage magnetic flux will be described, and then the stator voltage command value V ^* _S in consideration of field change will be described. <Stator voltage command value considering leakage flux> Now, substituting equations (12a, b) into equation (20), is,
By eliminating ir, substituting equation (11), and considering the conditions of theorems 1 and 2, the voltage command value V ^* _S to be obtained is expressed by the following equation. V ^* _S = (Rs/LmE−Ls/LmωJ)CφΦ ₀ −LrRs/LmRrω
sJCφΦ ₀ − (LrLs−Lm ² /LmRr) {ωωsE+P(ωs)J}Cφ
Φ ₀ ...(24) This is expressed as I ₀ and I ₂ using equations (18a, b). V ^* _S CφRs − (LsLr−Lm ² )ω/
Lr Lsω+(LsLr−Lm ² )P(ωs)/Rr RsI ₀ I ₂ ...(25) Therefore, in equation (25), the component generated by the interaction between field current I ₀ and torque current I ₂ is It is represented by the off-diagonal elements of the matrix on the right side. Then,
It can be seen that by adopting equation (25), it becomes possible to control the induction motor by taking leakage flux into account. Also, the differential term of the slip angular velocity P(ωs)
It can be seen that vector control is performed correctly even in response to sudden fluctuations in torque. Here, based on this method, the vector calculation circuit 6
When configured, a circuit configuration as shown in FIG. 19 is obtained. In the figure, blocks C ₅ , C ₆ , and C ₇ are the circuits shown in FIGS. 5, 6, and 7, respectively, and are the first, second, and third circuits, respectively. On the other hand, block C ₁₀ is the circuit shown in FIG. 10 mentioned above, and block C ₁₁ is the circuit shown in FIG. 11, and the calculation of equation (25) is executed by these circuits C ₁₁ and C ₁₀ . In such a vector calculation circuit 6, the field current I ₀ and torque current I ₂ determined by the circuit shown in FIG. 5, the slip angular velocity ωs determined by the circuit shown in FIG. When the angular velocity ω of the rotor magnetic flux determined by the circuit in Figure 7 is input to the circuit in Figure 11, the amplitudes of the stator voltage command values V〓, V〓
is required. The amplitude of this stator voltage command value
When V〓, V〓 and the angle of the rotor magnetic flux Φr determined by the circuits of FIGS. 6 and 7 are input to the circuit of FIG. 10, the stator voltage command value V ^* _S is required. Therefore, according to the vector calculation circuit 6 based on this method, the drive control of the induction motor can be made accurate through voltage control that takes leakage magnetic flux into consideration. <Voltage command value considering field change> Stator voltage command value considering field change
V ^* _S is given by: V ^* _S = AP ² (Φ ₀ ) + BP (Φ ₀ ) + C ... (26) Here, A, B, C are coefficient matrices including ω, ωs, Φ ₀ , and P ² is the second-order time derivative ( d ² / dt ² ) Operator A= ^XCφ ……(27) AP(ωs) JCφ−ωωsACφ −LrRs/LmRrωsJCφ+(Rs/LmE −Ls/LmωJ)Cφ (30). At this time, torque T and slip angular velocity ωs
The following relationship holds true between them. T=1/Rr{ωsφ ^t _r Φr−P(Φ ^t _r )JΦr)……(31
) Therefore, according to the above equations (26) and (31), even if the field changes, controllability is not lost and the desired torque can always be obtained. Therefore, by controlling the magnetic field, an energy saving effect can be obtained. That is, the strength of the magnetic field that minimizes heat generation varies depending on the generated torque. Therefore, if the field is controlled according to the above conditions for the desired torque,
It is possible to minimize heat generation, that is, energy loss. Here, based on this method, the vector calculation circuit 6
When configured, a circuit configuration as shown in FIG. 20 is obtained. In the figure, blocks C ₆ and C ₇ are the circuits shown in FIGS. 6 and 7, respectively, and are the second and third circuits, respectively. On the other hand, block
C ₁₀ is the circuit shown in Fig. 10 described above, and the block
C ₁₂ is a circuit shown in FIG. 12, and this circuit C ₁₂ is constituted by the circuits shown in FIGS. 13 to 16, respectively, and equation (26) is executed by these circuits C ₁₂ and C ₁₀ . In such a vector calculation circuit 6, when the absolute value Φ ₀ of the rotor magnetic flux is input to the circuit shown in FIG. 12, the amplitudes Vα and Vβ of the stator voltage command values are determined. At this time, in the circuit shown in Fig. 12, the contents of X (=Y') are shown in Fig. 13, and the contents of Y are shown in Fig. 14.
The contents of Z' are shown in Figure 15 and the contents of Z' are shown in Figure 16.
Each is represented in the figure. Therefore, the amplitudes Vα, Vβ of the stator voltage command value and the
When the angle of the rotor magnetic flux Φr determined by the circuit shown in the figure is input into the circuit shown in FIG. 10, the stator voltage command value V ^* _S is determined. Therefore, according to the vector calculation circuit 6 based on this method, it becomes possible to reliably control the drive of the induction motor by voltage control that takes field changes into account, and also enables efficient operation. As described above, according to the present invention, the stator voltage command value is given according to an equation that takes leakage magnetic flux and field changes into consideration, so that the vector of the induction motor drive control device that can be expected to perform highly accurate control. An arithmetic circuit can be provided.

[Brief explanation of drawings]

Figure 1 is a block diagram showing a general servo system, Figure 2 is a diagram showing the relationship between current and magnetic flux, Figure 3 is a diagram regarding output torque, Figure 4 is a diagram regarding rotor magnetic flux, and Figure 5 is a diagram showing the relationship between current and magnetic flux. FIG. 8 is a circuit diagram based on the conventional current control method, FIGS. 9 and 10 are circuit diagrams based on the conventional voltage control method, FIG. 11 is a circuit diagram based on the voltage control method of the present invention, and FIG. 12 16 is a circuit diagram based on another voltage control method of the present invention, FIG. 17 is a circuit diagram showing the configuration of a vector calculation circuit based on a conventional current control method, and FIG.
The figure is a circuit diagram showing the configuration of a vector calculation circuit based on a conventional voltage control method, FIG. FIG. 2 is a circuit diagram showing the configuration of a vector calculation circuit based on a voltage control method that takes field changes into account according to the present invention.

Claims (1)

[Claims] 1. The resistance of the stator and rotor windings of the induction motor is Rs, Rr, and the self-inductance and mutual inductance of the stator and rotor windings are Ls,
This is a vector calculation circuit for the drive control device of the induction motor, which is Lr and Lm, and from the input of the absolute value Φ ₀ of the rotor magnetic flux and the torque command value T ^* , the formula I ₀ = Φ ₀ /Lm, I ₂ = Lr / Lm・From the first circuit that calculates T ^* / Φ ₀ and outputs the field current I ₀ and torque current I ₂ , and the input of the absolute value Φ ₀ of the rotor magnetic flux and the torque command value T ^* , the formula ωs = Rr / Φ From the input of ^the rotor angle θ and the slip angular velocity ωs output from the second circuit, the formula ψ=∫(ωs+ωr)dt where _ωs = It is equipped with a third circuit that calculates ω−ωr, ω=ωs−ωr and outputs the angular velocity ω of the rotor magnetic flux and the angle ψ of the rotor magnetic flux, and when the torque command value T ^* is input, the formula V ^* _s = CφRs − (LsLr−Lm
² ) ω/Lr Lsω+(LsLr−Lm ² )P(ωs)/Rr RsI _{0 I} 2Where, P is a time differential operator, and the value of V ^* _s is obtained by calculating Cφ=cosψ sinψ −sinψ cosψ. , a vector calculation circuit for a drive control device for an induction motor, which outputs a voltage command value V ^* _s applied to a stator winding. 2 The resistance of the stator and rotor windings of the induction motor is Rs, Rr, the self inductance and mutual inductance of the stator and rotor windings are Ls,
This is a vector calculation circuit for the drive control device of the induction motor, which is Lr and Lm. From the input of the absolute value of the rotor magnetic flux Φ ₀ and the torque command value T ^* , the formula ωs = Rr / Φ ₀ T ^* is calculated, and the slip angular velocity ωs From the input of the rotor angle θ and the slip angular velocity ωs output from the second circuit, the formula ψ=∫(ωs+ωr)dt where ωs=ω−ωr, ω=ωs−ωr A third circuit calculates and outputs the angular velocity ω of the rotor magnetic flux and the angle ψ of the rotor magnetic flux, and the time differential operator is P, and Cφ=cosψ sinψ sinψ −cosψ X=LrLs−Lm ² /LmRr A =X・Cψ, B={(A+LrRs+LsRr/LmRr)E−2ωAJ}Cφ C=−AP(ωs)JCφ−ωωsACφ −LrRs/LmRrωsJCφ +(Rs/LmE−Ls/LmωJ)Cφ E=1 0 0 1 J = 0 - 1 1 0, calculate the value of V ^* _s by calculating the formula V * s = AP ^{2 (} Φ ₀ ) + BP (Φ ₀ ) + C, and calculate the voltage command value V applied to the _stator winding. ^* A vector calculation circuit for an induction motor drive control device that outputs _s .