JPH0356088A - Controlling method for induction motor, and film taking-up method using its controlling method - Google Patents

Abstract

PURPOSE:To perform rotation control with simple composition by controlling voltage from conditional equations for keeping exciting current constant. CONSTITUTION:On the equivalent circuit of a three-phase induction motor, R1, R2 are primary and secondary resistances, and x1, x2 are primary and secondary leakage reactances, and xm is an exciting reactance, and S is slip, and when a mutual inductance is set as M and primary and secondary leakage inductances are set as l1, l2, then angular frequency is set as omega, and x1=omegal1, x2=omegal2, xm=omega(3M/2) hold on the equivalent circuit, frequency is set as f, and an equation I and an equation II hold. In order to keep exciting current ¦I0¦ constant, E/f may be kept to be a constant value.

Description

Detailed Description of the Invention (Industrial Application Field) The present invention provides a method for controlling the torque and rotational speed of a three-phase induction motor, and a polyethylene film using the control method.
This relates to the method of winding up films such as polypropylene film. (Prior technology) Conventionally, a method was adopted in which the magnetic flux φ interlinking with the rotor of an induction motor was detected and the vector amount of the drive current was controlled. Conversion and vector calculations were performed, and the understanding of the control system was beyond an intuitive level, and the level of handling and processing was also high, making it unsuitable for on-site use. (Technical Problem) The present invention was made in view of the shortcomings of the prior art, and its technical problem is to control the rotation of the rotor at low cost with a simple configuration. (Technical means) In order to solve the above technical problem, the present invention uses a T-type steady-state equivalent circuit of a three-phase induction motor to
Condition for keeping l constant E/f=co = [(V+ -R+2+ 2tt
fl+ ) 2)/fl ● Effective value of the necessary voltage that satisfies I1, that is, V+ = C
o llf+R+2+ (2πfJl1) 2 *
I'm trying to force you to give it to me. (a) About the circuit equation of induction motor. In general, most of the induction motors in practical use are symmetrical three-phase motors (the circuit constants of each phase are equal). In a squirrel cage induction motor, each bar on the squirrel gauge corresponds to one phase, and the number of phases on the secondary side is much greater than three phases, but it can be equivalently replaced with a three-phase wound induction motor. I can think.

(See Figure 1) The symbols are explained below. a, b, c・●●Stator phase (stator phase) r, s, t
●・●Rotor phase (rotor phase) ω. ●●・Rotor angular velocity (rad/see) θ1 ・・Spatial position angle Ll between the central axes of the a phase and r phase ・・Total self-inductance of the primary coil phase L2 ・・Total self inductance of the secondary coil phase Self-inductance fLi ・●●Leakage inductance M●●●Mutual inductance θ●●●Electrical angle θ= CP/2) θ, P●●・Number of poles ω●●●Power source angular frequency (ω=2πf) S●●● Suberi S=(ω2-ω-e) /ωeωme
=dθ/dt=Pθ (+) @ =ω/ (P/2) (electrical rad/sec)
Input d...Enter the magnetic flux linkage of the a-phase coil 9a●●●Enter the interlinkage of the rotating magnetic field in the gap applied to the a-phase coil r ●●・Enter the magnetic flux linkage of the r-phase coil qr●●● Regarding the linkage of the rotating magnetic field in the gap applied to the r-phase coil, first assume the following relationship with respect to Figure 1. Ll
=Ki1 +M L2 =Ki2 +M i, +ib +ic =0 (Three-phase current has three-fold symmetry)
ir +is +tt =0 (three-phase current has three-fold symmetry)
Input d: Sentence 1・ia 10in 9a Input r = Intersection 2・i `` +λqr Input qa=M (ia + ih cos (
2π/3)+iccos(-2π/3))+M{ir
cosθ+fsCOS(θ+2π/3)+itcos
(θ−2π/3)} Input qr=M (ir + is cos (
2π/3) + i 1cos(-2π/3) }
+M (ia cos (10)+ibcos
(10+2π/3)+iccos(1θ-2π/3)} la=il i b= i d6-021K/3)=i (
6-j(2TC/3)ic = i, 6j(
21C/. 1) = i l6N2m/3)ir=
i 2 i , = i , 6-j (2TL/3) =
i 2 6 -1(2'lu/3)i t= i
, e4(2TL/3) = i2 6j(
2'tC/3) Considering the circuit equation based on the above relationship, the circuit equation for the primary a phase is Va = Rl ia + d input. /dt (
t) The quadratic r-phase circuit equation is 0=R2 ir +ci, /dt (
2) (Short-circuited at the end ring). Here, fla●● primary resistance R2 ●●● secondary resistance D●●● d/dt. Equations (1) and (2) above can be replaced as follows. Va = R1 ia +u+ D ia + (
3M/2)Dia(3M/2)D(ir e
'0) (1)'0=R2 ir +
Jl2 D ir + (3M/2) D ir (3M
/2) (D i.)e-jθ-j(i)ge(3M
/2)i,1 e−iθ (2
)'fr' = fr e'', then dejρ
/dt=(dθ/dt) (dei'il/dθ)=
j (d O/dt) ej−= jω●ee
Since Je, D ir' = (D ir ) el' + j
ωseir' Therefore, (ly formula and (2)' formula are Va = R+ ia + (u+ + (
3M/2))Dia(3M/2)D i%
(1)″0=R2 ir + (sentence 2 + (
3M/ 2)) (D −j ωoe) i r'
+ (3 M/2) (D jω-e)ia(
2)'. Equations (1) and (2) include only one phase each, the primary a phase and the secondary r phase. Therefore, if we consider that the a phase represents the three phases on the primary side and the r phase represents the three phases on the secondary side, (ω2 + ωmaro = ω1 = ω power supply angular frequency) Va = V +
, ia = it , ir' = i2 and the slip S is S = (ω8-ωIle) /ωe, then
(1)'/Equation (2) and Equation 4 are Vl = RI・il+jω2 (sentence 1 + 3 M/
2) i 1+j~e (3M/2) i 2
(1) f'0=R2・i2+j S(1
)I! Cl2 +3M/2)i2/1, + j Soe (3M/2)i1- (2). Here, the next real vector f V + ,I +
When + I 2 is introduced, the above formula becomes V, = R+ I+ +j (x+ +xs )I+
'+jXa I2(3) 0= jXs I+ + (R2 /S+ j (X
2 +Xl )'j・I 2
−(4).

"Vl = Wl v1 1 ej(ω"'+) = JE
v 1 6 CJtr l = M I I
11 6 j (uJtl de') = JE I
l e j'L? 2 =J l 1, 1ej(
ωt-%) 4 7 2 6 1+4+t where X
l = ω intersection 1 ●●● Primary leakage reactance x2 = ω
Sentence 2 ●●●Secondary leakage reactance XI1=ω(3M/
2) Let ●● excitation reactance. From equations (3) and (4) above, we obtain the T-type steady-state equivalent circuit of the induction motor as shown in Figure 2. Incidentally, it can be understood that 0 in the circuit represents the excitation current (Io = I+ + I2). In the T-type stationary equivalent circuit in Figure 2, I+ = v+ / ((R+ +jx+) + jxa
(R2 S+jx?)/ (R/S+j(X2 +x
．． )))■(5) r2=-jxs xl / (R2 /2+j (X
2 +xs ) (6) IO =I1 +I2 = (R2 /s+jx2)
I+ / (R2 /s+ j (X2 +Xs)
)(7), and the total secondary copper horizontal Pc of the induction motor is Pc = 3R
2 1I2 12 Secondary power P that crosses the re-gap and enters the secondary side? teeth
P2 =3R2 1 I2 l 2 /
S, and the motor output PO is Po = P2 - Pc = 3R (I S) l I
2 M/S. Therefore, the torque of the motor is PG = ωm T , ω,
= (1-s) ω/ (P/2) (rad/sec), T=Po /ωm = (3P/2) (R2 /sω
) I I 2 1 2 (N-m) - (8). Here, P●●◆Number of poles ω●●●Power supply angular frequency ωI...This is the angular rotation speed of the motor, and the same periodic speed of the motor ω,,. is ωsyn
=41)/(P/2) (rad/sec
) Delete the above (6)
=-jxa Io/(R2/S+jx2)
(9), so by substituting it into the torque equation (8), T
= (3P/2) (R2 /3ω) { (
Sxs ) 2/ (R22+ (SX2 ) 2))
We obtain l IO l2 (N-m)(IO). Exciting electric current with this equation (10)! If IIol is kept constant, the motor torque T becomes Sω(=2πfS). In other words, it can be understood that it is a function only of the slip frequency (S - f). Figure 3 shows the torque T in equation (10) expressed as a function of the rotational speed of the motor, using the frequency f as a parameter. Therefore, it can be understood that if control is performed to keep the excitation current constant, the characteristic curve between motor torque and rotational speed will be extremely linear. Figure 3 shows the characteristic curve of a 3.7kW, 3-phase, 200V, 50Hz rated motor, with lIol constant, and is based on the T-type steady-state equivalent circuit of Figure 2. 3 mentioned above
The specific circuit constants of the phase, 200V, 50Hz, 3.7kW, 4-pole motor are as follows. x+ =0.408
2 (Ω)4X2 =0. 269 (Ω)Xs=13
．． 2 (Ω) R+ =0.463 (Ω), R2 =0.432 (
Ω) As mentioned above, if the excitation current IIo1 is kept constant, the magnetic flux density of the rotating magnetic field in the gap is kept constant, so the degree of utilization of the magnetic material of the motor is kept almost constant, and the influence of iron saturation is reduced. It can be understood that this can be ignored in practice, and that the torque-rotation speed characteristic has linearity.

Also, 3. Figure 4 shows the torque T as a function of the slip frequency (S●f) for a 7 kW (4F) motor when the excitation voltage iiiIol is kept constant. [From equation (10)] As can be seen from Figure 4, torque and slip frequency are directly proportional up to about three times the rated torque. Therefore, it is expressed as T=k● (S●f) (1 1), where k is a constant of proportionality. (b) Control of torque and rotational speed of induction motor. From the T-type steady-state equivalent circuit of the three-phase induction motor in Figure 2, E=
j Xs io = j (2πf) (3M/2)I
oE/f=j3πMIo (12)
and E=V1 − (R+ +jx+)It
=V+ − (R+ +j (2πf) look+
) I+ E/f= (V+ − (R+ +j2πf statement+)I+)/f (
13) is obtained.

From equation (l2), it can be understood that in order to keep the excitation current IIo1 constant, (E/f) should be kept constant. From equation (13), the value CO that should be kept constant (E/f) can be calculated from the circuit constants of the motor. That is, as an example, 3 phase, 200V, 3.7kw, (4P)
, when considering control of a motor rated at 50 Hz, f = 50 (Hz) from the motor circuit constants. R+ =0.463 (Ω), x
+ =0.4082 (Ω). V+ =200 (V)
Since I+ = 15.4 (A) is given by the manufacturer, the value Co that E/f should satisfy can be found by substituting it into equation (l3). IE/fl= <200--E Ding Ding Chitomi) 24-stone "4
082)2 X15.4}/50=3.81=Co(!
;L+=0. 4082/ (2π50),',2
πf+=8. l 64X 1 0-3Xf
(Ω)) Therefore, the effective value V of the voltage required to keep the excitation current lIol constant when the frequency f and the current ■1 is E/f=Co = (V+ −.・V1 is specified as Vl because it is sufficient that the voltage is ■1 that satisfies ・II}/f
=Go − f+R+2+ (2 π fJ
It can be understood that it is sufficient if it is l+ ) 2 ・I+ (;Lbto) (l4). At this time, the torque generated by the motor for the slip frequency S◆f is T=k (S- f) (15)
becomes. Therefore, the above equations (14) and (15) are the basis of control of the induction motor. For actual control, a sine wave PWM voltage type inverter is used as the drive power source. The control calculation interval is assumed to be t (seq), which is generally 10 msec or less. (c)
Embodiment (Application example) (Fig. 5) In this embodiment, the induction motor control method described above is applied to the winding speed and winding tension control of a film winding machine. l is a three-phase voltage type inverter and is electrically connected to the three-phase induction motor 2. A winding roller 3 is connected to the rotating shaft of the three-phase induction motor 2 to wind up a film 4 such as polyethylene film, polypropylene film, etc.
A is a tacho generator for measuring the rotational speed of the induction motor 2, and the rotational speed current value frequency signal f@(n-
+) to be input to the next operating frequency command calculation circuit 7. In addition, the current sampling frequency signal f e (
n-1) to be input to the next operating frequency command calculation circuit 7. Therefore, the current rotational speed frequency signal f of the induction motor 2
*(n-1) and the current sampling frequency signal fe(n-1) of voltage type inverter 1, the current sampling frequency signal (S●f) (nu is (S*f) (I+-1) = fe(n-+)-
fern-n-(1 6). At this time, if H/f=Co (constant value) control, the current torque T rq (n − 1) of the induction motor 2
is Tra(n-1) = k (S e f) <n-
+> = k {fe(n-n -f*(n-+))
There is a proportional relationship of (1 7). A tension meter 6 detects the tension of the film 4 which is wound up by a winding roller 3 using a tension roller 5. This tension meter 6 provides a current value voltage signal T en (n - 1) of the winding tension. (
n-1) is a suffix representing the current value, and (n) is a suffix representing the next command value. This current value voltage signal Ten < n - 1) is input to the next operating frequency command calculation circuit 7. Here, the current torque T r q (
n − 1) and winding tension command value voltage signal T
e n (s), the next required torque command value T r Q ( n ) is Trq (n) : Tz
(n-H (Ten(s) ten α) / (Ten(n
1)+α) l8), which gives a functional form with no deviation and convergent motion command. (Here, α is the control constant for tension.) This is the variable gain P・D operation (proportional, integral, differential operation)
This shows the characteristics of this control. Therefore, the next command frequency signal fe(n) is obtained from equations (l6), (l7), and (l8). That is, f e(n) = ( f l!(IT-1) f
a(n-+)) (Ten(s) + α)/ (
T e n (n − + ) + α) + fa (
n) Obtain (1 9). On the other hand, the speed of the film 4 is determined by a yard oscillator 9 via a pinch roller 8 as a film current winding speed signal U(.

-1) to be input to the next operating frequency command calculation circuit 7. Letting the film winding speed command value signal be U(s), the motor's next rotational speed command frequency signal f, (.)
As with torque, we give the following functional form. Fa
(n) = fs(n-u (U(S)+β)/(U(
nn + β) (20) Here, β represents the control constant for speed. Therefore, (l
From formulas 9) and (20), in the next operation frequency command calculation circuit 7, f e (n) = ( f e (n-1) f s (
n-+)) (Ten(s)+ a)/ (Ten(
n-n + a) + f s(n-1) (U(S)
+β) / (U(n-n +β) (21)
is found. That is, the next command frequency signal fe(n) to the voltage type inverter 1 is determined from the current sampling information value (suffix of (n-1)). IO is the next operating voltage command calculation circuit and the next command voltage signal V e (n
) is Ve(n)=Co fe(n)+R+2+ (2ff
fe(n)Ill ) 2◆I (n-1>
(2 2).

Here, R1 is the stator θ winding resistance (primary resistance) in the induction motor, and like the secondary resistance R2, it is not affected by temperature changes because it is small. I (n-1) is the current value signal of the primary side 1 current obtained from the current sensor CT, and due to the existence of the primary leakage reactor varnish Xi, the variation can be ignored if the sampling time (talons e c) is taken into consideration. Therefore, equation (22) can be considered to be the defining equation for determining the next command voltage signal Ve(n). (Effects) Since the present invention has the above-mentioned 4S power and function, it has the following effects. In the statement of claim l. Effective signal of voltage to keep excitation current IIo1 constant ■l
can be easily obtained, and the motor is easy to control. In the statement of claim 2. The next command voltage signal V e (.) can be easily obtained, and control with extremely high precision can be performed quickly.

[Brief explanation of drawings]

Figure 1 is an equivalent principle diagram of a three-phase wound induction motor, Figure 2 is a T-type steady-state equivalent circuit diagram of a three-phase induction motor, and Figure 3 is the relationship between motor rotation speed and torque using frequency as a parameter. FIG. 4 is a diagram showing the relationship between slip frequency and torque when the excitation current IIol of the motor is kept constant. Figure 5 is a block diagram showing the film winding method. l・●●Three-phase voltage type inverter 2●●●Three-phase induction motor 4-●C film 7●●●Next operation frequency command calculation circuit 10-●●Next operation voltage command calculation circuit fe(n)・●・Next time Command frequency signal V e (n)●...Next command voltage signal Fig. 2

Claims (2)

[Claims] (1) Based on the T-type steady-state equivalent circuit of a three-phase induction motor, find the effective value V_1 of the necessary voltage that satisfies the conditional formula ▲There are mathematical formulas, chemical formulas, tables, etc.▼ to keep the excitation current |I_0| constant. ▲There are mathematical formulas, chemical formulas, tables, etc.▼ How to control an induction motor given the formula (2) In cases where the film winding speed and tension are controlled by an induction motor via a voltage inverter, the current film winding speed signal U_(_n_-_1) and the current value of the film winding tension are Voltage signal T_e_n_(
_r_)_(_n_-_1_), motor rotational speed current value frequency signal f_m_(_n_-_1_), and current sampling frequency signal f_e_(_n_-_1_) are respectively input to the next operation frequency command calculation circuit 7 and calculated. , the next command frequency signal f_e_(_
n_) to the voltage type inverter, while
The next command frequency signal f_e_(_n_) is input to the next operating voltage command calculation circuit 10 and calculated, and the next command voltage signal V_e_(_n_) is sent to the voltage type inverter using the formula ▲There are mathematical formulas, chemical formulas, tables, etc.▼ A film winding method developed to control an induction motor by inputting it