Vector controlling method and apparatus for induction motor

A vector controlling method and apparatus for an induction motor is disclosed in which a rotator magnetic flux is reliably obtained by using a newly deduced equation. The apparatus includes a rotator magnetic calculator and does not require a tachogenerator so that the rotator magnetic flux can be obtained by calculation.

BACKGROUND OF THE INVENTION 
The present invention relates to a vector controlling method and apparatus 
for an induction motor, and more particularly, to a vector controlling 
method and apparatus for an induction motor which does not require a speed 
detector. 
An induction motor is most widely used as a power source for various 
mechanisms and apparatuses in industrial fields. This is because the 
induction motor has peculiar advantages in that it has a simple structure, 
needs little maintenance and exhibits excellent durability and low 
production costs. 
The induction motor is, however, very difficult to control because the 
dynamic characteristic thereof is clearly nonlinear, with many interactive 
variables present. Much investigation into techniques of controlling the 
induction motor for high performance has been widely carried out. In the 
1980s, with the advent of the rapid development of semiconductors, 
complicated control theories were applied to actual systems to further 
advance induction motor control techniques. Especially, the vector control 
method developed in the early 1970s provided for the characteristics of 
the induction motor to be divided into a magnetic flux component and a 
torque component, so that the induction motor could be controlled with the 
high performance of a direct-current motor, which greatly broadened the 
scope of application of induction motors. However, the vector controlling 
method needs data on the angular velocity of a rotator and therefore 
requires a speed detector such as a tachogenerator and encoder. This 
complicates a system, deteriorates the durability and reliability of the 
induction motor, destabilizes the system, and increases production cost. 
A method of detecting the magnetic flux of a rotator has been proposed by 
Ohtani in a paper entitled "Vector Control of Induction Motor without 
Shaft Encoder" (IEEE Transactions on Industry Application, Vol. 28, No. 1, 
January/February, 1992). This method will be explained below. 
Provided that the d axis of the d-q coordinates rotating at the angular 
velocity (electrical angular velocity .omega.) of induction motor 
coincides with the magnetic flux vector of the rotator, the relationship 
between the magnetic flux .phi..sub.r of rotator, generated torque T.sub.e 
and the angular velocity .omega..sub.r of induction motor can be expressed 
as follows. 
##EQU1## 
where M is mutual inductance; I.sub.d1 is the d-axis component (magnetic 
flux component) of the primary-side (stator) current; I.sub.q1 is the 
q-axis component (torque component) of the primary-side (stator) current; 
T.sub.2 is a time constant (L.sub.2 /R.sub.2) of the secondary-side 
(rotator); L.sub.2 is rotator inductance; R.sub.2 is rotator resistance; 
and P is an operator (d/dr) for differentiation. 
In other words, the generated torque T.sub.e and angular velocity 
.omega..sub.r of an induction motor are determined by magnetic flux vector 
.phi..sub.r of the rotator and primary-side currents I.sub.d1 and 
I.sub.q1. The generated torque and torque-component current, i.e., the 
main control variables, can be given as the following equations (4.1) and 
(5.1) on the orthogonal coordinates (.alpha.-.beta.) fixed coordinates or 
x-y fixed coordinates) of the stator. 
##EQU2## 
where .phi..sub..alpha. =.phi..sub.r cos(.omega.t+.rho.); .phi..sub..beta. 
=.phi..sub.r sin(.omega.t+.rho.); i.sub..alpha. =I.sub.1 
cos(.omega.t+.gamma.*+.rho.); and i.sub..beta. =I.sub.1 
sin(.omega.t+.gamma.*+.rho.). 
Assuming that .rho. is the angle of the d axis with respect to the .alpha. 
axis when t=0 (and may be given as zero), then .gamma.* and I.sub.1 can be 
expressed as follows. 
EQU .gamma.*=tan.sup.-1 (I.sub.q1 /I.sub.d1) 
EQU I.sub.1 =(I.sub.d1.sup.2 +I.sub.q1.sup.2).sup.1/2 
The calculation equation for the rotator magnetic flux, used by Ohtani, is 
as follows. 
##EQU3## 
where V.sub..alpha. and V.sub..beta. are stator voltages on .alpha. and 
.beta.; i.sub..alpha. and i.sub..beta. are stator currents on .alpha. 
and .beta.; R.sub.1 is the primary-side stator resistance; L.sub.rl.alpha. 
and L.sub.rl.beta. are the total leakage inductance on .alpha. and 
.beta. or L.sub.1 (1-M.sup.2 /L.sub.1 L.sub.2); and L.sub.1 is the 
primary-side stator reactance. 
FIG. 1 is a block diagram of the rotator magnetic flux calculator proposed 
by Ohtani. 
Referring to FIG. 1, the calculator comprises a current-controlled inverter 
1, an induction motor 2, a subtractor 3, a multiplier 4 having the 
variable value of R.sub.1 +L.sub.rl P, an integration circuit 5 having the 
characteristic value of 
##EQU4## 
an integration circuit 7 having the characteristic value of 
##EQU5## 
and an adder 6. 
A rotator induction voltage e is applied to integration circuit 5, and the 
magnetic flux command .phi.* of rotator is applied to integration circuit 
7. The outputs of integration circuits 5 and 7 are summed to detect the 
rotator magnetic flux. 
The output e of subtractor 3 is expressed as the following equation (8.1). 
EQU e=V.sub.1 +(R.sub.1 +l.sub.p)i.sub.1 ( 8.1) 
where V.sub.1 =V.sub..alpha. +jV.sub..beta. and i.sub.1 =i.sub..alpha. 
+ji.sub..beta.. 
Therefore, equations (6.1) and (7.1) are expressed as the following 
equation (9.1). 
##EQU6## 
where .phi.*=.phi..sub..alpha. +j.phi..sub..beta.. 
As shown in equations (6.1) and (7.1), Ohtani's method of calculating the 
magnetic flux of rotator requires integration. In implementing the method, 
if a pure integrator is used and a direct-current offset or drift is 
present in the input value, the calculated value of the magnetic flux 
diverges and is rather unreliable. For this reason, Ohtani instead used a 
lag circuit similar to the integrator. In low-speed operation, however, 
the calculation value of the lag circuit is considerably different from 
the actual value and interferes with the rotator speed so that a complete 
vector control is impossible. In Ohtani's method, the problem was solved 
by inhibiting the control of magnetic flux at low speeds. This solution is 
imperfect for enabling a proper vector control throughout the speed 
ranges. 
Further, the Ohtani method needs additional external hardware such as an 
accelerator for initially driving the motor, because the calculated value 
of the rotator magnetic flux is unstable in initial driving. 
SUMMARY OF THE INVENTION 
Therefore, it is an object of the present invention to provide a vector 
controlling method for an induction motor enabling a high-performance 
dynamic response characteristic by calculating the magnetic flux and 
angular velocity of the rotator by using stator voltage and current 
information, without a speed detector, and applying the calculated 
information to the non-interference control of the induction motor. 
It is another object of the present invention to provide a vector 
controlling method for an induction motor which does not require external 
driving initially. 
It is still another object of the present invention to provide a vector 
controlling circuit for an induction motor which is capable of detecting a 
reliable magnetic flux for the rotator. 
To accomplish the first object, there is provided a vector controlling 
method for an induction motor having a rotator and stator, comprising the 
steps of: 
calculating voltages and currents i.sub.xs, i.sub.ys, V.sub.xs and V.sub.ys 
for the stator; 
calculating variables .alpha..sub.x and .alpha..sub.y by using the 
equations 
EQU .alpha..sub.x =i.sup.. xs+a.sub.1 i.sub.xs -a.sub.0 V.sub.xs 
EQU .alpha..sub.y =i.sup...sub.ys +a.sub.1 i.sub.ys -a.sub.0 V.sub.ys 
estimating .phi..sup...sub.xr and .phi..sup...sub.yr by using the equations 
##EQU7## 
and 
EQU .phi..sup...sub.xr .phi..sub.xr +.phi..sup...sub.yr .phi..sub.yr =-a.sub.4 
(.phi..sub.xr.sup.2 +.phi..sub.yr.sup.2)+a.sub.5 (.phi..sub.xr i.sub.xs 
+.phi..sub.yr i.sub.ys); 
updating .phi..sup...sub.r by using the equation 
##EQU8## 
calculating the angular velocity of the rotator according to the equation 
##EQU9## 
where P indicates a value of the number of phase divided by two; 
calculating control inputs u.sub.1 and u.sub.2 by using the equations 
##EQU10## 
where k.sub.pj and k.sub.ij (for j=1, 2) are control gain values for the 
controller, and .omega..sub.r * and .phi..sub.r * are command inputs of 
.omega..sub.r and .phi..sub.r ; and 
substituting the values obtained in the preceding step into the equation 
##EQU11## 
and thereby obtaining current commands i.sub.xs and i.sub.yr. 
To accomplish the second object of the present invention, there is provided 
a vector controller for an induction motor having a rotator and stator, 
comprising: 
rectifying means for obtaining a direct-current voltage from an alternate 
voltage; 
speed controlling means for performing a control operation with a user's 
speed command .omega..sub.r * and a speed feedback estimated value 
.omega..sub.r, thereby outputting a control output value u.sub.1 ; 
magnetic flux controlling means for performing a control operation with a 
user's magnetic flux command .phi..sub.r * and a magnetic flux feedback 
estimated value .phi..sub.r, thereby outputting a control output value 
u.sub.2 ; 
non-interference controlling means for converting a nonlinear interference 
system into a linear non-interference system, by forming a nonlinear 
feedback and outputting stator current commands i.sub.xs * and i.sub.ys * 
on stator fixed coordinates; 
current controlling means for performing a proportional integration control 
with the current commands i.sub.xs * and i.sub.ys * and actual feedback 
currents i.sub.xs and i.sub.ys flowing through the induction motor, and 
converting the result into a voltage signal; 
first phase converting means for converting a two-phase voltage of the 
current controlling means into a three-phase voltage signal; 
switching means for driving the induction motor in response to the 
three-phase voltage signal output from the first phase converting means; 
second phase converting means for converting a three-phase current signal 
from the induction motor into a two-phase current signal; and 
calculating means for receiving the output signals of the current 
controlling means and the second phase converting means and calculating a 
rotator speed and rotator magnetic flux value for the induction motor 
control.

DETAILED DESCRIPTION OF THE INVENTION 
Referring to FIG. 2, a vector controlling circuit for an induction motor 
300 comprises a rectifier 100, a switching device 200, a speed controller 
400, a magnetic flux controller 500, a noninterference controller 600, a 
current controller 800, a converter 700 for converting two phases into 
three phases, a converter 900 for converting three phases into two phases, 
and a state variable calculator 1000. 
The functions of the respective components will be explained below. 
The rectifier 100, to which a reactance L and a capacitor C are 
additionally connected, is designed to reduce a direct-current ripple 
voltage. Speed controller 400 performs a control with a user's speed 
command .omega..sub.r * and a speed feedback estimated value 
.omega..sub.r, thereby outputting a control output u.sub.1. Magnetic flux 
controller 500 performs a control with a user's magnetic flux command 
.phi..sub.r * and a magnetic flux feedback estimated value .phi..sub.r, 
thereby outputting a control output u.sub.2. Noninterference controller 
600 formed in a nonlinear feedback converts the induction motor, a 
nonlinear interference system, into a linear noninterference system. Here, 
the induction motor is divided into an electromagnetic system and a 
mechanical system. The final output thereof is a stator current command 
(i.sub.xs *, i.sub.ys *) on the stator fixed coordinates Current 
controller 700 performs a proportional integration control with the 
current command (i.sub.xs *, i.sub.ys * ) and an actual feedback current 
(i.sub.xs, i.sub.ys) flowing through the induction motor. The output of 
the proportional integration control is compared with a trigonometric wave 
and becomes a voltage-modulated signal through a pulse-width modulation. 
Switching device 200 outputs a tri-phase voltage modulating signal for 
driving the induction motor through the switching operation. Phase 
converter 800 converts the voltage-modulated signal on the x-y coordinates 
into a tri-phase coordinates signal and drives the gate of switching 
device 200. Current controller 700 and phase converter 900 detect the 
actual current flowing through the induction motor via a current sensor 
and convert the tri-phase current signal into the signal on the x-y 
coordinates for easy control. State variable calculator 1000 calculates 
the rotator magnetic flux and rotator speed which are internal variables 
necessary for the induction motor control, with the input variable and 
output variable of the induction motor. 
Referring to FIG. 3, the stator voltage and current are calculated in step 
10. 
The dynamic equation of the induction motor taking the stator fixed 
coordinates (hereinafter referred to as the x-y coordinates) as a 
reference axis is given as follows: 
EQU i.sup...sub.xs =-a.sub.1 i.sub.xs +a.sub.2 .phi..sub.xr +a.sub.3 
P.omega..sub.r .phi..sub.yr +a.sub.0 V.sub.xs (1) 
EQU i.sup...sub.ys =-a.sub.1 i.sub.ys +a.sub.2 .phi..sub.yr -a.sub.3 
P.omega..sub.r .phi..sub.xr +a.sub.0 V.sub.ys (2) 
EQU .phi..sup...sub.xr =-a.sub.4 .phi..sub.xr -.phi..omega..sub.r .phi..sub.yr 
+a.sub.5 i.sub.xs (3) 
EQU .phi..sup...sub.yr =-a.sub.4 .phi..sub.yr +.phi..omega..sub.r .phi..sub.xr 
+a.sub.5 i.sub.ys (4) 
EQU .omega..sup...sub.r =-a.sub.6 .omega..sub.r +a.sub.7 (T.sub.e -T.sub.L)(5) 
where i.sub.xs is the x-axis current of the stator; i.sub.ys is the y-axis 
current of the stator; .phi..sub.xr is the x-axis magnetic flux value of 
the rotator; .phi..sub.yr is the y-axis magnetic flux value of the 
rotator; .phi..sub.r is the angular velocity of the rotator; T.sub.e is 
generated torque; and T.sub.L is load torque. 
Here, V.sub.xs (the x-axis voltage of the stator) and V.sub.ys (the y-axis 
voltage of the stator) are control inputs. Torque T.sub.e is given as in 
the following equation (6). 
EQU T.sub.e =K.sub.T (.phi..sub.xr i.sub.ys .phi..sub.yr i.sub.xs)(6) 
Given that various induction motor constants and rotation direction are 
known in the deriving process of the estimating equation of the magnetic 
flux and rotation speed for rotator, magnetic fluxes .phi..sub.xr and 
.phi..sub.yr for x-y axis rotator can be expressed with the magnitude 
.phi..sub.r of the rotator magnetic flux and position angle .theta..sub.r 
of the rotator magnetic flux, as shown in the following equations (7a) and 
(7b). 
EQU .phi..sub.xr =.phi..sub.r cos.theta..sub.r (7a) 
EQU .phi..sub.yr =.phi..sub.r sin.theta..sub.r (7b) 
Instead of directly deriving rotator magnetic flux information .phi..sub.xr 
and .phi..sub.yr necessary for control, the values of cos.theta..sub.r, 
sin.theta..sub.r and .phi..sub.r are estimated. 
In step 20, which is a characteristic feature of the present invention, 
.alpha..sub.x and .alpha..sub.y are calculated by using the following 
equations (8) and (9). 
EQU .alpha..sub.x =i.sup...sub.xs +a.sub.1 i.sub.xs -a.sub.0 V.sub.xs(8) 
EQU .alpha..sub.y =i.sup...sub.ys +a.sub.1 i.sub.ys -a.sub.0 V.sub.ys(9) 
Here, .alpha..sub.x and .alpha..sub.y are rotator variables and can be 
calculated through the estimation of rotator current and voltage. 
First, equations (1) and (2) are multiplied by .phi..sub.xr and 
.phi..sub.yr, respectively, and then summed to become the following 
equation (10). 
EQU .phi..sub.xr (.sup...sub.xs +a.sub. i.sub.xs -a.sub.0 
V.sub.xs)+.phi..sub.yr (i.sup...sub.ys +a.sub.1 i.sub.ys -a.sub.0 
V.sub.ys)=a.sub.0 (.phi..sub.xr.sup.2 +.phi..sub.yr.sup.2)(10) 
When equations (7), (8) and (9) are substituted for equation (10) and both 
sides are divided by .phi..sub.r (assuming of course that .phi..sub.r 
.noteq.0), a nonlinear algebraical expression such as the following 
equation (11) is derived. 
EQU .alpha..sub.x cos.theta..sub.r +.alpha..sub.y sin.theta..sub.r =a.sub.2 
.phi..sub.r (11) 
Using equation (11), .theta..sub.r can be expressed as a function of 
.alpha..sub.x, .alpha..sub.y and .phi..sub.r. If the above equation is 
considered to be a nonlinear equation with respect to .theta..sub.r and a 
solution of .theta..sub.r is to be obtained therefrom, two solutions are 
produced. One of the two roots is an unrelated one which is generated when 
a term relative to .omega..sub.r is removed from equations (1) and (2) to 
form one equation. Therefore, the root does not coincide with the actual 
value of .theta..sub.r. 
When equation (11) is solved by additionally using the rotational direction 
of the induction motor in order to discriminate a single appropriate root, 
cos.theta..sub.r and sin.theta..sub.r are calculated as follows. 
Step 30 is designed to estimate .phi..sup...sub.xr and .phi..sup...sub.yr 
according to equations (12), (13) and (14). 
##EQU12## 
Now, in order to derive the estimated equation of .phi..sub.r, equations 
(3) and (4) are multiplied by .phi..sub.xr and .phi..sub.yr, respectively, 
and summed to obtain the following equation (14). 
EQU .phi..sup.19.sub.xr .phi..sub.xr +.phi..sup...sub.yr .phi..sub.yr =-a.sub.4 
(.phi..sub.xr.sup.2 +.phi..sub.yr.sup.2)+a.sub.5 (.phi..sub.xr i.sub.xs 
+.phi..sub.yr i.sub.ys) (14) 
If both sides of the above equation are divided by .phi..sub.r, the left 
side becomes equal to .phi..sub.r, and therefore equation (14) can be 
modified into equation (15) as follows. 
EQU .phi..sup...sub.r =-a.sub.4 .phi..sub.r +a.sub.5 (cos.theta..sub.r i.sub.xs 
+sin.theta..sub.r i.sub.ys) (5) 
If equations (12) and (13) are substituted for equation (15), the following 
dynamic equation is obtained. 
In step 40, .phi..sup...sub.r is updated from the following equation (16). 
##EQU13## 
Equations (12), (13) and (16) are estimated equations for the rotator 
magnetic flux without using speed information. 
An estimated equation for rotation speed is derived as follows. 
Equations (1) and (2) are multiplied by .phi..sub.yr and .phi..sub.xr, 
respectively, and equation (2) multiplied by .phi..sub.yr is subtracted 
from equation (1) multiplied by .phi..sub.xr to obtain the following 
equation (17). 
EQU .phi..sub.yr (i.sub.xs +a.sub.1 i.sub.xs -a.sub.0 V.sub.xs)-.phi..sub.xr 
(i.sub.ys +a.sub.1 i.sub.ys -a.sub.0 V.sub.ys)=a.sub.3 P.omega..sub.r 
(.phi..sub.xr.sup.2 +.phi..sub.yr.sup.2) (17) 
Equations (8) and (9) are substituted for equation (17) and rearranged with 
respect to P.omega..sub.r to obtain equation (18). 
##EQU14## 
If equations (12) and (13) are substituted for equation (18), the following 
calculation equation for the rotation speed will be obtained. 
In step 50, the rotator angular velocity is calculated according to the 
following equation (19). 
##EQU15## 
In the above equation (19), P indicates a value in which the number of 
phase is divided by two. 
From here on, an indirect vector control based upon of the rotator magnetic 
flux and rotator speed expressed by equations (12), (13), (16) and (19) 
will be described below. 
Suppose that stator currents i.sub.xs and i.sub.ys are directly controlled 
and approximate current commands i.sub.xs * and i.sub.ys * (in other 
words, i.sub.xs .apprxeq.i.sub.xs * and i.sub.ys .apprxeq.i.sub.ys *) , 
equations (1) to (5) are simplified as follows. 
EQU .phi..sup...sub.xr =-a.sub.4 .phi..sub.xr -P.omega..sub.r .phi..sub.yr 
+a.sub.5 i.sub.xs * (20) 
EQU .phi..sup...sub.yr =-a.sub.4 .phi..sub.yr -P.omega..sub.r .phi..sub.xr 
+a.sub.5 i.sub.ys * (21) 
EQU .omega..sup...sub.r =-a.sub.6 .omega..sub.r +a.sub.7 [k.sub.T 
(-.phi..sub.yr i.sub.xs *.sup.. +.phi..sub.xr i.sub.ys *)-T.sub.L ](22) 
In the simplified system, if .phi..noteq.0, a condition for noninterference 
is satisfied. 
For the noninterference of the system, a nonlinear feedback such as the 
following equation (23) is applied. 
##EQU16## 
where u.sub.1 and u.sub.2 are new inputs. According to the above equation, 
the input/output dynamic characteristic of the whole system derived from 
the following equations (24) and (25) is linear and noninterfering. 
EQU .omega..sup...sub.r =-a.sub.6 .omega..sub.r +a.sub.7 (k.sub.T u.sub.1 
-T.sub.L) (24) 
EQU .omega..sup...sub.r =-a.sub.4 .phi..sub.r +a.sub.5 u.sub.2 (25) 
In order to obtain an intended transient response and a normal-state 
response, control inputs u.sub.1 and u.sub.2 of noninterference controller 
600 are set as the outputs of speed controller 400 and magnetic flux 
controller 500 as described below. 
In step 60, control inputs u.sub.1 and u.sub.2 are calculated by using the 
following equations (26) and (27). 
##EQU17## 
where k.sub.pj and k.sub.ij (for j=1,2) are control gain values for the 
controller, and .omega..sub.r * and .phi..sub.r * are command inputs of 
.omega..sub.r and .phi..sub.r. 
In step 70, current commands i.sub.xs and i.sub.ys are calculated by 
substituting the value obtained in step 60 in equation 23. 
In step 80, the rotator magnetic flux is calculated by using equations (20) 
and (21). 
According to the above method, rotator time constants for an induction 
motor are determined. 
Accordingly, the vector controlling method and apparatus for an induction 
motor of the present invention is advantageous in that, first, a rotator 
speed can be precisely detected without a speed detector; second, there is 
no need for an external driving means for initially driving the induction 
motor; and third, the apparatus can operate with precision at low as well 
as high speeds.