CA1103755A - Induction motor control system - Google Patents

Abstract

INDUCTION MOTOR CONTROL SYSTEM

ABSTRACT OF THE DISCLOSURE
A variable frequency power supply device supplies an AC power to a squirrel-cage motor through an AC parameter control. The control receives a command active current resulting from a command torque and a command exciting current to generate a resultant current and its phase. The command torque is produced from the actual and command motor speeds and the exciting current is caused from the actual motor speed. The control also receives a command frequency determined by the actual motor frequency and a command slip frequency also resulting from the command torque. The control controls the firing phases of thyristors in the power supply device in response to the command current, phase and frequency. The control may generate a voltage for supplying the active current and an exciting voltage to similarly control the firing phases of the thyristors.
In the latter case, the exciting voltage may be added with its differential to compensate for a rapid change in active current.

Description

S~ ~

BACKGROUND OF TilE INVENTION
I
¦ This invention relates to a control system for ¦ controlling a frequency of an AC power supplied to a ¦ primary winding of an induction motor including a ¦ shortcircuited secondary conductor, for example, a squirrel-¦ cage motor.
In conventional induction motor control systems ¦ the variable frequency power supply device, for example, the ¦ inverter or cyclo-converter has supplied ~ electric power I to an induction motor with a shortcircuited secondary ¦ conductor, typically, to a squirrel-cage motor so that the electric power has a frequency as determined by ¦ the algebraic sum of an output from a command slip ¦ frequency generator responsive to a command torque and I an output from a speed sensor for the motor. A voltage ¦ for supplying the electric motor is proportional to the absolute value of the frequency thus deter~lined. Such ¦ control systems have more or less improved the character-I istics of the generated torque but the slip of the motor ¦ does not fast respond to the required torque. In ¦ addition, an air gap flux on the motor has been changed and long time has gone until this change in gap flux is ¦ settled.
¦ In order to soive those problems, the motor has ¦ been provided with an air g~p-magnetic sensor thereby to control the AC power supply to the motor in response to tlle sensed position of the gap flux or a phase of an internal electromo~ive force. This measure has resulted in a 7~5 complicated, expensive structure.
It is an object of the present invention to ¦ provide a new and improved induction motor control system for controlling a frequency of elec:trical energy supplied to a primary windin~ of an induction motor including a shortcircuited secondary conductor, having a fast response and a simple circuit configuration without the necessity of providing a gap -flux sensor and subordinate controls.
SUMrlARY OF THE INVENTION
The present invention provides an induction motor control system comprising variable frequency power supply means for supplying an AC power to a primary winding of an induction motor includillg a shortcircuited secondary conductor, slip frequency control means for controlling a frequency o-f the AC power and a slip frequency of the induc-: tion motor, a command slip -frequency gener.ltion means for generating a command value of the slip frequency in response to a required torque, and AC parameter control means for commanding and controlling the absolute value and phase angle of the AC power in connection with the slip frequency whereby the power supply is controlled independently o-f a gap flux on the induction motor.
In a preferred embodiment of the present invention, the AC parameter control means may include a first function generator for generating a command a~solute value of the supplied alternating current in connection with the command slip frequency, and a second function generator for generating 1 ~37~i~

a command phase angle of the supplied alternating current in connection with the command slip frequency means.
In the voltage controlled power supply, the AC
parameter control means may include two function generators C~p 0 ~7e~
for generating a first voltage t~ffl~e*~ and a second voltage compornent respectively, and a differentiating and adding means for differentiating the second voltage cO ~ >O n c ~
com~e~*e~ with respect to time and for adding the differentiated second voItage compornent to the exciting voltage.
BRIEF DESCRIPTION OF TIIE DRAWINGS
The present invention will become more readily apparent from the following detailed description taken in conjunction with the accompanying drawings in which:
Fig. la is a block diagram of a conventional induction motor control system;
Fig. lb is graph useful in explaining the operation of the arrangement shown in Fig. l;
Fig. 2 is a block diagram of an embodiment according to the induction motor control system of the present invention;
~`igs. 3 and 4 are respectively a graph cf three AC parameters and a vector diagram useful in explaining the principles of the present invention;
Fig. 5 is a schematic diagram of space conductor current distributions for a primary and a secondary current flowing through an induction motor controlled by the present invention;

~ ~r 3t;~

Fig. 6 is a diagram illustrating tl-e simplified equivalent circuit to induction motors including the shortcircuit secondary conductor;
Fig. 7 is a block diagram of a modification of the present invention;
Fig. 8 is a vector diagram ~seful in explaining the operation of the arrangement shown in Fig. 7;
Fig. 9 is a circuit diagram oE the details of one portion of the arrangement shown in Fig. 2;
Fig. 10a is a circuit diagram of another modification of the present invention;
Fig. 10b is a circuit diagram oE the solid state switch shown in Fig. 10a;
Fig. ll is a block diagram of still another modification of the present invention;
Fig. 12 is a block diagram of the AC waveform ; generator shown in Fig. 11;
Fig. 13 is a block diagram of the first function generator shown in Figs. 2 and 9;
Fig. 1~ is a diagram similar to Fig. 13 but illustrating the second function generator shown in Figs.

2 and 9; and Fig. 15 is a diagram similar to Fig. 13 but illustrating the AC waveform generator shown in Figs. 2 and 9.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
In a conventional induction motor control system shown in Fig. la an induction motor 10 includes a primary ~ 375~ ~

l winding ~not shown) suppliecl by a variable ~requency power ¦ supply device 12 and a shortcircuited secondary conductor `~not shcwn). The induction motor 10 in this case is a squirrel-cage motor while the supply de~ice 12 may be an ¦ iff~PeeP*e~ or a cyclo-converter. In this case, the torque control of the motor 10 has exhibited ~ complicated ¦ nonlinear response characteristics because o-f the presence ¦ of the shortcircuited secondary conductor. That is~ as ¦ compared with DC mOtOTS or commutator-less motors ¦ employing synchronous motors, the generation of a torque ¦ has been attained with a time lag, and the generated torque ¦ has changed in an oscillatory manner. Accordingly conven-¦ tional variable requency control systems ~or induction ¦ motors have been unsuitable for its use requiring a fast ~; 15 ¦ response.
¦ In order to eliminate the abovementioned ¦ objections, the arrangement illustrated in Fig. la has ¦ comprised an adder 16 receiving both an output ~N from a ¦ speed detector 14 such as a tacho-generator connected to ¦ the motor 10 and an output ~S from a command slip frequency ¦ generator 18 applied with a command torque I to produce the alge~raic sum ~ of both outputs that, in turn, determines a frequency ~ o~ an electric power supplied to the motor 10.
The alge~raic sum ~ is applied to both the variable frequency power supply device 12 and a voltage generator 20 acting as a square law detector which generate a voltage V~ propor-tional to the absolute value of the frequency ~. Thus 11~3~55 the power su ly device 12 controls the induction motor 10 in response to the voltage VM and the frequency ~
applied thereto. This measure is known as a slip frequency control system.
Conventional slip frequency control systen!s(such as shown in Fig. la have been disadvantageous in that an angle governing a torque does not fast respond to a change in torque. The term "angle governing a torque means a deviation angle of a primary from a secondary current distribution. More speci:Eically, when a command torque changes stepwise as shown in Fig. lb(i), an angular slip frequency WS immediately respond to the torque as shown in Fig. lb~ii) but a change in angle ~T that is an integrated ¦
value oE the slip frequency ~S oscillates with the system natural frequency as shown in Fig. lb(iii). That natural frequency is determined by both a coefficient of generation o-f a steady-state torque and the system inertia, and the oscillation decays as determined by a secondary resistance and inductance of the particular induction motor. The term "secondary inductance" used herein means a leakage inductance as viewed fro~ the secondary side of the ; induction motor for voltage controlled power supply devices connected to voltage sources, or a sel-f-inductance on the secondary side thereof for current control type power supply devices connected to current sources. Frankly speaking, a magnetic flux flowing through the particular motor in this oscillation has not been changed within a short time interval because of the presence of the short-lil}3'75~;

circuit of the secondary conductor thereof and acted on transient phenomena relatively short in duration as if it would resemble the magnet rotor o~ synchronous motors.
Therefore excessive power swings have occurred as in syn-chronous motors. In additions, a change has occurred in an air gap-magnetic flux and long time has gone until this change is settled.
Also in order to solve the problems just described, there have been previously proposed systems including gap flux sensor means and controlling a power supplied to the induction motor in response to a position of the sensed gap flux or a phase of an internal electromotive force.
; Those systems, however, have been cornplicated and expensive ; in sensing the magnetic flux.
Accordingly, the present invention contemplates to provide an induction motor control system having a simple cons~ruction and a fast response without the necessity of using gap flux sensor means and subordinate controls.
Fig. 2 wherei~ like reference numerals designate the components identical or corresponding to those shown in Fig. la illustrates an embodiment of the present invention employing a current controlled power supply device. A command speed NS and the actual speed N
from the speed sensor 14 are applied to a comparator 22a where the actual speed N is subtracted from the command speed NS to form a command torque T. The command torque T

~ 3~7SS

~ is applied to a block 22b forming a ~peed control circuit ¦ generally designated by the reference numeral 22 with the i comparator 22a. The block 22b is responsive to the torque ~ T to generate a command active current component I~
¦ corresponding to the desired torque r. That active current component ~ (~) is supplied to the command slip frequency generator 18.
lAlso a command excitation generator 24 is responsive to the actual speed ~ applied thereto to generate a command exciting current IE corresponding to a ¦ gap flux (~ in a high speed range. The command exciting current IE is supplied to the command slip frequency generator 18 where it along with the active current component ¦
~ I~ is converted to a command angular slip -frequency ~S
That slip frequency ~S is supplied to the adder 16 with the actua-l angular rotating frequency ~N supplied also from the speed sensor 14 to provide a command angular l 5e r~ v'e S
frequency ~. Thus the adder 16 ~crvicJc as a command ¦ frequency generator.
¦ The term "angular rotating -frequency" means an angular frequency into which a rotational speed is converted and which gives an synchronous speed equal to the rotational speed. The angular frequency may be called merely a "frequency" hereinafter.
As shown in Fig. 2, the speed con-trol circuit 22, the command excitation generator 24 and the command -frequency generator 16 are connected -to a three AC parameters-control Il g .1 11~2755 ¦ circult 26. The three AC parameter contr~l circuit 26 ¦1 includes a first :Euncti.o11 generator 2~, a second :Eunction generator ~ and a polyphase ~C waveEorm generator 32 1 connected to both function genera-tors 2~ and 30.
The active current component Ir rom the speed ; control circuit 22 and the command exci.-ting current : component IE from the command excitation generator 24 are :~ ¦ applied to the first function generator 28 where a command : ¦ fed current IM is generated. The command current IM is a ¦ composition of the acti.ve and exciting current components [r and 133 res ctively and holds the expression I = K ~
: I
lS ¦ where K1 designates a propor-tional constant. It will readily ~ ¦ be understood that, under the constant flux conditions that .: ¦ the exciting current component IE remains unchanged, IF may ¦ be also regarded as a proportional constant.
The second function generator 30 also receives the active current component Ir and the exciting current component IE to form a command phase angle ~r which is ¦ imparted to the composed current IM. That is, ~r designates ¦ a phase angle of the composed IM current on the basis of the ¦ exciting current component IE and satisfies the following ¦ expression:

~ an ~ 33 ~ , ,,.................. ~2) `~ - 10-.1 i~lC137~i~

Further the expression WS = K2 I~ ......................... (3) ..
is held by the command slip frequency ~S provided by the command slip frequency generator 18 where 1~2 designates a proportional constant. Considering a magnetic saturation~
K2 changes Wit}l either IE or I~ and particularly with IE
so that the more the magnetic saturation the greater the K2 will be.
Fig. 3 graphically shows the above expressions ~ 2) and (3) labelled IM~ ~T and ~S respectively, with IT or T plotted in abscissa. It is desirable that the slip frequenc~ ~S will be saturated in a high torque region and in either of the motoring and braking modes of operation as shown at dotted-and-doshed line wsl (which indicates a flat saturation curve) or at dottecl line ~S2 (which indicates a square root-proportional curve) in Fig. 3.
This is because the induction motor 10 has a power factor rather reduced with excessively high slips.
Fig. 4 is a vector diagram illustrating the exciting current component IE, the active current component I~, the fed current IM as above described. In Fig. 4, the induction motor produces a motoring torque ~ in the motoring mode of operation illustrated in their first quadrant o Fig. 4 and a braking torque ~ in the braking mode of operation illustrated in the fourth quadrant thereof.

~ S 5 The torque is positive when the motor is operated in the motoring mode and ne~ative when operat:ed in the braking mode. Also, the exciting current ~ and an internal electro-motive force E~ are put in quadrature relationship and remain unchanged as reference vectors. Further the exciting and active current componen-ts IE and I~ are put in quadrature relationship. When the torque I or the active current component I~ is changed, the extremity of the composed current IM depicts a straight line lI-H perpendicular to the exciting current component IF while an angle between the exciting current IE and the current IM or the command phase ~ changes.
Referring back to Fig. 2, the command supplied current IM and the command phase ~T thereof are applied to the polyphase AC waveform generator 32 which also receives the command frequency ~ from the command frequency generator 16. Then the polyphase AC waveform generator 32 applies to the power supply device 12 command AC information or the three command parameters or the command absolute value IIMI, the command phase angle ~ and the command frequency . In this case, the device 12 serves a power stage which, in turn, supply a command alternating current IM having the three command parameters to the induction motor 10 thereby to drive the latter as commanded.
While the present invention has been illustrated and described in conjunc~ion with the current control type it is to be understood that the same is equally applicable to the voltage control type. In the latter case, a voltage 11~3~S~i controlled power supply device is used, and the first function generator 28 is modified to generate a command fed voltage V~ while the command excitation generator 24 is arranged to generate a command first S voltage compornent VE for forming the command exciting current IE with the active current I replaced by a command second voltage compornent V Çor forming the same. Thereby the process as above described is repeated.
Further if it is desired to effect the positional control then a position sensor 34 is connected to the speed sensor 1~ and hence to the induction motor 10. The actual position XM of the motor 10 sensed by ~he position sensor 34 is deliverecl to a position comparator 36 where it is substracted from acommand position X applied to the comparator 36. A difference between the command and actual position X and XM respectively is applied as an equivalent to a command speed NS to the speed comparator 22a. Therea-fter the process as above described is repeated.
The induction motor 10 controlled in the manner as above described has current distributions for a primary and a secondary current flowing therethrough as shown in Fig. 5. In Fig. 5 an outer circular array o-f circles shows a space distribution of the primary current or fed current IM to the primary side and an inner circular array of ~circles shows that of a secondary current i~ flowing through the secondary side. The arrow ~g designates a direction of distribution of a gap flux flowing through an associated secondary conductor and iron core on the secondary side. The primary current I~l is resol~ed into -the exciting current component IE and the active current component IT which are, in turn, shown typically by lumped conductors labelled the corresponding reference characters IE and Il respectively. ~lso the crosses indicate currents flowing into the plane o:f Fig. 5 and the dots indicate currents flowing out -from that plane. The fed phase angle is shown in Fig. 5 as being a angle between the central axis of the gap flux or a magnetic axis a of the exciting current I~ distribution and a magnetic axis b of the supplied or composed current IM distribution which angle has been called previously the angle governi.ng tlle torque or the deviation angle of the primary :from the secondary current distribution. Also, a direction of rotation is shown at the arrow ~N.
~here a rapid change in torque is required, the control as above described is effected so that the exciting current component IE remains unchanged while a phase angle thereof and, in turn, the magnetic axis _ thereof is maintained to coincide with the central axis of the gar, flux ~g. Further the induction motor is applied with that component of the primary current inducin~. a secondary current i for producing the command torque T, that is to say, the acti~e current component Il and the latter is caused to change rapidly. In addition, the command slip frequency ~S is caused ~o interlock and change in a predetermined relationship in such a manner that the secondary current i is held under the conditions for the constant gap flux ~g and also that the space current and magne-tic distributions are maintained in their states 11~37S5 at-tained after the distribu-tions have challged.
As a result, the control effected by the arrangement of Fig. 2 completely Eulfils the steady state conditions af~er the torque has been changed and the magnetic ~lux is scarcely changed ~ith respect to a rotor involved. (It is noted that the magnetic flux is changed by a leakage magnetic flux of interlinkage attended upon a change in secondary current iT).
Induction motors have the well known equivalent circuit shown in Fig. 6. In Fig. 6 the current IM flows through a primary leakage inductance Ql' a resistance rl of primary winding and a mutual incluctance M between the primary and secondary windings to induce a secondary current ir across the mutual inductance M. The secondary current iT
flows -through an equivalent load resistance RL~ a resistance r2 of the secondary winding and a secondary leakage inductance Q2.
A change in primary active current component is larger than that in secondary current iT by ~IQ2 and the active current component Ir may be expressed by Ir = iT -~ ~IQ2 (4) In other words, the secondary current irr induced is less than the primary active current I by ~IQ2. This means that, in the equivalent circuit o-f Fig. 6, a current component through th~ mutual inductance ~ is mad~ of (IE ~ ~IQ2) 50 as to increase an gap flux of interlinkage s~;

by an amount corresponding to a flux (Q2iT) oE interlinkage with the secondary leakage inductance Q2 due -to the secondary current i (see Fig. ~. That increment serves to compensate for a voltage drop across the secondary leakage reactance and to maintain a cons-tant voltage ET across the equivalent load resistance ~L. These respects are somewhat dif-ferent from the conventional established t~eory that a secondary voltage Eg (see Fig. 4) is controlled to be constant, alternatively, that a voltage- to -frequency ratio is controlled to be constant.
From the Eoregoing it will readily be understood that the three parameters or the torque T, tlle slip frequency ~S and the active current component IT are linearly proportional to one another.
As a result of the immediate supply of the AC
current IM having the command phase angle ~T, it is possible to induce -tile secondary current iT that coincides with the gap flux ~g or a gap flux density distribution due thereto ensuring that the torque is produced without any time delay.
In this way the linear fast responsive control can be accomplished which has the command -torque T and the command active current component IT as inputs applied thereto.
In addition, the gap flux weakening control (or the field weakening control) may be accomplished by changing the command exciting current component IE or the gap flux ~g or by the command excitation generator 24.
The qualitative description for the dynamic characteristics of the present invention has a limit but>

il~3~55 it is summarized that, in order to cope wi-th tlle desired change in torque, the active current component IT j S
generated to be orthogonal to a no-load exciting current component while the first and second function generator 2 and 30 and. the command slip :frequency generator 18 have been provided so that those currents fulfill both the condi-tions that the steady state be reached and the initial conditions.
In order to positively prove the abovementioned matters, it is required to re-fer to the fundamental theory of induction motors. The fundamental equations for induc-tlon motors having the shortcircuited secondary conductor may be expressed by Vds rl + PLl ~Ll ~M ids VqS = ~Ll rl -~ PLl -~M -PM iqs ...~5 O _ P~l ~ M r2 + PL2 -~SL2 idr O ~SM PM ~sL2 r2 PL2 iqr and T - pM(idS iqr - iqs idr)................. (6) transEormed to d and _ coordinates where Vds = voltage in d coordinate across stator Vqs = voltage iJI _ coordinate across stator ids = current in d coordinate through stator iqs = current in q coordinate tllrough stator 110~

idr = current in d coordinate through ro-tor iqr = current in q coordinate t:l~rough rotor p = number of pole pairs P = differential operator Ll = primary self-inductance L2 = secondary sel-f-inductance and ~ ~S' rl and r2 have been previously defined.
The preferred embodiment of the presen-t invention as shown in Fig. 2 includes the -first and second function generators 28 and 30 and the command slip :Erequency generator 1~ operative to follow the expressions (1), (2) and (3) respectively. Generally speaking, the present invention is put under the control conditions expressed by ids = IE cos 30 ~ IT sin ~O--,-----(7a) T S ~0 ~ IE sin ~o........... ~7b) and ~ 2I~/L2 IE K2 I~IE ...................... (7c) respectively where aO designates any angle and thereEore any constant meaning that re:Eerence axes -for axis trans-forma~ion or an initial phase angle is optional. That is, it may be selected at will. I-t is noted that the expression (7c) is identical -to the e~pression (3).
I Assuming that ~O is null only for the purposes of facilitating an understanding of the theory? substituting ~he expressions (7a), (7_) and (7c) into the fundamentional equation (5) and rearranging it can yield the following il~3755 expression:

ids = IE

iqs = I~
................. (8) iqr = I~M/I.2 = i idr = O

and Vds rlIE - ~Ll~l-M /L1L2) IT
~Vqsi ~Lll~ rllT+PL (l-M /L 1~) T

Thu it is seen thst he c~n rol con itions defined by the expressions (7_), (7b) and (7c) cause the ¦ secondary current to be subordinately controlled to values ¦ given by the expressions (8) while a term including the ¦ differential operator P or a transient term is cancelled out.
¦ Also it is seen that the expression (4) is nothing but to ¦ mean the expression (8).
On the other hand, the voltage equation (9) has ¦ rows on the rotor sidè equal to zero with the result that ¦ the shortcircui-t requirements are met without the ¦ occurrence of all transient and steady-state unbalanced voltages.

~ 3~SSi Fur~her from the voltage equation ~9) it is seen that, on the stator side, the only and one transient term that includes the diffeTential operator P is left on the axis. However, a coefficient ~1 - M~/L1~2) associated with the differential operator P means a leakage coefficient and therefore ~Ll means a leakage inductance. Therefore ~LlI means that only a change in leakage flux of inter-linkage is a -factor of delaying a response.
On the other hand, the torque ~ is given by T = pM IEIT/L2 ~ lOa) P IE~S/r2 = K4IE~S (lOb) and proportional to I or ~S' By trans-forming the control requirements according to the expressions ~7a) and ~7b) bacX
to the AC system having the -Frequency ~, it is seen that phase currents are supplied to the AC system with peak values or effective values defined by the expression ~1) and a phase angle of their reference-phase sequence component defined by the expression (2).
Also, the components on the d and q axes defined by ~he expressions ~7a) and ~7b) or the expressions ~8) may be regarded to be current components on the imaginary and real axes of the vector diagram shown in Fig. 4 with proportional constants omitted.
From the expressions (8) through (10) it will readily be understood that, by setting the parameters as .~. .

11-3'7~i5 predetermined~ the present invention exhibits the completely linear control characteristics as above described in conjunc~ion with the operation of the embodiment thereof whosn in Fig. 2 which characteristics resemble the torque control characteristics exhibited by separately excited D~ motors with compensating windings.
In Fig. 7 wherein like re-ference numerals designate the components identical or corresponding to those shown in Fig. 2, there is illustrated a modification of the present invention supplying a voltage controlled power to an induction motor involved and also adapted to optimally supply a current controlled power to the motor. In Fig. 7 the three AC
paramete-r control circuit 26 includes, in addition to the polyphase AC wavefor generator 32, a first function generator serving as a command first voltage generator 38, a second function generator serving as a command second voltage generator 40, and a differentiator 42. The command first voltage generator 38 receives both an electrical quantity coTresponding to a gap flux ~, in this case, the exciting current component IE from the command excitation generator 24 and the command frequency ~ from command frequency generator or the adder 16 to generate an exciting voltage VE -for supplying a gap flux and, in turn, a first phase voltage component proportional to an exciting current component IE. The command second voltage generator 40 is responsive to the command torque ~ from the speed control circuit 22 or the command torque generator and the command frequency ~ from the adder 1~ to generate a second ~ ~ 3~

phase voltage component VT for supplying the active current component.
The di-fferentiator 42 is operative to rapidly change the active current component in response to the command torque T applied to the induction motor 10, To this end~
the differentiator 42 has an input connected to the speed control circuit 22 to ef-fect the differentiation with respect to time as will be apparent later. The differentiated exciting voltage VE is added to the exciting voltage component VE by an adder 44. The exciting voltage component VE thus compensated is applied to the polyphase AC waveform generator 32. Also the second voltage component VT that may be called an active voltage is applied to the wave-form generator 32.
In other respects, the arrangement is substantially identical to that shown in Fig. 2 excepting that in Fig. 7, the command slip frequency generator 18 receives the command torque T alone.
The operation of the three AC parameter control circuit 26 shown in Fig. 7 will now be described with reference to a vector diagram illustrated in Fig. 8.
Command values of the gap flux ~, the exciting current component IE there-For, the active current component ll contributing to the torque T provided by the induction motor 10~ the secondary voltage ~g for the gap flux ~ in the motor 10 and the frequency ~ can be produced in the similar manner as above described in conjunction with Fig. 2 wherein the current contro:l type is illustrated.

~1a?3 ~b~i In Fig. 8 the exciting current component IE applied to the induction motor 10 produces a voltage (IErl + jIExl) across a primary leakage impedance ~rl + jxl) thereo~ where xl designates a primary leakage reactance and 1 designates the unit of imaginary numbers. Tha~ voltage is added to the secondary voltage Eg to form a no-load motor voltage VMo~ By making the extremity of the no-load motor voltage VMo the center of the operation, a voltage VM supplied across the motor is controlled along a straight line fl2-ll2 passing through the center of the operation. The voltage VM supplied across the motor under loading is the vector sum of the no-load motor voltage VMo and a voltage drop (I rl + j~ z~ across a motor impedance (~1 + jx) due to a load current component IT . When the on-load motor voltage VM has its extremity lying on that portion of the straight line H2-H2 extending in an upward direction as viewed in Fig. 8 from the center of the operation, the motor is operated in the motoring mode. On the other hand, when the motor voltage VM is tilted downwardly to the secondary voltage Eg, the motor is put in the regenerated mode oE
operation.
From the foregoing it is seen that the on-load motor voltage ~ has a second phase voltage ~ component r and a first phase voltage component VE given by the following expressions:

VE Eg IExl + Irrl .................. ~11) and 1~ 5~i ~

T Erl ITX ..................................... (12) Alternatively VM ~~ ~ ~ l and .................... (13) ~ = tan 1VT/VE

hold where VM designates the absolute value o~ the on-load motor voltage VM and ~T designates a phase angle formed between the voltages VM and VE.
On the other hand, the command slip frequency ~S
is defined by the expression (3) or ~lOb). Since the voltage concerning the magnetic flux is proportional to the -frequency ~, these proportional multiplication inputs are applied to the function generators (38) and (40).
Also~ as the expressions (13) has the equivalent interchangea~ility with the expressions (11) and (12) in the arrangement of Fig. 7, the three AC parameter control circuit (26) shown in Fig. 7 may be modi,Eied to that shown in Fig. 2.
In the latter case, the function generators 2~ and 30 may be additionally provided with respective multiplication elements to effect the multiplication by the frequency ~.
~n the other hand, the expressions (11) and (12) correspond to the equation for a stator voltage described by the expression (9). Therefore VE = V~S and VT = -Vd5 hold.
In the steady-state o~eration it may be re~arded that - 2q -~ 7~;~

~LlIE = Eg ~i IEXl and . ............. (14) ~Ll(l - M /I,lL2) = x hold. I-lowever, since VqS appearing the expression (9) includes a term including the differenti.al operator, the differentiator and compensation adder 42 alld 44 respectively are operated to add a clif-ferentiated compensation voltage VE to the command exciting voltage component VE in response to a change in torque or command torque ~. '['hereby the required component IT has an improved fast response -to a rapid change in torque.
From the expressions (9), (lOa) and (10_) it is seen that this differentiated compensating voltage VE of the first phase voltage component VE may be defined by V~ = (1 - M2/LlL2)dI~/dt = K5(dIT/dt) = (L2/pM2IE) (1 - M2/LlL2)dl/dt = K5(d /dt) ........................ (15) where K5 and K5 are constants. In other words 7 one obtains ~VE dt - (1 - M /LlL2) I = ~Q(I~ ---(16) \.

There-fore, by adding a voltage VE having the product of voltage and time to the first phase voltage component VE
one may obtain leakage flux of interlinkage 'PQ~I~) due to the active current IT' S From the foregoing it will be appreciated -that the present invention as described in conjunction with Fig. 7 may be extended to be applicable to voltage controlled power supply devices wherein fast response characteristics are required.
Fig. 9 shows the details of the power supply device 12 and the three AC parameter control circuit 26 as shown in Fig~ 2. In Fig. 9 the power supply device 12 includes a DC source 50 and a rectifier group 52 including m/2 (where _ is any even integer, in this case m, having a lS value of six) pairs of serially connected semiconductor diodes connected in parallel circuit relationship across the source S0 so that their anode and cathode electrodes are connected to the negative and positive sides of the source 50 respectively. Also m/2 pairs of serially connected solid state switches 54 connected in parallel circuit relationship across the source 50. The solid state switch 54 may be any of a transistor, thyristors and other semi-conductor elements. The switches 5~ include respective control electrodes (not shown) controlled by a group of preamplifiers 56 which may be gate pulse or base curren~
limiting amplifiers. The junction of diodes in each pair is connected to that o-f the solid state switches 54 in the corresponding pair and thence to the induction motor 10.

3'~55 Thus the rectifier group 52 and the solid state switch group 54 form an inverter bridge including m/2 AC output terminals. In the example illustrated m is of six as above described and the three switches labelled ordinal odd number 1, 3 and 5 are connected at their anode electrodes to the positive side of the source 50 and at the cathode electrodes to the switche Nos. 4, m and 2 respectively.
The latter switches have the cathode electrodes connec~ed to the negative side of the source 50.
The power supply device 12 further includes a current sensor 58 such as a current transformer coupled to both a lead connecting the negative side of the source 50 to the cathode electrodes of the lower solid state switches as viewed in Fig. 9 alld a lead connecting the positive side of the source 50 to the cathode electrodes of the lower rectifier elements as viewed in the same Figure. The current sensor 58 senses the sum of a current flowing ; through the rectifier group and that flowing through the switch group. This measure results in a simplified r~ C I r ~ ~ I t K 20 -cur-c~ configuration.
The ~hree AC parameter control circuit 26 is arranged to effect the phase and frequency control with digital pulse trains. The command fed current IM
from the first function generator 28 is applied to an absolute-~alue comparator 60 forming one part of the polyphase AC waveform generator 32. In the comparator 609 the command fed current IM is applied to a summing point 62 to subtract a current IMp seilsed by the current sensor ~ ., ...

11~ 5S

58 therefrom and a di.fference there~etween is supplied to a comparing element 64 to form a chopping signal S(c~l).
Further a carrier generator 66 generates a triangular or a saw-tootlled wave which is, in turn, applied to the comparing element 64 through the summing point 6Z to be suporposed on the chopping signal S~cH) thereby to impart a predetermined carrier period to the signal. T~us the chopping control that is the ON-OFF time ratio control or pulse width modulation control is effected.
If desired, the sensed current IMp may be formed by separately rectifying respective phase currents supplied to the induction motor 10.
The command phase angle ~ from the second function generator 30 is applied to a conduction control-signal distributor 70. The control signal distributor 70 includes an m-mal reversible ring counter 72 having outpu-ts 1,2, m and a pair of forward and backward inputs F and B, two frequency dividers 74 and 76 connected to the inputs F and B of the counter 72 respectively, two "O~" gates 7S and 80 connected to the frequency dividers 14 and 76 respectively and a carrier pulse generator 82 connected to one input o-f each "OR" gate 74 or 76. Each of the "OR" gates 74 or 76 includes the remaining three inputs connected to the speed sensor 1~, a pulse generator 84 and the second fllnction generator 30 respectively.
The speed sensor 14 in this case is, for example, an incremental rotary encoder for generating a train of rotating frequency adding pulses P(~N) having a. pulse repetion frequenc)r ~N~P) indicating the actual frequency ~N of the iL1~)3'75~j induc-tion motor 10. The pulse generato-r 8~ is connected to the command slip frequency generator 18 to genera-te a train of slip :frequency control pulses P(os) having a pulse peti-tion :Erequency ~S(P) in response to the command slip frequency ~S T}le second function generator 30 generates a train of phase control pulses P(~) representative o:f the comn~and fed phase angle 3~ and the carrier pulse generator 82 generates a train of carrier pulses PcQ having a pulse repetition freauency WPcQ Each of the pulses P(~N)~ P(~S)~
P(~) and P~Qhas either a positive or a negative value and the pOsitioll ~ulses are applied to the "OR" gate 78 while the negative pulses are applied to "OR" gate 80.
The ring counter 72 cooperates with the frequency dividers 7~, 76, the "OR" gates 78, 80 and the carrier pulse generator 82 to perform both the function o-f controlling a phase angle and the function o:E composing .Erequencies.
Only for purposes of illustration, t~e pulses appearing from the "OR" gates 78 and 80 are designates by +P
and -P respectively and the pulses delivered from the :Erequency dividers 7~ and 76 are clesignated by P~ and PB
respecti-vely. Also the pulses P~ and PB are called :Eorward and backward shift pulses respectively. The -forward and backward shift pulses are also known as a clockwise and a counterclockl~ise rotation pulse designated ~y C~ and CC
respectively or as a count-up and a count-down pulse respectively.
Each pulse train is frequency divi.decl by a factor of R through either of the frequency dividers 7~ and 76 and ~3~

further by a factor of m through the ring counyer 72. For example, the pulse train P(~N) is frequellcy divided by a factor o-f m.R to have a pulse repe-ti-tion ~requency N ~N(p)/m~R.
The pulses P~N), P~) and P(~s) entering the "OR"
gate 78 are operati~e to cause the fed phase angle to move forward by an electrical angle of ~ = 2~/m.R radian that is one control uni-t per each pulse. That is, the phase angle is caused to rotate stepwise in a positive direction by that angle to lead. On the contrary, these pulses entering the "OR" gate 80 are operative to cause the -fed phase angle to move backward by an electricaL angle of = 2~/~.R radian per each pulse. That is, the phase angle is caused to rotate stepwise in a negative direction to lag. On ~he other hand, the carrier pulses PcQ can not step the fed phase but determine pulse repetition frequencies of the forward and backward shift pulses PF and PF in the abscence of all the other pulses applied to the both "OR"
gates 78 and 80. In other words, the pulses PcQ determine a pulse phase modulation carrier frequency ~c expressed by ~c = ~PcQ/R In the absence of the pulses P(~N), P(~), and P(~s) applied to the two "O~" gates 78 and 80, the forward shift pulses PF are equal in pulse repeti-tion frequency to the backward shift pulses PB.
Each time any one o-f the phase control pulses P(~) or ~P(~) and -P(~), the slip -frequency control pulses P(~s) or +P(ws) and ~P(~s) and the rotating -frequency adding N (~N) and -P(~N) is applied to the 1~1C\3~5~ , associated "OR" gate 78 or 80, a relative phase difference is caused between the corresponding forward and backward shift pulses PF and PB respectively and determines a ratio of a conduction time or oE a pulse width between each solid state switch and the adjacent one while the mean value thereof determines the effective fed phase angle or an angle of rotation oE vector. The term "angle of rotation of a vector" means an angle of rotation of an magnetic axis caused in a gap in an induction motor involved by a current or voltage supplied to the motor in the particular power supply state. Thus the fed phase angle means that angle of rotation o~ the vector.
Further the pulses P(t~, P(t~s) and P(~N) applied to the "OR" gates 78 and 80 have an algebraically time-integrated value that determines an added angle of rotation of the vector integrated with respect to time while the algebraic sum of their frequencies determines a frequency difference (~PF - t~PB) between the frequency t~p~ of the forward shifted pulse PF and that t~pB f the backward shift pulse PB and, in turn, the supplied freauency t~.
That is, ( PF ~PB)/m ~ [~S(P) + ~N(P)]/m.R

holds. Further the phase control pulses P(~ ave an added number of pulses Np(~) that determineis a shif-ted value ~ a fed phase angle ~T or shifted value of a phase angle. That is, 3~iS
*

~ T= ~Np (~) ~ 2~Np(~)/m R
holds.
The details of the power supply control u-tilizing the forward and backward pulses as above described may be found in U.S. Patent Nos. 3,992l 657, issued Nov. 16, 1976 (Akamatsu) and

4,002,958, issued Jan. 11, 1977 ~Akamatsu).
In this way, the function of adding the command rotating frequency ~N to -the command slip frequency ~S and the function of controlling the command fed phase angle 3 T have been performed with the digital pulse trains.
The results of -the processes as above described are supplied to a frequency distributory 86 for determining an output frequency modulated with the carrier caused from the carrier pulse generator 82. The frequency distrihutor 86 forms the other part of the AC waveform generator 32 and includes a plurality of "AND" elements 88 one for each output of the ring counter 72.
Each "AND" element 88 has one input applied with the chopping signal S(CH) from the absolute value comparator 60, the other input connected to a corresponding one of the outputs 1, 2, ......
m of the ring counter 72, and an output connected to one input of an associated "OR" element 90. Each "OR" element 90 has the other input connected to that output of the ring counter 72 adjacent to the output thereof in a direction that the ordinal numbers identifying the outputs of the ring counter 72 increase in value.
For example, the "OR" elemen-t connected to the 11(33'~5Si output 1 of tlle ring counter 72 tllrough the matillg "~ND"
element 88, has the other input connected to the output 2 of the ri.ng counter 72. I`he "AND" element 88 connected to the last output _ of the ring counter 72 is connected to the "OR"
element ~0 having the other input connected to the first output 1 of the ring counter 72.
Then each "O~" element 90 is connected at the output to that preamplifier 56 identified by the same ordinal number as that designating the output of the ring counter 72 connected to the mating "AND" element 88. As above described, the preamplifiers 72 are connected to the solid state switches 54 respectively so that the ordinal numbers identifying the preamplifi.ers 56 is e~ual to those identl fying the solid state switches 54 respectively.
The outputs of the distributor 86 or the "OR"
elements 90 deliver output signals -from the outputs 1,2, m of the ring counter 72 to the preampli-fiers 56 in a predetermined order. The output signals from the preamplifiers 56 circulate along the out~uts of the preamplifiers 56 at the supplied Erequency ~ on the average whi.le their frequency rises and falls from the pulse phase moduration carrier freqUency ~c When the chopping signal S(cll) is an ''ONI' signal, the two or three solid state switches 54 is conducted in a predetermined order to permit the source 50 to supply an electric power to the induction Tnotor 10 through the conducting switches 5~. When the chopping signal S(cl-l) is an "OFF" signal, one or two oE the conducting switches is or are turned o:Ef t^ suspend the power supply to the li~3~SS

induction motor 10. The chopping mode o:E opera-tion as above described is repeated to control the absolute value c~:E the fed current IM.
l From the foregoing it is seen that the control ¦ Gf the three AC parameters or the absolute value of the current I~,l, the supplied phase angle ~ and the slip frequency ~S (and the output frequency ~) is accomplished by the embodiment of the present inventi.on as shown in Fig. 7 including both the simplest digital electronic circuitry and the simple main circui.t.
Fig. 9 also illustrates positional control means as shown at dotted line ln Fig. 2 at dotted line extending lrom the speed sensor 12 serving as the positional sensor , 34 to a dotted circle located between the con~mand slip lS frequency generator 18 and the pulse generator 84.
In this case the sensor 34 produces the pulse repetion frequency ~N of the frequency adding pulses.
Fig. lOa shows another modifica~ion of the present invention wherein a three-phase induction motor is controlled in the current control mode of operation. A
three-phase AC generator 92 supplies a current controlled power to the three-phase induction motor 10 through current c.ontrolled power supply device 12' that may be an inverter or a cyclo-converter. In the example ill.ustrated the power supply device 12' forms a cyclo-converter for supplying a three-phase current to the motor 10. The power supply device 12' comprises three-rectifier circuits 94_~ 94_ and 94w one for each phase. The rectifier circuit 94_ is shown in 11~3~:~S

~ig. lOa as including a first set of tilree series combina-¦ tions of two similarly poled semiconductor rectifiers 94uP
¦ such as thyristors lnterconnec-ted in parallel circuit ¦ relationship and a second set of three similar series ¦ combinations of two similar rectifiers 94_N connected in ¦ anti-parallel circuit relationship with the first set of the three series combination. Then a rector 96_P connects ¦ cathode electrodes of the rectifiers 94uP to anode electrodes ¦ of the recti-fies 94uN on the uppers side as viewed in Fig.
¦ lOa and a rector 96uN connects ca~hode electrodes of the ¦ rectifiers 94uP to anode electrodes of the rectifiers 94uP
¦ on the lower side. The junctions of -the serially connected ¦ rectifiers 94uP or 94uN in each set are connected to the ¦ similar junctions in the other set and also AC outputs of the lS ¦ three-phase generator 92.
¦ Each of the remaining rectifier circuits 94v and 94_ is identical to the rectifier circuit 94_ and schematically shown by two pairs of two serially connected rectifiers connected in anti-parallel circuit 2U relationship with each other through two reaction 96vP and 96uN or 96wP and 96wN.
_ _ _ The rectifier curcuits 94u, 94_ and 94w include individual pairs of DC outputs connected across three primary windings u, v and w of the open-delta connection of the induction motor 10 respectively. Three current sensors 9~_~ 98v and 9~w such as current transformers are coupled to leads connecting the primary windings _, v and _ to the rectifier circuits 94_, 94v and 94w respectively and also li(~3~SS

connected to one input o:f three recti.fier -fi.ring phase controls 100_, 100_ and lOOw respec~i.vely to apply the sensed currents iu~ iv and iw with nega-tive polari.ty to the latter respectively. Then the firing phase controls 100_, 100_ and 100 are connected to the rectifier circuits ~4u, 94v and 9~w respectively as shown at the arrows whereby à closed loop control circuit is prepared Eor the induction motor 10.
As shown on the lower portion of Fig. I.Oag the induction motor 10 includes voltage sensors 102_, 102_ and 102w which are, in turn, connected to respective filters symbollically shown by block ln4u-v-w. Those voltage sensors may be search coils buried in the induction motor 10.
The filters 104u-v-w supply the sensed, filtered voltages Vu, Vv and Vw to second inputs of the firing phase controls 100u, 100v and 100w with the positive polarity respectively :Eor comparison purposes. The positive feedback of the motor voltages Vu9 Vv and Vw is very e-ffective for reducing or substantially elimi.nating deviations o:E the absolute motor voltage values and phases angle thereof Erom the command values thereof.
In order to provide command waveforms with which instantaneous waveforms o-f the sensed phase currents are compared, ~he firing phase controls 100_, 100_ and lOOw are connected at the third inputs to a command waveform generator 32. That genera-tor 32 :Eorms the center of the three AC
parameter control ci-rcuit 26 as above described and, in this case, utilizes the conduction control signal distributor 70 as shown in Fig. 9.
If desired, the command waveform generator 32 may employ any of various analog and digital means and also may utilize any of various digital-to-analog converters.
In Fig. 10a, the conduction control signal distributor ^;2 receives the command phase angle ~l~ the command slip frequency ~S or ~S(P) and the command rotating frequency ~N
or ~N(P) ~see also Fig. 9) and selectively provides at its outputs 1,2,..... , m (where is any e-ven integer and in this case m has a value of six) ON-OFF signals pulse-width rnodulated with the forward and back shift pulses PF and PB
~espectively as above described in conjunction with Fig. 9.
In the example illustrated, the ON-OFF signals have pulse widths e~ual to phase differences between the pulses PF and ~B-Then the ON-OFF signals thus produced are applied to a plurality of multipliers lQ6 one for each of the m outputs of the signal distributer 70. The command supplied current IM is applied to the multipliers 106 and switching-modulated with the ON-OFF signals to provide an AC half-wave pattern at Olltputs o~ the multipliers 106. The switching-modulation is one sort of the multiplication.
Fig. lOb shows an analog switchsuitable for use as the multiplier 106. As shown, the multiplier 106 includes a common emitter NPN type transistor Tr having a base connected to a corresponding output, in this case, the output 1 of the signal distributor 70 through a base :: .

3'i'~S

resistor r~ and a collec-tor connectecl -to a collec~or resistor _~. A vol.tage V corresponding to the supplied current I~1 is applied be~ween the coll.ector resistor -c and the emitter of the transistor Tr while an output is deli.vered from the collector -thereo:E.
The outputs o-f the _ multipliers 106 where m = 6 are connected to m/2 analog adders 108 so that every two outpu-ts thereof are connected to a positive and a negative input of each adder 108 assuming tllat the l.ast output is adjacent to the -first output. Thus each adders 108 composes ~he two associated outputs from the multipliers 108 into a command AC waveform iuS' ivS or iwS :Eor each phase which is subsequently supplied to the associa-ted Eiring phase controls 100_, lOOv and 100_. In each phase control 100_, lS 100_ or lOOw, the command AC waveform iUS7 iVS or iwS is compared ~ith the sensed phase current iu' iv or iw respec-tively, and a difference current therebetween is applied to the associated rectifier circuit 94_, 94_ or 94_ to control the firing phase of the rectifiers disposed therein.
Ripple components developed in the pulse width modulation as above described decay or may decay by both the adders 108u, 108v and 108w and the firing phase controls lOOu, 100_ and 100_ also acting as current limi-ters.
From the foregoing it is seen that tlle control : 25 of the supplied phase angle ~ and the composition of the slip -frequency ~S and the rotating :Erequency wN can be accomplished in the similar manner as above described in conjunction wi-th Fig. 9 and that the absolute current value 3'i'5~ ~

can be con-trolled with the command supplied current IM applied to the multipliers 10~.
The reactors 9~uP through 96wP and 96uN through 9l)wN disposed in the power supply circuit 12 can supress ripple components due to the rec~ification and current components circulating through the rectifier circuits without the occurrence of AC voltage drops across impedances involved.
Although the waveform generator 32 may generate a sinusoidal wave, a sinusoidal wave appro~ima~ed by broken lines or a trapezoid wave, the same employing the signal distributor 70 including the reversible ring counter 72 ~see Fig. 9) generates a trapezoid waveform. This cooperates with the reactors included in the rectifier circuits to permit three phase currents in the form of trapezoids to be supplied to the induction motor 10. Further, if the inductance of coupling reactors is selected to a low magnitude, t;nen the induction motor may ~e applied with a three-phase curren-t with sinusoidal waveform in place of the trapezoiclal waveform.
In still another modification oE the l)resent invention illustrated in Fig. ll wherein like reference numerals designate ~he components identical or similar to those shown in Fig. 2 or 7 and Figs. 9 and lO, the power supply circuit 12' is identical to that shown in Fig. 9 and acts as a pulse width modulation inverter to supply a ~oltage waveform controlled power to three-phase induction motor 10 as will be described hereinafter.

1~(};1 75 j Voltage sensor means 102 are operatively coupled to the induction motor 10. The voltage sensor rnay be a voltage transformer or a search coil buried in the motor 10.
rhree phase motor voltages are sensed hy the voltaKe sensor means 102 and after having been filtered or smoothed by filter means 10~, applied to voltage controls 100. The absolute value comparator 60 as shown i.n Fig. 9 may be substituted for the voltage control 100. The filter 104 may be an integrator or a simple delay circuit with the first order or any o.E delay circuits ~ith higher orders.
If desired, the voltage control 100 may be replaced by a voltage parity-converted-to-magnetic flux control that controls a voltage wave:Eorm having a voltage value proportional to a freauency by controlling a voltage integrated with respect to time. In the latter case, the filter means 10~ are required only to act as an integrator.
The three AC parameter control circuit 26 in this case may compri.se a reference vo:Ltage or a reference :Elux waveform generator because of the voltage or interlinkage flux wave:Eorm control type.
The three AC parameter control circuit 26 comprises proportional coeEficient elements 110 and 112 having applied thereto a command torque ~ formed in the same manner ..
as above described in conjunction with Fig. 2 to -form constants concernings Q and rl respec-tively. A multiplier 11~ is suppl.ied with an output ~Q (see the expression (].6)) from the proportional coef:Eicient element 110. Also the 11~3'7~

command frequency ~ as above described is applied to the multiplier 114 to cause the latter to deliver a voltage ITX appearing in the expression ~12J which voltage is applied to an adder 116. Then the gap flux ~ as above described in conjunction with Fig. 2 is applied to a proportional coefficient (r/m) element 118 connected to the adder 116. In the adder 116, the output from the multiplier 114 is added to an output with the genative polarity from the proportional coefficient ~r/M) element 118 to produce the command active voltage VT defined by the expression (12).
In order to produce the -first phase voltage component VE as defined by the expression (11), the proportional coefficien-t element (r/M) 112 is connected to another adder 120 that is connected to another multiplier 122 having applied thereto both the ga~ flux ~ and the command frequency ~`. As a result, the adder 122 provides the voltage component VE (see the expression ~11)).
From the foregoing it is seen that the components 110 through 122 :~orm function generators to generate two AC components in quadrature relationship having respective amP1itUdeS VT and VE in the voltage control mode or ~ and ~PE in the interlin~age flux mode of opera-tion. ~`hat is, the two AC components thus generated are expressed by the d and q coordinate system.
Since the multipliers 114 and 122 effect the multiplication by the frequency ~ in the voltage waveform control mode o-f operation, they may be omitted in the flux waveform control mode of operation performed a-fter the 1103~5S

conversion to magnetic flux, that is to say, when the components 102 and 104 function as an integrator and a gap -flux sensor respectively.
The three AC parameter control circuit 26 further comprises a reference waveform generator 106 that may be identical to the generator lOh shown in Fig. lOa. In Fig.
11, however, the waveform generator 106 has a circuit configuration as best shown in Fig. 12. As shown, the wave~orm generator 106 comprises an analog-to--frequency converter 124 applied with a command frequency ~ formed through the addition of analog signals ~S and ~N as above described in conjunction with Fig. 7. The converter 124 delivers phase shifted pulses P~) having a pulse repetition frequency proportional to the command -frequency ~ to a reversib~e ring counter 72. That counter 7Z is similar to the counter 72 as shown in ~ig. 9 but has the number of counter stages equal to twice that oE the latter.
In other words, the counter 72 is shown in Fig. 12 as including six output terminals la, 2a, 3a, 4a, 5a and 6a alternating six output terminals 6b, 1_, 2b, 3b, 4b and 5b.
Outputs at the output terminals la through 6a are put in quadrature rela~ionship with those at the output terminals lb through 6b respectively.
Then the outpu~ terminals la through 6a oE the ring counter 7Z are connected to a plurality of multipliers 124a one for each output terminal while the remaining output terminals lb through 6b thereof are similarly connected to multipliers 124b. The AC component VT or ~T as above described is supplied to all the multipliers :106a and the other AC component VE or ~E is supplied to all the multipliers 106b.
Then the six multipliers 106a are connected -to three adders 108a (only one o-f which is shown) in the same m~nner as above described in conjunction with Fig. lOa and the six multipliers 106b are similarly connected to three adders 126c (only one of which is shown). Those adders 108b and 108c coupled to each pair of the counters outputs labelled the identical reference numerals with the su:E:Eixes a and b are connected at the outputs to an output adder 108 for each phase, :Eor example, the adders 108_ and 108c cou~led to the counter's output la and lb are connected to the output adder 108.
lS Each set of the counter portion including the output terminals la,..... , 6a or lb,..... , 6b and the associated components 108a and llOa or 108b and llOb is operated in the s~me manner as above described in conjunction with the waveform generator 106 shown in ~ig. lOa to generate a waveform put in quadrature relationship with another wave:Eorm generated by the other set thereof.
The waveform developed from the adders 108a represents a command second phase voltage component having an amplitude as determined by the i.nput V~ applied to the multipl.iers 106a and the waveform from the adders 108b represents a command first phase voltage component having an amplitude as determined by the input ~E applied to the mu].tipliers 106b. Both waveforms are added to each other ~ 3~

¦ by the adcler 108 for each phase resulting in a command resultant voltage or a command voltage-converted-to-flux ¦ waveform Vus, Vvs or Vws. Those resultant voltages or flux ¦ ~aveforms are supplied to the associated voltage controls ¦ }00 to be compared with the sensed motor voltages respectively.
The voltage or firing phase controls 100 supply differences between the command and sensed voltages to the associated pairs of solid state switches to control their l firing angles thereby to supply a three-phase voltage control-¦ led power to the induction motor 10.
From the foregoing it wilL be appreciated that ¦ the arrangement as shown in Figs. 11 and 12 per~orm the ¦ voltage controlled power supply as above described in conjunc-¦ tion with Fig. 7.
¦ As above described, the converted Elux control I system includes the three AC parameter control circuit 26 ¦ having no multipliers 11~ and 122 shown in Fig. 11. If the ¦ magnetic fluxes ~ and ~ are replaced by the currents I~
I and IE res-pectively, then the AC parameter control circuit 2n I 26 without the multipliers 11~ and 122 may be suitable for ¦ use with current controlled power supply systems.
¦ The function generators 28 and 30 and the ¦ polyphase AC ~avegenerator 32 as shown in Fi~s. 2 and 9 I and coupled to Fig. lOa may have circuit con~igurations ¦ illustrated in Figs. 13, 14 and 15 respectively.
In Fig. 13 the first function generator 2~
¦ includes two oscillators 130a and 130b for generating I ~wo-phase high frequency signals ~1 and ~2 respectively and li~37S5 multipliers or modulators 132a and 132b connected to the ¦ oscillators 130a and 130b respective:Ly. The multiplier ¦ 132a receives the first phase current component IE and the l multiplier 132b receives the second phase current component ¦ I . Both multipliers 132a and 132b are connected at the out-I puts to an adder 134 subsequently connected to a rectifier or I ¦ s~uare law detector 136. An output from the rectifier 136 is filtered or smoothed by a filter 138 to provide a l command absolute current value IM in the analog form satisfy-I ing the expression (1).
In Fig. 14 an adder 140 receives both a command second phase current component IT and an output with a negative polarity from a multiplier 142 applied with a ¦ command first phase current component I~. The adder 140 ¦ has its output connected to an operational amplifier 144 the output of ~hich is connected to the multiplier 142. The ¦ components 140, 142 and 144 form a divider that ~roduces ¦ I /IE at the output. The output of the operational amplifier I 144 is also connected to a nonlinear function generator 146 ¦ ~or generating an inverse tangent o-f IT/I~ with the first ¦ phase current component IE remaining unchanged. The function ¦ generator 146 produces an output forming an analog signal ¦ for a command supplied phase angle ~ .
I The analog signal from the -function generator ¦ 146 is applied to a positive input of an adder 14g including ¦ an output connected to a coincidence comparator 150. The ¦ comparator 150 includes two outputs +~ and -e connected to one input of two "AND" gates 152 including the other inputs 3'75~i ¦ applied with a train of clock pulses cl. Tlla-t AND gate ¦ 152 connected to the output +~ of the comparator 15n includes ¦ an owtput connected to a count-up input CU of a reversible ¦ counter 15~ and the other "AND" gate 152 includes an output S ¦ connected to a count-down input CD of tile reversible ¦ counter 154. Then ~he counter 154 is connected to a ¦ digital-to-analog concerter 156 subsequently connected ¦ to a negative input of the adder 148.
¦ The components 148, 150, 152, 154 and 156 form ¦ an analog-to-pulse number converter. The coincidence ¦ comparator 150 is operative to cause the reversible counter 1 154 to count pulses applied thereto by apporting the ¦ clock pulses cl between the inputs CU and CD of the rebersible ¦ counter 154 a-fter having selectively passed through the two ¦ AND gates 152, so as to equal analog output from the I converter 156 to the analog output al from the function ¦ generator 146. ~\s a result, phase shifted pulses ~P~) and ¦ -P~) appear at the outputs of the u~per and lower "A~D"
I gates 152 as viewed in Fig. }4 and have the abgebraic sum ¦ proportional to the command phase angle ~T.
¦ Where the field weaking control or a variation in the first phase current IE i9 enabled, the function generator 30 of Fig. 14 effects the calculation of the I expression ~2) while transforming the command phase angle ¦ ~ to a phase shifted pulses P~
¦ The AC waveform generator or function generator ¦ 32 shown in Fig. 15 can calculate the expression ~3) to ¦ generate a command slip -Frequency ~S In Fig. 15, an adder I

1 ~3~t137~;

160 has a positive input receiving a command second p}lase current component Ir and an OlltpUt connected to an opera-tional ampli-fier 162 that is connected at the output to a multiplier 164 receiving a commancl first phase current component IE. The multiplier 164 applies an OlltpUt to a negative input of the adder 160 and cooperates with the ~dder 160 and the operational amplifier 162 to form a divider. Thus the quotient of the second phase current component I~ divided by the first phase current component lE appears at the output of the operational amplifier 162.
That quotient IC/IE is also supplied to a proportional coefficient (r2/I.l) element 164 to provide an analog slip Erequency ~S at the output of the latter. The analog slip frequency ~S is applied to analog-to-pulse number converter 120 to form a pulse signal P(ws) having a pulse repectition frequency proportional to the slip ~requency ~S
While the present invention has been illustrated and described in conjunction with a few preferred embodiments thereof it is to be understood that numerous changes and modifications may be resorted -to without departing from .he 5pi~ it a scope of the present invention.

'`;
~:

Claims (11)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. An induction motor control system comprising variable frequency power supply means for supplying AC power to a primary winding of an induction motor including a short-circuited secondary conductor, slip frequency control means arranged to control a frequency of said AC power and the slip frequency of said induction motor, a command slip frequency generation means for generating and arranged to generate a command value of said slip frequency in response to a command torque and controlling said slip frequency control means in accordance with said command value, and AC parameter control means arranged to command and control the absolute value and phase angle of said AC power in predetermined relationship with said slip frequency with said phase angle controlled independently of a gap flux on said induction motor.

2. An induction motor control system as claimed in claim 1, wherein said power supply means supplies a first AC
component having a first phase and a second AC component having a second phase to said induction motor, and said AC parameter control means controls said second AC component in predetermined relationship with said command slip frequency.

3. An induction motor control system as claimed in claim 2, wherein said second phase of said second AC component leads ahead or lags behind said first phase of said first AC
component by an electrical angle of .pi./2 radians.

4. An induction motor control system as claimed in claim 3, wherein there are a first phase component IE and a second phase component IT and said second phase component IT has a linear functional relationship with said command slip frequency.

5. An induction motor control system as claimed in claim 3, wherein there are a first phase component VE and a second phase component VI and said second phase component VT has a linear functional relationship with said command slip frequency.

6. An induction motor control system as claimed in claim 5, wherein said variable frequency power supply means is a voltage controlled power supply device and said first phase component VE includes a differentiated component VE for compensating for transients.

7. An induction motor control system as claimed in claim 4, wherein said AC parameter control means includes a first function generator for commanding the absolute value of a current supplied to said induction motor in predetermined relationship with said command slip frequency, and a second function generator for commanding a phase angle of the current in predetermined relationship with said command slip frequency generation means.

8. An induction motor control system as claimed in claim 7, wherein said first function generator generates the command absolute value of the current IM satisfying .

9. An induction motor control system as claimed in claim 7, wherein that said second function generator generates the command phase angle .theta.T satisfying .theta.T = tan-1IT/IE or .theta.T = tan-1VI/VE.

10. An induction motor control system as claimed in claim 5, wherein said AC parameter control means includes a first function generator for commanding the absolute value of a voltage supplied to said induction motor in predetermined relationship with said command slip frequency, and a second function generator for commanding a phase anyle of the voltage in predetermined relationship with said command slip frequency generation means.

11. An induction motor control system as claimed in claim 10, wherein said first function generator generates the command absolute value of the voltage VM satisfying .