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United States Patent [191 [11] [45] Ueda et al. - [54] [75] Oct. 15, 1991 OTHER PUBLICATIONS Inventors: Yoshihim Ue da_ Takaaki Yamada Lawrence A. Jones, Jeffery H. Lang “A State Observer ’ for the Permanent-Magnet Synchronous Motor” ' IECON 1987 Conference, Cambridge, MA, Nov. 2-6, [73] Assignee: Omron Corporation, Kyoto, Japan [21] APP]_ NO’: 544,427 1987 Yoshihiro Ueda, Takaaki Yamada “A State Observer . for the Permanent Magnet Synchronous‘Motor w1th [22] Flled‘ J'm' 27’ 1990 [30] Foreign Application Priority Data Jul. 14, 1989 [JP] Inductance Variations and its Characteristics” Proceed ings of the 33rd Ann. Conf. of the Inst. of Systems, Japan ................................ .. l-l80407 s ISCIE’ 1989‘ Primary Examiner—Paul Ip . """"""""""""" " Attorney, Agent, or Firm—Dickstein, Shapiro & Morin 318/561; 318/800; 318/803 [58] Date of Patent: AC MOTO R C0 NTR OL both of Tsukub’a Japan 5,057,759 Patent Number: I [57] Field of Search .............................. .. 331188//576709—_6g66 [56] ABSTRACT In a discrete_time a1 ternatingcurren t motor control apparatus having a state estimation observer estimating , References Cited a rotor angle and a rotor angular velocity based on a Us PATENT DOCUMENTS direct ‘quadrature transformation model of the motor, the gam of the observer is changed over dependmg on an estimated angular velocity. As a result, the apparatus gtischke et a1‘ """"""" " 3 4Issoi51s 7/1987 Kur§k;£;';{;ii"j.... I: 318/561 4,695,780 . . . .. 318/561 9/1987 Kurakake et al. . . . . . slicker CI 31. ----...-.. is applicable in a wide range of the mom’ Speed ‘Furthermore, the phase difference between the winding voltages and the winding currents Suppligd to the State .- - - 11;"; gnso}? """" 4’825’773 5/1989 M2138}: t: Z: :1‘ ' ' 313/11); """ 8/187 X estimation observer is compensated depending on the estimated angular velocity, thereby improving the con ....... .. 318/616 "01 accuracy 4,s51,754 7/1989 4,943,759 7/1990 Sakamoto et al Sakamoto ct al. . 4,958,114 9/1990 Ogawa I4 . 318/565 X .. ... . . . .. .. . . . . . . . .. 318/616 . / 4 Claims, 8 Drawing Sheets I3 'MH I9 /v / 20 / a'kq 4* SPEED/ POSITION CONTROLLER CURRENT CONTROLLER Vb'kq ?' --> PWM CIRCUIT “INVERTER Vc 'n+1 w\!> -’ S/ H iq,1+1 A wk,‘ ' an 61 1 V . V Vd'k ‘ Vq'k '5 I6 STATE ESTIMATION I If 22 OBSERVER l8 . . '0 ‘b ' T_.,_J V / 17 '“1 iii k Gun g % LPF OBSERVER GAIN ?le 'b-I‘ S/H SWITCH UNIT \. , DISCRETE-TIME AC MOTOR CONTROL ‘APPARATUS ‘IO US. Patent 52.5..:08350 Oct.15, 1991 ' Sheet3 0‘f8 - 5,057,759 l ‘n ' ANGULAR (“"1 VELOCITY & US. Patent Oct. 15, 1991 ' Fig.6 Sheet 6 qr s - 5,057,759 US. Patent Oct. 15,1991 ' V Sheet 7 o_f8 - 5,057,759 I| S STATE 24 / ESTIMATION OBSERVER . DELAY ‘M CIRCUIT it)’k US. Patent Oct. 15, 1991 " Sheet8 0_f8 I 5,057,759 _mO Zmw .HZMEDU mOzm mBgzH @31 2> v. I 1 ! xmeg.m 6zoE<.Ham m.!i mo. 2. I 1 5,057,759 2 angular velocity thus estimated include estimation er DISCRETE-TIME AC MOTOR CONTROL APPARATUS rors. SUMMARY OF THE INVENTION BACKGROUND OF THE INVENTION 5 It is therefore an object of the present invention to provide a discrete-time alternating-current motor con 1. Field of the Invention trol apparatus capable of controlling the motor in a The present invention relates to a control apparatus wide range of the motor speed. of an alternating-current (AC) motor operating in a Another object of the present invention is to provide discrete-time fashion. a control apparatus of a permanent-magnet altemating 2. Description of the Related Art current motor, said control apparatus unnecessitating When achieving a positioning control in a control apparatus of a permanent-magnet (PM) alternating-cur sensors to measure information items of the angle, the rent motor, an angle of a rotor of the motor is required to be sensed for a feedback of information of the rotor angular velocity, and the magnetic pole. angle. For this purpose, the conventional technology carry out an estimation with a high precision or accu has employed a sensor such as an encoder or a resolver. racy even when phase differences exist in association Still another object of the present invention is to Furthermore, in the alternating-current motor, it is with the inputs of the winding voltages and winding necessary to change a phase of a current flowing currents. through each winding of the motor depending on the In accordance with the present invention, there is rotation angle of the rotor. In order to sense the mag 20 provided a discrete-time alternating-current motor con netic pole positions of the rotor, the conventional sys trol apparatus including a state estimation observer tem employs a sensor such as a pole sensor. which receives as inputs thereto voltages and currents However, these sensors above cannot be used in gen of windings of the alternating-current motor to estimate eral at a high temperature and is moreover not satisfac a rotor speed and an angular velocity of the alternating torily resistive against vibration and shock. In conse 25 current motor based on a model of the motor. The quence, the conventional motor control apparatus using observer is characterized by further comprising ob such sensors has been attended with a problem that the server gain switch means for setting an optimal gain in desired control operation cannot be achieved in such an the state estimation observer according to the estimated environment. angular velocity. On the other hand, a state estimation observer has 30 been proposed by Lawrence A. Jones et al. in “A STATE OBSERVER FOR THE PERMANENT MAGNET SYNCHRONOUS MOTOR”, IECON 1987 Conference, Cambridge, Mass., Nov. 2-6, 1987. In this observer, a direct quadrature (dq) transformation model of a permanent-magnet alternating-current motor and a linear observer theory are applied to esti mate a rotor angle and an angular velocity thereof from winding current and voltage values of the altemating In accordance with the present invention, since the estimation state observer means is assigned with an optimal gain in association with a rotation angular ve locity of the motor by means of the observer gain switch means, a predetermined control performance can be continuously accomplished in a broad velocity range. Preferably, the observer gain switch means employs a hysteresis with respect to the estimated angular velocity current motor. Furthermore, advantages associated 40 for a gain switch. As a result, the unstable operation is prevented from being developed in the gain switch with the direct quadrature transformation model has operation. been described in the article. The alternating-current (AC) control apparatus in However, in an actual case where a control apparatus accordance with the present invention further com is con?gured with a state estimation observer to control an alternating-current motor, if the state estimation 45 prises origin angle sense means for sensing an origin position of a rotor of the AC motor and a controller for observer has a ?xed gain, there have been problems that controlling the motor based on the estimation result an estimation value produced by the observer becomes attained from the state estimation observer means and unstable when a speed of the motor is changed in a wide the origin position sensed by the origin angle sense range and that the response time to obtain the observer estimation value becomes to be longer. Namely, the 50 means. alternating-current motor cannot be controlled in a stable state at a high speed. For example, in a case where the observer gain of such a motor control system is set to a value suitable for a speed substantially equal to With the provision of the above constitution, when controlling a permanent-magnet alternating-current motor, there are unnecessitated an angle sensor such as and encoder or a resolver, an angular velocity sensor 1,500 rotations per minutes (rpm), if the control appara 55 such as a tachometer generator or a frequency-to-volt age (F/V) converter, and a rotor pole sensing device tus attempts to control an alternating-current motor rotating at 500 rpm, the state estimation observer cannot obtain a converged estimation value. such as a pole sensor. Furthermore, signal lines to feed back signals from the various sensors to the respective Furthermore, the rotation angle estimated by the signal processing components associated therewith Can state estimation observer is an electric angle, which 60 be dispensed with. Since these sensors are removed, the motor above can be employed under various environ leads to a problem that assuming the number of rotor mental conditions such as the high temperature, the poles to be N (22), a unique mechanical angle cannot be determined. vibration, the shock in a wider variations as compared with the conventional case. Owing to the elimination of In addition, the state estimation observer receives as inputs thereto winding voltages and currents of the 65 the signal lines for the sensors, there can be attained advantages that the resistivity against noises and the alternating-current motor, which results in a problem that when a phase difference is found in association with operation reliability are improved in the control appara the currents and the voltages, a rotation angle and an tus and that the cost thereof is lowered. In accordance 3 5,057,759 with the present invention, there is implemented a con trol apparatus of a permanent-magnet alternating-cur rent motor, said control apparatus unnecessitating the sensors of the angle, the angular velocity, and the mag netic pole positions. ‘4 origin sense switch 22. Some components above, for example, the observer 11, the gain switch unit 12, and the controllers 13 and 14 are implemented by use of a computer loaded with an appropriate program. Of the parameters (physical quantities) used in the Moreover, in accordance with the present invention, there is provided a discrete-time alternating-current cated by codes marked with" thereover, estimated val motor control apparatus including a state estimation ues are designated by codes with ~ thereover, and vec observer which receives as inputs thereto winding volt tors are denoted by underlined codes. ages applied to the motor and currents of the motor windings measured by current sensors to estimate a rotor speed and an angular velocity of the alternating current motor based on a model of the motor. The system is characterized by further comprising means for compensating phase differences associated with the voltages and currents of the windings depending on the estimated angular velocity. In the constitution according to the present inven tion, the state estimation observer means can estimate motor control apparatus 10, measured values are indi As will be shown later, parameters (for example, currents id and i[,) of the motor 30 are transformed in accordance with an orthogonal coordinate system of a two-phase stator. Transformed parameters are repre sented by use of subscripts a and B as ia and i;;, for example. Furthermore, for an estimation processing, the parameters are subjected to a direct quadrature (dq) transformation based on an estimated rotator angle 0 (a transformation into a biaxial orthogonal coordinate system rotating in synchronism with the rotor). The with a higher precision the values of the rotor speed, the 20 parameters after the direct quadrature transformation angular velocity, and the winding currents of the alter are expressed, for example, as id and Iq with subscripts d nating-current motor. and q. First, a brief description will be given of an alternat BRIEF DESCRIPTION OF THE DRAWINGS ing-current motor model adopted in the state estimation These and other objects and advantages of the pres 25 observer. As described in the article above, based on a ent invention will become apparent by reference to the voltage 2 applied to a winding and a sensed windving following description and accompanying drawings current'i, the observer estimates a winding current i, a wherein: rotor angular velocity (2», and a rotor angle 3 from ex FIGS. 1 to 3 are diagrams for explaining an embodi pressions (1) to (3) as follows. ment according to the present invention; 30 FIG. 1 is a functional block diagram showing a con ceptual structure of a discrete-time alternating-current motor control apparatus; FIG. 2 is a schematic diagram showing a switch table adopted to switch a gain of an observer; 35 FIG. 3 is a graph showing a hysteresis of the gain of (1) the observer; FIGS. 4 to 6 are diagrams for explaining an alterna tive embodiment according to the present invention; FIG. 4 is a functional block diagram showing a con ceptual structure of a discrete-time alternating-current motor control apparatus; FIG. 5 is a graph illustratively showing relationships of phase differences between winding currents and volt 45 ages in the motor; FIG. 6 is a diagram schematically showing a table containing phase correction angles; and FIGS. 7 and 8 are block diagrams showing further alternative examples of phase compensate means to 45/71: ‘= (3 (3) Where: L: Winding inductance, R: Winding resistance, K: Torque constant, B: Viscosity friction C: Coulomb friction, H: Inertia, 1': Torque, N: Number of pole pairs compensate phase differences of the winding currents and voltages. DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows an embodiment of the altemating-cur 55 rent motor control apparatus of the discrete-time type in accordance with the present invention. The con?guration includes a permanent-magnet al ternating-current motor 30 as a control object, which is a three-phase motor associated with phases a, b, and c. v V 6 l v I ll i = (I... 1B)’ 1 = (Va, "[91 Currents and voltages of the respective phases are rep resented as ia, i[,, and ic and V“, VI, and vs, respectively. A discrete-time AC motor control apparatus 10 in cludes a state estimation observer 11, an observer gain switch unit 12, a current controller 13, a speed/position 65 controller 14, current sensors 15 and 16, a low-pass ?lter 17, sample-and-hold circuit 18 and 19, a pulse width modulation (PWM) circuit 20, an inverter 21, and an 811812 62x2 _ [821822] The coulomb friction, the viscosity friction, and the inertia vary depending on the magnitude of load im 5 5,057,759 ék+1 and 6k+1 are delivered to the current controller 13 and the upper-level controller (speed/position con In the expressions above, i=(ia, i3)T is obtained by transforming a sensed winding current (i1, i[,) in accor dance with a coordinate system of a two-phase stator. Assuming the transformation to be T (0), the result can be expressed as follows. i: (in, iB)T= 7(5) (Ia 179T 6 The estimated values i¢k+1 and iq,k+1 are fed to the current controller 13. Moreover, the estimated values posed on the motor. In addition, the inertia expressed above is associated with the mechanical system includ ing the motor and the load. troller) 14. The current controller 13 can decide, based on the estimated value 01<+1, phases to be assigned to the wind ing voltages to supply a current in association with magnetic pole positions of the rotor. In consequence, 10 the magnetic pole sensor ca be dispensed with. Moreover, the current controller 13 compares the The description above also applies to the expression current instruction values idyk+l and iq,k+1 fed from the ppper-level controller 14 with the values id,k+1 and X=( Va’ VB)T~ In a discretized form, the expressions (1) to (3) are iq,k+1 estimated by the state estimation observer 11 to compute based on a predetermined control algorithm respectively represented by expressions (4) to (7) as follows. the direct-quadrature transformation values ing/(+1 and {IL/(+1 of the voltage applied to the motor windings, for example, to minimize the deviations associated there with. In addition, the current controller 13 computes, in accordance with the value 9k+1 described above volt ages va,k+1, vb,k+1 and vc,k+1 to be applied to the motor windings. The resultant voltage values are passed via the sample-and-hold circuit 19 to the pulse-width modu lation (PWM) circuit 20, which in turn transforms the 25 received values into pulse widths. The obtained signals are delivered via the inverter (switch circuit) 21 to the motor windings. In a case where the upper-level controller of the 30 current controller 13 is the speed/position controller 14 as shown in FIG. 1, since the values (Ii/(+1 and ¢I>k+1 estimated by the state estimation observer 11 are fed to the speed/position controller 14, the angle and angular velocity sensors become to be unnecessary for the con Where: 35 trol of the speed and positions. In this connection, since the rotor angle forecasted by the state estimation observer 11 is an electric angle, the At: Sampling time obtained value 9k+1 cannot be directly adopted to achieve the position control. However, a rotor angle necessary for the current control is an electric angle; furthermore, the convergence in the operation of the The Subscript k denotes that the associated value is state estimation observer 11 can be accomplished at a attained at a sampling time (point of time) k, whereas high speed, which is satisfactory with respect to a time the subscript k+ 1 indicates that the value is obtained at constant of the motor. In consequence, at an initiation of a point of time when a sampling period of time At is 45 the motor operation, the motor can be started by use of elapsed after the point of time k. the current controller and hence the origin angular p The motor winding currents in and i1, respectively position can be sensed by the origin sense switch 22. attained from the current sensors 15 and 16 are sent via The origin sense signal is fed from the origin sense the low-pass ?lter 17, which removes noises from the switch 22 to the current controller 13 and the speed/po received Signals, to the sample-and-hold circuit 18. The sition contrpller 14. Based on the origin sense signal and circuit 18 achieves a sample-and-hold operation at a the value 0k+| forecasted by the state estimation ob sampling time k on these signals to be supplied respec server 11, the mechanical angle is computed. As de tively as imk and ib,k to the state estimation observer 11. scribed above, through the calibration above at the start The observer 11 then conducts a direct quadrature point of the motor operation, the position control can be transformation on the received current values imk and accomplished without using an angle sensor. ilnk based on the rotor angle 0k estimated at the time Subsequently, a description will be given of the ob 14-1 to generate current values Lu and lq'k. The state estimation observer 11 is also supplied with voltage values V“ and vqJc obtained by the current controller 13 through the direct quadrature transformation con ducted on the voltages applied to the windings,“ which will be described later. Based on the values 6k, idyk, iq,k and 0k estimated at the time k-l and the transformed values Vd'k, v“, i4_;; and ilyk, the state estimation ob server 11 estimates values id,k+1, i1,k+1, é:k+1, and server gain switch unit 12. The state estimation ob server 11 develops a nonlinear dynamics characteristic with respect to an angular velocity éik as represented with the expressions (1) to (3) or (4) to (7). The dynam ics characteristic alters depending on the observer gain values 62x2 and 61x2. Consequently, in a general motor control apparatus in which the control speed range is not limited, in order to 0k+1 at the tlme k+1 from the expressions (4) to (7). In 65 retain the control performance of the apparatus, the gain of the state estimation observer is required to be consequence, the rotor angle and the angular velocity switched according to the speed. For the observer gain, can be obtained without using the angle and angular velocity sensors. an optimal value can be in advance computed by use of 7 5,057,759 linearized error equation (expression (8) below) associ ated with the expressions (1) to (3). 8 circuit 20 and the inverter 21. Due to delays associated with these circuits, precisely, the values 0d,], and v91‘ are (8) A"?ee, N) Furthermore, éd stands _for a differentiated value of ad. This also applies to a, em, and eg. According to results from experiments, it has been con?rmed that the observer gain need not be switched different from the voltages applied to the motor wind ings at the point of time k. Namely, the values v,“ and a”, are applied to the motor windings at a point of time or changed over between the respective values for each 20 t; succeeding the point of time k as shown in FIG. 5. speed, namely, the switch operation of the observer On the other hand, the state estimation observer 11 is gain is t be conducted between predetermined appropri supplied with the currents ink and ibyk, which are motor ate speed ranges. 'In consequence, there is prepared a winding currents undergone the sampling at the point of table, as shown in FIG. 2, containing values of the ob time k. However, these currents are sent through the server gain associated with the angular velocity 60 be 25 current sensors 15 and 16 and the low-pass ?lter 17 to forehand computed from the expression (8). The table is loaded in a memory of the observer gain switch unit 12. the sample-and-hold circuit 18. Owing to the phase lags associated with these circuits, exactly, the currents iLk In this table, for the respective estimated angular veloc and ibyk are different from the motor winding currents of ity ranges wito mi+1(i=1~n), gain values gm, gm, g2“, the motor 30 at the point of time k. In actual operation, 822i, g'1 “and g'lzi are stored in association therewith. In 30 there are supplied the currents ?owing in the motor operation, a value (bk estimated by the state estimation windings at a point of time t1 following the point of time observer 11 at a point of time k is delivered to the ob k as shown in FIG. 5. I server gain switch unit 12, which acquires from the As above, the winding voltages in), and v” and the table an optimal gain associated with the value (bk to winding currents id'k and ihk are different from the re supply the obtained value as a gain (Gk+1)at a point of 35 spective actual values developed at the point of time k time"+1 to the state estimation observer 11. Based on and hence a phase difference AT exists between the the optimal gain given by the observer gain switch unit winding voltages and currents, which leads to the fol _12, the observer 11 computes the estimation values lowing problem. Since the state estimation observer 11 id,k+1iq,k+1, G>k+1 and §k+1 at the point of time k+1, thereby developing a predetermined control perfor treats the winding currents and voltages as ones sensed at the same point of time, due to the phase difference AT mance in the overall control speed range. therebetween, the estimated rotor angle, the angular velocity, and the winding currents include estimation At boundaries (m2, m3, etc.) of the speed for switching the observer gain, when the angular velocity rises and falls, the‘ observer gain is frequently changed over. This errors. In order to remove the problem above, a phase com causes the state estimation observer 11 to carry out an 45 pensating unit 23 is disposed in a discrete-time alternat unstable operation and hence exerts a disadvantageous in?uence on the motor control characteristic. To cope ing-current motor control apparatus 10A of FIG. 4. The phase compensator unit 23 may also be implemented by with the problems above, the observer gain is supplied use of a computer provided with an appropriate pro gram. In the constitution of FIG. 4, the same constitu shown in FIG. 3, thereby removing the problems 50 ent components as those of FIG. 1 are assigned with the above. In this situation, the observer gain switch unit 12 same reference numerals and a redundant description need only conduct a decision processing to determine thereof will be avoided. whether or not the received angular velocity rink is The phase compensating unit 23 is supplied with with a hysteresis with respect to the angular velocity as within the hysteresis width. When the angular velocity winding current imk and ib,k from the sample-and-hold is within the range, it need only be achieved to produce 55 circuit 18 and with the estimation values 0k and {bk a gain with a value identical to the value of the previous estimated by the state estimation observer 11. The phase output. . compensator unit 23 advances the phases of the re Referring next to FIGS. 4 to 6, a description will be ceived winding currents ink and iq,k by the phase differ given of the discrete-time alternating-current motor control apparatus including a phase compensating unit. In the motor control apparatus 10 of FIG. 1, the values {1d,}: and ‘7%,, supplied to the state estimation ob ence AT and conducts a direct quadrature transforma tion on the obtained signals to resultantly'supply the state estimation observer 11 with values id'k and iqyk having a phase identical to the phase of the winding serve 11 are resultant values of the direct quadrature voltages a“ and m. That is, since the state estimation transformation produced at the point of time k from the observer 11 conducts the operation based on a direct current controller 13 which outputs the value via the 65 quadrature transformation model, by use of a value sample-and-hold circuit 19. Actually, the motor wind ings of the alternating-current motor 30 ar supplied with these voltages through the pulse width modulation obtained by adding a correction angle A0 associated with the phase difference A T to the rotor angle 0k estimated by the state estimation observer 11, the coor 9 5,057,759 - dinate transformation is accomplished according to the following expression (9) to equivalently equalize the phase between 'the voltage values m and m and the While particular embodiments of the invention have been shown and described, it will be obvious to those skilled in the art that various changes and modi?cations may be made without departing from the present inven tion in its broader aspects. What is claimed is: 1. A discrete-time alternating-current motor control current values idyk and iq,k, respectively. [5112,1.,]: (9) Where, T(ék+Aék) is a matrix employed to transform apparatus comprising: the winding currents ink and ilLk in accordance with an orthogonal coordinate system of a two-phase stator. Thekcorrection angle Aék to be added to the rotor state estimation observer means for receiving as in puts thereto winding voltages and winding cur angle 0k varies depending on the rotor angular velocity (Bk and can be determined in advance. In consequence, 15 it is favorable to store the correction values associated with the values of the rotor angular velocity (Bk in a form of a table as shown in FIG. 6. Namely, from this table, the phase compensating unit 23 obtains a correc tion angle 130k associated with the rotor angular veloc thereby conducting the com utation based on the ex pression (9). Fixed values A k may be naturally deter mined for the respective appropriate ranges of the rotor the alternating-current motor; and observer gain switch means for setting an optimal gain to said state estimation observer means ac— cording to the estimated angular velocity. ity for a gain switch operation. 25 FIGS. 7 and 8 are schematic diagrams showing alter native embodiments according to the present invention. In the constitution of FIG. 7, in order for the state estimation observer 11 to acquire the winding currents imk and ibyk at a point of time when the voltages v“ and 3. A motor control apparatus in accordance with claim 1 further comprising: origin angle sense means for sensing an origin posi tion of a rotor of the alternating-current motor; and a controller for controlling the alternating-current motor based on an estimation result from said state estimation observer means and an origin position v,” are actually applied to the windings, a delay circuit 24 is disposed to delay the current lqyk and ilhk. The delay time of the delay circuit 24 is controlled depending on the angular velocity (bk estimated by the state estimation observer 11. rents of an alternating-current motor and for esti mating based on a model of the alternating-current motor a rotor angle and a rotor angular velocity of 2. A motor control apparatus in accordance with claim 1 wherein said observer gain switch means assigns a hysteresis with respect to an estimated angular veloc ity (Bk supplied from the state estimation observer 11, angular velocity (bk. 10 server 11 The sensed voltages vabyk vbak are transformed into vdyk and vq,k in the state estimation observer 11. sensed by said origin angle sense means. 4. A discrete-time alternating-current motor control apparatus comprising: 35 state estimation observer means for receiving as in puts thereto winding voltages applied to an alter nating-current motor and winding currents sensed The con?guration of FIG. 8 includes voltage sensors 26 and 27 respectively measuring voltages vab and vbc actually applied to the windings of an altemating-cur by a current sensor and for estimating based on a model of the alternating-current motor a rotor rent motor 30. Current values in and i1, respectively sensed by the current sensors 15 and 16 and voltages val, and vbc respectively obtained by the voltage sensors 26 and 27 are supplied to the sample-and-hold circuit 25 to be sampled at an identical point of time. The sampled values are delivered as sensed values ia,k, ibJc, vabJ‘ and angle and a rotor angular velocity of the alternat ing-current motor; and means for compensating based on the estimated angu lar velocity a phase difference between the wind ing voltages and the winding currents. vbgk at the point of time k to the state estimation ob 45 50 55 65 ‘ it t It ‘I ‘I