Sensorless Control of Permanent Magnet AC Motors Kaushik Rajashekara*, Atsuo Kawamura**
* DeIco Remy, Electric Propulsion Systems, P.O. Box 2439, Anderson, IN 46018 - USA phone: (3 17)841-4825;fax: (3 17)577-9008; e-mail:
[email protected]
** Department of Electrical Engineering, Yokohama National University, Yokohama, 240 Japan phone: +81-45-335-1451; fix: +81-45-338-1157; e-mail:
[email protected]
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Absrrad This paper presents a brief review of the different position sensorless strategies reported in the literature. The sensorless schemes are classified based on the method of position detection and control strategy. The schemes for both PM brushless de motor and for PM synchronous motor are discussed The advantages and limitations are presented 1. INTRODUCTION
Permanent magnet brushless motors have found wide applications due to their high power density and ease of control. The brushless motors are generally controlled using a three phase power semiconductor bridge. The motor requires a rotor position sensor for starting and for providing proper commutation sequence to turn on the power devices in the inverter bridge. The position sensors such as resolvers, absolute position encoders. and Hall sensors incrcost and size of the motor. A special mechanical arrangement needs to be made for mounting the sensors. These sensors, particularly Hall sensors, are t e m p t u r e sensitive, limiting the o p t i o n of the motor to below about 75°C. The absolute position sensors are speed limited to about 6000 rpm. The resolvers need special extend circuit to obtain the correct position information. In some applications, it may not be possible to mount any position sensor on the motor. Due to these limitations of the motor operation with position sensors, sensorless operation of PM brushless motors is receiving wide attention. Permanent Magnet motors are generally classified as Pemanent Magnet Brushless DC motors with trapezoidal back em€, and Permanent Magnet synchronous motors with sinusoidal back emf. The dc brushless motor employs a dc power supply switched to the stator phase windings of the motor by power devices, the switchmg sequence being determined from the rotor position. The PM synchronous motor employs a sinusoidal variable frequency, with a voltage regulated or current regulated PWM inverter to achieve control of the motor speed and torque. Several schemes for sensorless operation of PM motors are reported in the literature. In this paper, various position sensorless operation of PM motors are reviewed and the advantages and limitations are presented. As the PM motor is not a self starting motor, starting strategies without using position sensors are also briefly discussed.
0-7803-1328-3/94$03.0001994 IEEE
2.0 POSITION SENSORLESS OPERATION OF PM BRUsaLESS DC MOTOR [ 1-81
In a permanent magnet brushless dc motor, only two of the three motor phases are excited at any instaut of time. For example, the current flows inphase A during the period 0 to 120 and from 180 to 300 electrical degrees. Phase A is not excited h m 120 to 180 and fbm 300 to 360 electrical degrees. The back emf of each motor phase is trapezoidal with two 120 degree conducting intervals of wnstant voltage as shown in Fig. 1. The back emf voltage in the unexcited phase can be measured to establish a switching sequence for commutation of the power devices in the three phase bridge inverter. Based on the rotor position, the power devices are commutated sequentially every 60 degrees to continually synchronize the phase excitation with the magnet mmfwave. The commutation is typically initiated at the beginning and end of the flat top portion of the back emfwaveform. The electrical phase of the back emf should be the same as the stator currents for optimal control and maxi" torquelampere. The back emf is the direct indication of the torque production capability of the motor. Several algorithms are reported in the literature to obtain the position information for proper motor commutation.
2.1 Terminal Voltage Sensing [4] In this method, the three terminal voltages VA, VB, VC, and the neutral voltage v~ of the motor with respect to the negative dc bus voltage are measured. At the instants of the zero crossing of the back emfwaveform, the terminal voltages is equal to the neutral t h a VA= y~ voltage. When the back emf of phase A = V&. In order to use this zero crossing point to derive the switching sequence,this point has to be phase shifted by 30 degrees. In order to achieve this,the tenniaal voltages are first converted to triangle waveforms and then compared with the neutral voltage. The output of the comparators detennine the switching sequence. The position detection scheme based on tenninal voltage sensing is simple and practical for steady state operation. The output signals of the terminal voltage sensing circuits have large phase dif€erences compared with actual position signals, resulting from speed variations of brushless dc motor. Because of the phase shift variations and the incorrect rotor position signals, the optimal torque operationscannot be obtained.
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2.2 Third harmonic voltage integration [54]
2.3 Back emf integration [ 3 , 1
The rotor position is determined based on the third harmonic voltage component. To detect the third harmonic voltage, a three phase resistance is connected cross the motor windings. The voltage across the two neutrals V m determines the third harmonic voltage. This voltage is integrated and input to a zero crossing detector. ThC output of the zero crossing detector &tennines the switchurg sequence for turning on of the devices.
The hack emf k ~ t e p t i o napproach has the advantage of reduced swinoise sensitivity and automatic adjustment of the inverter switching instants to changes in rotor speed. A signal selector circuit selects the plmc-to-ncutral motor voltage of the unexcited phase winding. The selected phase voltage equals the desired back emf for position sensing as soon as the residual inductive current flowing in the unexcitedwin* immediately following the removal of excitation decays to zero. This absolute value of this selected back emfis instarting fium the ZQO cros~ing. The next "mutation of the device is initiated whcn this integrated value Vint reaches a set threshold value. The choice of the threshold value and the inregmtor constant dcpends on the motor and the alignment of phase current wavefonn with the back emf voltage.
The main disadvantage is the relatively low value of the third harmonic voltage at low speed. It is difl[icult to detect the right relative phase position between the third harmonic and the corresponding phase. If the sequence is lost, the system has to be restarted again. The amplitude and phase of the third harmonic is directly related to the saturation.
The hack emfwaveform integration still suffers at low speeds like the other techniquesmentioned above.
'*a 0
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2 4 Position Sensorless operation based on tbe conducting state of free-wbeeling diodes [8] The position i n f d o n is detamined based 011 the conducting state of b w h e e l i a g diodes in the unexcited phase. The inverter gate drive signals axe choppea during each 120 degrec operation. Thc0pcn phase current undcrdtapper operation d t s from the bsck emfproducedin the motor windings. The current waveform in an open phase is shown in Fig. 2. Thc position information is obtained evay 60 degree by detectrng whether the ficc-whccling diodes axe d u c t i n g or not. Since the detected position signal leads next commutation by 30". the cammutation signals are phase shifted using a phase shiftcr. The system has been tested from 45 rpm to 2300 rpm. -& -
4
The motor is started by exciting two arbitrary phases for a preset timc. The rotor turns to the direction * totheexcited phescs. Next,the cornmuatation signal that advances the switching pattan by 120" is provided. Oncc the motor starts accelerating, the open-iaop "muatation is switched to the sc~~sotless strategy.
The starting -still has the same dra*b ofmany schemes mentioned in the litaaturr. Low speed operation is a problem. 2 5 Position detection using pb8re current sensing [9]
The magnetic flu of the motor is in phase with the stator current. 'Ihcrcforc. near exact rotor position signals cau be obtained just by 1590
detecting and procesSing the phase current waveforms. Using a current signals can be converted signal processing circuit, the into thi required rotor position signals. Establishingthe Starting Switchtng strategy could be a problem. The system can be noise sensitive. It also depends on the arbitrary reference level for comparing the current signals to obtain the position information signals. 3.0 POSITION SENSORLESS OPERATION OF PM
SYNCHRONOUSMOTOR The ideal back emf for this type of motor is Sinusoidal, so that when sinusoidal currents flow, a constant torque is produced with very low ripple. The stator of the Sinusoidal-fed PM ac motor and that of the wound rotor synchronous motor arc similar. The motor requires continuous rotor position fdback to power the motor with sinusoidal voltages or currents frmn the inverter system. At any instant of time, three power devices of the three phasc bridge inverter are conducting. Several techniques are proposed to control this type of motor without using position sensor. Some of these techniques can be extcnded to PM brushless dc motor system. In sinusoidal back emf motors, the rotor position is nqukcd continuously and in trapezoidal back emfmotor, it is enough to have the rotor position every 60 degrees to obtain the proper switching sequence. 3.1 Position information based on the measurement of voltqer and currents [lo-131
In these methods, the basic principle of controlling the PM synchronous motor is based on the field orientation, which is illustrated in Fig. 3. Stator voltage and current signals are used to construct a flux linkage position signal through which the phase angle of the stator current can be controlled. q-uir
I
= lWab
- 4(ia - i b W
ea = tan-l(-T)A', Aid
r1 is the stator resistanceper p k , ia, it,, and ic arc the currents in the phases A, B, C respectively.
If the stator power factor has to be unity, the stator current space vector
should lead the stator phase flux lkrkage space vector 2,
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by No, that is it should lead the line space vector /2, by 60 *. The three phase current commands have the instautaneous values
i,' = i,' cos 8, i,' = i,' cos(8, - 120") .e
1,
e
.
=-(in +i, )
8,= ea f 60" 8,is the space angle ofthe line flux linkage A,. In [14], the position infinmation is detamincd based on the motor taminal voltages and line m t s with the aim of estimating the flux Iinkaga. At each time step, using the previously predicted papition information and the flux linkages. the line ament of the motorisescimatcdm twu stages tocmecttheprrdicted position and the estimated flux linkage respectively. The calculations are based on the ABC refer" frame model of the mache. The position estimator block d i q " is shown in Fig. 4. The proposed algorithms have ben applied for both trapaoidal back emf PM motors and sinusoidal back emfPM motors. The & o " x of the algorithms prrsented above depends on the qualtty and BCCUBC~of the estimated flux linkages and measured values of voltage and cuments. The parameter variations due to temperaand saturation shall also affect the accuracy of the positionillfdm 3.2 Position information based on the hypothetical rotor position [IS 19)
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In the proposed amtrol strategies, the difference between the detected actual state variables and the estimated state variables is used to obtain the papition infarmation. Thc controlla detamines the applied voltage-to the motor acardiq to the hypothetical rotor 3 Space vector diagnm of PM synchronous motar position, which is not n d y coincident with the actual rotor position. The ideal applied voltage is calculated using the vector Tis determined tiom the emf instantansous voltage equation of the motor and the detected n e stator line flux current. The difference between the actuai and ideal voltage is vector e, Proportional to the angular ditrerence between hypothetical and - actual rotor positions. S e l f - s y n c h " is possible by reducing
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AI = leldt = 'ld'
The stationary
+
%qS
d- and q-axis line-to-lie fluxlmkages are:
thisangular difference to zao. The following procedure is reported in [IS]. 1591
I
1
(a) The detected three phase voltages and currents are transformed to a hypotheticai coordinate system, y 6 axis voltage and current, to obtain vy and ~ 6 .
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(b) The hypothetical voltages v i and v i are determined based on the detected current and motor model. (c) The angular diflirence A V ~= vv vy' a AO. The andifference between the actual and hypothetical axes is estimated by the voltage dB'ence between the actual and the hypothetical axes. Self synchronization is achieved by making this angular difhmce zero, by changing the speed of the motor.
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In [ 161, the position estimation based on current model of the motor is presented. The estimation of position and speed is performed using a current error between an actual current, and the calculated current using the motor model. In [17], a comparative study of the self synchronization based on voltage error and current error is presented.
In [18-191, the strategy used is almost similar to those used in [IS171, the difference being two hypothetical reference frames are used instead of one. These two coordinated axes[ (XI, y1); (x2. y2)] are 90" apart from one another. The rotor position angle is calculated using the equation
e= tan- '(L), here
vel is
the m r
ve2
between the actual voltages based on measurements and the calculated voltages in (XI, y1) reference fiame, and Ve2 is the error in (x2, y2) reference fiame. The rotating speed of the motor is determined using the value of 8. 3.3 Sensorless Operation Based on Kalman Filtering [20-251 A Kalman filter provides an optimum observation from noisy sensed
signals and processes that are disturbed by random noise. This
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assumes that measurement noise and disturbance noise are llllcomIBted Knlmnn filter approach is a viable and computationally efficient candidate for the on-line estimation of the speed and rotor position. This is possible since a mathematical model, describing the PM motor dynamics is sufficiently well knom The rotor position can be dttamincd based on the voltages and currents. The measured voltages and currents are tnrnsfomed to stationary 6ame components. va, vp,i, and ip. Using the state equations and Kalman filter, the missing states (rotor position and velocity) are estimated. The estimated rotor position is used for commutation.
Kalman filter is an optimum state estimator. The filter's estimation
is constantly comctcd by an additional tam originated from the "remat. The estimated state x'(n) is the minimum variance estimate of x(n). The Kalman filter consists of two step process prediction and filtering. The predictor talres states from k+ to @+I)-, whaea~the mter taka states iimn time @+I)- to @+I>+. The prediction part of the algorithm calculates the next estimate values for x and the state covariance matrix P before the new "merit is made. In doing SO, the predictor uses the state
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variable equations, state transition matrix, disturbance covariance Q andmeasurementcovarianceR
The function of the filter is to w m c t the estimation process in a recursive manna. The filter umstantly works on the output and camcts its quality in a recursive manner based on the measured values. Based on the deviation h m the estimated value, the filter provides an optimum output value at the next output instant. The critical step in Kaknan filter design is to select the coefficient values to yield the best estimation performance possible. The Katman filter approach is computationally intensive, depends on the ~ccuracy of the parameters of the model and the motor.
REFERENCES
An estimation of the rotor position based on a state observer is proposed in [26], by combining the ideas of a linear observer with
P.C. Krause, R.M. Voyles, et al, " Analysis and Simulation of a Brushless DC Servomotor," MotorXon m - s , April 1984, PP. 86-94. K.J. Binns, D.W. Shimmin, and K.M.AI-Auhidi, " Implicit Rotor Position Sensing using Motor Winfor a Self Commutating Permanent Magnet Drive system", IEE P r ~ t ~ e d l nPart g ~ , B, Vol. 138, NO. 1, January 1991, PP. 2834. M.D. Erdman, H.B. Harms, and J.L. Oldenkamp, " Electronically Commutated DC Motors for the Appliance Industry", lEEE IAS Conference Record, 1984, PP. 13391345. K. Jizuka, H.Uzuhashi. et al, "Microcomputer Control for Sensorless Brushless Motor", IEEE Tran. on Industry Applications,May/J~ne1985,PP. 595-601. P. Ferrais. A. Vagati, and F. Villata, " P.M. Brushless Motor Drives: a self commutation system without rotor-position sensors", Proceedings of the Ninth Annual Symposium on Incremental Motion Control Systems and Devices. June 1980, PP. 305-312. M. Nagata, S. Yanase , et al, " Control Apparatus for Brushless Motor," US Patent Number 4,641,066, February 3, 1987. R.C. Becerra, T.M. Jahns, and M. Ehsani, " Four Quadrant Sensorless Brushless ECM Drive". IEEE Applied Power Electronics Conference and Exposition 1991, PP. 202-209. S. Ogasawara and H. Akagl, " An Approach to Position Sensorless Drive for Brushless DC Motors", JEEE Trans. on Industry Applications. Vo1.27, SeptembedOctober 1991, PP. 928-933. R. Lin, U T . Hu, C.Y. Lee, and S.C. Chen, " Using Phase Current Sensing Circuit as the Position Sensor for Brushless DC Motors Without Shaft Position Sensor", IEEE IECON proceedings, 1989, PP. 215-218. R. Wu and G.R. Slemon, " A Pennanent Magnet Motor drive Without a Shaft Sensor", Confmence Record of IEEE IAS Annual Meeting, 1990, PP. 553 - 558. T.H. Liu and C.P. Cheng, " Adaptive Control for a Sensorless Permanent Magnet Synchronous Motor Drive", EEE IECON 1992.PP.413 -418. T.H. Liu and C.P. Cheng, " Controller Design for a Sensorless Permanent Magnet Synchronous Drive System," IEE ProceedingS-B, Vol. 140, NO. 6, November 1993, PP. 369378. M. Naidu and B.K.Bose, " Rotor Position Estimation Scheme of a Permanent Magnet Synchronous Machine for High Performance Variable Speed Drive", Conference Record of lEEE - IAS Annual Meeting 1992, PP. 48 53 N. Ertugrul and PP Acamley, " A New Algorithm for Sensorless Operation of Permanent Magnet Motors," IEEE Trans. on Industry Applications, Vol. 30, No. 1, JanuaryfFebruary 1994, PP. 126-133. N. Matmi and M. Shigyo, " Brushless DC Motor Without Position and Speed Sensors", IEEE Trans. on Industry
the dq transformation. In a state obmer, the output is defined as a combination of states, and this output is compared with the equivalent measured output of the real motor. Any error between the two signals is used to correct the state trajectory of the observer. The stability of an observer is an important issue in providing the accurate position information. Loss of observer stability would result in erratic and possibly destructive motor operation. 4.0 STARTING STRATEGIES
The position sensorless schemes are not self starting. In order to sense the back emf or to calculate the position based on measured voltages and currents, the motor first must be started and brought up to a certain speed where the terminal quantities can be detected. In [4,29], to start the motor, the currents in the motor phases are injected corresponding to a certain increasing frequency profile. Then at some instant, the rotor aligns itself to the desired position to provide accelerating torque capability. Once the speed reaches a threshold value and back emf is developed, it is used for position information and the required switchingsequence is established. In [15], the motor is started by applying a specific PWM pattern (say, devices T1, T2,and T6 are turned on and of€) to the inverter for about 200 ps. This is repeated s e v d times to align the rotor in the direction of A-phase winding. The regular sensorless control strategy is then followed. Most of the starting strategies presented are based on arbitrarily energizing the two or three windings and expecting the rotor to align to a certain definite position. This has a poor dynamicresponse, and the rotor can be in the hunting mode. The INFORM (Indirect Flux Detection by On-line Reactance Measurement) proposed in [24] claims to offer a high dynamic performance even at standstill. The rotor is brought into a defined position by applying a stationary armature current. Hence, the d-axis of the rotor is turned into the direction of the space phasor of the annature current. Now a torque producing current of about maximum value is applied to the q-axis to accelerate the rotor. 5.0 CONCLUSIONS
This paper presents a brief review of the position sensorless control strategies for PM motor. The sensorless control strategy for a PM brushless dc motor seems to be simpler than for a PM synchronous motor. The position detection calculations based on tennihal voltages and currents need faster computation and hence need a Digital Signal Processor. Position detection error can result due to quantization, truncation errors, and measurement inaccurscies. The variation of the motor parameters due to tempemture and saturation also afTects the estimated position informaton.
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[ 161
[17]
[18]
(191
I201
[21]
[22]
Applications, Vo1.28, No. 1, JanuaryEebruary 1992, PP. 120127. N. Matsui, T. Takeshita, and K. Yasuda, " A New Sensorless Drive of Brushless DC Motor", IEEE ECON 1992, PP. 430 435. N. Matsui, "Sensorless Operation of Brushless DC Motor Drives," IEEE IECON93 proceedings, PP.739-744. H. Katsushima, S. Miyazaki et al, " A measuring Method of Rotor Position Angles of the Direct Drive Servo Motor," Proc. of IPRCPO, Tokyo, PP. 724-73 1. H. Watanabe, H. Katsuishima, and T. Fujii. " An Improved Measuring System of Rotor Position Angles of the Sensorless Direct Drive Servo motor", IEEEECON 1991, PP. 165-170. R. Dhaouadi, N. Mohan, and L. Norum, " Design and Implementation of an Extended Kalman Filter for the State Estimation of a Permanent Magnet SynchronousMotor", lEEE Trans.on Power Electronics, July 1991, PP.491497. M. Schroedl, " An Improved Position Estimator for Sensorless Controlled Permanent Magnet Synchronous Motors", 4th European Conference on Power Electronics and Applications, 1991, PP. 418423. A. Bado, S. Bolognani, and M. Zighotto. " Effective estimation of Speed and Rotor Position of a PM Synchronous Motor Drive by a Kalman Filtering Technique," EEE Power Electronics SpecialistsConference ,1992, PP. 951-957.
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[23] B.J. Brunsbach, G. Henneberger, and Th. Klepsch, " Position Controlled Permanent Excited Synchronous Motor without Mechanical Sensors",5th European Power Electronics and Association, EPE 93, PP. 3843. [24] M. Schroedl, " Digital Implementation of a Sensorless Algoritbm for Permanent Magnet Synchronous Motors," EPE Conference, 1993, PP. 430435. [25] S.Meshkat, " Sensorless BrushlessDC Motor using DSPs and Kalman Filtering,"DSP Applications, June 1993, PP. 59-63. [26] L.A. Jones and J.H. Lang, " A state. observer for the Permanent Magnet Synchronous Motor", EEE Trans. on IndustrialElectronics, Vol. 36, NO. 3, August 1989,374-382. [27l A.B. Kullrarni and M. Ehsani, " A Novel Position Sensor Elimination Technique for the Interior Permanent Magnet Synchronous Motor Drive", IEEE Trans. on Industry Applications, JanuaryEebruary 1992, [28] 0. Shinkawa, K. Tabata, et al, " Wide Operation of a Sensorless Brushless DC Motor Having an Interior Permanent Magnet Motor", Proceedings of Power Conversion Conference - Yokohsma, 1993, PP. 364-370. [29] R. Krishnan and R. Ghosh, " Starting Algorithm and Performance of a PM DC Brushless Motor Drive System With No Position Sensor", IEEE Power Electronics Specialists Conference 1989, PP. 815-821.
