New Integration Algorithms for Estimating Motor Flux ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 5, SEPTEMBER 1998

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New Integration Algorithms for Estimating Motor Flux over a Wide Speed Range Jun Hu and Bin Wu, Member, IEEE

Abstract— Three new integration algorithms for motor flux estimation are proposed in this paper. These algorithms are developed for use in high-performance sensorless ac motor drives. The first algorithm is used to elaborate the basic operating principle. The second one is designed for the drives that require a constant air-gap flux during operation. The third algorithm, in which an adaptive controller is used, can have wide industrial applications. The proposed algorithms can effectively solve the problems associated with pure integrators. These algorithms can be used to accurately measure the motor flux including its magnitude and phase angle over a wide speed range (1 : 100). The performance of the algorithms is investigated, compared, and verified experimentally. Index Terms— Adaptive control, flux estimation, integrator, sensorless drive.

I. INTRODUCTION

F

LUX ESTIMATION is an important task in implementing high-performance motor drives [1]–[6]. There are, in general, two methods for flux estimation: one is based on measured motor currents, and the other is based on measured voltages [1], [2], [5]. In the current-based method, the motor air-gap flux is identified by solving a set of equations in which motor parameters are required as well as measured motor currents, speed, or position [1]. One of the problems associated with this method is that the parameters change with motor operating conditions, e.g., variations in rotor temperature and magnetic saturation level. In order to overcome this problem, an on-line motor parameter identification scheme should be implemented, which increases the complexity of the drive system. Furthermore, the motor speed or position has to be detected, an undesirable practice in most industrial applications since the use of tachometer will deteriorate the reliability of the drive. In the voltage-based method, the motor flux can be obtained by integrating its back electromotive force (emf). The only motor parameter required is the stator winding resistance, which can be easily obtained and in most cases can be considered constant. Taking into account the fact that the motor speed signal is not required, this method is much preferred [3], [4].

Manuscript received June 3, 1997; revised February 24, 1998. This work was supported by the Natural Sciences and Engineering Research Council of Canada and Rockwell Automation-Allen Bradley, Inc. Recommended by Associate Editor, D. Torrey. The authors are with the Department of Electrical and Computer Engineering, Ryerson Polytechnic University, Toronto, Ont., M5B 2K3, Canada (e-mail: [email protected]; [email protected]). Publisher Item Identifier S 0885-8993(98)06489-8.

Fig. 1. Algorithm 1: modified integrator with a saturable feedback.

However, implementation of an integrator for motor flux estimation is no easy task. A pure integrator has dc drift and initial value problems [3], [5]. A dc component in measured motor back emf is inevitable in practice. This dc component, no matter how small it is, can finally drive the pure integrator into saturation. The initial value problem associated with the pure integrator can be explained as follows. When a sine signal is applied to the integrator, a cosine wave is expected at its output. This is true only when the input sine wave is applied at its positive or negative peak. Otherwise, a constant dc offset will appear at the output. This offset, representing a constant dc flux in a motor, does not exist during motor normal operation. The dc offset can also be generated when there is a rapid change in the input signal. A common solution to these problems is to replace the pure integrator with a first-order low-pass (LP) filter. Obviously, the LP filter will produce errors in magnitude and phase angle, especially when the motor runs at a frequency lower than the filter cutoff frequency. Therefore, motor drives using LP filters as a flux estimator usually have a limited speed range, typically 1 : 10 (6–60 Hz) [1]. In this paper, three modified integrators using proposed algorithms are developed to solve the above mentioned problems. The performance of these integrators is studied and verified through simulation and experiment. II. NEW INTEGRATION ALGORITHMS As discussed in the previous section, both pure integrator and LP filter have application problems when they are used for motor flux estimation. To solve these problems, three modified integrators are proposed. The output of these integrators can be generally expressed as (1) where is the input of the integrator and is a compensation signal. Assuming that the compensation signal is set to zero,

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 5, SEPTEMBER 1998

Fig. 2. Algorithm 2: modified integrator with an amplitude limiter.

Fig. 3. Algorithm 3: modified integrator with an adaptive compensation.

the modified integrator essentially serves as a first-order LP filter which is usually adopted to replace the pure integrator in practice. If, on the other hand, the compensation is taken from ), the modified integrator the integrator’s output (i.e., ]. performs the same function as a pure integrator [ It can be seen from the above analysis that with a properly designed compensation, the modified integrator may achieve a better performance than the LP filter while the problems associated with the pure integrator may be avoided. The detailed discussions on the modified integrators are as follows.

A. Algorithm 1: Modified Integrator with a Saturable Feedback The block diagram of a modified integrator with a saturable feedback is shown in Fig. 1. The output of the integrator is composed of two components: a feedforward component and feedback component . If the frequency of the input of the signal is much higher than the cutoff frequency modified integrator, the gain of the feedback block is close is trivial to zero. As a result, the feedback component is essentially composed of the and the integrator output feedforward component only. At low frequencies, however, the functional blocks in the feedback loop play an important role in eliminating dc drift or saturation. Assuming that the in the saturation block is not exceeded, the limiting level compensation signal is equal to the integrator output , and

a pure integrator function is obtained. If the limiting level is reached, the integrator output becomes (2) is the output of the saturation block, whose where amplitude is limited to . It is interesting to note that the level of nonlinear distortion produced by the saturation block can be reduced at the output of the feedback block since this block is essentially an LP filter. Now, let us assume that a pure dc signal is applied to the input. The maximum output of the integrator is (3) which implies that the modified integrator will not be driven into saturation provided that the limiting level is properly set. The main difficulty associated with this algorithm is to determine the limiting level . In order to eliminate dc component at the output, the limiting level should be set at a value equal to the actual flux amplitude. When the limiting level is greater than the flux amplitude, the flux waveform may be shifted up or down due to the dc bias at the input until its amplitude reaches either positive or negative limiting level. Hence, the output waveform is composed of an ac flux signal and a dc offset. The larger the difference between the

HU AND WU: NEW INTEGRATION ALGORITHMS FOR ESTIMATING MOTOR FLUX

Fig. 4. Vector diagram showing relationship between

~ and emf. ~

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Fig. 6. Flux waveforms produced by Algorithms 1 and 2 when the limiting level is not correctly set show that Algorithm 2 does not produce distorted flux.

Fig. 7. Response of the pure integrator and Algorithm 2 to a sine input with a dc offset. Fig. 5. Comparison of flux waveforms estimated by different integration algorithm (the motor is running under steady conditions when the LP filter and integrators are put into operation).

actual flux amplitude and the limiting level, the larger the dc drift will be. If the limiting level is set below the actual flux amplitude, the output flux waveform will not contain any dc component, but will be distorted. More discussions will be given in Section III. B. Algorithm 2: Modified Integrator with an Amplitude Limiter To avoid the possible waveform distortion discussed above, a new integration algorithm is developed. This algorithm, shown in Fig. 2, is specially designed for ac motor flux estimation. In ac motor drives, it is a common practice to transform a set of three-phase variables in a-b-c frame into two-phase variables in – frame for various purposes. The and in the – frame can be obtained motor fluxes by integrating motor back emf’s in the – frame, which transform. The flux can be obtained through abc to , is a dc signal and so amplitude, defined as is the limiter output. The flux magnitude and angle can be transformed back to its – form through a Polar to Cartesian transform block, whose outputs are sinusoidal waveforms with a limited amplitude. The nonlinear distortion caused by the saturation block in Fig. 1 is eliminated, resulting in an improved performance of this modified integrator. However, the accuracy of the estimated flux still depends on how the limiting level is set. If the motor operates at various flux levels, the limiting level should be adjusted accordingly. Therefore, this algorithm is suitable for applications where the motor flux is not required to vary during operation.

(a)

(b) Fig. 8. Response of modified integrator using Algorithm 3, where the motor is running under steady-state conditions when the modified integrator is put into operation: (a) estimated flux waveforms and (b) compensation level.

C. Algorithm 3: Modified Integrator with an Adaptive Compensation Algorithm 3 is designed for motor drives with variable flux operations. Fig. 3 shows a block diagram of this algorithm in which an adaptive controller is used. This scheme is developed based on the fact that the motor flux is orthogonal to its back emf. A quadrature detector is proposed to detect the orthogonality between the estimated flux and back emf. A proportional–integral (PI) regulator is used to generate an

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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 13, NO. 5, SEPTEMBER 1998

(a)

(b)

(c)

(d)

Fig. 9. Response of modified integrator using Algorithm 3 to a step change in magnitude of emf : (a) input signal emf , (b) compensation level emf , (c) estimated flux showing no dc offset flux after the step changes in emf , and (d) estimated flux using pure integrator showing that the flux contains a dc offset due to step changes in emf .

appropriate compensation level, which is given by emf

emf

(4)

and are the constants of the PI regulator. The where , which corresponds to the limiter output in magnitude of Fig. 2, is no longer fixed. It is now governed by (4). The operating principle of the adaptive scheme can be explained by using a vector diagram shown in Fig. 4. The estimated flux vector is a sum of two vectors, a feedforward which is the output of the LP filters ( and ) vector which is composed of and . and a feedback vector Ideally, the flux vector should be orthogonal to the back emf vector, and the output of the quadrature detector is zero. When an initial value or dc drift is introduced to the integrator, the above orthogonal relation is lost, and the phase angle between the flux and emf vectors is no longer 90 , which yields an error signal defined by emf emf

emf

Fig. 10. Experimental setup for verifying the proposed integration algorithms.

emf (5)

III. SIMULATIONS is Assuming that the magnitude of the feedback vector as shown in Fig. 4 due to a dc offset or initial increased to will be greater that 90 . value problem, the phase angle The quadrature detector will generate a negative error signal. is reduced and so is the The output of the PI regulator moves toward feedback vector. As a result, the flux vector the original position of 90 until the orthogonal relationship between and emf is reestablished. If is less than 90 for some reason, an opposite process will occur, which brings back to 90 Therefore, the modified integrator with the adaptive control can adjust the flux compensation level automatically to an optimal value such that the initial value and dc drift problems are essentially eliminated.

The performance of the proposed integration algorithms is investigated by Matlab/Simulink. It is assumed in the following simulations that the motor is already running in steady state with a stator frequency of 10 rad/s when the LP filter or integrators are put into operation. The cutoff frequency ( ) used in the LP filter and proposed algorithms is 20 rad/s. The magnitude of motor back emf is adjusted such that the actual flux amplitude is equal to one per unit for the convenience of discussion. Fig. 5 shows the waveforms estimated by the LP filter, component of the pure integrator, and Algorithm 1. The , is shown in the figure. It can be observed that flux, the LP filter produces a large error both in phase angle and

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(a)

(b)

m

Fig. 11. Results of Algorithm 3 when the motor runs at 60 Hz: (a) measured voltage, current, and estimated fluxes and (b) measured position  sd and estimated flux angle 'est .

(a)

(b) Fig. 12. Results of Algorithm 3 when the motor runs at 0.5 Hz: (a) measured voltage, current, and estimated fluxes and (b) measured rotor position msd and estimated flux angle 'est .

in magnitude, the pure integrator holds a dc offset due to the initial value problem since the sinusoidal back emf is applied to the integrator at its zero crossing, and the output of Algorithm 1 converges to the actual motor flux within one and a half cycles. Fig. 6 shows the results of Algorithms 1 and 2 with a limiting level of 0.5 per unit which is improperly set on purpose (the ideal limiting level should be equal to the

amplitude of actual flux which is one per unit in this case). The flux waveform estimated by Algorithm 1 is distorted while that by Algorithm 2 is not. However, Algorithm 2 still produces some errors due to the improper limiting level. It should be noted that the errors have been substantially reduced compared to the output of the LP filter in Fig. 5. For motor drives which require a constant flux operation, the limiting level can be set at a value equal to the flux reference of the drive.

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(a)

(b)

m

Fig. 13. Results of the LP filter when the motor runs at 1 Hz, showing unacceptable errors between  sd and 'est : (a) measured voltage, current, and estimated fluxes and (b) measured rotor position msd and estimated flux angle 'est .

(a)

(b) Fig. 14. Estimation results of Algorithm 3 during the motor startup: (a) measured voltage, current, measured position msd , and estimated flux angle 'est and (b) estimated fluxes.

To investigate the dc drift problem, a dc bias with an amplitude of 0.5 per unit is superimposed to sinusoidal emf inputs. Fig. 7 shows the responses of the pure integrator and Algorithm 2 to such input signals. It can be observed that the output of the pure integrator diverges while the flux estimated by Algorithm 2 is a stable sine wave with a negligible dc offset. Fig. 8 shows the response of the modified integrator using Algorithm 3 to the same operation conditions as those in

, which represents the Fig. 5. The transient waveform of adaptive compensation level, is illustrated in Fig. 8(b). As shown in the figure, the output of this modified integrator quickly converges to the actual flux. The initial transient dies away in about a half cycle. Fig. 9 shows the behavior of Algorithm 3 to a step change and in emf magnitude. The transient waveforms of are illustrated in Fig. 9(b) and (c), respectively. The

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(a)

(b) Fig. 15. Estimation results of Algorithm 3 when the motor speed reverses (10 to and estimated flux angle 'est and (b) estimated fluxes.

Fig. 16. Estimation results of the LP filter when the motor speed reverses (10 to can be observed.

response of the pure integrator is also presented in Fig. 9(d) for comparison. Obviously, there is no dc offset in the flux waveform produced by Algorithm 3, whereas the pure integrator generates an undesired positive dc offset after a step increase in emf and then a negative dc offset after a step decrease. It can be concluded that Algorithm 2 can be used in a drive with a constant flux control while Algorithm 3 is most suitable for the motor flux estimation under variable flux control. IV. EXPERIMENTS To verify the proposed integration algorithms, a synchronous motor drive was constructed. Fig. 10 shows the block diagram of the drive system where a conventional fieldoriented control is implemented. The front-end converter of the drive system is a silicon-controlled rectifier (SCR), and the synchronous motor (6 hp, 6 poles) is fed by a gate turn-off

010 Hz):

010

m

(a) measured voltage, current, measured position  sd ,

Hz), where substantial differences between `msd and 'est

thyristor (GTO)-based pulsewidth modulation (PWM) current source inverter. The rotor speed and position are detected by a shaft encoder (2500 pulses per revolution) for field-oriented control. The measured rotor position is also used for verification purposes. To evaluate the performance of the proposed algorithms, two flux estimators shown in the dotted block were built and tested. A TMS320C31 DSP board is used for real-time control. The sampling time is set at 1 ms due to a relative low-switching frequency required by GTO devices. Since the synchronous motor does not have a built-in flux sensor, comparison between the estimated flux and the actual flux in the motor may be difficult to make. However, the proposed integration algorithms can be verified based on a phenomenon that the rotor axis is coincident with the air-gap flux axis when the motor operates under no-load conditions. Therefore, a comparison between the estimated flux angle

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(a)

(b) Fig. 17.

Estimation results of Algorithm 3 when the motor flux varies: (a) measured voltage, current, and estimated flux and (b) compensation level

and measured rotor position can be used to evaluate the performance of the proposed integrators provided that the motor is unloaded. A. Steady-State Performance Fig. 11(a) shows the measured stator voltage, current, and rad/s) when the estimated fluxes using Algorithm 3 ( motor runs at 60 Hz. Fig. 11(b) gives a comparison between and estimated flux angle the measured rotor position which is calculated by . It can be observed and measured position are that the estimated angle and . These discrepancies are well matched except at simply display errors due to the fact that the ratio of sampling frequency (1 kHz) to stator frequency (60 Hz) is low, and also these frequencies are not synchronized. Therefore, the discrepancies do not reflect the accuracy of the algorithm. Fig. 12 shows the estimated motor fluxes when the motor runs at 0.5 Hz at which most other flux estimation algorithms fail to work. The estimated and measured angles are in good agreement. Clearly, Algorithm 3 can be used to accurately estimate fluxes at both high- and low-motor speeds. The rad/s) when estimation results using the LP filter ( the motor runs at 1.0 Hz are given in Fig. 13 for comparison. The LP filter produces large errors in both flux angle and Wb is expected). magnitude ( B. Dynamic Performance The dynamic performance of the modified integrator using Algorithm 3 is illustrated in Figs. 14 and 15. The estimated in Fig. 14 follows the detected rotor position flux angle very well during the motor startup. The same phenomenon can be observed when the motor changes its speed from 200 (10 Hz) to 200 rpm ( 10 Hz) as shown in Fig. 15.

cmp .

If an LP filter is employed as a flux estimator, the accuracy of the estimated flux is expected to reduce, especially when the motor runs at a vicinity of zero speed. Fig. 16 demonstrates such a case where a substantial discrepancy between the estimated flux angle and measured rotor position occurs when the motor reverses its speed. when the actual Fig. 17(a) shows the measured flux motor flux is increased by 50%. Fig. 17(b) shows the adaptive ) at the output of the PI regulator, compensation level ( which is automatically adjusted such that the potential dc offset is eliminated. in V. CONCLUSIONS Three integration algorithms for motor flux estimation are proposed, investigated, and compared in this paper. These algorithms are developed to solve practical problems associated with pure integrators for motor flux estimation. The basic operating principle is elaborated through Algorithm 1. Using reference frame theory, Algorithm 2 is developed to eliminate the nonlinear distortion produced by Algorithm 1. This algorithm is suitable for applications where the motor flux should be kept constant during operation. Algorithm 3, evolved from the above two, uses an adaptive controller, resulting in a superior dynamic and steady-state performance. This algorithm is particularly suitable for high-performance sensorless motor drivers where motor flux may vary during operation. The performance of the proposed algorithms is verified by simulation and experiment. REFERENCES [1] W. A. Hill, R. A. Turton, R. J. Dungan, and C. L. Schwalm, “A vectorcontrolled cycloconverter drive for an icebreaker,” IEEE Trans. Ind. Applicat., vol. 23, no. 6, pp. 1036–1042, 1987.

HU AND WU: NEW INTEGRATION ALGORITHMS FOR ESTIMATING MOTOR FLUX

[2] I. Takahashi and T. Noguchi, “A new quick response and high efficiency control strategy of an induction motor,” IEEE Trans. Ind. Applicat., vol. 22, no. 5, pp. 820–827, 1986. [3] R. Wu and G. R. Slemon, “A permanent magnet motor drive without a shaft sensors,” IEEE Trans. Ind. Applicat., vol. 27, no. 5, pp. 1005–1011, 1991. [4] X. Xu, R. Doncker, and D. W. Novotny, “A stator flux oriented induction machine drive,” in IEEE PESC Conf. Rec., 1988, pp. 870–876. [5] H. Tajima and Y. Hori, “Speed sensorless field oriented control of the induction machine,” in IEEE IAS Conf. Rec., 1991, pp. 385–391. [6] C. Schauder, “Adaptive speed identification for vector control of induction motors without rotational transducers,” IEEE Trans. Ind. Applicat., vol. 28, no. 5, pp. 1054–1061, 1992.

Jun Hu was born in Zhejiang, China, in 1966. He received the B.Sc., M.Sc., and Ph.D. degrees from Tsinghua University, Beijing, China, in 1988, 1991, and 1995, respectively, all in electrical engineering. He was appointed as a Lecturer in Electrical Engineering at Tsinghua University in April 1994. From 1995 to 1997, he worked as a Post-Doctoral Fellow at Ryerson Polytechnic University, Toronto, Ont., Canada. He joined Rockwell Science Center (RSC), Thousand Oaks, CA, in October 1997, where he is currently a Member of Technical Staff in information technology. His research interests include power electronics, ac drives, and motion control.

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Bin Wu (S’89–M’91) received the M.A.Sc. and Ph.D. degrees in electrical engineering from the University of Toronto, Toronto, Ont., Canada, in 1989 and 1993, respectively. After being with Rockwell Automation/AllenBradley, Inc., Cambridge, Ont., as a Senior Development Engineer, he joined Ryerson Polytechnic University, Toronto, Ont., where he is currently an Associate Professor. His research interests include power converter topologies, motor drives, computer simulation, and DSP applications in power engineering. Dr. Wu was awarded the Gold Medal of the Governor General of Canada in 1990. He is a Registered Professional Engineer in the Province of Ontario, Canada.