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Published in IET Electric Power Applications Received on 21st May 2007 Revised on 16th August 2007 doi: 10.1049/iet-epa:20070234

ISSN 1751-8660

Sensorless permanent-magnet synchronous motor drive using a reduced-order rotor flux observer

T.F. Chan1 W. Wang1 P. Borsje2 Y.K. Wong1 S.L. Ho1

Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, Republic of China 2 Motion Control Department, ASM Assembly Automation Ltd, Hong Kong, 4/F, Watson Centre, 16 Kung Yip Street, Kwai Chung, Hong Kong SAR, Republic of China E-mail: eetfchan@polyu.edu.hk

1

Abstract: A sensorless permanent-magnet synchronous motor (PMSM) drive is developed. A second-order Luenberger observer is used to estimate the position of the rotor flux and hence the rotor speed. The observer is computationally efficient as it has a simple structure and does not involve mechanical parameters. An integral-feedback method is adopted for the estimation of the rotor speed. The inner current loop is realised using a decoupling and diagonal internal model control algorithm. Details of the sensorless control system are given and the feasibility of the proposed method is verified through simulation and experiments. Satisfactory estimation accuracy is obtained even when the drive operates at very low speeds and also during rotor speed reversals.

Nomenclature

B iA , iB , iC id , iq ia , ib J Ls P Rs s Te TL vA , vB , vC vd , vq va, vb damping constant stator phase currents stator currents in rotor reference frame stator currents in stationary reference frame rotor inertia stator winding self inductance number of pole-pairs stator winding resistance differential operator electromagnetic torque load torque stator phase voltages stator voltages in rotor reference frame stator voltages in stationary reference frame rotor position in electrical rad

l v vn

?

^

flux linkage angular velocity in electrical rad/s nominal speed reference quantities estimated quantities

1

Introduction

u

Permanent-magnet synchronous motor (PMSM) drives are widely used in high-performance applications. These machines are preferred because of the brushless construction, absence of rotor windings, high efficiency and improved power density. A major drawback of the classical PMSM, however, is the need for a rotor position sensor, such as a high-resolution encoder, for proper control of the inverter switches. The rotor position sensor affects the reliability of the drive system and increases the system cost. These disadvantages may be overcome by developing sensorless PMSM drives in which the rotor position is estimated through terminal voltage and current

88 / IET Electr. Power Appl., 2008, Vol. 2, No. 2, pp. 88– 98 doi: 10.1049/iet-epa:20070234

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measurements. Sensorless drives are particularly useful in applications such as electric traction, aerospace systems, oil-rigs and remotely operated vehicles [1]. Sensorless control of PMSM drives may be realised by using saliency-based position estimators or model-based observers. Saliency-based position estimation methods derive the rotor angle information from positiondependent inductance variations [2]. For example, injection signals may be exploited to estimate the rotor position [3], but this method is not effective for surface-mounted PMSM, while the injected signal may cause undesirable side effects, such as increased harmonic losses and acoustic noise. Model-based observers can be divided into those which exploit electrical dynamics only [4–13] and those which exploit both electrical and mechanical dynamics [14–16]. The latter method in general gives better estimation accuracy, but at the expense of a more complex control structure. Besides, the mechanical parameters are difficult to determine accurately and they may not be constant during drive operation. In flux linkage estimation methods [4], the rotor flux is estimated by using the integral of the machine terminal voltages. These methods are sensitive to machine parameter changes, especially the phase resistance. Drift and saturation problems may cause the controller to lose its synchronisation ability consequently. Other methods utilise the EMF or extended EMF information for computation of the rotor position [5, 6]. Owing to the close coupling of the speed and rotor position in the estimation algorithms, it may be difficult to realise rotor speed reversal. Adaptive sliding-mode observers [7–10] are generally used to handle parameter uncertainty problems, but large switching gains have to be selected. Noisy speed and speed estimates may result as it is not easy to get smooth control signals. Batzel and Lee [11] employed a full-order Luenberger observer to estimate the flux linkage and hence the rotor position. Problems of motor operation at low speeds were tackled by setting the observer gain to zero when the speed is below a certain threshold value. Shinnaka [12] put forward a sensorless control approach that could be applied to both salient-pole and non-salient-pole machines. The approach provides satisfactory sensorless control for PMSMs, but sophisticated theory is involved. Other schemes employed state estimators, such as the extended Kalman filter [13], to determine the rotor position and speed. Kalman filter based methods also require the complete set of machine parameters to be known and the algorithms are computationally intensive. It is often difficult to determine the noise covariances and the Kalman gain. This paper develops an effective sensorless PMSM drive by using a reduced-order Luenberger state observer for the rotor flux. The observer is based on the stator a – b frame dynamic model and no mechanical parameters are involved. Its structure is therefore very simple, and it can be realised at a low computation burden. Simulation and experimental results will be presented to demonstrate the feasibility of the proposed drive system.

2

Estimation strategies

2.1 Mathematical model of the PMSM

The currents and voltages of a non-salient-pole PMSM in the a – b stationary reference frame are related to the phase quantities by a linear transformation [17] 2 1 1 32 3 ! 1 ? ? iA 26 ia 2 p2? ?? p??? 74 iB 5 (1) ? 4 5 ib 3 3 3 iC ? 0 2 2 ! 2 26 ? 4 3 1 0 1 1 32 3 ? ? vA 2 p2? ?? p??? 74 vB 5 5 3 3 vC ? 2 2

va vb

(2)

The circuit equation [9] of a cylindrical PMSM in the a – b reference frame is given by (3) 2 3 2 R v s 3" " # # ? s 0 " # 0 _a lpm a i 6 Ls 7 ia Ls 7 6 7 ?6 5 4 Rs 5 ib ? 4 vs _b lpm b i ? 0 0 ? Ls Ls 2 3 1 0 " # 6 Ls 7 va ?6 1 7 4 5 v b 0 Ls (3) where u is the rotor position in electrical radians. The PM flux linkage lpma,b projected onto the a – b axis can be represented as ! ! lpm a cos(u) (4) lpm b ? l sin(u) The dynamics of the PM flux can then be determined as " # ! ! ˙ l pm a 0 ?v lpm a (5) ? ˙ lpm b v 0 l pm b where v is the rotor speed in electrical rad/s.

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To develop the ?model for a?T rotor position observer, the vector lpm a lpm b defined in (5) is considered to be a disturbance state that satisfies a known differential equation. Combining the disturbance state vector with the state variables defined in (3), we obtain the state vector x as follows ? ?T x ? x1 x2 x3 x4 ? ?T ? ia ib lpm a lpm b (6) The input vector u is the applied phase voltages in the stationary a – b reference frame ? ?T ? ?T u ? u1 u2 ? va vb and the output vector y is the measurable currents ? ?T ? ?T y ? y1 y2 ? ia ib The PMSM state and output equations are x ? Av x ? Bu _ y ? Cx where 2 R v 3 ? s 0 0 6 Ls Ls 7 6 7 Rs v 6 7 ? 0 7; Av ? 6 0 ? 6 7 Ls Ls 6 7 4 0 0 0 ?v 5 0 C? 0 ! 21 6 Ls 7 6 7 17 6 7 B?60 6 Ls 7 6 7 40 05 0 0 (8) 0 3 (7) where D ? A22 ? HA12 F ? DH ? A12 ? HA11 G ? B2 ? HB1 Fig. 1 shows the block diagram of the Luenberger state observer to estimate the rotor flux. Supposing the matrices A12 and A22 are observable, H can be chosen to place the poles of the observer matrix D at the desired locations in the complex plane. The observer matrices D, H, F and G are determined as ! 1 0 D?d 0 1 2 3 d ?1 ? ? 6 7 H ? ?D ? A22 A?1 ? Ls 4 d v 5 12 ? ?1 v 2 3 d ? ? ? ?6 ?1 7 F ? DH ? A21 ? HA11 ? dLs ? Rs 4 d v 5 ? ?1 v 2 3 d ?1 ? ? 6 7 G ? B2 ? HB1 ? ?4 d v 5 ? ?1 v ? where xm ? ia R ? s 6 Ls A11 ? 6 4 0 A21 ? 1 6L B1 ? 6 s 4 0 2 2 ib ?T h ? , xu ? l pm a ^ 3 2 ? l pm b 0 iT

v3 7 Ls 7 6 7 5 Rs 5 A12 ? 4 v ? 0 ? Ls Ls ! ! 0 0 0 ?v A22 ? 0 0 v 0 3 ! ! 0 7 1 0 7 B2 ? 0 0 I? 15 0 0 0 1 Ls

0

^ In (9), xm denotes the measurable states and xu the unknown states. From the Luenberger observer theory [18] and the state model of the PMSM, a reduced-order observer is constructed as follows z ? Dz ? Fy ? Gu _ xu ? z ? Hy ^

v

0

1 0 0 0 0 1 0 0

The subscript v in Av indicates that the latter is dependent upon the rotor angular speed.

2.2 Luenberger observer of PM flux

The state model (7) has four states and the last two ? ?T states lpm a lpm b are not measurable. Therefore instead of a complex full-order observer, a reducedorder observer will be used for the stable estimation of the PM flux linkage states. The state model of the PMSM and output equation can be partitioned as ! ! ! ! xm _ A11 A12 xm B1 ? u _ ? A xu ^ B2 xu ^ 21 A22 ! ? ? xm (9) y? I 0 xu ^

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Figure 1 Block diagram of Luenberger observer to estimate the PM flux

When v is close to zero, the computed observer matrices may become ill-conditioned. To avoid this undesirable effect, we choose the observer poles as d ? gjvj, hence the observer matrices are calculated as ! 1 0 D ? gjvj 0 1 ! ?1 g sign?v? H ? Ls ?g sign?v? ?1 ! ? ? ?1 g sign?v? F ? gjvjLs ? Rs ?1 ?g sign?v? ! g sign?v? ?1 (10) G?? ?1 ?g sign?v? In the proposed sensorless PMSM drive scheme, the observer matrices are computed with the estimated ? speed v instead of the actual rotor speed v, as illustrated in Fig. 2.

Figure 2 Application of Luenberger flux state observer to estimate the rotor position

In this work, the integral feedback speed estimation method introduced by Shinnaka [12] is adopted. The block Argfexp( j1)g in Fig. 3 is needed to return the rotor position error 1 within the range (2p, p) rad for both simulation studies and experimental work. Neglecting this block, the relationship between estimated rotor speed and estimated rotor position is given by

v? ^

C(s) ^ su s ? C(s)

(12)

Equation (12) implies that the low-pass-filtered differential ? estimated position su can be used to estimate the rotor position. In this work, the transfer function C(s) is chosen so that C(s) 2v s ? v2 c ? c (s ? vc )2 s ? C(s) (13)

2.3 Estimation of rotor position and speed

^ ^ From the flux estimates l pm a and l pm b , the rotor position may be computed as follows ^ ^ ^ (11) u ? atan2 l pm b , l pm a Fig. 2 shows the configuration of the Luenberger flux state observer to estimate the rotor position. A typical PMSM drive system possesses considerable moment of inertia and operates with short sampling intervals, and hence the angular speed v can be regarded as constant over the system sampling period. With this assumption, the resulting control model may be linearised. For sensorless control of the PMSM, the estimated speed can be derived from the estimated rotor position. Conventional approaches achieve this by employing adaptive feedback loops which assume that the estimated rotor positions are the same as the actual values [8–11].

where 2vc is the cutoff angular frequency of the lowpass filter. We may exploit the natural relationship between rotor position and rotor speed as follows 1 ^ ^ uf ? v s (14)

Figure 3 Integral feedback speed and position estimator IET Electr. Power Appl., 2008, Vol. 2, No. 2, pp. 88– 98/ 91 doi: 10.1049/iet-epa:20070234

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Figure 4 Schematic diagram of the proposed sensorless PMSM drive

The estimated rotor position can thus be given by the ? low-pass-filtered signal uf as illustrated in Fig. 3.

3

Speed and current controller

Figure 6 Current controller

The schematic diagram of the proposed sensorless PMSM drive is shown in Fig. 4. Compared with the standard sensor-based vector control system, the main difference is the presence of the ‘estimator’ block which implements the rotor position and speed estimation algorithms as discussed in Section 2. The reference voltages generated by the controller are applied to a space vector pulse-width modulation inverter. The speed controller is given by [19] i? ? 0 d ki ? iq ? kp ? (v? ? v ) ? Ba v ^ ^ s

The PI speed controller outputs the q-axis current reference i*, and the d-axis current reference i* is set q d to zero in normal operation to give the maximum torque-to-current ratio. To prevent integrator windup and inverter saturation, back-calculation is used in the speed controller. The block diagram of the speed controller is shown in Fig. 5. The current controller block is given in Fig. 6. The inputs are the current reference and the estimated rotor speed, whereas the outputs are the reference voltages. As with the speed controller, backcalculation is introduced to avoid integrator windup and inverter saturation. In a standard PI current controller, the command voltages are expressed as v? d kid ? (id ? id ) ? kpd ? s kiq ? ? vq ? kpq ? (iq ? iq ) s

(15)

If a denotes the bandwidth of the speed controller, the PI gains kp and ki , and the load torque reject gain Ba , are tuned as follows kp ?

aJ 3=2P 2 l

(16)

(17)

ki ? akp Ba ?

aJ ? B 3=2 P 2 l

where kpd , kid , kpq and kiq are PI gains for the d- and qaxes currents, respectively. The controller is difficult to

Figure 5 Speed controller 92 / IET Electr. Power Appl., 2008, Vol. 2, No. 2, pp. 88– 98 doi: 10.1049/iet-epa:20070234

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tune during implementation when d- and q-axes current coupling terms exist. To overcome this problem, we use the decoupling and diagonal internal model control (DIMC) [20] structure for current control in the drive. The DIMC regulates the stator current by ? employing the back EMF term vl, and this feedforward control decouples the dynamics between the applied voltages and the currents. The command voltages are now given by v? d Rs ? ? b Ls ? ^ (i ? id ) ? v Ls iq s d Rs ? ? (i ? iq ) ? v Ls id ? vl vq ? b Ls ? ^ ^ s q

Table 1 Parameters of PMSM drive used in simulation and experiments Parameter nominal power stator winding self inductance stator winding resistance back EMF constant number of pole-pairs Symbol Pn L R ke P J Value 1130 W 0.0369 H 12.3 V 0.979 V s/rad 4 0.2 ? 1023 kg m2 314 rad/s 3.6 N m 2.36 A (rms) 6.5 A (rms) 400 V 4 ? 2000 p/r 7.5 A 400 V 314 rad/s 2p rad/s

(18)

rotor inertia nominal speed (mech.) rated torque rated current drive current limit drive voltage limit effective resolution of encoder base current base voltage base speed (mech.) base angle (elect.)

vn

Tn In Imax Vmax n IB VB

where b is the desired closed-loop bandwidth as determined by the specified rise time of the current controller. Unlike the conventional PI controller with two parameters kp and ki , the DIMC involves only a single parameter b, and so tuning of the controller to give specified performance is easier. Instead of the measured phase voltages, the reference voltages are used as the estimator input. This will improve the drive robustness against noise and filtering can be omitted.

vB

QB

4

Simulation study

To check the feasibility of the proposed rotor position and speed estimation algorithms, a simulation study was carried out with reference to a 1.13 kW, nonsalient-pole PMSM manufactured by Brusatori Spa, Italy. The machine data are given in Table 1. A PI speed controller bandwidth a of 200 rad/s and a stator-current controller bandwidth b of 2000 rad/s were chosen. The convergence of the Luenberger flux observer depends critically upon the parameter g, which should be negative in order that the poles are placed on the left of the complex plane. On the other hand, pole placement to the far left of the complex plane improves the convergence rate, but system stability may be lost. As a general rule, the Luenberger observer poles gjvj must be chosen such that its magnitude is two to five times larger in magnitude than the speed controller poles a. This will ensure that the estimation error decays sufficiently fast compared with the desired dynamics and the speed controller poles are predominant. Simulation results indicate that satisfactory performance is guaranteed if the following pole placement conditions are satisfied ? gjvjrated ! 5a g ?0:80

This implies that g should be within the range [22.41, 20.80]. For fast convergence, the value g ? 22 was chosen for the experimental PMSM drive. The rotor position was estimated by using (11). The cutoff frequency was selected as 2512 rad/s, which is equal to the number of pole-pairs times the nominal rotor mechanical speed. From (13), the integral-feedback speed estimation low-pass filter was given by C(s) 2512s ? 12562 ? (s ? 1256)2 s ? C(s) (19)

The controller transfer function was therefore designed as C(s) ? 2512s ? 12562 s (20)

The PMSM was assumed to run on no load with the following speed commands (mech.) 8 0 s t 0:1 s < 314 rad=s, ? v ? 314 to ?314 rad=s, 0:1 s , t 0:9 s : ?314 rad=s, 0:9 s , t

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Figure 7 Actual speed, estimated speed and speed error of sensorless PMSM drive: simulation results

Figure 9 Actual speed, estimated speed and speed error of 0 sensorless PMSM drive: simulation results with Rs ? 0.6Rs , 0 Ls ? 0.6Ls

Figs. 7 and 8 show the simulation results of the sensorless PMSM drive using the Luenberger observer. With the proposed estimation algorithm, both the speed error and the position error tend to zero at steady state. Despite the initial speed and position errors, the sensorless PMSM drive is able to startup from standstill. Estimation errors also occur immediately after a zero-speed crossing operation. This phenomenon is due to the fact that the pole position of the flux observer depends upon the speed, as inferred by (10). Convergence of the estimated flux is slow at low speeds, and it is not guaranteed when the rotor speed is zero. Figs. 9 and 10 show the simulation results for the proposed sensorless PMSM drive in which the winding resistance and synchronous reactance are each equal to 60% of the nominal value. The results indicate that the speed estimation accuracy is satisfactory despite the change in motor electrical parameters. The

robustness of the sensorless drive against parameter variations is advantageous in practical applications.

5

Experimental results

5.1 Steady-state performance

Steady-state and transient tests were carried out on the sensorless PMSM drive using the experimental setup shown in Fig. 11. The estimation algorithms described in Section 3 were realised by software implementation on a digital signal processor, the fixed-point TMS320F2812 with a sampling frequency of 10 kHz. A shaft-mounted encoder was provided for monitoring the actual rotor position and to yield the rotor speed signals for evaluation of the estimation accuracy. A DC dynamometer was used as the load machine. To improve the drive performance at very low speeds (say at 3 rad/s or 1% of nominal value) the speed

Figure 8 Actual position, estimated position and position error of sensorless PMSM drive: simulation results 94 / IET Electr. Power Appl., 2008, Vol. 2, No. 2, pp. 88– 98 doi: 10.1049/iet-epa:20070234

Figure 10 Actual position, estimated position and position error of sensorless PMSM drive: simulation results with 0 0 Rs ? 0.6Rs , Ls ? 0.6Ls

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Figure 13 Performance of sensorless PMSM drive with a speed command of 5 rad/s and a load torque of 3.6 N m

Figure 11 Experimental setup of sensorless PMSM drive

estimation controller was designed with a cutoff frequency of 24 rad/s. At rotor speeds above 3 rad/s, a cutoff frequency of 2512 rad/s was used. For each case study on the sensorless PMSM drive, the response curves are presented in the following order: ? the speed command v? , the estimated speed v, ? the actual speed v, speed error v 2 v, the estimated ? rotor position u, the actual rotor position u, q-axis current component iq , and the phase A stator current iA . The y-axis quantities are normalised to the base values given in Table 1, whereas time is measured in seconds. Fig. 12 shows the PMSM performance at a command speed of 3 rad/s, which corresponds to 1% of the nominal speed. At such a low speed, the dynamometer machine could only exert a load torque of 1.8 N m (which corresponds to half of rated load) to the motor. To ascertain the accuracy of position estimation,

? the rotor position error u 2 u and the filtered position ? f 2 u response are also given in Fig. 12. The error u speed estimation error was 0.5 rad/s, or 16.7% of the command speed. Both the estimated rotor positions ? ? u and uf match well with the actual position, which ? confirmed that the filtered estimated rotor position uf given by (14) could be used as the rotor position signal. This approach was therefore adopted in all subsequent investigations. Fig. 13 shows the PMSM performance at a rotor speed of 5 rad/s and with the rated torque of 3.6 N m applied. The estimated rotor position also matches well with the actual value. The rotor speed, however, experiences more pronounced fluctuation due to the heavier load torque and also due to the higher cutoff frequency of the speed estimator used. The speed estimation error is 1.0 rad/s, or 20% of the command speed. Fig. 14 shows the performance of the sensorless PMSM drive at a rotor speed of 188.5 rad/s (or 60% of nominal value) and with rated torque applied. Both the rotor position and speed estimation accuracies are

Figure 12 Performance of sensorless PMSM drive with a speed command of 3 rad/s and a load torque of 1.8 N m

Figure 14 Performance of sensorless PMSM drive with a speed command of 188.5 rad/s and a load torque of 3.6 N m IET Electr. Power Appl., 2008, Vol. 2, No. 2, pp. 88– 98/ 95 doi: 10.1049/iet-epa:20070234

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Figure 15 Transient response of sensorless PMSM after a sudden application of rated load torque at 10 rad/s

Figure 17 Motor response to a trapezoidal speed command waveform: slow rotor speed reversals with load

very good. The speed estimation error is 3.0 rad/s, or 0.96% of the command value. The effectiveness of the sensorless controller is therefore verified from the results of Figs. 12 –14.

5.2 Load change

Fig. 15 shows the transient performance of the sensorless PMSM drive subsequent to the application of rated load at a command speed of 10 rad/s. The initial no-load stage demanded a small q-axis current and phase current for overcoming the frictional losses of the load machine. When rated torque was applied, both the q-axis current and phase stator current were regulated so that the electromagnetic torque developed restored the rotor speed back to the command value. The sensorless controller was able to maintain stable operation when the drive was subjected to a large load disturbance.

Fig. 16 shows the transient performance of the sensorless PMSM drive subsequent to removal of rated load at a command speed of 10 rad/s. In this case, the currents were decreased in order to maintain the rotor speed at the command value. It is observed that the transient response subsequent to removal of load was faster than that subsequent to application of load. This was due to the delay in torque response of the dynamometer machine when loaded as a generator.

5.3 Slow rotor speed reversal with load

Fig. 17 shows the PMSM drive performance at low speeds. A trapezoidal command speed waveform with an amplitude +15.7 rad/s and an acceleration of +30 rad/s2 was used in this investigation. The dynamometer was loaded in such a way that rated torque was developed at a rotor speed of +15.7 rad/s. During a rotor speed reversal, a variable load torque would be applied to the PMSM drive. The results indicated that the PMSM drive performed satisfactorily at low speeds with zero-speed crossing while driving a variable load. The maximum estimated speed error occurred at zero speed as the estimated rotor position converged slowly. Compared with the speed command, the estimated speed has a time delay due to the actions of the PI controller and the speed low pass filter for estimating the rotor speed (12).

5.4 Rapid rotor speed reversal

To evaluate the speed estimation accuracy during rapid rotor speed reversals, the sensorless PMSM drive was operated on no load by using a trapezoidal speed command waveform with an amplitude of +251.3 rad/s (+80% of nominal speed) and an acceleration of +840 rad/s2 during speed reversal operations. The load machine was uncoupled from the

Figure 16 Transient response of sensorless PMSM after a sudden removal of rated load at 10 rad/s 96 / IET Electr. Power Appl., 2008, Vol. 2, No. 2, pp. 88– 98 doi: 10.1049/iet-epa:20070234

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7 Acknowledgments

The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 5201/03E).

8

References

[1] SNARY P., BHANGU B. , BINGHAM C.M., ET AL .: ‘Matrix converters for sensorless control of PMSMs and other auxiliaries on deep-sea ROVs’, IEE Proc., Electr. Power Appl., 2005, 152, (2), pp. 382 – 392 [2] KULKARNI A., EHSANI M.: ‘A novel position sensor elimination technique for the interior permanent magnet synchronous motor drive’, IEEE Trans. Ind. Appl., 1992, 28, (1), pp. 144– 150 [3] JANG H., SUL S.K., HA J.I., ET AL .: ‘Sensorless drive of surface-mounted permanent-magnet motor by high-frequency signal injection based on magnetic saliency’, IEEE Trans. Ind. Appl., 2003, 39, (4), pp. 1031 – 1039 [4] WU R., SLEMON G.: ‘A permanent magnet motor drive without a shaft sensor’, IEEE Trans. Ind. Appl., 1991, 27, (5), pp. 1005 – 1011 [5] ANDREESCU G.D. : ‘Adaptive observer for sensorless control of permanent magnet synchronous motor drives’, Electr. Power Compon. Syst., 2002, 30, pp. 107 – 119 [6] KIM J.-S., SUL S.-K. : ‘High performance PMSM drives without rotational position sensors using reduced order observer’. Conf. Rec. IEEE – IAS Annual Meeting, October 1995, vol. 1, pp. 75– 82 [7] FURUHASHI T., SANGWONGWANICH S., OKUMA S.: ‘A positionand-velocity sensorless control for brushless DC motors using an adaptive sliding mode observer’, IEEE Trans. Ind. Electron., 1992, 39, (2), pp. 89 – 95 [8] HAN Y.-S., CHOI J.-S., KIM Y.-S.: ‘Sensorless PMSM drive with a sliding mode control based adaptive speed and stator resistance estimator’, IEEE Trans. Magn., 2000, 36, (5), pp. 3588 – 3591 [9] CHEN Z., TOMITA M., DOKI S., ET AL .: ‘New adaptive sliding observers for position- and velocity-sensorless controls of brushless DC motors’, IEEE Trans. Ind. Electron., 2000, 47, (3), pp. 582– 591 [10] ELBULUK M., LI C.: ‘Sliding mode observer for widespeed sensorless control of PMSM drives’. Conf. Record IET Electr. Power Appl., 2008, Vol. 2, No. 2, pp. 88– 98/ 97 doi: 10.1049/iet-epa:20070234

Figure 18 Motor response to a trapezoidal speed command waveform: rapid rotor speed reversals without coupled load

PMSM drive since its rated speed (157 rad/s) is much lower than the maximum rotor speed being attempted. Fig. 18 shows the motor performance under the above testing conditions. The speed estimation accuracy of the experimental PMSM drive was also satisfactory during rapid acceleration/deceleration transients and the speed tracking capability was good. Fig. 16 confirms the validity of the simulations illustrated in Figs. 7 and 8. From (10), the pole locations of the flux state observer depends on the speed, and the rate of convergence of the estimated flux to the actual flux is zero at zero speed. This implies that the control scheme cannot work properly if zero command speed is applied for a prolonged period. Nevertheless, the results in Sections 5.3 and 5.4 indicate that the sensorless PMSM drive is capable of zero-speed crossing operations, a useful feature for practical servo applications.

6

Conclusions

This paper has presented a speed sensorless PMSM drive using a Luenberger observer for PM flux states. The proposed observer has a reduced order and does not involve mechanical parameters. Details of the rotor position and rotor speed estimators are given. The feasibility of the proposed method is verified and confirmed through simulation and extensive experiments. The experimental sensorless PMSM drive gives satisfactory performance even when operating at a rotor speed of 3 rad/s, or 1% of the nominal value.

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IEEE – IAS Annual Meeting, October 2003, vol. 1, pp. 480– 485 [11] BATZEL T.D., LEE K.Y.: ‘Electric propulsion with the sensorless permanent magnet synchronous motor: model and approach’, IEEE Trans. Energy Convers., 2005, 4, (4), pp. 818– 824 [12] SHINNAKA S.: ‘New sensorless vector control using minimum-order flux state observer in a stationary reference frame for permanent-magnet synchronous motors’, IEEE Trans. Ind. Electron., 2006, 53, (2), pp. 388– 398 [13] BOLOGNANI S., ZIGLIOTTO M., ZORDAN M.: ‘Extended-range PMSM sensorless speed drive based on stochastic filtering’, IEEE Trans. Power Electron., 2001, 16, (1), pp. 110–117 [14] SEPE R.B., LANG J.H.: ‘Real-time observer-based (adaptive) control of a permanent-magnet synchronous motor without mechanical sensors’, IEEE Trans. Ind. Appl., 1992, 28, (6), pp. 1345– 1352 [15] DE ANGELO C., BOSSIO G., SOLSONA J., ET AL .: ‘Mechanical sensorless speed control of permanent-magnet AC motors driving an unknown load’, IEEE Trans. Ind. Electron., 2006, 53, (2), pp. 406– 414 [16] WALLMARK O., HARNEFORS L., CARLSON O.: ‘An improved speed and position estimator for salient permanent-magnet synchronous motors’, IEEE Trans. Ind. Electron., 2005, 52, (1), pp. 255– 262 [17] PILLAY P., KRISHNAN R.: ‘Modeling of permanent magnet motor drives’, IEEE Trans. Ind. Electron., 1998, 35, (4), pp. 537– 541 [18] STEFANI R.T., SHAHIAN B., SAVANT C.J.JR., ET AL .: ‘Design of feedback control system’ (Oxford University Press Inc., New York, USA, 2002) [19] HARNEFORS L., PIETILAINEN K. , GERTMAR L.: ‘Torquemaximizing field-weakening control: design, analysis, and parameter selection’, IEEE Trans. Power Electron., 2001, 48, (1), pp. 161– 168 [20] HARNEFORS L., NEE H.-P.: ‘Model-based current control of AC machines using the internal model control method’, IEEE Trans. Ind. Appl., 1998, 34, (1), pp. 133 – 141

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