1. Back EMF Sensorless-Control Algorithm for High-Dynamic Performance PMSM
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 6, JUNE 2010,P.2092~2100
Fabio Genduso, Rosario Miceli, Member, IEEE, Cosimo Rando, and Giuseppe Ricco Galluzzo
Adviser : Y.S. Kung
Student :Jin-Mu Lin

2. Outline Abstract Introduction Control-algorithm description
Experimental results
Conclusion
Appendix
References

3. Abstract
1. a low-time-consuming and low-cost sensorless-control algorithm for high-dynamic performance permanent-magnet synchronous motors.
2. This control algorithm is based on the estimation of rotor speed and angular position starting from the back electromotive force space-vector
determination without voltage sensors by using the reference voltages given by the current controllers instead of the actual ones.

4. 3. This choice obviously introduces some errors that must be vanished by means of a compensating function.
4. The mathematical structure of the estimation guarantees a high degree of robustness against parameter variation as shown by the sensitivity analysis reported in this paper.

5. Introduction
1. in field-oriented control for brushless machines, the exact knowledge of the rotor angular position is needed.
2. when the rated power of an electrical machine is small or fractional,the electrical-drive comprehensive cost will raised.
field-oriented control 磁場定向控制

6. 3. the signal transmission between sensor and control systems can be subjected to electromagnetic interference (EMI) coming from external sources, producing an error in measurement that may be significant for feedback control.
4.So in this paper, a novel low-time-consuming and low-cost sensorless-control algorithm for PMSM drives, both surface or IPM mounted.

7. Control-algorithm description
A. PMSM Mathematical Model

8. id=0,是必須的，這樣可以簡化，

9. the torque expression in (1) becomes
Because of the constant PM flux, the torque depends only on the quadrature component of the stator current.

10. B. Description of the Estimator
Assuming a balanced three-phase system, the expression of the back EMF space vector components is

11. The argument of the back EMF clearly is not the real rotor position.

12. A simple analysis on the machine model at steady state with id = 0 gives the following expression for correct rotor position:

13. Let T be the lag time introduced by the inverter and be the first term of (4),

14. Now, after substitution, considering a well-known calculus formula for the increment of functions, we can write

15. and developing the partial derivatives of the incremental term
(𝜕 𝐹 /𝜕𝑣 𝛼 )𝛿𝑣 𝛼 + (𝜕 𝐹 /𝜕𝑣 𝛽 )𝛿𝑣 𝛽
, we get

16. Now, neglecting all harmonics, consider that 𝑣 𝛼 and 𝑣 𝛽 are, respectively, cosine and sine functions of ωt. The same can be
said for 𝑣 ∗ 𝛼 and 𝑣 ∗ β . In particular, it is
where V is the rms value of the stator voltage.

17. It is now clear that T being very small compared with 2π/ω

18. In this way, our previous expansion of (8) reduces to

19. that in a more compact form becomes
cos(ϕ) being the power factor in the motor operation and V , I,and E are, respectively, the rms values of the stator voltages,currents, and back EMF.

20. Equation (12) may be written also in complex-number form
where ( ∗ ) denotes the complex conjugate.

21. Furthermore, as with 𝑖 𝑑 = 0, the motor drive operates with near-unity power actor, (12) can be further simplified as follows:
Equation (12) expresses the correction term to be used to
estimate the argument of the back EMF when the reference
voltages are used.
---投影片---
It is clear that E depends not only on the motor speed but also
on the current. Therefore, the term (V/E)ωT in (14) depends
simultaneously on speed and on stator current (by means of E).
This term is referred as the “speed offset” because ω appears
explicitly, even if E depends on the stator current.

22. Introducing these speed- and current-offset corrections in (4), one finally gets a suggestion for the first expression of
“estimated” position

23. Fig. 2 shows the sum of speed and current offsets
Fig. 2 shows the sum of speed and current offsets (V/E)ωT + arctan(λ P M /L q I q ) as a function of speed and
current i q at steady state with reference to the IPMSM used for the experiments in this paper (see Table I for nameplate ratings).

24. Equation (15) may be rewritten in a differential form by substituting 𝜔 with the derivative of 𝜃 est

25. C. Estimator Realization
Taking the presence of the PI into account, the ultimate estimator-equation form is
This ensures that the position-estimation error 𝜃 − 𝜃 est vanishes.

26. Estimator block diagram.(Fig.3.)

27. Experimental results A. Description of the Test Bench 1) an IPMSM;
2) a controlled hysteresis brake;
3) a digital signal processing and control
engineering(dSPACE) board;
4) a resolver (used only for comparison purpose).
A master Power PC 604E and a Ti slave DSP of the type TMS320F240.

28. Test bench for IPMSM electrical-drive machine.(Fig.4.)

30. B.Results and Discussion
1) step change in motor speed from 400 up to 4000 r/min (nominal speed) and back again to 400 r/min.
2) sudden application of a 1.8-N · m load torque while the motor runs at 4000 r/min speed.

31. Comparison between (solid line) real and (dashed line) estimated speed during the execution of test n. 1.
Fig. 5.

32. (Solid line) Real and (dashed line) estimated position during the execution of test n. 1.
Fig. 6.

33. Comparison between (solid line) real and (dashed line) estimated rotor position during the execution of test n. 2.
Fig. 7.

34. Comparison between (solid line) real and (dashed line) estimated rotor speed during the execution of test n. 2.
Fig. 8.

35. Estimation error for rotor speed during the execution of test n. 2.
Fig. 9.

36. Conclusion
this paper, a low-time-consuming and low-cost sensorless-control algorithm for PMSM without voltage probes for position and speed estimation has been introduced, discussed, and experimentally verified.
Drive starting is made with open-loop operation.
使用開回路

37. in the proposed control systems, the reference voltages instead of the actual voltages are used for the back-EMF estimation,therefore eliminating the presence of voltage probes.
量測反電動勢使用參考電壓，取代真實電壓，所以電壓感測器勢必移除。

38. Clearly, the presented correction method is intended, above all, to make the electrical drive cheaper and suitable for industrial drives both surface or internal mounted PM working within the nominal speed range, as, for example, for spindle drives, while the field weakening is not taken into account.
顯然，提出的校正方法的目的是，首先，使電力驅動便宜，適合工業驅動器的表面或內部安裝時的額定轉速範圍內工作，例如，主軸驅動器，而弱磁不考慮。

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