Luenberger Position Observer Based on Deadbeat-Current Predictive Control for Sensorless PMSM

Round 1

Reviewer 1 Report

This manuscript proposes a sensor-less control of permanent magnet synchronous motors. The authors discuss a deadbeat current predictive control including current compensation methods and compare its efficiency to that of more conventional sensor-less control methods that neglect current fluctuations.

In general, this manuscript is well written, and the method proposed is discussed in a detailed and rigorous way. This manuscript deals with an important topic since permanent magnet synchronous motors can be found in a wide range of applications where their control demands a high level of precision, especially when operating at high speed. Here, the implementation of a two order phased-Locked-Loop position to track the rotor position and speed, in combination with the proposed deadbeat current predictive method, demonstrates a generally higher accuracy with respect to the traditional ones. Indeed, the discussion is supported by a solid experimental validation, which evidences an improved speed response and current accuracy, as well as a reduced error in estimating the rotor position. For all these reasons, I would recommend this paper for publication after addressing a few comments.

The acronym PLL, which should stand for “Phased-Locked Loop”, is used on page 1, line 36, but it is explained only in line 131 on page 4.
Page 6, line 186: the sentence “The sampling current i(k-1) and are used to predict...” seems to miss a word after “and”.

Line 278-280 page 11. Figure 9 is introduced mentioning the first step at 0 seconds. Actually, from the panel a, the first step is at about 5 s. The graph shows a clear improvement in terms of a quicker response to the imposed speed. It is interesting to note that the deadbeat current predictive method introduces also a small but notable spike in the speed, which seems to grow as a function of the desired speed. A similar “quick-peak” response is shown by the current value in figure 11b. I would like to know the authors’ opinion about that.

Figure 10 shows the current error of both conventional and deadbeat current predictive method. While the later shows a smaller amplitude and a clear improvement, the line width used is too large and the oscillations are partially superimposed, giving the impression of much quicker fluctuations with the new method of current prediction.

I know this is not the final layout of the article, but figure 13 is mentioned in paragraph 4.2 on page 13 line 319 but shown only after the next paragraph. Besides, figure 13d shows an improved average current value, but once more, a larger amplitude for the individual spikes. This is an interesting behavior the authors should comment about.

The panels in figure 14 should be rescaled to avoid to cut out part of the data like in panel a. The caption reports 1000 rpm for panel c but I think it is representing data at 2000 rpm.

Author Response

Dear Professor:

        Thank you for your suggestions and comments on our paper. Firstly, I am sorry for some mistakes caused by our carelessness, we will correct it in later manuscript. Besides, we are gald to explain the fluctuations on speed response and current response. Due to the integrator in current closed-loop, the order of system has risen to the third order system from original second order system. By designing appropriate gain of integrator, the system achieves a faster response but the overshoot of system is bigger than before. Noticing the settling time of system is too short, the overshoot of new algorithm would not make too much difference on control performance. In general, the steady-state error of the system is smaller than before. Furthermore, the Luenberger observer used to track rotor position information is applied. Due to the small back EMF in PMSM starting stage, the back-EMF cannot be estimated precisely ,which causes the fluctations in low speed stage. Another question is about the "quick peak" of speed response at the moment of speed switch. We think the Back EMF in different speed stage is different, the observer is discrete, and the control progress is affected by the inverter and temperature, which cause small fluctuations at state switching moment.

     Thank you again for your suggetions and comments.

Reviewer 2 Report

The contribution of the manuscript is reasonable, and thus it is potentially publishable from this viewpoint. However, the English language and style must be thoroughly revised in the final version.

Author Response

Thank you for your suggestions and comments on our paper.  I am sorry for some linguistic errors caused by our carelessness, we will correct it and in later manuscript.

Reviewer 3 Report

This manuscripts contains a Luenberger rotor sensorless observer based on a proposed current control
350 method. The analytical approach and correspponding results presented here are sound.

This should be accepted as it is.

But the english language and style should be  corrected.

Author Response

Thank you for your suggestions and comments on our paper. I am sorry for some linguistic errors caused by our carelessness, we will correct it and in later manuscript.