計畫成果及自評

本計畫成果說明如下：

1. 在 96 年 7 月於台灣科技大學舉辦交流電動機設計及驅動產業論壇，由相關的子計畫主持人報告計畫執行成果，以一天的時間進行報告，並邀請產、官、學研相關研究人員參加。

2. 獲得中華民國專利一件：

發明第工 246822 號

開關式磁阻馬達及直流無刷馬達轉軸角/速度估測方法

3. 相關成果已投稿至 International Journal of Electronics 期刊及 IEE proc.-Electr. Power Appl. 期刊

參考文獻

[1] P. C. Sen, “Electric motor drives and control-past, present, and future,” IEEE Transactions on Industry Applications, vol. 37, no. 6, pp. 562-575, December 1990.

[2] B. K. Bose, “Power electronics and motion control-technology status and recent trends,” IEEE Transactions on Industry Applications, vol.

29, no. 5, pp. 902-909, September/October 1993.

[3] G. C. Verghese and S. R. Sanders, “Observers for flux estimation in induction machines,” IEEE Transactions on Industrial Electronics, vol. 35, no. 1, pp. 85-94, February 1988.

[4] P. Pillay and R. Krishnan, “Application characteristics of permanent magnet synchronous and brushless dc motors for servo drives,” IEEE Transactions on Industry Applications, vol. 27, no. 5, pp. 986-996, September/October 1991.

[5] D. E. Cameron, J. H. Lang, and S. D. Umans, “The origin and reduction of acoustic noise in doubly salient variable-reluctance motors,” IEEE Transactions on Industry Applications, vol. 28, no. 6, pp. 1250-1255, November/December 1992.

[6] G. S. Buja and M. I. Valla, “Control characteristics of the SRM drives-part I: operation in the linear region,” IEEE Transactions on Industrial Electronics, vol. 38, no. 5, pp. 313-321, October 1991.

[7] G. S. Buja and M. I. Valla, “Control characteristics of the SRM drives-part II: operation in the saturated region,” IEEE Transactions on Industrial Electronics, vol. 41, no. 3, pp. 316-325, June 1994.

[8] T. J. E. Miller, Switched Reluctance Motors and Their Control, New York: Oxford, 1993

torque production,” IEEE Transactions on Industrial Electronics, vol.

39, no. 2, pp.168-174, April 1992

[10] 王健鴻, “開關式磁阻電動機的無轉軸偵測跑步機驅動系統性能改善之研究,” 碩士論文, 國立台灣科技大學電機工程研究所, 2004 年六月.

[11] B. Andreycak, Power factor correction design consideration and the uc3854n PWM controller, Unitrod Inc. Product & Applications Handbook, 1997.

[12] 新華電腦, DSP 從此輕鬆跑<以 TI DSP 320LF2407A 為主題>, 台科大圖書股份有限公司, 2003 年十月.

參加2006年IEEE-IECON’2006研討會報告

1. 前言

2006年第32屆國際電機電子學會工業電子分會(IEEE-IECON’2006)係在法國巴黎舉行，地點在 Conservatoire National des Arts et Metiers大學，時間由11月6日(一)至11月10日(五)，共計五天。此次會議共約有1700篇論文投稿，接受959篇。接受率約為56%，參加人員來自世界各地64個國家。

此次會議共有七個領域，分別涵蓋：控制系統及應用，電機機械及驅動、電力電子、感測器與致動器及系統整合、信號及影像處理、工業資訊、微機電及機器人等七個主題。同時有七場並行進行，

參加人員可以選擇有興趣的場次進行聆聽及討論，氣氛相當熱絡，充分達到交流目的。

2. 參加研討會經過

第一天

11月6日(一)為短期課程(tutorial)，時間為上午9:00至下午5點，包括：

1. 電動車電力電子與電動機驅動在混合車及燃料電池電動機的應用。

2. 使用 MATLAB 在電力電子系統及電動車驅動的模式建立及模擬 3. 大學教育在電力電子、電動機驅動及電力系統的改進

4. 被動式控制在功率轉換器及電動機控制的應用 5. 使用 VHDL 及 FPGA 在功率變頻器的應用 6. 感應式功率轉換

7. 電動機及發電機的熱分析

8. 高功率轉換器：拓樸，控制及應用

9. 工業資訊化時代，自動化的合作及服務架構 10. 以網路為基礎的控制系統及應用

11. 智慧控制應用在功率電子系統及電動機驅動

第二天

11月7日(二) 上午8:00~12:00 上午8:00~10:00 註冊

上午10:00~10:45 開幕式

上午11:15~12:00 大會專題演講(一)：法國傳輸系統操作的發展

上午11:15~12:00 大會專題演講(二)：衛星導航服務的整合

下午3:00~4:40

論文發表

z 功率電子元件 I z 控制

z 能源系統

z 開關式磁阻電動機及驅動 z 分數微分及其應用 I z 整合光電及其相關技術 z 系統判別及估測 I z 非線性及最佳控制 II z 能源系統的控制 I z 三維影像處理 z 汽車影像處理 z 致動器

z 視覺

第三天 11月8日(三) 上午8:00~10:00 z 功率電子元件 II z 功率轉換器的控制 z 電動機驅動(感應)

z 永磁電機無轉軸偵測元件驅動 z 分數微分及其應用 II

z 工程及工業技術教育 z 微機電系統

z 風力整合系統 I z 系統判別及估測 II z 非線性及最佳控制 III z 能量系統控制 II z 影像處理 I

z 圖形描述及電力系統控制

z 感測器

z 網路為基礎的控制系統 I 上午11:00~下午1:00

z 電動機驅動 II z 電力電子元件 III z 電力轉換器控制 II

z 無轉軸偵測元件的電動機驅動 z 類神經網路應用在主動功率濾波器 z 產品中的人類因素

z 電力電子中 MATLAB/Simulink 應用 z 風力整合系統 II

z 系統判別及估測 III z 智慧型控制 I z 網路為基礎的控制 z 影像處理 II

z 圖形描述及電力系統控制 z 類神經網路及模糊邏輯 I z 網路為基礎的控制系統 II

第四天 11月9日(四) 上午8:00~10:00

z 功率轉換器控制 III z 主動濾波器

z 滑動模式及基因法則

z 感應電動機的無轉軸元件驅動系統 z 電機機械 III

z 永磁電動機控制 z 智慧型感測器 z 再生能源 I z 非線性控制 I z 運動控制

z 交流驅動器的先進控制及觀測

z 影像處理 III z 高精度運動控制 I z 類神經及模糊邏輯 II

z 電機機械及驅動器的熱分析上午11:00~下午1:00

z 燃料電池及直接功率控制 z 矩陣轉換器

z 整流器 z 觀測技術 z 電機機械 II

z 功率發電機的應用 z 系統整合

z 再生能源 II z 非線性控制 II z 程序控制

z 交流驅動系統的先進控制及觀測 z 語音及信號處理 I

z 高精度運動控制 II z 行動機器人

z 電機機械及驅動的熱分析下午3:00~5:00

z 波寬調變

z 直流/直流轉換器 z 功率轉換器 I z 感應電動機驅動 z 電機機械 I z 電機機械 IV

z 智慧型微感測器及致動器 z 分佈系統及機器人

z 非線性及最佳控制 I

z 行動系統控制

z 工業程序

z 語音及信號處理 II

z 低功率電力電子及 SOC-I z 定位系統

z 人類調適及人性化微機電-I

第五天 11月10日(五) 上午8:00~10:00 z 共振式轉換器

z 交流/交流轉換器及主動濾波器 z 實現

z 估測技術

z 双饋及特殊感應機驅動 z 交換協定

z 網路感測器 z 再生能源-III

z 自我最佳化系統及其先進控制-I z 電機系統的偵錯及可靠度 z 新型控制架構

z 分佈式發電機系統 z 微機電

z 行走及抓取 z 生醫電子及光電上午11:00~下午1:00 z 電力轉換器控制 z 電源供應系統 z 功率轉換器 II

z 電動機驅動的容錯及偵測 I z 電動機驅動的控制技術 II z 量測與控制

z 控制

z 再生能源 IV

z 自我最佳化系統及其先進控制 II z 電機系統的偵錯及可靠度

z 控制的即時應用 I z 分佈發電系統 II z 微機電

z 協助及服務機器人 z 生醫及光電

下午3:00~5:00

z 電力轉換器控制 V z 功率轉換器 III z 電源供應系統 II z 電動機驅動的偵測 II z 電動機驅動的控制技術 I z 正式的工業方法

z 電力轉換器控制 VI

z 自我最佳化系統及其先進控制 III z 電機系統的偵錯及可靠度

z 控制的即時應用 II

z 超寬頻檢測器及 RFID 的技術與應用 z 控制技術

z 具人類適應及人性化的微機電 II

此次研討會申請人共發表兩篇論文：Adaptive controller design for sensorless IPMSM position

control system以及Field weakening with nonlinear controller design for an interior permanent magnet

synchronous motor。此外，申請人也擔任TPC2-2 section : Sensorless PM machines的主持人。在發表

完論文後得到熱烈的迴響並與多位教授如Rahman教授等充分討論，也有多位德國教授對申請人的

論文具有濃厚興趣，留下名片日後聯絡。

3. 攜回資料 1. 議程1本 2. 光碟1片

4. 建議

參加IEEE IECON-2006收穫甚多，不但發表2篇論文，主持一場議程，且認識多位國際間知名的教授，達到充分交流的目的。

5. 所發表的兩篇論文附錄如下

Field Weakening with Nonlinear Controller Design for an Interior Permanent Magnet Synchronous Motor

Ji-Liang Shi Tian-Hua Liu Shih-Hsien Yang

National Taiwan University of Science and Technology 43 Keelung Road, Section 4

Taipei 106, Taiwan

Abstract – This paper proposes a field weakening control algorithm with a nonlinear speed-loop controller for an interior permanent magnet synchronous motor. By using the proposed method, the adjustable speed range can be extended to 1.6 times that of the based speed. The method includes the constant torque region and the constant power region. In addition, an adaptive backstepping speed-loop controller is designed to improve the transient response and load disturbance rejection capability. A DSP based full digital speed-control system is implemented. Several experimental results validate the theoretical analysis.

I. INTRODUCTION

The interior permanent magnet synchronous motor (IPMSM) has been widely used in industry due to its high torque to current ratio, large power to weight ratio, high efficiency, and superior robustness. The rotor of the IPMSM has complex geometry. This feature allows the motor to be operated in a high-speed operating range by incorporating the field-weakening technique. Several researchers have discussed the field-weakening technique for an IPMSM. For example, Morimoto et al. proposed a combining method to achieve a maximum torque-per-amp control and constant power control [1]. Soong et al. compared the experimental field-weakening performance of five rotors, including the induction motor, the IPMSM, and the synchronous reluctance motor [2]. Uddin et al. investigated the performance of an IPMSM over a wide speed range for high precision industrial applications [3]. Pan et al. proposed a linear torque control strategy for an IPMSM drive to fully utilize the reluctance torque and simplify the controller design [4]. Kim et al.

proposed a novel flux-weakening scheme for an IPMSM drive system, which is based on the output of the synchronous PI current regulator-reference voltage to the PWM inverter.

The flux level can be adjusted inherently by the outer voltage regulation loop to prevent saturation of the current regulator [5]. Rahman et al. proposed a novel control scheme for a direct-controlled IPMSM drive incorporating field weakening technique [6]. In addition, Rahman et al. proposed a nonlinear control for an IPMSM. This paper, however, focuses on the constant torque region only and does not consider the constant power region [7].

--- This project is supported by National Science Council, the R. O. C., under Grant NSC 94-2213-E-011-074.

Generally speaking, only very few papers discuss the controller design for an IPMSM which is operated in field weakening region [4]. This motivated us to design an advanced nonlinear controller, which takes the system nonlinearities into account in the controller design.

In this paper, an adaptive backstepping controller with a maximum torque/ampere control is designed to overcome motor mechanical parameter uncertainties and to improve the dynamic responses of an IPMSM. The operation ranges of the motor include constant torque region and constant power region. The experimental results show that the proposed method can work well in both the constant torque region and the field weakening region. To the authors’ best knowledge, this is the first time that an adaptive backstepping controller is applied to the field-weakening control and constant torque for an IPMSM. The details are shown follows.

II. MATHEMATICAL MODEL

In d-q axis synchronous frame, the dynamic equations of the IPMSM, can be expressed as:

) Where d/dt is the differential operator,

i

_d is the stator d-axis equivalent current, and i_q is the stator q-axis equivalent current,L is the d-axis self- inductance, _d L is the q-axis _q self- inductance,

v

_d is the d-axis voltage,

v

_q is the q-axis voltage,

r

_s is the stator resistance, ω_e is the electrical speed, and λ_m is the flux-linkage of the permanent magnet in the d-axis rotor. The electro-magnetic torque expressed in the d-q synchronous frame is

where T is the electro-magnetic torque of the motor, and _e P is the number of poles of the motor. In this paper, the maximum torque algorithm is used to achieve a maximum torque/ ampere ratio. According to equation (3), the difference between L and _d L is negative. As a result, a _q negative of

i

_d is required to increase the electro-magnetic torque. The rotor speed and position of the motor can be expressed as: constant of the motor and load, T_l is the external load torque, B is the viscous frictional coefficient of the motor and load, and θ is the mechanical rotor position. The electrical rotor _r speed and position are expressed as:

III. FIELD WEAKENING ALGORITHM When the motor is operated in the constant torque region, a maximum torque/ampere is required in this paper. The d-axis current command and q-axis current command are selected as [3]:

When the motor exceeds base-speed, the field weakening technique is required. To fit the voltage limit constraint, the d-axis and q-axis current commands have to satisfy the following equation [1]:

)

The voltage _V_am is the maximum available output voltage of the inverter depending on the dc-link voltage. The current Iamis a continuous rated armature current or a maximum available current of the inverter.

Fig.1 shows the current trajectories of the d-q axis currents in different operating modes. In this figure, there are three regions: region I, region II, and region III. In region I, the speed is below base speed. The terminal voltage is below Vom, the motor is only limited by the maximum current of the inverter. As a result, a MTPA control algorithm can be applied. When the motor speed increases and exceeds the base speed, the region II is achieved. Region II is the range between base speed ω_base^andω_c. The speed ω_cis the speed of rated voltage with

i

_d and

i

_qequal to zero. In region II, if the MTPA can be satisfied and the terminal voltage is below the allowed voltage, then the MTPA is selected. For example, in Fig. 1, the C point is in the MTPA mode and the C point terminal voltage is below the voltage-limit at speed ω₂ . Then, the C point is chosen. However, in the real world, we can not on-line measure the constant torque curve. As a result, we use a DSP to determine the d-axis current

i

_dB. When MTPA control is satisfied, the B point is selected at the speed of ω₂ by setting d-axis current command as

i

_dB. On the other hand, the DSP determines the d-axis current

i

_dD by using the field weakening control algorithm. From Fig.1, we can observe that i_dD is smaller than i_dB and then the MTPA can be selected. For implementation, we use the DSP to compare

idD^andi_dB ^{. If}i_dD < i_dB , the MTPA algorithm is used. However, if

dD dB

i > i , the field weakening algorithm is applied. When the speed exceedsω_c, only the field weakening algorithm can be used. The d-q axis current command in different operating modes is shown in Fig.2.

ωbase

Fig. 1 The current trajectories of the d-q axis currents in different operating modes.

base

Fig. 2 The d-q axis current command in different operating modes.

IV. CONTROLLER DESIGN

The PID controller is widely used in industry due to its simplicity. In addition, by suitably adjusting the gains: K_P, K_I, and KD, the PID controller can achieve the required performance of the closed-loop control system. As we know, the variations of the system parameters and load can heavily influence the performance of a PID controller. To eliminate the disadvantage, in this paper, an adaptive nonlinear controller is proposed. The details are as follows.

In this paper, first, the speed error is defined as :

e =

ωr^*

−

ω (10)

where ω_r^* is the speed command. By taking the derivative of equation (10), one can obtain

)

Then, define a Lyapunov function

2 1Je

V= (12)

By taking the derivative of equation (12) and substituting (3)(4) into the derivative of equation (12), one can obtain :

⎟⎠

In order to on-line adjust the d-axis and q-axis currents, in this paper we select the two currents as :

e parameter with a negative value. Substituting (14)(15) into (13), one can derive:

According to equation (16), we can see that the Lyapunov is semi-negative definite. As a result, the whole control system is stable. Unfortunately, in the real world, the inertia

J and the external load T can not be measured precisely. In _l addition, the inertia J and the T can be varied abruptly to _l the external load. As a result, it is better to obtain the parameters J and the T by using on-line tuning. _l

The d-axis current and q-axis current are redefined as:

By substituting (3)(4) into (11) and substituting (17)(18) into the previous result,we can obtain

To consider the influence of the tuned parameter error, we should redefine the Lyapunov function as:

2 taking the derivative of equation (20), one can obtain

)

In this paper, we assume that the variations of the inertia, viscosity, and load are slow as compared to the variation of the current slope. As a result, dJ dt , dB dt , and dT dt are _l neglected. Then, substituting (19) into (21), one can obtain

After some mathematical processes, we can derive )

Finally, we can set the parameter adaptive law as follows:

1 0

From (24)-(26), we can derive the adaptive law of the speed controller as:

By substituting (27)-(29) into (23), we can obtain

2 0

From (30) and using Barbalat’s lemma, we can show that the whole control system is asymptotically stable [8]. Then, the speed error can reach zero in the steady-state condition.

The whole control algorithm is shown in Fig. 3. The system parameters and controller parameters are on-line tuned. The implemented system is shown in Fig.4. The system is based on a digital signal processor TMS2407. The system includes two major parts: software and hardware. Most of the functions are implemented by a DSP. As a result, the hardware is very simple.

Fig. 3 The closed-loop drive system.

ωr

Fig. 4 The implemented control system.

As mentioned in section III, when the motor is operated

derive：

According to equation (32), we can use the iterative method to adjust α , and then to obtain the current commands i , ^*_d i_q^* to achieve the maximum torque/ ampere control.

On the other hand, when the motor is operated in the field weakening mode, rearranging equation (9), we can obtain

Substituting (17)-(18) into (33), we can derive

)

Finally, we can obtain

)

According to equation (35), we can also use the iterative method to adjust α , and then to obtain the current commands

i , d i_q^* to achieve the field-weakening control. The controller is impossible for a sensorless control system. The major reason is that the precious shaft position and speed are required.

V. EXPERIMENTAL RESULTS

In this paper, the commercial IPMSM parameters are ：

B 0.0341 N.m.sec/rad, J = 0.0227 Kg-m2, λ_m= 0.31V.sec/ rad., L_d=15.1 mH, L_q= 31mH, L /_q L_d =2.05.

The base speed is selected as 2300 r/min. Several experimental results are shown here. The parameters of proposed controller are: K_s= 2, γ₁= ^0.00001,γ₂= ^0.01,

γ 1. Fig. 5 shows the speed response at 1 r/min. In constant torque region, the proposed system works well at a speed as low as 1 r/min. Fig. 6 shows the transient responses at 500 r/min. Fig. 7 shows the transient responses at 1500 r/min and 3500 r/min. Fig. 8 shows the variation of the adaptive parameters in transient state at 3500 r/min.. The experimental results show that the on-line tuned parameters have fast convergence behavior. Fig. 9(a)(b)(c) show the speed and current responses and current trajectories at 2500 r/min with a 1.5 N.m load. Fig. 10 (a)(b) show the speed and current

responses without using field weakening technique.

Fig.11(a)(b) show the speed and current responses by using field weakening technique. Fig. 12 shows the measured torque-speed capability curves. The proposed method performs better than the traditional method by setting the d-axis current as zero.

Fig .5 The measured response from standstill to 1 r/min

B c J c1= 2=

B c J c1=0.5 2=0.5

B c J c₁=1.5 ₂=1.5

Fig.6 The transient responses at 500 r/min.

Fig.7 The transient responses at 1500 r/min and 3500 r/min.

) 10 ( ⁻³

Fig.8 The measured results of adaptive parameters.

(a)

(b)

(c)

Fig. 9 The transient response and load response at 2500 r/min (a) speed (b) d-axis and q-axis currents (c) current

trajectories.

(a)

(b)

Fig. 10 The responses without using field weakening (a) speed (b) current.

(a)

(b)

Fig. 11 The responses using field weakening (a) speed (b) current.

ωr

Fig. 12 The measured torque-speed capability.

VI. CONCLUSIONS

In this paper, a field-weakening technique and a nonlinear speed-loop controller are proposed for an IPMSM.

The proposed method can be applied in both the constant torque region and the field-weakening region. Several experimental results are shown to validate the theoretical analysis. This paper proposes a new direction to control the IPMSM in a wide speed range.

REFERENCES

[1] S. Morimoto, M. Sanada, and Y. Takeda, “Wide-speed operation of interior permanent magnet synchronous motors with high-performance current regulator,” IEEE Trans. Ind. Appl., vol.

30, no.4, pp. 920-926, July/ Aug. 1994.

[2] W. L. Soong and N. Ertugrul, “Field-weakening performance of interior permanent-magnet motors,” IEEE Trans. Ind. Appl., vol.

38, no. 5, pp. 1251-1258, Sep./ Oct. 2002.

[3] M. N. Uddin, T. S. Radwan, and M. A. Rahman, “Performance of interior permanent magnet motor drive over wide speed range,”

IEEE Trans. Energy Conv., vol. 17, no.1, pp. 79-84, Mar. 2002.

[4] C. T. Pan and S. M. Sue, “A linear maximum torque per ampere control for IPMSM drives over full-speed range,” IEEE Trans.

Energy Conv. , vol. 20, no.2, pp. 359-366, June 2005.

[5] J. M. Kim and S. K. Sul, “Speed control of interior permanent magnet synchronous motor drive for the flux weakening operation,” IEEE Trans. Ind. Appl., vol. 33, no. 1 , pp. 43-48, Jan./ Feb. 1997.

[6] M. F. Rahman, L. Zhong, and K. W. Lim, “A direct torque-controlled interior permanent magnet synchronous motor drive incorporating field weakening,” IEEE Trans. Ind. Appl., vol. 34, no. 6, pp. 1246-1253, Nov./ Dec. 1998.

[7] M. A. Rahman, D. M. Vilathgamuwa, M. N. Uddin. and K. J.

Tseng,“Nonlinear control of interior permanent magnet synchronous motor,” IEEE Trans. Ind. Appl., vol. 39, no.2, pp.

408-415, Mar./ Apr. 2003.

[8] J. J. E. Slotine, and W. Li, Applied Nonlinear Control. New Jersey: Prentice Hall,1991.

Adaptive Controller Design for a sensorless IPMSM Position Control System

Ji-Liang Shi, ^*Tian-Hua Liu, and Yung-Chi Chang Department of Electrical Engineering

National Taiwan University of Science and Technology 43, Section 4, Keelung Road

Taipei 106, Taiwan Abstract - This paper proposes a novel advanced

controller design for a sensorless interior permanent magnet synchronous motor position control system. An adaptive controller is proposed to obtain a good transient response and a good load disturbance rejection capability.

The proposed control method can be applied in a position control system without using any position sensor. By using the Lyapunov stability theory and Barbalat’s lemma, the closed-loop sensorless position control system can be proven to be an asymptotical stable system. A 32-bit digital signal processor is used to execute the rotor estimating algorithm and the control algorithm.

Experimental results validate the theoretical analysis and show the correctness and feasibility of the proposed system.

I. INTRODUCTION

The permanent magnet synchronous motor (PMSM) has been widely used in industrial applications due to its high efficiency, high performance, and simple control characteristics. Generally speaking, an encoder is required for the PMSM control system. The encoder needs extra cost and increases size. In addition, the signal of the encoder is easily polluted by noise. To solve the disadvantages, a sensorless drive system is required. Recently, elimination of the shaft position sensor from PMSM applications has resulted in the development of several techniques. These techniques can be divided into several categories. However, the current slope has shown to be a very useful method to detect the rotor position for salient ac motors [1]-[6]. For example, Matsuo and Lipo used the current slope to obtain the rotor position of a synchronous reluctance motor. This method, however, is applied to synchronous reluctance motors but not PMSMs. In addition, at a high speed operating range, the back EMF is not easily compensated for [1]. Akagi et al. proposed the magic saliency to estimate rotor position [2]. An INFORM estimating technique, allowing to operate the motor at a standstill or in the low speed operating range, has been proposed by Schroedl et al. However, when the motor speed increases to a middle or a high speed operating range, the back EMF detecting method is required to replace the INFORM method [3]-[5].

--- This research was supported by the National Science Council of the Republic of China under grant NSC 92-2213-E-011-026.

Recently, Liu et al. propose a sensorless technique by detecting the current slope with a back EMF compensation [6].

This rotor position estimating technique can work well from standstill, transient, and steady-state conditions for an IPMSM.

In this paper, the adaptive control combined with the sensorless technique is applied in the position control system.

To the best of the authors’ knowledge, the idea discussed in this paper is original. In fact, this is the first time a sensorless IPMSM position control system, using an adaptive controller, has been implemented.

II BASIC POSITION ESTIMATING PRINCIPLE

A. Dynamic Model of an IPMSM

In this paper, the IPMSM dynamic mathematical model in the a-b-c axis stationary reference frame is established. The

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