Nonlinear integral sliding mode control of PMSM based on load observer Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

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Original article / Оригинальная статья УДК 613.6

NONLINEAR INTEGRAL SLIDING MODE CONTROL OF PMSM BASED ON LOAD OBSERVER © Weihua Chen, Pengfei Nan, Ye Pan

Academy of Electrical and Control Engineering, Liaoning Technical University, Liaoning Huludao, 125105, People's Republic of China.

ABSTRACT. Based on the mathematical model of the surface PMSM, this paper proposes a nonlinear integral sliding mode controller based on a torque observer. The nonlinear integral sliding mode controller realizes high precision control and has better transient performance. At the same time, extended state observer is used to evaluate the load torque of the system online, and disturbance feed forward compensation is taken as an observation result. The load torque disturbance impact on the control system performance can be inhibited. Theoretical analysis and experimental results show that the effectiveness of the proposed method. the system has satisfactory dynamic and static performance. According to the permanent magnet synchronous motor speed control system design a sliding mode load torque observer control strategy based on the traditional integral sliding mode surface with nonlinear integral, improve static and dynamic performance of permanent magnet synchronous motor; extended state observer through real-time observation of the load disturbance, can effectively improve the performance of the load disturbance. The simulation results show that the designed controller improves PMSM speed tracking performance and resistance to load torque disturbance. As a result of the offered system risks of traumatizing in workplaces where movements of any freights are carried out are practically excluded.

Keywords: permanent magnet synchronous motor (PMSM), nonlinear integrator, sliding mode control, exception of risks of traumatizing

For citation: Weihua Chen, Pengfei Nan, Ye Pan. Nonlinear integral sliding mode control of PMSM based on load observer // XXI century. Technosphere Safety, 2017, vol. 2, no. 4, pp. 10-18. (In English)

НЕЛИНЕЙНЫЙ ИНТЕГРАЛ, УЛУЧШАЮЩИЙ КОНТРОЛЬ ЗА ПОСТОЯННЫМ МАГНИТОМ СИНХРОННОГО ДВИГАТЕЛЯ НА ОСНОВЕ УПРАВЛЕНИЯ ГРУЗОМ

1 2 3

Веихуа Чен , Пенгфеи Нан , Е Пан

Академия электротехники и автоматики, Ляонинский Технический Университет, Ляонин Хулудао, 125105, Китайская Народная Республика.

Аннотация. На основе математической модели поверхности вентильного двигателя в статье рассматривается нелинейное комплексное скользящее управление с контролем нагрузки. Нелинейное комплексное управление со скользящим контролем позволяет добиться высокоточного контроля и повысить эффективность переходного режима. Для оценки момента нагрузки системы в режиме онлайн используется расширенный контроль. Итогом является компенсация нарушений: воздействия на эффективность системы контроля в результате нарушений нагружающего момента могут быть устранены. Теоретический анализ и экспериментальные данные доказывают эффективность предлагаемого метода. Динамическая и статическая эффективность системы является удовлетворительной. Результаты моделирования показывают, что разработанный контроллер заставляет PMSM хорошо отслеживать скорость и устранять возникающий крутящий момент. В итоге практически исключаются риски травмирования и чрезвычайные происшествия на рабочих местах, где проводятся перемещения любых грузов. Ключевые слова: постоянный магнит синхронного двигателя (PMSM), нелинейный интегратор, управление со скользящим контролем, исключение рисков травмирования.

1Weihua Chen, PhD, e-mail: [email protected]

Вейхуа Чен, e-mail: [email protected] Pengfei Nan, e-mail: [email protected] Пенгфей Нан, e-mail: [email protected]

3Ye Pan, e-mail: [email protected] Е Пан, e-mail: [email protected]

Том 2, № 4 2017 XXI ВЕК. ТЕХНОСФЕРНАЯ БЕЗОПАСНОСТЬ Vol. 2, no. 4 2017 XXI CENTURY. TECHNOSPHERE SAFETY

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Формат цитирования: Вейхуа Чен, Пенгфей Нан, Е Пан. Нелинейный интеграл, улучшающий контроль за постоянным магнитом синхронного двигателя на основе управления грузом // XXI век. Техносферная безопасность. Т. 2. № 4. С. 10-18.

Introduction

Permanent magnet synchronous motor (PMSM) has many advantages, such as small volume, high power factor and low rotational inertia. Vector control and direct torque control are usually used in PMSM control system. Because the PI controller is more fragile to the external disturbance and parameter perturbation, it is difficult to obtain satisfactory dynamic performance.

In recent years, in order to improve the system dynamic and static performance of domestic and foreign scholars, the sliding mode variable structure control [1 -3], back-stepping control [4-6], passive [7-8] control, intelligent control and [9-10] control method of permanent magnet synchronous motor control system. Sliding mode variable structure control is an effective control method for nonlinear uncertain systems. It has strong robustness to parameter perturbation and external disturbance, simple structure and fast response. The [11] uses a novel reaching law of sliding mode variable structure control, effectively improve the system's static and dynamic characteristics and robustness. Integral sliding mode controller in [12] design speed, realize high precision control of PMSM; no overshoot, but because of the whole sliding surface dynamic process and the initial conditions are closely related, lead to a rise in long time; literature [13] sliding mode variable structure control is applied to the permanent magnet synchronous motor directly.

In the moment control system, the dynamic and static performance of the system is improved and the pulsation of torque is reduced. The [14] is proposed by using adaptive sliding mode control with extended state observer design of speed controller, the proposed method achieves high speed estimation accuracy and realize the speed estimation by q axis current expectations, the control system has good dynamic and static performance.

Based on the nonlinear integral sliding mode control proposed by [15], a new nonlinear integral sliding mode controller is designed. A class with large error saturation, small error amplifier nonlinear integral term into the sliding surface, the system get higher tracking accuracy and has good dynamic performance, the accurate estimation of the load torque observer will be extended; out of the observed disturbance torque compensation; reduce the switching parameters of robust sliding mode controller; effectively reduce the chattering and enhance the system robustness to external load disturbance. Matlab simulation results show that the controller designed in this paper improves the dynamic and static performance of the system, and further improves the robustness of the system.

Mathematical model of PMSM

Based on synchronous rotating rotor d q coordinate system of the surface permanent magnet synchronous motor mathematical model [16] is as follows: (its direct axis inductance is approximately equal, that is, Ld = Lq = L) equation variables and parameters of the definition as shown in Table 1.

did R. .1 „X

-± = -- ld + Pmiq+-ud; (1) dt L L

m-q R ■ ■ РФГ 1 .

(1)^ =-Tlq -P®ld---T®+TUq ; (2)

diq R. • РФГ 1 — = — i - pmi,--r- m + —

dt Lq L L

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ЩМ

dcu 3 рфг В Tr -= r i--c—- . dt 2 J q J J (3)

Symbol definition of motor parameters Условное обозначение параметров двигателя Table 1 Таблица 1

Symbolic / Символ Physical meaning / Физическая величина Unit / Единица измерения

ud,uq D, q Axis Stator Coltage V

id,iq DЛ qC A

R stator resistance / сопротивление статора ù

Фг Permanent magnetic flux / Постоянный магнитный поток Wb

L stator inductance / индуктивность статора H

p pole pairs / полярные пары 1

J moment of inertia / момент инерции kgm

B viscous friction coefficient / коэффициент вязкости NmS

Tl load torque / момент нагрузки Nm

w rotor mechanical angle / механический угол двигателя rad/s

Load torque observer design

Since the frequency of load change is much smaller than the switching frequency of the controller, it is considered that the load torque changes slowly during the control period, fL= 0. Combined with the torque equation, motion equation, load torque, rotor position and speed as the state variable, the augmented system.

CO =

Ърфг

TL= 0

B

Tr

-7--со- —

2 J 9 J J

(4)

Extended torque observer:

л Зрфг В TL ,

со = 7,--со—- + клсо-со)

2 J q J J

fL =-k2(co-co)

(5)

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<

Hü

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ОХРАНА ТРУДА И ПРОМЫШЛЕННАЯ БЕЗОПАСНОСТЬ LABOR PROTECTION AND INDUSTRIAL SAFETY

ЩМ

вы

Type: cc for motor rotor mechanical angular velocity estimation value; fL load torque estimation ^ > 0, £2 > 0.

Stability analysis of observers:

By formula (4) and formula (5), the observation error equation is

--IL

CO

J

i = k2co

(6)

Lyapunov function:

V =-ô2+—Г-

L ,

(7)

1 ~ ~ T

Vo = Jcoâ-i--TLTL = Jco(— -kx<a) + TLS> = -kxJä2 < 0 .

кn J

(8)

By formula (8), the observation error can asymptotically approach zero, i.e l/mib ~c;

lim TL = TL . t—

Controller design

Define system speed tracking error for

e = a -a.

a

(9)

The type of type (3) and (9) derivative, available

. » 3 рф В Tj e„=o — со = со---/'„ h—со-' —

2J J J

(10)

Take the system sliding surface [17] as

\s = ea+ktt \à- = g(ej

(11)

In the formula, a class of nonlinear functions with small error amplification and large error saturation.

g (eJ

JTQ . .

ßsm(^), \em\<ß

ß,

-ß,

ea~ß ea — -ß

(12)

ШМ

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ОХРАНА ТРУДА И ПРОМЫШЛЕННАЯ БЕЗОПАСНОСТЬ LABOR PROTECTION AND INDUSTRIAL SAFETY

When the error is small (i.e. when |e| < p)), |g (E) | > |e|; and when the error is large when (i.e. when |e|> beta), |g (E) | < |e| and saturation in ±p. The p is a design parameter of error shaping, and the nonlinear function of "small error amplification and large error saturation" can conveniently obtain the desired error state by selecting the appropriate p value. The system has higher tracking precision and better dynamic performance.

Take the derivative of (11):

3 РФ,

B T

* = ea + kg(ea) = cb - i+-ca + ^- + kg(eco).

2 J

J

J

(13)

Using the exponential reaching law, ensure reach sliding surface in finite time, improve dynamic quality reaching movement.

S = — PS — E sgn(s) .

(14)

Among(14) p> 0, s> 0.

The control law can be obtained by combining (13) and (14)

2 J

lq =

Ърфг

в т

со + — co + -j- + kg(e£0) +ps + ssgn(s)

(15)

The saturation function sat(s,S) is used instead of the sign function sgn(s) in the control law (15) to weaken the chattering of the system and replace the control law with the observer's o b-servation results.

1, s > 5

sat(s,S) = <js / S, Isl <5 .

-1, s <-5

(16)

2 J

lq =

3M

В T

со* + —со+ + kg(eco) + ps + ssatCs1, S)

(17)

Real time estimation and compensation of load torque by state observer. When the load is disturbed, the controller can compensate the load disturbance timely, and can achieve better disturbance rejection effect under the condition of smaller robust switching parameters. Therefore, the nonlinear integral sliding mode control strategy of load torque observer can not only restrain the load disturbance of the system control performance based on adverse influence, and can reduce the gain of sliding mode control, to further weaken the chattering phenomenon of sliding mode control system.

Simulation results and analysis

The correctness and effectiveness of the sliding mode load torque observer based on control strategy in order to verify the proposed, the simulation of permanent magnet synchronous motor vector control system,the motor parameters are shown in table 2.

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Table 2

Motor physical parameters

Таблица 2

Физические параметры двигателя_

Symbol / Символ Name / Наименование Value / Показатель

R Stator resistance / Сопротивление статора 1.6Q

фг Permanent magnet flux / Постоянный магнитный поток 6.365x10'3Wb

L Stator inductance / Индуктивность статора 0.1852 H

P Polar logarithm / Полярный логарифм 2

J Moment of inertia / Момент инерции 1.854*10"4kgm2

B Coefficient of viscous friction / Коэффициент вязкости 5.396x10"5Nms

Given the rotor speed is given, the rise time is 0.05s, the stable value is 100 rad/s. Motor no-load start, loading 2 N■ m at 0.1s, when 0.25s becomes 0 N■ m.

From the simulation results 1-2 can be seen in the PI control load disturbance, the speed of about 5 rad / s fluctuations, speed recovery time is longer.

Figures 3-5 show the control effect of motor load observer integral sliding mode control based on the design, the load observer can accurately observe the load torque. The feedforward compensation load observation, load speed change is very small, the speed error is about 2 rad/s, and the adjusting time is very short.

П И (

Fig. 1. PI control speed response Рис. 1. Реакция управления скоростью вентильного двигателя

шш

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Fig. 2. PI control speed response error Рис. 2. Ошибка реакции управления скоростью вентильного двигателя

Fig. 3. The response speed based on integral sliding mode control with load observer Рис. 3. Скорость реакции на основе комплексного скользящего управления с контролем нагрузки

8 г 6 -

4 -

-4 -

-6 -

-8-1-1-1-1-1-1-1-1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

WH ( S)

Fig. 4. The speed response error based on integral sliding mode control with load observer Рис. 4. Ошибка скорости реакции на основе комплексного скользящего управления

с контролем нагрузки

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2.5 2 1.5 1

0.5 0

•ürnrnrn

-0.5 t_С_С_С_с

0 0.1 0.2 0.3 0.4

w га ( о

Fig. 5. The estimated load torque based on integral sliding mode control with load observer Рис. 5. Расчетный момент нагрузки на основе комплексного скользящего управления с контролем

нагрузки

Through simulation analysis, this paper designed the control method and PI control are compared, when load disturbance or mutation, the load observer can well compensate the load caused by the impact; speed change has a smaller and faster recovery, has better dynamic and static performance and good robustness.

Conclusions

According to the permanent magnet synchronous motor speed control system design a sliding mode load torque observer control strategy based on the traditional integral sliding mode surface with nonlinear integral, improve static and dynamic performance of permanent magnet synchronous motor; extended state observer through real-time observation of the load disturbance, can effectively improve the performance of the load disturbance. The simulation results show that the designed controller makes the PMSM have good speed tracking performance and strong resistance to load torque disturbance.

References

1. Lai C K, Shyu K K. A novel motor drive design for incremental motion system via sliding-mode control method[J]. IEEE Transactions on Industrial Electronics, 2005, 52(2):499-507.

2. Jian-Jun H E, Duan Y, Shou-Yi Y U. Rotor Position and Speed Estimate of SPMSM Using Sliding Mode Estimator[J]. Control Engineering of China, 2012. 19(3):527-530.

3. Li Min H,Jin Peng Z et al.Passivity-based Control for IPMSM Based on Nonsingular Terminal Sliding Mode Observer [J]. Control Engineering of China, 2015. 22(6):1131 -1136.

4. Ouassaid M, Cherkaoui M, Maaroufi M. Improved nonlinear velocity tracking control for synchronous motor drive using backstepping design strategy[C]// Power Tech, 2005 IEEE Russia. 2005:1-6.

5. Jian-Hui H U, Zou J B. Adaptive Backstepping Control of Permanent Magnet Synchronous Motors with Parameter Uncertainties[J]. Control & Decision, 2006, 21(11):1264-1269.

6. Zhou G R, Yong-Feng L I. Backstepping Based Adaptive Sliding Mode Control for PMSM[J]. Control Engineering of China, 2009, 16(1):49-51.

7. Xiao-Long J I, Shen C W, Meng Y Q, et al. A Passivity-based Stator Field-Orientation Controller for Induction Mo-tors[J]. Power Electronics, 2007, 41(9):15-16.

8. Jing Wei X,Yi Xin X.Fuzzy Self-Adaptive PI Control Method for PMSM Drive[J]. Micromotors, 2015, 48(11):58-61.

9. Ma L. Induction Motor Tracking Control Based on Passivity Principle with Unknown Time-varying Load Torque[J]. Transactions of China Electrotechnical Society, 2004, 19(1):12-17.

10. Hong Ru LI, GU Shu sheng Liaoning. Neural-network-based adaptive sliding mode control for PMSM[J]. Control

Том 2, № 4 2017 XXI ВЕК. ТЕХНОСФЕРНАЯ БЕЗОПАСНОСТЬ Vol. 2, no. 4 2017 XXI CENTURY. TECHNOSPHERE SAFETY

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Theory & Applications, 2005.

11. Lin F J, Chiu S L. Adaptive fuzzy sliding-mode control for PM synchronous servo motor drives[J]. Control Theory and Applications, IEE Proceedings, 1998, 145(1):63-72.

12. Zhang X, Zhao K, Sun L, et al. A PMSM Sliding Mode Control System Based on A Novel Reaching Law[J]. Proceedings of the Csee, 2011, 31(24):77-82.

13. Zheng L I, Guangda H U, Cui J, et al. Sliding-mode Variable Structure Control With Integral Action for Permanent Magnet Synchronous Motor[J]. Proceedings of the Csee, 2014, 34(3):431-437.

14. Jia H. Variable Structure Sliding Mode Control for PMSM DTC[J]. Transactions of China Electrotechnical Society, 2006.

15. Hou L M, Wei W. Speed sensorless system of passivity-based control strategy for SPMSM[J]. Kongzhi Yu Juece/control & Decision, 2013, 28(10):1578-1567.

16. Peng Li, Jianjun Ma, Zhiqiang Zheng. Sliding mode control approach with nonlinear integrator[J]. Kongzhi Lilun Yu Yinyong/Control Theory and Applications, 2011, 28(5):619-624.

17. Pillay P, Krishnan R. Modeling of permanent magnet motor drives[J]. Industrial Electronics IEEE Transactions on, 1988, 35(4):537-541.

Authorship criteria

Weihua Chen, Pengfei Nan, Ye Pan have equal authors' rights and responsibility for plagiarism.

Критерий авторства

Вейхуа Чен, Пенгфей Нан, Е Пан обладают равными авторскими правами и несут равную ответственность за плагиат.

Conflict of interests

The authors declare no conflict of interests.

Конфликт интересов

Авторы заявляют об отсутствии конфликта интересов.

Received on 23 November 2017 Поступила 23 ноября 2017 г.

Том 2, № 4 2017 XXI ВЕК. ТЕХНОСФЕРНАЯ БЕЗОПАСНОСТЬ Vol. 2, no. 4 2017 XXI CENTURY. TECHNOSPHERE SAFETY

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