http://dx.doi.org/10.11142/jicems.2015.4.4.1

Journal of International Conference on Electrical Machines and Systems Vol. 4, No. 4, pp. 17~22, 2015

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A Sensorless Vector Control System for Permanent Magnet Synchronous Motor Based on Line Active Disturbance Rejection Controller Jinliang Zhang*, and Longyun Kang** Abstract –This paper presents line active disturbance rejection controller (LADRC) for closed-loop speed, current, and speed estimation of the permanent magnet synchronous motor (PMSM) to achieve the sensorless vector control system. The controller is not overly dependent on the accurate mathematical model of the motor. The disturbance is observed and then compensated by the LADRC, which leads to good dynamic and static performances and is robust to the load. In order to estimate the rotor speed and position, a speed observer based on LADRC is also designed. Compared to a conventional active disturbance rejection controller (ADRC), the LADRC reduces the number of the arithmetic operations. Simulation and experimental results show good dynamic and static performances on the PMSM speed. And the current regulation is also achieved by this method.

Keywords: PMSM, Sensorless, Vector control, ADRC 1. Introduction Owing to their characteristics of high efficiency, high power density, and reliability, AC machines, more recently especially permanent magnet synchronous machines have obtained dominance[1]. To control the torque and flux levels of the PMSM, the rotor flux oriented control is seen as an industry standard[2, 3]. The AC speed regulation system of the PMSM has good static and dynamic performance. Its speed regulator is generally the proportional integration differencetlal (PID) [4, 5], which is one of the early developed controlling strategies. The PID control is very popular and useful for a PMSM current control with a precise mathematical model, where the controller makes the decisions according to the error information. It does not rely on a detailed mathematical model of the motor. It is widely used in AC speed regulation systems since its simple algorithm, good robustness, and higher merit of reliability. However, because the PID control is based on the mathematical model of the controlled object, and its ability of restraining the parameter perturbation is not ideal, it is difficult for the PMSM servo system to realize high precision control. The auto-disturbance rejection controller (ADRC), proposed by Han in [6], maintains the advantages of PID, and was introduced into the motion control system by Feng * School of Electric Power, South China University of Technolog-y, China. ([email protected]) Received 15 April 2014; Accepted 15 November 2014

[7] and Gao [8], respectively. The ADRC concept is derived from the idea of using the nonlinear feedback configuration based on the process control strategy. It is initially applied to industrial applications such as timevariant, highly-coupled systems [9, 10]. Because it is not depend on the accurate mathematical model of the PMSM, and it can also estimate and compensate the internal dynamics and the external disturbance, the ADRC has strong robustness and adaptability. Past works prove its successful implementation on the permanent magnetic motors [11, 12] and induction motors [13]. It can also be applied to different kinds of motion systems with satisfactory results [14, 15]. Therefore, the motor is much more robust and more resistant to external disturbances. So far, there has been no relevant article discussing the implementation of the new control method on a PMSM. Although ADRC is superior to the classic PID, the number of the tuned parameters increases. The tuning methods, discussed in[16, 17], are too complex to be used in practice. The linear active disturbance rejection controller (LADRC) was proposed by GAO in[18]. This paper introduces LADRC into the sensorless vector control system of the PMSM. The purpose is to make the controller design and the tuning of the PMSM more easy and effective. The paper is organized in five sections. Section 2, describes the linear active disturbance rejection controller. In Section 3, a dynamic model of the PMSM is illustrated and the estimated rotor speed based on the LADRC is introduced. In Section 4, experimental and simulation results are discussed. Finally, a conclusion wraps up the

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A Sensorless Vector Control System for Permanent Magnet Synchronous Motor Based on Line Active Disturbance Rejection Controller

to a unit gain double integrator as (6) ⎧ x1 = x2 ⎪ ⎨ x2 = bu0 ⎪y = x 1 ⎩

paper.

2. Mathematic Mode of LADRC For the sake of simplicity, a second-order plant is considered as follows ⎧ x1 = x2 ⎪ ⎨ x2 = f ( x1 , x2 , t , ω ( t ) ) + bu ⎪ ⎩ y = x1

(1)

(6)

The above controller (3) and (4) combines with the LESO in order to actively compensate for the disturbances and is, therefore, denoted as the linear active disturbance rejection controller (LADRC). The architecture of the LADRC is shown in Fig.1.

Where, y and u are the output and the input respecttively, and ω ( t ) is the external disturbance. Here, f ( x1 x2 t ω (t ) ) refers to the generalized disturbance,

including the unknown internal dynamics and the external disturbance ω ( t ) . Rewrite (1) as (2)[2]. ⎧ x1 = x2 ⎪ x = x + bu ⎪ 2 3 ⎨  ⎪ x3 = h ⎪⎩ y = x1

Fig. 1. The block diagram of LADRC (2)

Where, x3 = f ( x1 , x2 , t , ω (t ) ) = f is an augmented state, and h = f . f can be estimated using a state observer, i.e. (3), which is denoted as the linear extended state observer (LESO). ⎧e = z1 − y ⎪ z = z − β e ⎪ 1 2 01 ⎨  z = z − β 3 02 e + bu ⎪ 2 ⎪⎩ z3 = − β 03e

(3)

Where β 01 , β 02 , β 03 are the state observer gains. For each state(from z1 to z3 ), it can track corresponding input states correctly. So that z1 (t ) → x1 (t ) , z2 (t ) → x2 (t ) , z3 (t ) → f . With the state observer properly designed, the

control force input u = u0 −

z3 (t ) , where u0 is easily b

(4)

Where v is the set-point. kp , kd are the gains. Rewrite (1) as (5) ⎧ x1 = x2 ⎪ z3 (t ) ⎞ ⎛ ⎪ ⎨ x2 = f ( x1 , x2 , t , ω (t ) ) + b ⎜ u0 − b ⎟⎠ ⎝ ⎪ ⎪⎩ y = x1

On the synchronous rotating frame of the PMSM, the dynamic mathematical model is shown as (7) Rs ud ⎧ ⎪id = − L id + Pn ωiq + L ⎪ ⎪ uq R Pϕ ⎪⎪iq = − s iq − Pn ωid − n f ω + L L L ⎨ ⎪ Pϕ Bω TL ⎪ω = n f iq − − J J J ⎪ ⎪ ⎪⎩θ = ω

(7)

Where, θ is the rotor position, J is the moment of inertia, B is the friction coefficient, ω is the rotor speed, Pn is the number of pole pairs, TL is the load torque, ϕf is the rotor magnetic linkage, Rs is stator resistance, ud uq is the voltage of d-axis and q-axis, L is the inductance

controlled with a PD controller: u0 = kp (v − z1 ) − kd z2

3. Design of the PMSM Drive System Based on the LADRC

(5)

Ignoring the estimation error in z3 , the plant is reduced

of the stator inductance. From equation (7), the rotor speed B T ω is influenced by id , iq , and TL . − − L can be J J regarded as the disturbance of the speed loop denoted by Pϕ w1 (t ) . − Pn ωid − n f ω is regarded as the disturbance L of the q-axis current loop, denoted by w2 (t ) . w1 (t ) , w2 (t ) will be regarded as the disturbances of the system

and then can be estimated and compensated by the LESO. Thus (7) can be reduced to the following form.

Jinliang Zhang, and Longyun Kang

Rs ud ⎧ ⎪id = − L id + Pn ωiq + L ⎪ u ⎪⎪i = − Rs i + w (t ) + q q q 2 (8) ⎨ L L ⎪ Pnϕf iq + w1 (t ) ⎪ω = J ⎪ ⎪⎩θ = ω There are two first-order LADRCs for regulating the qaxis stator current and velocity respectively. The block diagram of the system is illustrated in Fig. 2.

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Fig. 3. The block diagram of LADRC speed observer. Bω TL − J J can be regarded as the disturbance of the speed loop which is denoted by w3 (t ) . The disturbance item w3 (t ) can be observed and then compensated by the LADRC. So Pϕ B TL ω = n f iq − − becomes J J J Pϕ ω = n f iq + w3 (t ) (14) J

by TL and iq . According to LADRC theory, −

Fig. 2. The LADRC control system structure of PMSM . By analyzing (3), (4), (5), we can obtain the first-order LADRC of the q-axis stator current as following.

LESO:

⎧e = z21 − iq ⎪⎪ Rs z21 + buq ⎨ z21 = z22 − β 02 e − L ⎪ ⎪⎩ z22 = − β 03e

(9)

(10)

The control law: uq = u0 −

z22 (t ) Rs z21 − b L

Bω TL − . The block diagram of the J J

LADRC speed controller is shown in Fig.4. In Fig.4, ω ∗ is the reference rotor speed, ξ is the speed error, z21 is the tracking signal for ω , z22 is the observed value of disturbance, u0 is output of the P controller. iq* is the reference torque current.

P controller: u0 = kp (v − z21 )

Where w3 (t ) = −

(11)

The rotor speed ω is included in w2 (t ) , In order to be

The LADRC parameters are obtained from simulation and experimental results. As well as this, the following steps should be observed. First, according to the characterristics of the control object, system stability should be ensured. Then, the parameters of PD and LESO are regulated to evaluate the reference inputs, the variables of each state and the disturbances, quickly and correctly.

convenient for analysis, the estimated value of w2 (t ) is denoted as w2 (t )∗ . Z 22 = w2 (t )∗ . The estimated rotor speed is Lq Z 22 ω∗ = − (12) Ld id + ψ f By integrating both sides of (2), the rotor position can be derived as follows

∫

θ ∗ = ω ∗dt

Fig. 4. The block diagram of LADRC speed regulator.

(13)

Fig. 3 shows the block diagram of the LADRC speed observer. The first-order LADRC of Speed regulator is similar to the above. From equation (7), the rotor speed is influenced

4. Simulation and Experiment Results In this section, the simulation and experimental results are presented to verify the feasibility of the sensorless vector control system of the PMSM based on the LADRC.

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A Sensorless Vector Control System for Permanent Magnet Synchronous Motor Based on Line Active Disturbance Rejection Controller

The nominal parametric values of the simulation and experimental 330V/1.2kW PMSM are listed in Table 1. Table 1. PMSM prototype specification Quantity

Value

Nominal torque

10N·m

Nominal speed

3000r/min

Stator resistance Rs

1.2Ω

d axes inductances Ld

0.03mH

q axes inductances Lq PM Flux linkageψ f

0.03mH 0.13Wb −3

2

Rotor inertia

1.1×10 kg·m

Poles pairs

4

Fig. 7. Simulation results of the Real position and estimated position .

Fig.5 to Fig.9 shows the responses when ω ∗ =100rad/s. The speed dynamic response of the sensorless drive is shown in Fig.1. The machine is accelerated from 0 rpm to 100rad/s. During transient, the LESO has good tracking performance (speed and position). Fig .2 and Fig. 4 show the differences of the speed and the position between the real values and the estimations. Fig. 5 shows the response of the current in q axis. The simulation results indicate that the proposed Fig. 8. Simulation results of the errors between Real position and estimated position .

Fig. 5. Simulation results of the Real speedand estimated speed.

Fig. 6. Simulation results of the errors between Real speed estimated speed

Fig. 9. Simulation results of the current responses of q axes PMSM servo system has high precision, and is more robust to the parametric variation and the load torque disturbance. In the experimental hardware, a controller based on DSP TMS320C6713 with a clock speed of 225MHz is applied. The actual rotor position and speed are obtained from an incremental encoder with 10000 pulses per revolution. The inverter space-vector PWM control, the d axis current PI regulator, and the LADRC algorithm are operate with a 100 us sampling time step. The currents flowing in the stator windings are measured with two hall-effect current sensors. In the experiments, the load torque is 1N·m, the speed is set from 600r/min to 900r/min, then to 500r/min. Fig.10

Jinliang Zhang, and Longyun Kang

shows the rotor speed estimated by the LADRC speed observer, Fig.11 shows the rotor estimated position at the system starting moment, Fig.12 shows the experimental results of the current responses of d and q axes. The experimental results indicate that the proposed PMSM servo system has high precision in the position control.

Fig.10. Experimental results of the real speed and estimated speed

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position sensorless vector control system of the PMSM based on the LADRC. The current and the speed regulator and the speed observer are designed based on the LADRC. The variations of the motor rotational inertia and the stator resistance, and other unknown disturbance are observed and compensated by the LADRC current controller, and the system has a good robustness against parameter variations. The LADRC current controller also provides a transient process for the input signal, which results in fast response and no overshooting. The sensorless vector control system of the PMSM based on the LADRC described in the previous sections is implemented in Matlab/Simulink environment and the proposed scheme is implemented by using DSP TMS320C6713. Simulation and experiments results show that the speed can be accurately estimated with the load or not. A good dynamic and static performance of the PMSM speed regulation is achieved by this method.

Acknowledgements This work is supported by National Natural Science Foundation of China (Grant no. 51377058) and Youth Fund ofNational Natural Science Foundation in China (Grant no.61104181).

References

Fig. 11. Experimental results of the real position and estimated position

Fig. 12. Experimental results of the current responses of d and q axes

5. Conclusion In this paper, we propose a novel approach to the

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A Sensorless Vector Control System for Permanent Magnet Synchronous Motor Based on Line Active Disturbance Rejection Controller

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Jinliang Zhang received his B.S., M.S. degree in Shandong University of Technology, Zibo, China, in 2008 and 2011, respectively, both in College of Electrical and Electronic Engineering. He is currently working toward the Ph.D. degree at the school of Electric Power of South China University of Technology. His current research interests include motor drives, electric vehicle, and power electronics. Longyun Kang was born in Jilin, China, in 1961. He received his B.S., M.S. and Ph.D. degree in physics from Yanbian University, China, in 1982, and electrical engineering from the Engineering Department of Kyoto University, Japan, in 1996 and 1999, respectively. From 1999 to 2001, he was a Researcher with the Department of Engineering, Tokyo Institute of Technology. From 2001 to 2006, he was an associate professor with the Institute of Mechanical Engineering, Xi’an Jiaotong University. Since 2006, he has been with the School of Electric Power, South China University of Technology, where he is currently a Professor. He is supervisor of a Ph.D. student, a director of Guangdong key laboratory of Clean Energy Technology. Her current research interests are in the area of renewable energy and electric vehicle, including wind energy, solar energy conversion, Hybrid Energy System and Hybriddrive Technology of electric vehicle.