Minghui Wang, Yongxiang Xu, Member, IEEE, Jibin Zou, Senior Member, IEEE, Hua Lan. Department of Electrical Engineering, School of Electrical Engineering ...
2017 IEEE Transportation Electrification Conference and Expo, Asia-Pacific (ITEC Asia-Pacific)
An Optimized I-F Startup Method for BEMF-based Sensorless Control of SPMSM Minghui Wang, Yongxiang Xu, Member, IEEE, Jibin Zou, Senior Member, IEEE, Hua Lan Department of Electrical Engineering, School of Electrical Engineering and Automation Harbin Institute of Technology, HIT Harbin, China Abstract—BEMF-based methods, with the purpose of estimating the position and speed of the permanent magnet synchronous machine (PMSM), cannot be applied in low- speed range. Though the high frequency injection (HFI) methods can be operated in low- speed range, they are complicated. For low cost SPMSM applications, it is not necessary to be operated in low- speed range. Thus, an I-f starting method was introduced to accelerate the machine to a desired speed. This paper proposes an optimized starting procedure for sensorless control of SPMSM. The proposed transition procedure, including a nonlinear current reduction function, allows a more smooth transition between the startup accelerating mode (low- speed range) and the back-EMF-based sensorless control mode (medium- and high- speed range). The simulation results verify the effectiveness and robustness of the proposed method. Keywords—SPMSM; sensorless control; I-f starting method; nonlinear current reduction function.
I. INTRODUCTION Permanent magnet synchronous machine (PMSM) has been widely used in industrial and domestic applications over the last several decades. Compared to other kinds of electrical machines, PMSM has higher power density and efficiency. The angle position and speed of PMSM are needed for its vector control. Typically, a position sensor, such as encoder and resolver, is equipped to detect the position and calculate the speed. However, the position sensor is expensive and may be ineffective in high temperature or high humidity. In recent years, many researchers have devoted to studying sensorless control methods. Sensorless control methods can be divided into two series. The first is based on the electromotive force (EMF) machine model for the medium- and the high-speed range, such as the Luenberger observers [4], flux observers [25], sliding mode observers [5], model reference adaptive observers [6], and extended Kalman filters [7], which are suitable for medium- and high- speed ranges because the BEMF signal is small in low- speed range. The second is the high frequency injection (HFI) methods, such as rotating signal injection methods [8], pulse signal injection methods [9], and square signal injection methods [10], which are suitable for low- speed range. Though pulse signal injection methods are suitable for SPMSM, they are difficult to be implemented. This work was supported in part by the National Natural Science Foundation of China under Grant 51437004, and in part by the National Natural Science Foundation of China under Grant 51577036.
Fortunately, for some low cost applications, such as fans, pumps, and compressors, operation in low- speed range is unnecessary. Some simple startup methods that could accelerate the machine in low- speed range were introduced. Open loop V/f control method has been widely used for induction machine control. It can be utilized to start the machine, but it may be unstable when applied to synchronous machine. Some papers have proposed the I-f method that is more suitable for synchronous machine. Unlike the open loop V/f control method, a single current loop is used in I-f control. However, when the control mode changes from I-f startup method to BEMF-based method, there will be short-time speed and torque oscillations, even startup failures. So smooth transition methods should be paid attention. For solving the above-mentioned issue, a first-order compensator was used in [1]. A transition procedure with linear current reduction rate was proposed in [2]. A smooth transition method by resetting the current controller references was proposed in [3]. In this paper, the control system is shown in Fig. 1. A sliding mode observer (SMO) and a PLL (phase locked loop) are implemented in medium- and high- speed range, and a smooth transition method is proposed in low- speed range. The rest of this paper is organized as follows. Mathematical model, sliding mode observer and PLL are described in Section II. A detailed analysis for I-f startup procedure is in Section III. The proposed transition method is discussed in Section IV. Lastly, in Section V, the proposed method is tested by simulations. II. MATHEMATICAL MODEL AND BEMF-BASED METHOD A. Mathematical model The mathematical model of SPMSM in αβ axis is expressed as eαβ = jω e eαβ
diαβ dt
=
R 1 1 uαβ − s iαβ − eαβ Ls Ls Ls
978-1-5386-2894-2/17/$31.00 ©2017 IEEE
978-1-5386-2894-2/17/$31.00 ©2017 IEEE
(1)
(2)
2017 IEEE Transportation Electrification Conference and Expo, Asia-Pacific (ITEC Asia-Pacific)
Fig. 1 Control system for PMSM
where iαβ is the current in αβ reference frame, uαβ the voltage in αβ reference frame, eαβ the BEMF in αβ reference frame, and ωe the electrical speed. Ls is stator inductance, and Rs is the stator resistance. By Park transformation, the model given in dq axis is
u d = Rs id + Ls
u q = Rs iq + Ls
diq dt
Ls
did − ω e Ls i q dt
(3)
+ ω eψ f + ωe Ls id
(4)
The electromagnetic torque is:
where iˆαβ is the estimated current value in αβ axis.
dt
= − Rs iˆαβ + uαβ − k sgn( sαβ )
(7)
where k is the observer gain, and sgn(x) is sign function.
Ls
diˆαβ dt
= − Rs iˆαβ + uαβ − k sat( sαβ )
(8)
Moreover, the following equation can be acquired by the equivalent control.
(5)
B. Sliding Mode Observer and PLL A sliding mode observer is implemented for medium- and high- speed ranges. Firstly, the sliding surface is selected as sαβ = iˆαβ − iαβ
diˆαβ
In order to reduce the chattering phenomenon of the observer, the saturation function is implemented in this paper. Thus, the observer can be expressed as
where id and iq are current variables in dq axis, ud and uq voltage variables in dq axis, ψf the permanent flux.
Te = 1.5ψ f niq
Secondly, by using the mathematical model in αβ axis, the sliding mode observer (SMO) is expressed as
eˆαβ = k sat( sαβ )
(9)
Thirdly, the constant k should be selected to keep the stability of the observer by the Lyapunov function. The Lyapunov function is selected as
V=
(6)
To keep stable,
1 T s s 2
(10)
2017 IEEE Transportation Electrification Conference and Expo, Asia-Pacific (ITEC Asia-Pacific)
V = s T s < 0
(11)
As a result, k > max(| eα |, | eβ |)
(12)
After the BEMF values are estimated, the position and speed information can be acquired by arc-tangent algorithm,
θˆe = − arctan(
eˆα ) eˆβ
(13)
1.5 pψ f iq* cos θ L − Tl = Jω
dθˆ ωˆ e = e dt
I-f startup method without speed loop can be divided into three stages. Firstly, a constant i*d and θ* are set to align the machine in the electrical angle θ*. Typically, i*d is selected to be enough large to rotate and θ* is 0. An instantaneous reverse may occur, but it is acceptable in most actual applications. Secondly, the reference i*d is set to 0. The reference i*q is set to a constant value and ωe* is a linear ramp-up value. In this procedure, the speed reference ramp-up rate and the current reference should be designed. In low- speed range, the motor cannot be in speed control mode. The SMO and PLL start to calculate the speed and angle, but they are not used in the control algorithm because they are not stable at this stage. The stage makes the motor accelerate from zero speed to the desired speed, so as to make the SMO to be stable. Thirdly, when the speed is large enough, a transition procedure can be used to acquire a smooth transition with less speed and torque oscillations. Then the speed control loop and SMO are used in the vector control system. During the I-f startup procedure, the motor is controlled in a virtual rotating reference frame because the actual angle is unknown. As is shown in Fig.3, We define θL to be the error between the virtual rotating reference frame and the actual rotating frame. During startup procedure, the virtual reference frame always lags behind the actual frame.
f
i q* c o s θ L
According to (16) and (17), the system keeps stable when 0< θL
