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Abstract
The inaccuracy and delay of speed feedback cause a vibration problem when the permanent magnet synchronous motor runs at low speed. As the low-speed smoothness is a key point of many applications of the permanent magnet synchronous motor, this article solves this problem by adding a real-time adjusted extended Kalman filter to low-precision-sensor vector control. In the mathematical model, the estimated speed of the extended kalman filter is significantly impacted by the deviations of the resistance and magnetic flux rather than other parameters. Thus, under id = 0 vector control, a Rs-ψf-identifier is designed to calculate the values of the resistance and flux simultaneously with a small compensating id. This algorithm runs on the platform in real time. Finally, the experiment results validate that when the velocity reaches as low as 1 r/min, the proposed method eliminates the vibration problem in the low-precision-sensor permanent magnet synchronous motor.
NOMENCLATURE
| iα, iβ | = | current in α-axis and β-axis |
| uα, uβ | = | voltage in α-axis and β-axis |
| L | = | inductance in αβ-axis |
| Rs | = | stator resistance |
| ωr | = | angular velocity |
| Pn | = | number of pole pairs |
| ψf | = | permanent magnet flux |
| Te | = | electromagnetic torque |
| B | = | friction coefficient |
| TL | = | load torque |
| J | = | rotor inertia |
| v(t), w(t) | = | system and measurement noises |
| Q(t), R(t) | = | covariances of system and measurement noises |
| Tc | = | sample period |
| I | = | identity matrix |
| δkj | = | Kronecker-δ function |
| Qk | = | non-negative symmetric matrix of system noise variance |
| Rk | = | positive symmetric covariance measurement noise matrix |
| = | value updated at t(k − 1) time | |
| = | predicted value of t(k) time at time t(k − 1) | |
| Pk − 1|k − 1 | = | covariance of state error |
| yk | = | measured value of output variables |
| γ20 | = | arbitrary positive finite constant |
| ω*r | = | given speed |
| n | = | number of sampling data |
Additional information
Notes on contributors
Dong Xu
Dong Xu was born in Hebei Province, China, in 1979. He received his B.S. in mechanical engineering from Beihang University, Beijing, China, in 2003 and his Ph.D. in mechatronic engineering from Mechanical Engineering and Automation Institute, Beihang University, China, in 2009. Since May 2009, he has been working for Beihang University as an assistant professor. His current research interests are in the fields of distributed control systems, adaptive control, computer-control systems, robotics control, and electric machine control.
Jingmeng Liu
Jingmeng Liu was born in Anhui Province, China, in 1967. He received his B.S. from the College of Electrical Engineering, Anhui Polytechnic University, Wuhu, China, in 1991 and his M.S. and Ph.D. from the Mechanical Engineering and Automation Institute, Beihang University, Beijing, China, in 2000 and 2004, respectively. He is currently with Beihang University as an associate professor. His research interests include missile guidance and control, robotics, and electrical engineering.
Shaoguang Zhang
Shaoguang Zhang was born in Hebei Province, China, in 1989. He now is studying for his B.S. in the School of Automation Science and Electrical Engineering, Beihang University. His current research interests are in the fields of robotic control and computer-control systems.
Hongxing Wei
Hongxing Wei received his B.E. from in the Department of Material from Inner Mongolia University of Technology, in 1995 and his M.S. and Ph.D. from College of Mechanical Electrical Engineering and College of Automation, Harbin Engineering University, in 1998 and 2001, respectively. He has been an associate professor with the School of Mechanical Engineering and Automation, Beihang University, Beijing, since 2004. His research interests include mobile sensor networks, modular robotics architecture, and embedded electromechanical control technology.