Abstract Sliding mode variable structure observers (SMOs) are widely used in sensorless drive systems due to their strong robustness and low sensitivity to changes in motor parameters. However, the discontinuities in real-world systems, the limited sliding mode switching frequency, and improper selection of the sliding mode switching gain lead to chattering issues in the quantities estimated by the SMOs. This paper addresses the chattering problem in SMOs in practical systems by proposing a multi-stage discrete control (SMO) approach to replace the sign function in the traditional SMO and achieve multiple state switching. This approach retains the advantages of traditional SMOs while effectively suppressing chattering in the estimated quantities. Simulation and experimental results show that this method effectively suppresses chattering in the SMO estimator and improves the performance of the vector control system for a positionless permanent magnet synchronous motor. Keywords : Permanent Magnet Synchronous Motor, Chattering, Discrete Sliding Mode Control, Multilevel A Novel Sliding Mode Observer for PMSM Vector Control Abstract Due to its robust estimation performance and low sensitivity to variation of machine parameters, SMO is widely used in sensorless drive systems. However, values ​​estimated by SMO do have a chattering problem because of the discontinuity and finite switching frequency of the real system. In this paper, a novel sliding mode observer is proposed to circumvent the chattering problem. A multilevel discontinuous control is applied to replace the sign function used in the conventional models. The method both preserves the well-known SMO features and effectively inhibits the chattering problem. Simulation and experimental results show that the method effectively inhibits the chattering problem and enhances the performance of the sensorless PMSM vector control system. Keyword : PMSM, chattering, discontinuous control of SMO, multi-level 1 Introduction Permanent magnet synchronous motors are increasingly used in servo control due to their advantages such as high power density, large torque-to-inertia ratio, and high efficiency. The realization of field orientation and vector control of permanent magnet synchronous motor requires rotor speed and rotor position information. In AC servo drive control, photoelectric encoders, resolvers and Hall sensors are commonly used to provide rotor speed and rotor position information. However, the use of these sensors increases the cost of the system and maintenance, and also reduces the stability and reliability of the system. Therefore, many sensorless technologies for estimating rotor speed and rotor position have been widely developed. Reference [1] directly calculates the speed and rotor position using stator terminal voltage and current. This method is simple to calculate, has fast dynamic response and small delay, but requires an accurate mathematical model of the motor. This method requires the combination of parameter self-identification to achieve a more accurate estimation of rotor speed and rotor position; in references [2-3], high-frequency injection method and other methods are used to estimate the speed and rotor position. This method can solve the problem of speed and rotor position estimation at low and ultra-low speeds, but it is relatively difficult to implement, especially when the nonlinear factors are prominent when the motor is running at low speed; references [4-6] use extended Kalman filter algorithm to estimate rotor speed and rotor position, but the algorithm has a large computational load for observing speed and rotor position, and the delay effect of the estimated value converging to the measured value during the start-up stage of permanent magnet synchronous motor is large; reference [7] uses neural network theory to estimate speed and rotor position. Such intelligent algorithms are particularly complex and the parameter design is difficult and not conducive to implementation. References [8-10] use sliding mode variable structure observer to estimate rotor speed and rotor position. It can be seen that the algorithm is robust and has low sensitivity to changes in motor parameters. The sliding mode variable structure observer can only achieve the theoretical effect when the switching frequency of the discrete system is infinite. In fact, both the limited switching frequency and the relatively low sampling frequency under ideal conditions will cause chattering in the system estimator. Among them, improper selection of sliding mode switching gain is the main reason for chattering. This paper reduces the sliding mode switching gain by multiplexing the sliding mode control signal to achieve multiple switching states, thereby effectively suppressing the chattering problem of the sliding mode variable structure observer estimator. The sliding mode variable structure observer described in this paper is implemented in a digital control system based on DSP2812 permanent magnet synchronous motor. Simulation and experimental results verify the effectiveness of the new sliding mode variable structure observer proposed in this paper. 2 Sliding Mode Observer with Multiplexed Discrete Control 2.1 Mathematical Model of Permanent Magnet Synchronous Motor 2.2 Traditional Sliding Mode Variable Structure Observer Based on equation (1), the sliding mode variable structure observer can be constructed as follows: Generally speaking, the smaller the region formed by the sliding mode and the switching surface during logic switching, the more beneficial it is to make the actual motion approach the ideal sliding mode motion. The maximum value of the width of the region formed by logic switching and the switching surface is determined by the frequency of discrete control and its switching gain. Under normal circumstances, it is only necessary to determine the sliding mode switching gain value in the full speed range to make the sliding mode motion run stably. However, the chattering range of the observed quantity varies with different operating conditions. When the motor is running at low speed, the relatively large switching gain at a fixed switching frequency may increase the estimation error of the stator current. As can be seen from the figure above, sliding mode discrete control usually has only two states. The system is linear and continuous within the region; however, it cannot be further verified whether it converges to zero. 2.3 Multivariable control sliding mode variable structure observer By transforming equation (3) into a discretized form, we can obtain: 2.4 Vector control system of permanent magnet synchronous motor based on sliding mode variable structure observer Figure 2 shows the sensorless permanent magnet synchronous motor vector control drive system, which includes a speed outer loop and two current inner loops as well as the adaptive sliding mode variable structure observer proposed in this paper. It also includes the traditional vector control part: Clark and Park transformations and their inverse transformations, SVPWM module, three-phase voltage source inverter and permanent magnet synchronous motor. The rotor position is estimated by the sliding mode variable structure observer, and the vector control adopts the control strategy of Id=0. [align=center]Fig. 2 The structure block diagram of control system[/align] 3 Experiment and Analysis The main parameters of the permanent magnet synchronous motor are: stator resistance 0.4Ω, AC and DC axis inductance 8.6mH, number of pole pairs 4, permanent magnet 0.213Wb, rated power 600W, rated torque 2.5 N•m, and rated speed 3000rpm. The system sampling frequency is 10kHz, the bus voltage is 310V, and the maximum phase current is 5.8A. In addition, a 2500-pulse incremental encoder is used to measure the initial rotor correction angle. Figures 2 and 3 show the simulation results of the permanent magnet synchronous motor under no-load and full-load conditions at a speed of 250rpm, respectively. [align=center] Figure 2 Simulation results of Multi-Level SMO: no load. Figure 3 Simulation results of Multi-Level Control SMO: 2.5-Nm load.[/align] Figures 4 and 5 show the experimental results of the permanent magnet synchronous motor under no-load and full-load conditions when the speed of the permanent magnet synchronous motor is 250 rpm, respectively. [align=center] (b) (d) Fig. 4 Experimental results of Multi-Level control SMO: no load (a) signal measured by encoder; (b) signal estimated by SMO (c) stationary-axis sliding control; (d) stationary-axis sliding control Fig. 5 Experimental results of Multi-Level control SMO: full load (a) signal measured by encoder; (b) signal estimated by SMO (c) stationary-axis sliding control; (d) stationary-axis sliding control[/align] Simulation results show that, regardless of whether the permanent magnet synchronous motor is unloaded or fully loaded, there is a significant error between the estimated rotor position and the measured rotor position within the first 0.05 seconds. This is because the motor speed is low at startup, resulting in a small back EMF and causing the SMO estimate to deviate from the actual value. After startup, due to the sufficiently large back EMF, the rotor position estimated by the SMO is almost identical to the measured value. In the experiment, mechanical friction on the motor shaft causes the motor speed to rise more slowly at startup than in the simulation, but the error between the estimated rotor position and the measured rotor position by the encoder is very small after one electrical cycle. Furthermore, under both simulation and experimental conditions, the estimated motor rotor position and the sliding mode control signal curves on the two-phase stationary coordinate axes are very smooth under both unloaded and fully loaded permanent magnet synchronous motor conditions, effectively eliminating chattering. This fully verifies the feasibility and effectiveness of the multi-level control proposed in this paper. 4. Conclusion This paper proposes a multi-level control sliding mode variable structure observer based on the traditional sliding mode variable structure observer vector control for permanent magnet synchronous motors. The rotor angle curve estimated by this method is smoother and more accurate, especially under load conditions, while retaining the advantages of the traditional sliding mode observer, such as strong robustness. The multiplicative sliding mode observer proposed in this paper has been successfully used in the vector control of permanent magnet synchronous motor. The above simulation and experimental results verify the correctness and effectiveness of the multiplicative control sliding mode variable structure observer. References [1] Malakondaiah Naidu, Bimal.Bose. Rotor Position Estimation Scheme of a Permanent Magnet Synchronous Machine for High Performance Variable Speed ​​Drive[J].Industry Applications Society Annual Meeting,1992,(1):48-53. [2] Jung-lk Ha; Seung-Ki Sul. Sensorless field-orientation control of an induction machine by high-frequency signal injection[J].Industry Applications, IEEE Transactions on Volume35, Issue 1,Jan-Feb,1999 Page(s):45-51. [3] Jia Hongping, He Yikang. Research on Initial Rotor Position Detection of Permanent Magnet Synchronous Motor Based on High-frequency Injection Method [J]. Proceedings of the Chinese Society for Electric Engineering, 2005, 27(15): 15-20. Jia Hong Ping, He Yi Kang. Study on Inspection of the Initial Rotor Position of a PMSM Based on High-frequency Signal Injection [J], Proceedings of the Chinese Society for Electric Engineering, 2005, 27(15): 5-20. [4] Zhuang Xu, Rahman MF An Extended Kalman Filter Observer for the Direct Torque Controlled Interior Permanent Magnet Synchronous Motor Driver. Power Electronics and Drive Systems [J], PEDS 2003, 1: 686-691. [5] HEN-GEUL YEH. Real-Time Implementation of a Narrow-Band Kalman Filter With a Floating-Point Processor DSP32 [J]. Industrial Electronics, IEEE Transactions on Volume 37, Issue 1, February 1990, Page(s): 13-17. [6]Rached Dhaouadi, Ned Mohan, Lars Norum. Design and Implementation of an Extended Kalman Filter for the State Estimation of a Permanent Magnet Synchronous Motor[J]. Power Electronics, IEEE Transactions on Volume 6, Issue 3, July 1991, Page(s): 491-497. [7]Li Hongru, Gu Shusheng. Design of a PMSM speed and position adaptive observer based on neural network[J]. Proceedings of the CSEE, 2002, 22(12): 32-35. Li Hong Ru, Gu Shu Sheng. Neural-Network-Based Adaptive observer of Position And Speed ​​of PMSM[J]. Proceedings of the Chinese Society for Electrical Engineering, 2002, 22(12): 32-35. [8] Wu Chunhua, Chen Guocheng, Sun Chengbo. Sensorless permanent magnet synchronous motor and vector control system based on sliding mode observer[J], Electrical Engineering and Power Technology, 2006, 25(2): 1-3. Wu Chun Hua, Chen Guo Chen, Sun Cheng Bo. PMSM Sensorless Vector Control Based on Sliding Mode Observer[J]. Advanced Technology of Electrical Engineering and Energy, 2006, 25(2): 1-3. [9] Vadim Utkin, J. Guldner and Jingxin shi, Sliding mode control in electromechanical systems, 1st ed, Taylor & Francis, 1999. [10] ZMPeixoto, et al, “Speed ​​control of permanent magnet motors using sliding mode observers for induced emf, position and speed estimation,” in Conf. Rec. IEEE – IAS Annu . Meeting , Vol . 2, 1995, pp. 1023-1028. About the author: Pang Tao (1981-) male, master, major research direction: engaged in the research of sensorless vector control of permanent magnet synchronous motors. Xu Zhuang (1972-), male, associate professor. His main research areas include: sensorless direct torque control of IPM motors, sensorless ultra-low speed operation of IPM motors, control research of megawatt-level permanent magnet direct-drive wind power generation systems, design of novel IPM motors in the 42V PowerNet ISA system of hybrid electric vehicles, and research on Z-source bidirectional converters. Contact address: Room 611-2, Apartment 11, Campus 1, Harbin Institute of Technology. Contact number: 13654583125