# High-Performance Speed Control of PMSM Using Fuzzy Sliding Mode with Load Torque Observer
## 5 Conclusions  
In order to improve the speed control performance for PMSM, an improved sliding mode control method based on load torque observer is proposed. The main contributions of this paper are as follows:  
1. A nonlinear smoothing function \(f(S,\gamma,\beta)\) with flexible shape adjustment is proposed to replace the symbolic function \(\mathrm{sgn}(\cdot)\), and the chattering caused by the discontinuity of the symbolic function \(\mathrm{sgn}(\cdot)\) is solved;
2. The fuzzy self-setting algorithm of equal speed switching item parameters \(\varepsilon\) and the self-setting rules of exponential switching term parameters \(k\) for exponential reaching law are proposed, the constant switching term \(\varepsilon\) and \(k\) affecting the system chattering, and the rapidity problem of reaching the sliding mode surface from the initial state are solved;
3. To achieve rapid suppression of load-torque disturbance, a load torque observer is designed, which only needs the electromagnetic torque and the actual speed of the motor to observe the load torque.  
Through the numerical simulation comparison between the strategy proposed in this paper and the conventional sliding mode control, the conventional sliding mode with  
Figure 17: Curve of torque observation.  
Figure 18: Speed tracking experimental curve.  
load torque observer (SMC + LO), as well as the PID control with load torque observer (PID + LO), it is found that when tracking step signals or staircase signals, the regulation time of the control strategy proposed in this paper is the same as that of SMC + LO, which is significantly shorter than that of ADRC and PID + LO, being only 29-20% of the regulation time of ADRC control and 23-13.8% of the regulation time of PID + LO. When a step load is suddenly applied, the dynamic speed drop of the control strategy proposed in this paper is 2.7 r/min, while the dynamic speed drops of SMC + LO, ADRC, and PID + LO are 3.2 r/min, 3.7 r/min, and 4.1 r/min, respectively, and the recovery time is also significantly shorter than that of the other three control strategies. The experimental results are basically consistent with the numerical simulation results. Based on the comprehensive analysis of the simulation and the experiment, the control strategy proposed in this paper can not only ensure the dynamic and static performance of the permanent magnet synchronous motor (PMSM) speed regulation system well, but also effectively improve the robustness of the system and weaken the system chattering.  
Conceptualization, P.X.; Methodology, P.X. and P.L.; Software, P.Q. and P.L.; Validation, P.X. and P.L.; Writing--original draft, P.X. and P.L.; Writing--review and editing, P.Q. All authors have read and agreed to the published version of the manuscript.  
This research was supported by Science and Technology Research Project of the Education Department of Jilin Province, grant number JKH20240083 KJ.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
Author [PERSON] was employed by the company Intelligent Connected Vehicle Development Institute China FAW Group Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.