## 1 Introduction  
Permanent magnet synchronous motor (PMSM) has been widely used in electric vehicle, ship electric propulsion system and other driving fields because of its advantages of simple structure, high power density and high operating efficiency [1, 2]. With the development of electronic technology, PMSM drive structures are also constantly updated to adapt to the needs of different operating conditions [3, 4]. In the detection of traditional drive system, the installation position of mechanical sensors such as photoelectric encoder and rotary transformer is not accurate. In addition, the aging of sensors restricts the drive system to achieve satisfactory control performance, which reduces the system reliability and economics of production [5, 6]. In order to solve the influence of traditional mechanical sensors on the drive system, the sensorless idea is developed and applied in PMSM drive system. PMSM sensorless drive system can construct the rotor position and speed information required by detecting the voltage and current signals of the motor port [7, 8]. At present, the sensorless control technology of permanent magnet synchronous motor can be roughly divided into two types based on fundamental wave observation and salient pole effect [9, 10]. The observation method based on salient pole effect has better observation performance for low speed operation condition [11; 12]. However, it is a pity that this method has some limitations for hidden pole machine [13; 14]. Therefore, the method based on fundamental wave observation is still used to obtain PMSM rotor information in more control occasions. The fundamental wave observation method is divided into four types: arc-tangent method, phase-locked loop (PLL) method, model reference adaptive method and intelligent algorithm according to the different methods of obtaining rotor information [15; 16]. Among them, the model reference adaptive method has the characteristics of simple structure. However, the accuracy of the observation is closely related to the design rules of the adaptive law, which is difficult to be applied in practical systems [17; 18]. In addition, it is difficult to realize in the actual system. Meanwhile, intelligent algorithm observation rotor information accuracy is closely related to the number of training samples, the control structure is very complex [19; 20]. On the contrary, the arc-tangent method can use the sliding mode variable structure method to obtain the inverse electromotive force information of the motor rotor, and directly construct the arc-tangent equation to obtain the required position information [21; 22]. However, this method has a low signal noise ratio (SNR) and is greatly affected by back EMF harmonics [23; 24]. Fortunately, the closed-loop feedback of rotor back EMF information based on phase-locked loop method is constructed by introducing PI controller [25; 26]. In the presence of harmonics, closed-loop self-adjustment process can be adopted to alleviate the disadvantages of arc-tangent method [27; 28]. It can be seen that the phase-locked loop method is an observation method with relatively good comprehensive performance. Meanwhile, PI regulator introduced by phase-locked loop method also aggravates the problem of integral saturation and integral drift of the whole system. Therefore, in order to achieve better performance of the sensorless system, it is necessary to perform integral saturation suppression on the driving system. In terms of integral saturation suppression, most engineering uses anti-saturation methods, such as variable speed integration and integral separation, to suppress the integral saturation state of the drive system [29; 30; 31]. In [32], the influence of saturation phenomenon has been suppressed to a certain extent, nonetheless it does not eliminate the accumulated integral error. Hence, the anti-saturation method is easy to fall into integral saturation again.