## 1 Introduction  
With the continuous advancement of science and technology, the degree of electrification within human society continues to deepen, and the utilization of electric energy has infiltrated every aspect of daily life [1]. Consequently, the modes of electricity transmission are evolving rapidly. In recent years, wireless power transfer (WPT) has been increasingly applied in domains such as underwater operations, consumer electronics, and modern medicine [2; 3; 4; 5; 6; 7], owing to its superior flexibility and convenience. Nonetheless, this technology encounters several challenges, particularly when system loads fluctuate or the mutual inductance between coils varies. These variations can negatively impact the system output voltage [8; 9; 10] and transmission efficiency [11; 12]. Therefore, researchers have proposed various methods to improve the system efficiency under the conditions of load and mutual inductance variations. To maintain the constant system output voltage, the method of cascading DC-DC converter at the input or output of the WPT system is usually adopted [13; 14]. [PERSON] et al., from Chongqing University in China, connected a DC-DC converter at the input of the WPT system, and a method was proposed to adjust the output voltage by varying the duty cycle of the Buck converter connected to the system input [15]. However, this method relies heavily on the accuracy of the identification algorithm and necessitates high sampling precision. The authors of [16; 17] describe an alternative approach where a DC-DC converter is connected to the output of the WPT system. The method adopts a Proportional-Integral (PI) controller to maintain constant current (CC) charging for the variable load. In addition, some methods without DC-DC converters have been proposed. The authors of [18] introduce a battery charging control strategy that needs no bilateral communication and an additional DC-DC converter. This approach achieves constant current output or constant voltage (CV) output regardless of load and position changes through phase shift control. Moreover, a prototype is built to demonstrate the CC/CV output over a transmission distance of 10-25 cm. The authors of [19] propose a strategy for pre-control calibration, in which the system mutual inductance is detected during the calibration stage, and the system output voltage is estimated in real time based on this mutual inductance value. Then, the output voltage is adjusted through the phase shift control of the inverter. The authors of [20] introduce a phase shift control method for a half-bridge rectifier and derive the equivalent impedance related to the phase shift angle of the half-bridge rectifier. This method allows for the adjustment of the system output voltage without DC-DC converters. At the same time, some methods have been proposed to improve the transmission efficiency of the WPT system during mutual inductance and load changes. [PERSON] et al., from the University of Hong Kong, propose a discrete sliding mode control for a series-series-compensated WPT system, enabling rapid maximum efficiency tracking and output voltage regulation [21]. In [22; 23], a control method by adjusting the phase shift angle of the active rectifier was proposed for real-time maximum efficiency tracking. The method can adjust the equivalent load impedance and output voltage to solve the efficiency reduction problem caused by load changes. This article proposes a control method for the WPT system, focusing on improving transmission efficiency while maintaining a constant output voltage. First, a Buck-Boost converter is cascaded after the diode rectifier of the WPT system to achieve a constant voltage output. Then, the output voltage of the rectifier is measured to estimate the mutual inductance and calculate the optimal phase shift angle for maximum efficiency tracking. Finally, the value of the optimal phase shift angle is sent to the controller of the WPT primary side to improve the system transmission efficiency.