## 1 Introduction  
Wireless power transfer systems can deliver electric power from the power supply side to the load side without requiring any physical connections [1]. Possessing the advantages of contactless operation, safety, low maintenance and environment friendliness [2], WPT systems have been widely used in many applications, such as transportation, medical electronics, consumer electronics, and aerospace [3; 4; 5; 6]. With the high nonlinearity [7], WPT systems are highly sensitive to many disturbances, such as input voltage fluctuation, coil misalignment and load variations [8; 9]. Therefore, many control strategies have been proposed to improve the output voltage quality. The PWM control strategy is one of the most commonly used control strategies in WPT systems. In [10], a control scheme without the secondary side measurement is proposed. It only uses the current and voltage measurements of the primary side to estimate mutual inductance and load in real time. The PWM driving pulse is adjusted according to the changes in mutual inductance and load to stabilize the output voltage. Authors in [11] proposed a multi-transmitter and multi-receiver (MTMR) WPT PWM-based control strategy that can balance current distribution and achieve high efficiency and stable output voltage. In [12], a novel control strategy combining one cycle control and proportional differential control (OCC-PD) is proposed to ensure the swiftness of the transient response of the WPT system. The approximated boundary of the start-up transient time of the WPT stage is solved analytically by dividing the resonant circuit into three equivalent parts and analyzing their transfer functions, respectively. Authors in [13] proposed a new duty cycle control (DCC) strategy for a dual-side LCC resonant converter with a semi-bridgeless active rectifier (SAR). With such a control strategy, the gate signals of the primary- and secondary-side circuits do not need to be synchronized, which could reduce the complexity and the cost of the WPT system. A novel system topology for WPT of fuel cell (FC) energy is introduced in [14]. The pre-regulating WPT system is developed with a quadratic boost converter (QBC) located on the transmitting side is applied between the FC unit and the inverter to increase the output voltage of the FC to a higher voltage level, which is sufficient for WPT transmission. However, the transient response speed of many WPT control strategies needs to be improved in order to meet the operational requirements in applications, such as mining and medical power supply [15; 16]. Concerning the well-established PWM-based methods, the advantage of the PT control method is its rapid-transient response speed and simple implementation [17]. The major characteristic of the PT control is that the error amplifiers and corresponding compensation circuits are not required, ensuring a relatively high response speed when the load varies [18]. Due to simple implementation, PT control methods have been applied in DC/DC power converters [19; 20; 21; 22]. However, when the PT controlled DC/DC converters are operated in continuous conduction mode (CCM) [23; 24], low-frequency voltage oscillations at the output side can be observed due to the phase difference between the control and the response. The tradeoff between improving response speed and increasing system stability is a challenge for PT control. Hence, many research efforts have been made on suppressing the low-frequency oscillations of PT controlled power converters. Authors in [25] proposed a PT control strategy with inductor current ripple injection feedback (ICRIF) to avoid such oscillations. The valley current-based PT (VCM-PT) control is proposed in [26] to ensure that the variation of inductor current in each switching cycle is equal to zero, and low-frequency oscillations can be eliminated. However, due to the use of preset valley current, the allowable output power range of the converter is limited.