## 1 Introduction  
In power electronic converters, high switching frequency is a highly desirable feature, which can not only reduce the volume and power density of converters, but also increase the dynamic response. However, high switching frequency brings about the problems of high switching loss and severe electromagnetic interference (EMI) [1; 2]. The soft switching technique is one of the best options to address the problems above. To date, a variety of soft-switching DC-AC topologies have been proposed. Among them, the zero-voltage-transition (ZVT) pulse-width-modulation (PWM) inverter is a typical soft-switching inverter [3; 4; 5; 6; 7; 8; 9; 10; 11]. An auxiliary circuit connected parallel to the main power path is employed in the ZVT PWM inverter, which only operates for a short interval before and after the commutation period of the main switches. This makes the ZVT inverter closest to the PWM converter counterpart. Compared with other soft-switching inverters, the voltage and current stresses and conduction losses are much lower [3; 4]. Contributing to these advantages, the ZVT PWM inverter is well accepted. Several topologies of the ZVT PWM inverter have been proposed. The auxiliary resonant commutated pole inverter (ARCHI) has been proposed with two auxiliary switches per phase [5; 6]. The ARCHI can meet the demand for high efficiency and low voltage and current stresses. However, the major drawback is the existence of the split capacitors, which cause the problems of capacitor charge unbalance. The auxiliary resonant snubber inverter (ARSI) has been proposed to eliminate the split capacitors, but the three-phase topology cannot utilize the conventional space-vector-pulse-width modulation (SVPWM) [7; 8]. Thus, they are more suitable for permanent magnet brushless DC motors instead of all types of motors. The single-phase topology is very attractive with only two auxiliary switches and well fit to the conventional PWM. Meanwhile, the ZVT inverter using coupled magnetics has been proposed to eliminate the split capacitors [9; 10; 11]. However, these topologies need coupled inductors and a large number of auxiliary switches, which increases the cost and difficulty of the circuit realization. The ZVT PWM converter has been synthesized and summarized in [3; 4]. In high-precision motor drive applications, an LC filter must be added in the ARSI to reduce the output current ripple. Moreover, the additional LC filter can solve problems of poor insulation that result from the overvoltage [12]. However, since the additional LC filter together with the inductor of the motor forms the LCL filter, a resonance peak occurs in the system, which makes the system unstable. Recently, the passive damping method has been used to stabilize the system [13; 14]. The passive components of resistors, capacitors, and inductors are parallel or series-connected to the filter capacitor to damp out the resonance. The method is easy to implement; however, it reduces the efficiency of the system. The active damping method can be used to damp out the resonance at no expense of efficiency. The state variable feedback, such as filter capacitor voltage [15; 16] or filter capacitor current [17; 18], is introduced to provide virtual resistance. Among them, the capacitor current feedback is a typical and widely used method. Most studies of the active damping method have focused on the grid with consideration of zero resistance. However, in the drive system, the load resistance should not be neglected. Until now, only a few researchers have studied the active damping in the motor drive system; however, they have not taken into consideration the digital control delays. In addition, previous studies on ARSI have focused on the circuit design and auxiliary current control but there has been a lack of research about the design of the closed-loop control. Thus, a step-by-step closed-loop controller design of the ARSI with LC filter is proposed in this paper, including the auxiliary current controller and the output current controller.