## 1 Introduction  
The advantages of the high-speed permanent magnet synchronous motor (HPMSM) include high power density, high reliability, fast operation, and the possibility of direct connection to the load. Therefore, it is widely used in industry, especially in compressor machines, vacuum cleaners, generators, etc. [1; 2; 3]. However, the structural characteristics and operating conditions of HPMSM determine that the stator inductance is generally designed to be small, and the electrical frequency is also much higher than that of conventional motors [4; 5]. The voltage source inverter (VSI) is a common driver device for motor control, which has a high switching frequency and will generate a large number of high-frequency current harmonics. The harmonics mainly appear around the switching frequency and its integer multiples, causing distortion of the current in the motor windings [6; 7; 8]. Abundant harmonic currents will induce large noise, iron loss, and torque turbulence, leading to the reduction of motor capability and system efficiency [9; 10; 11]. To restrain the current harmonics, increasing the equivalent inductance is the most simple and intuitive method. In [12], series inductors are connected in series in each phase of the stator winding to increase the equivalent inductance and successfully reduce the harmonic component of the stator current. Nevertheless, the series inductors will inevitably enlarge the volume and weight of the system. It has been proposed to add LC filters between the three-phase stator winding and the inverter, which can effectively reduce the increase in system size while providing filtering effects [13]. However, the introduction of the LC filter brings about a resonance peak in the system. Due to the low circuit impedance,the voltage and current oscillations will appear, which brings challenges to the stability of the drive system. To overcome this, many papers have proposed damping technologies for suppressing the resonant peak, which are mainly divided into two categories: the passive damping method and the active damping method. One of the most commonly used passive damping schemes is to connect the damping resistance with the filter capacitor in series, because of its simple design and implementation [14]. In order to obtain good high-frequency attenuation and very low damping loss, many improved passive filter topologies have been proposed and verified [15; 16; 17]. Additionally, in [18], the \"critical damping ratio\" metric is first introduced and solved, which provides an efficient and accurate method for the damping design of filters. However, although the passive damping method has the effect of suppressing resonance, it will inevitably cause additional power losses, which decreases the efficiency of the system [19]. As a result, the active damping scheme with no additional loss has been favored by the industry, and the active damping strategy has been widely studied and developed in academic circles. In [20], a virtual impedance system is built by using the transfer function equivalent method. The impedance is emulated using the feedback current of the filter capacitor to provide the damping effect, so it will not consume any extra energy of the system. Other active damping methods such as high-pass filters [21], hysteresis networks [22; 23; 24], infinite impulse response (IIR) digital filters [25; 26], weighted feedback currents (WAC) [27], etc. have been investigated. However, in most cases, those methods require additional sensors, which enlarge the system volume, increase cost, and enhance the possibility of interference. Subsequently, a filter-based active damping technique was proposed in [28]. It was achieved by simply inserting a low-pass filter or notch filter in the forward path of the current control loop; thus, no extra sensors are required, which makes the method emerge as a promising alternative to active damping. Actually, the trap filter concept was primarily implemented in [28], where a genetic algorithm was applied to regulate the trap filter.