## 1 Introduction  
Due to the aggravation of environmental pollution and the energy crisis, automotive products are required to be energy-saving, highly efficient, and environmentally-friendly [1; 2; 3]. Compared with traditional diesel locomotives, electric vehicles (EVs) which have several advantages such as no CO2 emission and energy efficiency have caught widespread attention in recent years [4; 5]. The propulsion configurations of EVs can be classified as a distributed motor driven layout and a centralized driven layout. Compared with centralized driven layout EVs, in-wheel motor (IWM) propelling EVs, as the distributed propulsion system, enjoy various additional structure and control merits [6; 7]. As in the IWM the brake and the reducer are integrated into the rim, the mechanical transmission system of hub-driven EVs is simpler and more efficient. Moreover, by controlling the torque of each electric motor precisely and independently, hub-driven EVs have played a significant role in enhancing the performance of existing vehicle stability/motion control systems, such as electronic stability control systems (ESC) and traction control systems (TCS) [8]. However, the development of hub-driven EVs has introduced some new technical problems. The integration of the driving system into the rim leads to an increase in the unsprung mass, which deteriorates road handling capacities and the ride comfort of vehicles [9,10]. What is more, the road surface roughness excitation and the coupling effect in IWM make the magnet gap deformed. The deformed magnet gap then leads to magnetic force oscillation which is a critical vibration source for vehicle dynamics [11,12]. In the past decades, some passive and active methods, such as optimization of the vibration isolator, redesign of the IWM, and active control for suspension systems, have been adopted to suppress magnetic force oscillation and improve the ride comfort. However, there are some deficiencies which remain to be solved. [PERSON] et al. [12] proposed a novel IWM topology scheme and studied the coupling effect of the IWM system. By mounting rubber bushings in the IWM device, the vibration energy from the road surface was absorbed and the deformation of magnet gap was restricted. However, the life of the rubber bushing was short due to the severe operating environment of the IWM, making it difficult for practical use. Moreover, due to neglect of the permanent magnet brushless direct current (PMBDC) motor model which could provide the phase current for calculating the unbalanced electromagnetic force (UEF), the established coupling model was simple and inaccurate. The transient characteristics of electromechanical coupling effect cannot be effectively studied under vehicle running conditions. [PERSON] et al. [13] designed the motor mount, making the motor mass as dynamic vibration absorber. The results show that the ride comfort was improved. However, there was a distinct axis relative displacement between the rotor and the stator, prompting magnet gap deformed and magnetic force oscillation. The active suspension control methods have been proposed to suppress the magnetic force oscillation. Nevertheless, the majority of the active suspension system of hub-driven EVs are based on switched reluctance in-wheel driven motors [14,15] or neglect the negative electromagnetic coupling effect in IWM [16,17,18,19]. Different from switched reluctance motors (SRM), the magnetic field in permanent magnet synchronous motors (PMSM) is provided by permanent magnets. Consequently, as a permanent magnet synchronous IWM, more complex multi-field coupling effects need to be studied to enhance the ride comfort of EVs. In brief, it is meaningful to suppress magnetic force oscillation and improve the ride comfort. However, for the PMSM, the passive methods to suppress magnetic force oscillation have some defects and the active methods are rarely studied.