## 1 Introduction
Furthermore, the electromagnetic coupling model of hub-driven electric vehicle based on PMSM that has been established by [PERSON] is inaccurate [12]. It is necessary to establish the complete electromagnetic coupling model, investigate the coupling mechanism of PMSM and study the active control methods for the suspension system of hub-driven electric vehicle to solve the negative coupling effect of the PMSM. Besides, failures of electrical components, sensors, and the actuator are fairly common to active suspension systems, which will lead to a series of problems, such as system instability, performance degradation, and even disaster traffic accidents. Therefore, it is of great significance to design the active suspension considering actuator failures. [PERSON] et al. [20] proposed a robust controller for a semi-active suspension system with actuator saturation. The vehicle vibration attenuation problem under two cases was addressed, namely, without actuator fault and with base oil leakage in MR damper. [PERSON] et al. [21] proposed a new adaptive fault tolerant control scheme by employing adaptive feed-back stepping technique which ensured the boundedness in probability of the considered systems. [PERSON] et al. [22] presented an application of a diagnosis and a fault-tolerant control method for an active suspension system. This method could improve the vehicle performance in the presence of road disturbances by identifying an actuator fault and reconfiguring the controller. In the literature [23,24,25], the fault-tolerant control was proposed for an active suspension system with an actuator fault. The results showed that the control effects of the active suspension system deteriorated without considering the actuator failure. Similarly, the control effects will be unsatisfactory if the model parameter uncertainties are neglected. In the literature [26; 27; 28], the robust control was proposed for vehicle active suspensions. The comparative simulations presented the availability of the designed controllers considering the model uncertainties. In addition, some other control methods were also proposed to suppress disturbance and obtain the better performance of the system, such as \(u\)-synthesis [29], neural network method [30], mixed \(H_{\infty}\)/\(H_{2}\)[31], slide-mode control [32; 33; 34; 35; 36], adaptive control [37], and nonlinear control [38; 39]. However, most of the control strategies are proposed for conventional vehicles and rarely for PMSM-driven EVs. From the existing studies, the issues of active suspension systems associated with actuator fault tolerance, model parameter uncertainties, and coupling effect in IWM based on PMSM have not been well studied in previous research. This paper focuses on the coupling effect in permanent magnet synchronous IWM and the robust control for active suspension of hub-driven EVs. The challenges and technical contributions are summarized as follows: (1) unlike studies in Ref. [11; 12], in which the established electromechanical coupling model was simple and inaccurate, in this paper, according to the electromagnetic field theory, the complete electromechanical coupling model of the hub-driven EVs composed of four sub-models is established. The transient characteristics of electromechanical coupling effect can be effectively studied under vehicle running conditions; (2) unlike studies in Ref. [15; 16; 24], in which the authors proposed active suspension controller for the SRM driven electric vehicle, the electric vehicle neglecting the coupling effect or the conventional vehicle, in this study, a multi-objective control is designed for the PMSM driven EV to obtain better ride comfort and restrict coupling effect of in-wheel PMSM.