# Hybrid Model Predictive Control of Semiactive Suspension in Electric Vehicle with Hub-Motor
## 1 Introduction  
Due to increased pressure for environmental protection and energy shortages, electric vehicles' development is being highly valued by many research institutions [1]. Electric vehicles are environmentally friendly and excel in terms of sporting performance due to the fast and precise torque of the electomotor [2, 3]. Hub-motor electric vehicles (HM-EVs) have the advantages mentioned above and eliminate the need for a powertrain, improving transmission efficiency and space utilization, making power control easier to achieve [4, 5]. Thanks to its unique technical advantages, HM-EV has received unprecedented attention and development. It has become one of the focuses and hotspots of electric vehicle technology research and has become a unique direction for electric vehicles' development. The industry also refers to the HMs as the final drive form of electric vehicles [6]. However, because the HM-EV highly integrates the motor, reduction mechanism, and brake in the wheel, it increases the unsprung mass of the vehicle and deteriorates the vertical performance of the vehicle [7]. Additionally, tire bounce, support shaft bending, bearing wear caused by the excitation of the road will cause the stator and rotor to be eccentric and cause uneven distribution of the motor air gap along the circumference [8, 9]. The unbalanced electromagnetic force generated by the uneven air gap will be transmitted to the wheels through the reduction mechanism or directly, which is equivalent to adding a certain external load to the wheels, thus affecting the dynamic characteristics of the suspension [10]. To solve these problems, many scholars have suppressed various adverse effects of HMs on vehicles from both structural and control perspectives. [PERSON] et al. [7] used special springs and dampers to connect the motor to the unsprung mass, to turn the motor into a dynamic vibration absorber (DVA) for the unsprung mass, reducing the vibration of the sprung mass and improving the smoothness of the vehicle ride, as wellas reducing the input to the motor vibration. [PERSON] et al. [11] proposed a new type of HM structure with rubber bushing between the stator and rotor. Through the comparison and simulation of two HM schemes with bushing and without bushing, it was concluded that the vertical performance of the motor with bushing was significantly improved. [PERSON] et al. [12] proposed a new method of vibration damping based on the DVA structure, and the simulation results show that the ride comfort and handling stability were effectively improved after adopting the new DVA structure. Finally, a multibody simulation was carried out using muti-body dynamic software (LMS motion) to verify the feasibility of the proposed DVA structure. There are many scholars already working on suppressing the adverse effects caused by HM from an active suspension perspective. [PERSON] et al. [13] proposed an optimal control strategy for electric vehicle wheels, which optimizes the parameters of the DVA structure according to the typical working conditions, and then adopts the fuzzy control method and linear quadratic regulator (LQR) method to control the actuator force of the DVA structure and suspension force, respectively, to reduce the impact on the HM and improve the ride comfort. [PERSON] et al. [14] present an HM-EV active suspension fault-tolerant fuzzy H\({}_{\infty}\) controller that takes into account sprung mass variation, actuator faults, and control input constraints, and verifies the effectiveness of the controller by simulation. [PERSON] et al. [15] proposed a fuzzy optimal sliding mode control method using normalization and hierarchical analysis to select weighting coefficients, and verified the superiority of using this control method for electric vehicles by simulation. [PERSON] et al.