# Fuzzy Sliding Mode Control of Vehicle Magnetorheological Semi-Active Air Suspension
Zhiyong Ruan  
Key Laboratory of Vehicle Intelligent Equipment and Control of Nanchang City, East China Jiaotong University, Nanchang 330013, China; [EMAIL_ADDRESS] (Z.R. ); [EMAIL_ADDRESS] (R.  
of replacing the mechanical behavior of the MR damper by the combination of a damping element, elastic element, mechanical element, etc. This type of model is relatively simple in structure, and there are many existing research studies, such as the Bingham model, Sigmoid model and hyperbolic tangent model, which are applied in semi-active control [11]. Non-parametric models, such as the differential equation model, neural network model and polynomial model, mainly simulate the mechanical properties of MR dampers by means of intelligent control [12]. However, these non-parametric models do not consider the rheological properties of MR fluid and have poor adaptability. [PERSON] et al. proposed the hyperbolic tangent model based on the study of the hyperbolic tangent function, which is mainly composed of three parallel structures of the hysteretic force element, damping element and spring element [13]. The hyperbolic tangent model can accurately describe the hysteretic characteristics of the MR damper by using the characteristics of the hyperbolic tangent function, but there are many parameters to be identified. [PERSON] et al. constructed an improved hyperbolic tangent model, which applies another hyperbolic tangent function and is composed of viscous damping elements and elastic elements in series and parallel [14]. Appropriate control algorithms can make the semi-active air suspension almost achieve the same vibration attenuation effect as the active air suspension. In recent years, the sliding mode control (SMC) with strong anti-interference ability and good robustness attracted more and more attention in related fields. [PERSON] et al. designed a sliding mode controller for the vehicle seat and considered the human body mass as the uncertainty factor of the system [15]. Through simulation analysis, it is concluded that the sliding mode controller has favorable robustness to the uncertainty of the system, and the ride comfort is also improved. [PERSON] et al. proposed an improved adaptive sliding mode-based fault-tolerant control design, the results showing that the dynamics performance of half vehicle active suspensions with parametric uncertainties and actuator faults in the context of external road disturbances are improved [16]. [PERSON] et al. presented a practical terminal sliding mode control framework based on an adaptive disturbance observer for the active suspension systems, which requires no exact feedback linearization about the suspension dynamics [17]. For the tracking control problem of vehicle suspension, [PERSON] et al. derived a robust design method of adaptive sliding mode control [18]. Under this approach, the influence of parameter uncertainties and external disturbances on the system performance can be reduced, and the system robustness is also improved. [PERSON] et al. proposed a terminal sliding mode control approach for an active suspension system, which has an ability to reach the sliding surface in a finite time to achieve high control accuracy [19]. Combining the principle of fractional order control with sliding mode control, [PERSON] et al. proposed a corresponding fractional order sliding mode control strategy for vehicle suspension and verified its effectiveness through simulation and experiment [20]. [PERSON] et al. combined the advantages of fuzzy control and sliding mode control and confirmed the effectiveness of the fuzzy sliding mode controller [21]. In addition, many other control strategies are applied to the control of suspension systems, which include switching control, adaptive robust control, linear-quadratic-Gaussian (LQG) control, and intelligent control methods [22; 23; 24; 25; 26; 27]. Sliding mode variable structure control has good robustness, strong anti-interference ability, and can be well adapted to air suspension systems.