## 2 Suspension System Model  
In this section, the 2-DOF suspension model is introduced to describe the vertical vibration and the schematic diagram of the vehicle dynamics model is shown in Figure 1. It is assumed that tire damper is ignored. The stiffness of the tire is represented as constant \(K_{t}\). \(m_{2}\) and \(m_{1}\) denote the sprung mass and the unsprung mass respectively. Suspension control force is denoted \(u\). \(z_{1},z_{2}\), and \(q\) represent tire vertical displacement, sprung displacement and road excitation respectively [33]. ECU representselectronic control unit which handles the sensors signals to achieve control signals. The positive direction is shown in Figure 1.  
Base on [PERSON]'s second law, the equation of the 2-DOF controllable suspension model which is illustrated in Figure 1 is expressed as Equation (1)  
\[\left\{ \begin{array}{l}m_{2}\ddot{z}_{2}=u\\ m_{1}\ddot{z}_{1}+K_{t}(z_{1}-q)=-u\end{array} \right. \tag{1}\]  
where \(\ddot{z}_{2}\) and \(\ddot{z}_{1}\) refer to the acceleration of sprung mass and unsprung mass respectively. **3. Hybrid Damping Control**  
The semi-active suspension system with hybrid control is shown in Figure 2 [34]. Because the spring-damper parallel connection structure connects between the sprung mass and unsprung mass, the desired hybrid control force is expressed as Equation (2)  
\[u(t)=-(u_{1}(t)+u_{td}(t)) \tag{2}\]  
where \(u_{1}(t)=K(z_{2}-z_{1})\) represents the spring force, \(K\) is the spring stiffness, \(\dot{z}_{2}\) and \(\dot{z}_{1}\) represent the sprung mass velocity and the unsprung mass velocity. The damping force is represented as \(u_{td}(t)=[1+k(S)]C_{sky}\dot{z}_{2}-k(S)C_{gr}\dot{z}_{1}\), where \(C_{gr}\) is the desired ground-hook damping coefficient. \(C_{sky}\) is the desired sky-hook damping coefficient. \(k(S)\) is the weight of the hybrid damping coefficient. Figure 1: 2-DOF vehicle controllable suspension model. Figure 2: Principle diagram of the hybrid damping control. As illustrated in Figure 2, based on the Equations (1) and (2), the equations of hybrid control suspension system which is illustrated in Figure 2 are represented as  
\[\left\{ \begin{array}{l}m_{2}\ddot{z}_{2}+K(z_{2}-z_{1})=-[1+k(S)]C_{sky}\dot{z}_ {2}+k(S)C_{gr}\dot{z}_{1}\\ m_{1}\ddot{z}_{1}-K(z_{2}-z_{1})+K_{t}(z_{1}-q)=[1+k(S)]C_{sky}\dot{z}_{2}-k(S)C_ {gro}\dot{z}_{1}\end{array} \right. \tag{3}\]  
However, it is difficult to realize the desired sky-hook control and the desired ground-hook control in reality. Therefore, the equivalent damping coefficient is adopted to realize hybrid control. The equivalent damping coefficients are written as  
\[\mathrm{C}_{\alpha\beta}=\left\{\begin{array}{l}C_{\max}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  
The parameters of the suspension system are shown in Table 1. The frequency responses of ride comfort and driving safety are illustrated in Figure 3 from the MATLAB/Simulink simulation when the vehicle drives over the C grade pavement at 40 m/s under the coefficient \(k(S)=-0.33\). Figure 3a describes that the body acceleration gain under the hybrid control is less than that under passive suspension. The frequency response of suspension dynamic displacement is illustrated in Figure 3b. The performance of hybrid control is better than the sky-hook control under high vibration (5-12 Hz), although hybrid control is still at a disadvantage to the passive suspension. Meanwhile, the ground-hook control performs best of all under high frequency (5-12 Hz), worst under low frequency (0-5 Hz). Figure 3c illustrates that the tire dynamic deformation gain of hybrid control is slightly higher than passive suspension under high frequency (5-12 Hz). However, compared with the sky-hook control, it has a significant decrease. The ground-hook control is superior to other control methods under high frequency (5-12 Hz). In low frequency (0-5 Hz), its gain is much higher than other control. Therefore, hybrid control can affect the amplitude-frequency of the suspension system.