# A Hydraulic Semi-Active Suspension Based on Road Statistical Properties and Its Road Identification
## 2 New Hydraulic Semi-Active Suspension  
Many suspensions for vehicles are equipped with hydraulic dampers with adjustable damping characteristics, for example, setting up three grades: \"soft\", \"moderate\", and \"hard\". They are usually called the shift-selected semi-active suspension system. Their use relies on the driver's road perception during a period for vehicles under changing conditions. According to the perceived information of the road conditions, the driver chooses the reasonable position that he thinks. In essence, the driver's road perception is mainly based on the statistical characteristics of road conditions. Thus, the basic assumption is that the road condition is constant during a limited period for the shift-selected semi-active suspension system. This paper adopts the assumption above, and then,proposes a novel hydraulic semi-active suspension system based on road statistical properties, as shown in Figure 1.  
In Figure 1, \(m_{2}\) and \(m_{1}\) are sprung mass and unsprung mass, respectively; \(K_{\rm s}\) represents the spring stiffness of the suspension system; \(K_{\rm t}\) represents the tire vertical stiffness; \(C\) represents the damping coefficient of the hydraulic damper; \(q\) represents the road input; \(G_{q}\) represents the PSD (power spectral density) of \(q\); and \(z_{1}\) and \(z_{2}\) are the vertical displacements of the wheel and the car body, respectively. The adopted controllable hydraulic damper is an important part of the semi-active suspension system, as shown in Figure 2, including: (1) stepper motor; (2) core bar; (3) protective cover; (4) outer tube; (5) piston rod; (6) controllable throttle hole; (7) piston; (8) inner tube; and (9) valve seat.  
The working process of the semi-active suspension system is as follows:  
**Step 1**: Based on the measured vertical vibration acceleration of the body \(\tilde{z}_{2}\) and the running speed \(v\), the PSD \(G_{q}\) can be obtained by an identification method.  
**Step 2**: According to \(\tilde{z}_{2}\) and \(G_{q}\), through a certain damping control method, the optimal damping ratio \(\xi_{\rm o}=\xi_{\rm o}(G_{q},v)\) of the semi-active suspension system can be obtained under the current running condition.  
**Step 3**: According to the relationship \(\xi_{\rm o}=C/2\sqrt{K_{\rm s}m_{2}}\), the current optimal damping coefficient \(C=C(G_{q},v)\) can be obtained.  
Figure 1: The new hydraulic semi-active suspension system.  
Figure 2: The controllable hydraulic damper.  
**Step 4**: Based on the damper oil circuit, the relationship among the throttle hole area \(A\), \(C(G_{q},v)\), and the rotation angle \(\theta\) of the stepper motor can be obtained, and then, \(\theta=\theta(G_{q},v)\) can be calculated.  
**Step 5**: According to \(\theta(G_{q},v)\) and the feedback signal \(\theta^{\prime}\) measured by an angle sensor, the stepper motor rotates a certain angle \(\triangle\theta=\theta(G_{q},v)-\theta^{\prime}\) to adjust the damper damping force.  
For the working process, the road identification method in Step 1 is the key, which will be investigation in the following in details. In addition, the mentioned damping control method in Step 2 can be offline or online, for instance, the optimal damping ratio control strategy proposed in the previous work [25]. Because the proposed suspension bases on the road statistical properties, the existing real-time control strategies [32; 33] are not totally applicable to the proposed suspension.