## 5 Semi-Active Control Analysis of the Multi-DOF Seat Damping Suspension
### Design of the Semi-Active Controller
#### 5.1.2 Fuzzy Skyhook Control Method  
Since an MRF damper was used as the output control force in this study, the output control force had to conform to the output law of the MRF damper. That is, the output control force had to be the opposite to the relative velocity of the MRF damper. As a classical control strategy for semi-active suspensions, the control force output of the skyhook control method conforms to this rule. This method has many advantages, such as simple implementation, few control variables, and easy measurement. The basis of the skyhook control method is the ideal skyhook control method. The principle of the ideal skyhook control method is shown in Figure 21.  
Figure 20: The one-way vibration model. As shown in Figure 21, the ideal skyhook control method assumes that a damper (\(c_{sky}\)) is installed between the sky inertial system and the platform on a seat. During movement of the seat, the method generates a skyhook damping force with an amplitude of \(c_{sky}\times v_{2}\) (\(v_{2}\) is the movement speed of the seat load \(m\)), and the direction is opposite to the direction of the seat load movement; thus, the vibration can be reduced in the seat load. However, in actual use, there is no damper connected with the sky inertial system, and the skyhook damping force needs to be output by the MRF damper. Therefore, in the actual skyhook control strategy, when the output damping force of the MRF damper is opposite to the direction of motion of the seat load, the current is added to output the skyhook damping force in order to generate the damping effect; otherwise, the skyhook damping force will not be output. The skyhook control strategy comprises the following equation:  
\[f_{MRF}=\left\{ \begin{array}{ll}c_{sky}\times v_{rel}&v_{rel}\times v_{s}\geq 0 \\ 0&v_{rel}\times v_{s}<0\end{array} \right. \tag{15}\]  
where \(c_{sky}\) is the skyhook damping controlled by the current, \(v_{rel}\) is the relative velocity of the MRF damper (upper rod velocity minus the lower rod), and \(v_{s}\) is the upper rod velocity of the damper. For traditional skyhook control, the damping force is generated by a fixed current; that is, when the motion of the suspension meets the requirements of the output damping force as shown in Equation (15), the current switch is turned on, a fixed current is input, and the damping force is output. Otherwise, the current switch is turned off, and only the minimum damping force is output. However, skyhook control also has disadvantages: (1) it produces an impact load on the suspension system during damping force switching; (2) the MRF damper can only change between fixed current and no current under skyhook control, so it is unable to fully utilize the ability of the MRF damper to continuously adjust the damping force; as a result, it consumes more electric energy. Therefore, a fuzzy algorithm-based skyhook control was examined, to maximize the MRF damper's continuously adjustable damping advantage. The input variables of a fuzzy controller are the upper rod velocity \(v_{s}\) and the relative velocity \(v_{rel}\), and the output is the damping force factor [24]. This factor is multiplied by the skyhook damping coefficient to obtain the desired damping force. Through multiple calculations on the suspension model, the skyhook damping coefficient was selected as 3000 Ns/m. This study controlled the damping force by the sign of \(v_{s}\times v_{rel}\). The fuzzifications of \(v_{rel}\) and \(v_{s}\) are Negative Big (NB), Negative Small (NS), Zero (ZE), Positive Small (PS), and Positive Big (PB), and the fuzzifications of the desired output are Zero (ZE), Small (S), Middle (M), and Big (B). The fuzzy logic control rules are based on the skyhook strategy, and when the \(v_{s}\) and \(v_{rel}\) are NB, the output is the maximum damping force that corresponds to B in the fuzzy control algorithm, and so forth. The final control rules are shown in Table 3, and the structure of the fuzzy controller is shown in Figure 22.  
Figure 21: The ideal skyhook control model.