# Advancements in Semi-Active Automotive Suspension Systems with Magnetroheological Dampers: A Review
## 4 Semi-Active Control of Suspension Systems
### Classical Control Strategies
#### 4.1.1 Skyhook Control  
Skyhook damping control, proposed by [PERSON] et al. in 1974, is a classic suspension control strategy [37]. Its core principle posits an ideal skyhook damper, affixed at one  
Figure 6: The illustration of the design of three-coil mixed mode MRD [6].  
Figure 7: Structure of the MRD with a piston head featuring bypass holes [36].  
end to the vehicle body and at the other end to the \"absolutely stationary\" sky, thereby transmitting damping force exclusively to the vehicle body without affecting the unsprung mass, thus achieving vibration reduction. However, practical vehicle suspension systems inherently retain coupling between the vehicle body and unsprung mass, precluding the isolation of damping forces solely to the vehicle body. Nonetheless, skyhook control has demonstrated significant enhancements in vehicle ride quality.  
[PERSON] et al. proposed integrating switch control into skyhook damping, where the damper's switching state is determined by the velocities of the unsprung and sprung masses [38]. The damper switches to the \"off\" state when the velocity of the unsprung mass exceeds that of the sprung mass and their directions align; otherwise, it remains \"on\". This constitutes a switching control strategy to adjust damping levels according to control demands, thereby accommodating vehicle body vibrations under different conditions. However, due to its toggling nature, this control approach may induce jitter in the suspension system.  
To eliminate jitter phenomena, [PERSON] and [PERSON] conducted in-depth research on switch-type skyhook control and proposed a jitter-free skyhook control method [10]. [PERSON] et al. devised a continuous linear skyhook control strategy to counteract the jitter induced by switch-type skyhook control [39]. [PERSON] and [PERSON] introduced an enhanced energy-efficient skyhook control that integrated active control and energy recovery technologies, effectively managing the system's dynamic performance and energy consumption issues through efficient switching conditions [40], as illustrated in Figure 8. [PERSON] et al. proposed an adaptive skyhook damping control algorithm and employed genetic algorithms to optimize the optimal control gain coefficients for skyhook damping control across varying vehicle speeds [41], as shown in Figure 9. [PERSON] et al. presented an advanced skyhook damping control method based on real-time estimation of road surface conditions, enabling optimal control parameters according to different vehicle speeds and road surfaces [42]. [PERSON] et al. developed a skyhook damping controller based on an inverse model of the MRD and refined it using the grey wolf optimization algorithm, thereby reducing vehicle acceleration, suspension travel, and tire dynamic loads [43].  
Figure 8: The proposed enhanced energy-efficient skyhook control [40]: (**a**) quarter-car model of a semi-active suspension system; (**b**) block diagram of the control system.  
For the convenience of signal acquisition, [PERSON] et al. proposed an Acceleration-Driven Damping (ADD) control strategy [44; 45]. This strategy's control logic parallels that of skyhook control, but instead of relying on the velocity of the sprung mass, it evaluates the relationship between the acceleration of the sprung mass and the relative velocity of the suspension. ADD control effectively attenuates high-frequency vibrations, while skyhook control excels in mitigating low-frequency vibrations. Consequently, [PERSON] and [PERSON] integrated these two control algorithms to propose a Hybrid Skyhook-ADD (SH-ADD) damping control strategy [46]. This approach employs a switching control methodology, adapting the control strategy according to the frequency of the current road excitation, thereby achieving superior ride comfort across the entire frequency spectrum.