## 4 Conclusions  
This study derived the torque modeling relationships for an MR fluid multi-plate clutch using MR fluid, and a HILS system was used to perform simulations and MR fluid multi-plate clutch link control.  
The flow properties of the MR fluid were changed by applying a current and forming a magnetic field to control the ensuing torque transmission ratio. Consequently, a maximum transmission torque of 16.7 Nm was obtained in fluid mode, and the torque value increased in proportion to the current. Accordingly, it was determined that power transmission can be achieved by controlling the current.  
A PID controller suitable for each driving condition was designed by receiving feedback regarding the dynamic changes in the vehicle in real time, and a HILS system was implemented via a co-simulation in CarSim and MATLAB/Simulink. As a result, a 0.02 s time delay occurred; however, the error rate was less than 3%. Therefore, it was deemed that smooth control is possible.  
The front/rear driveshaft torque difference changed owing to the changes in the power distribution ratio according to the drive motor's rotation speed in the longitudinally flat (0%) road driving experiments. As such, the driveshaft rotation speed of the power distribution system affected the power distribution ratio by at least 2.29 Nm and a maximum of 4.72 Nm according to the road friction coefficient. However, it was determined that stable driving can be achieved because of the response to the power distribution ratio based on the fact that the change in the road friction coefficient was quick at less than 0.1 s.  
In the lateral DLC driving experiments, the vehicle was unaffected by changes in the drive motor's RPM or the changes in the front/rear power distribution ratio when the  
Figure 11: Power distribution ratio: (**a**) 20 rpm. (**b**) 100 rpm.  
Figure 12: The vehicle lateral acceleration and yaw rate when DLC driving.  
lateral acceleration and lateral angular velocity changed rapidly, and it was determined that smooth control is possible at a maximum lateral acceleration of 0.51 g and a maximum yaw rate of 13.2 deg/s.  
A communications delay of 0.02 s occurred between the DAQ and the PC, which are components of the HILS system. It was also determined that unstable elements can be removed to ensure stable control by designing a digital controller that considers this time delay when conducting experiments.  
Conceptualization, [PERSON]-H.J. and [PERSON]-Y.P.; methodology, Y.-C.K.; software, J.-H.J.; validation, J.-Y.P., [PERSON]-H.J. and Y.-C.K.; formal analysis, J.-Y.P.; investigation, J.-H.J.; resources, Y.-C.K.; data curation, J.-Y.P.; writing--original draft preparation, J.-Y.P.; writing--review and editing, J.-Y.P.; visualization, J.-H.J.; supervision, Y.-C.K.; project administration, Y.-C.K.; funding acquisition, Y.-C.K. All authors have read and agreed to the published version of the manuscript.  
These results were supported by the \"Regional Innovation Strategy (RIS)\" through the National Research Foundation of Korea (NRF), which is funded by the Ministry of Education (MOE) (2021 RIS-004).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Author [PERSON] was employed by the company EPSTech Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.