# A Turning Brake System for Motorcycles via an Autoregulative Optimal Slip Ratio
## 6 Conclusions  
Considering motorcycle safety is insufficient when braking in a turn, this paper pro-posed a turning brake system based on an autoregressive optimal slip ratio. This brake system takes the optimal slip ratio as input, and uses a PID strategy to control the motorcycle brake behavior. The operational performance was evaluated through a collaborative simulation using MATLAB and BikeSim, with a comparative simulation also performed alongside a traditional anti-lock braking system (ABS). The research yielded the following outcomes:  
1. The system input--the optimal ratio--is autoregulative according to the vertical force of the tires and roll angle. The slip ratio refers to the optimal solution after combining brake performance and stability. The greater the vertical force is, the smaller the absolute value of the optimal slip ratio. As for the influence of the roll angle on the optimal slip ratio, the greater the absolute roll angle is, the closer the optimal slip ratio is to 0. In this way, the brake system has able to adapt to the motorcycle dynamics.  
2. The two main parameters used to generate optimal slip ratio, vertical force and roll angle, can be calculated and estimated via kinematic signals measured by IMU and a wheel speed sensor, and the estimated accuracy is perfect, which makes the practical application of the proposed brake system possible.  
3. The proposed brake system, based on the PID strategy, can perfectly ensure the front and rear tires follow the optimal slip ratio. It makes the motorcycle stop steadily during the turning period, and the sideslip angle is very small. Compared with a traditional brake system based on a fixed slip ratio, the proposed system has good brake performance and directional stability.  
This study employs software to simulate the roll angle estimation and braking systems for a motorcycle during a turn. To enhance the braking system, it is essential to develop a comprehensive motorcycle dynamics model that incorporates the influence of the driver and the transient behavior of the tire. To enable the tire to more closely follow the optimal slip ratio, it is advisable to explore advanced intelligent control algorithms, such as a fuzzy PID control algorithm. There is a significant discrepancy between the simulation environment and real-world conditions. To evaluate the practical performance of the system, future research should integrate the experimental setup onto an actual motorcycle, which is also part of the subsequent research agenda.  
Conceptualization, X.-D.Z. and C.-K.C.; methodology, X.-D.Z.; formal analysis, X.-D.Z.; investigation, Y.-J.M.; writing--original draft preparation, X.-D.Z.; writing--review and editing, X.-D.Z. and C.-K.C.; supervision, C.-K.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Ministry of Science and Technology of Taiwan, ROC, under grant number MOST 110-2622-E-027-008; National Taipei University of Technology, ROC, under grant number NTUT-SZU-109-07; Ningde Normal University Young and Middle-aged Research Project, PRC, under grant number 2020Q102 and the Natural Science Foundation of Fujian Province, PRC, under grant number 2022J011222.  
Data Availability Statement: Data is contained within the article.  
The authors declare no conflicts of interest.