# Steering Dynamic and Hybrid Steering Control of a Novel Micro-Autonomous Railway Inspection Car
## 4 Hybrid Steering Control System  
### Control Law  
The vehicle generated sufficient lateral forces at wheel-rail contact during cornering to make a turn. However, cornering was slow because of weak centrifugal force. Therefore, additional torque was required for the wheelset to turn in the steering yaw direction, which we achieved using the widespread differential speed steering shown in Figure 10. Self-steering and independent steering capabilities were combined to construct a unique hybrid steering control system.  
The fuzzy logic controller (FLC) in the proposed hybrid steering system utilizes lateral displacement and yaw rate as input variables to change the speed of the left and right motors. The rule-based decision-making process is designed to optimize vehicle stability by balancing self-steering effects and active control. The FLC enhances responsiveness by reducing overshoot and mitigating steady-state errors, ensuring the micro-autonomous railway inspection vehicle maintains track alignment with minimal deviation under varying operating conditions.  
Figure 10: The yaw angle of the car.  
Figure 9: Lateral forces in (**a**) front wheelset and (**b**) rear wheelset running on a right-cornering track in SIMPACK and SIMULINK.  
The fuzzy logic controller is the controller used for independent steering control on this vehicle. Table 2 shows the rules of the 5 \(\times\) 5 fuzzy controller. The input variables the fuzzy logic control system were the difference error lateral position of the vehicle center with a value 0 at the stable position in the center of the track and the rate of change of this error. Fuzzy control output was measured on the basis of the voltage of the left motor to produce a speed change at a constant vehicle speed of 30 km/h. For the vehicle to consistently move at a fixed speed of 30 km/h, the value of the left DC motor speed increase was required to be equal to that of the right DC motor speed decrease, and vice versa.  
Figure 11 presents the methodology for designing the steering control system. Because of the specific design of the micro-autonomous railway inspection car, assessing the vehicle's self-guidance was necessary before the steering system control could be designed. Therefore, an analysis was conducted of the vehicle parameters, structure, and working condition requirements to determine the factors affecting the steering system. Afterwards, a simulated vehicle dynamics model was created using SIMPACK 2022x, a software for analyzing the dynamics of vehicles that run on rails. Additionally, a horizontal dynamics model of the steering system was created on SIMULINK using the Hertzian normal contact theory and [PERSON]'s linear theory. The SIMULINK dynamics model was used to obtain the creep coefficients, contact area, and contact angle corresponding to the contact position between the wheel and rail on the basis of the wheel and rail profiles of the SIMPACK dynamics model. The results for the lateral position of the vehicle center and the lateral forces at the wheel and rail contact position were compared between the SIMULINK and SIMPACK models. Finally, the steering system for vehicle control was designed on the basis of the simulation results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**e**} & \multicolumn{5}{c}{\(\Delta\)**e**} \\ \cline{2-6}  & **NB** & **NS** & **Z** & **PS** & **PB** \\ \hline NB & InB & InB & InS & InS & Z \\ \hline NS & InB & InS & InS & Z & DeS \\ \hline Z & InS & InS & Z & DeS & DeS \\ \hline PS & InS & Z & DeS & DeS & DeB \\ \hline PB & Z & DeS & DeS & DeB & DeB \\ \hline \hline \end{tabular}
\end{table}
Table 2: Rules of the fuzzy controller.  
Figure 11: Diagram of the control design process of the vehicle’s steering system.