# Development of a New Test-Rig for Wheel-Rail Contact Experiments under Large Slip Conditions
## 3 Detailed Description
### Simulation of Precise Slip Control  
The test-rig is a complex dynamic system, with various non-linear disturbances such as wheel/rail adhesion, gear meshing vibration, wind resistance, motor torque fluctuation, etc. In order to study the system response of the test-rig and verify the slip control effect, a joint simulation model is built in MATLAB/Simulink [35], in which the mechanical part of the test-rig is built by SIMPACK. The simulation model is shown in Figure 9, where (1) is the creepage calculation module, module (2) injects target speed of Motor W to generate creepage, (3) is the motor controller module for two motors and (4) is the SIMPACK module of the test-rig mechanism.  
As the PID control algorithm is widely used in industry, it is applied to the motor controller module in both simulation and the test-rig in the laboratory. The basic structure of a PID controller is as follows:  
\[u(t)=k_{p}e(t)+k_{i}\int e(t)dt\,+k_{d}\frac{de(t)}{dt} \tag{20}\]  
where \(u(t)\) is the controller output, \(e(t)\) is the controller input, which is the calculation error between the actual value and the target value. \(k_{p}\), \(k_{i}\) and \(k_{d}\) are proportional gain, integral gain and differential gain, respectively. Ignoring the differential control item, the motor control algorithm is shown in Figure 10. A double closed-loop control system is adopted for precise slip control. The application of servo motors further improves the control accuracy compared with asynchronous motors.  
In Figure 10, the speed PI controller of the outer loop calculates target current \(i_{qref}\) according to speed error \(e_{v}=v_{cref}-v_{c}\) and the current PI controller of the inner loop calculates target voltage \(u_{q}\) according to current error \(\epsilon_{i}=i_{qref}-i_{q}\). PI controller parameters of two motors are calculated from the vector control motor model and the transfer function of the test-rig mechanism and the results are shown in Table 3.  
The parameters in Table 3 are used for simulation. The target vehicle velocity is constant at 20 km/h, and the target creepage is sinusoidal, varying from 0 to 0.3 (a) and 0.25 to 0.3 (b) with a period of 12 s. The actual value of the creepage is shown in Figure 11 with or without PID control. It can be seen that, in open-loop simulation, the creepage  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**PI Controller Parameters** & **Motor V** & **Motor W** \\ \hline speed PI controller & \(k_{p}\) & 8000 & 30 \\  & \(k_{i}\) & 20 & 600 \\ current PI controller & \(k_{p}\) & 0.3 & 0.7 \\  & \(k_{i}\) & 51.6 & 226.7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: PI controller parameters of two motors.  
Figure 10: The motor control algorithm of the simulation and test-rig.  
Figure 9: The joint simulation model of the test-rig built in MATLAB/Simulink.  
response fluctuates significantly due to gear meshing vibration. PID control can suppress the fluctuation, making the actual value of creepage close to the target value, and improve the accuracy of slip control eventually.