## 4 Electric Braking System and Fault Modes Simulation  
### Braking System Simulation Parameters  
Once the EMA has been integrated into an EBS, parameters are added to the model. Table 1 shows the EMA parameters used for the simulation. The required values were obtained from an existing actuator, that has been used as a baseline. Other parameters, such as motor armature inductance and motor rated speed were obtained from the base DC motor block parameter provided by MATLAB/Simulink. Figure 6: The integrated model of electric braking system combining EMA and anti-skid braking system (ABS) models. As for the physical blocks, damping, friction, and spring rate parameters were iterated until a suitable simulation was obtained. Controller values, such as gains and limits were modified accordingly to provide good actuator performance. Following the EMA definition, aircraft and ABS parameters are given in order to provide a suitable scenario for the actuator. As no specific aircraft is being targeted, the values selected for the model assure that the simulation is produced accurately. Table 2 shows various aircraft and ABS parameters used. The EBS model in the simulation is used to represent a realistic approach of a brake using an EMA, without considering any other means for braking in an ideal scenario. Using Equation (1), the approximate stopping distance can be calculated as a function of the initial velocity and the ratio of friction force and vertical load (MU), assuming the values we defined previously [22]. \[SD=\frac{v0^{2}}{(2*g*Mu*E)} \tag{1}\]  
where \(Mu\) is assumed as 1, \(E\) is the desired wheel slip 0.2 and \(g\) is the gravity constant 9.81 m/s\({}^{2}\). The results show that the aircraft will take about 2 km to achieve full stop, so a similar distance should be expected from the ABS simulation to verify the proper integration of the model. In order to estimate the power required by the brakes to stop the vehicle, Equation (2) obtained from [21], derived from a free body diagram of an aircraft, can be used:  
\[P_{\text{brakes}}=\dot{x}F_{\text{brakes}} \tag{2}\]  
where \(\dot{x}\) is the velocity of the aircraft, starting from \(v0\), and \(F_{\text{brakes}}\) is the braking force required to stop the aircraft. Using an expected and estimated average braking force of 19 kN similar to the one used by [21], the peak braking power required to achieve full stop is found to be 1.67 MW, whilst the average \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Units** & **Reference** \\ \hline PWM Frequency & 5 & kHz & [16] \\ PWM Voltage & 5 & V & [17] \\ Motor Operating Voltage & 36 & V & [18] \\ Motor Rated Load & 200 & W & [17] \\ Motor Temperature Range & \(-\)40 to 80 & \({}^{\circ}\)C & [18,19] \\ \multicolumn{3}{c}{Gear Reduction} & 6.25:1 \\ \multicolumn{3}{c}{Leadscrew Displacement per Revolution} & 0.015 & Mm & Assumed \\ \multicolumn{3}{c}{Motor Efficiency} & 99 & \% & Assumed \\ \multicolumn{3}{c}{Leadscrew Efficiency} & 99 & \% & Assumed \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of EMA used for simulation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Variable** & **Value** & **Units** \\ \hline Aircraft Initial Velocity [21] & v0 & 88 & m/s \\ Wheel Radius & Rr & 0.34295 & M \\ Force to Torque & Kf & 1000 & N/m \\ Mass of Aircraft & M & 8000 & M \\ Max. Brake Pressure & PBmax & 30,000 & Pa \\ Inertia & I & 0.0210701 & kg m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Different aircraft and ABS parameters for simulation. power stands at 0.84 MW. As seen on the ABS system diagram (Figure 5), the wheel slip can be obtained by dividing the aircraft longitudinal speed by the wheel angular speed, as shown in Equation (3):  
\[\mathit{slip}=1-\frac{w_{w}}{w_{v}} \tag{3}\]  
where \(w_{w}\) is the wheel angular speed and \(w_{v}\) is the aircraft longitudinal velocity. The wheel slip is 0 when both velocities are equal which means a non-braking condition exists.