## 5 Experimental Validation
### Installed Setup and Measurements  
The 96 V and 200 Ah LiFePO4 battery pack feed a Simrod inverter. The squirrel-cag IM with the four poles 15/45 kW (rated/max.) drives the rear axle through a reduction with a factor of 7.13. The outer diameter of the wheel was 576 mm [36].  
NEDC or other speed profiles can be applied as a reference speed. In this way, the designed controllers' performance can be investigated. Generally, the speed profile such as NEDC and WLTC are in km/h or m/s. However, the controller takes input reference speed in RPM. Therefore, it is essential to convert from m/s to the RPM using the relation represented in Equation (61). As an example of the NEDC speed profile, the speed of the motor (in RPM) has been attained as an average of both motorized wheel speeds, which is multiplied by a gearbox ratio of 7.13. The NEDC speed profile in RPM is shown in Figure 17.  
\[Speed\ (RPM)=\frac{30*Speed(\text{m/s})}{\pi*radius\ of\ wheel\ (\text{m})}\ G_{r} \tag{61}\]  
Figure 17: NEDC speed profile in RPM.  
As mentioned in Section 3.5.1 of speed control design, the rotational speed (RPM) can be calculated using the s-domain transfer function as represented in Equation (62). The relation is modeled in simulation to estimate the speed using load and electrical torque.  
\[Speed\ (RPM)=\frac{T_{e}-T_{l}}{Js+B} \tag{62}\]  
The thrust can be calculated using the relation of torque, thrust, and radius of the wheel, i.e., \(T\left[\mathrm{Nm}\right]=F\left[\mathrm{N}\right]\times r\left[\mathrm{m}\right]\). Using the above Equations (61) and (62), the dependency of speed (m/s) on thrust can be calculated as Equation (63).  
\[Speed\ \left(\frac{\mathrm{m}}{\mathrm{s}}\right)=\left(\frac{1}{Js+B}\right) \left(F_{e}-F_{l}\right)\ r^{2}\frac{\pi}{G_{r}} \tag{63}\]  
where \(T_{e}\) (Nm), \(T_{l}\) (Nm), \(B\), and \(J\) are electrical torque, load torque, coefficient of friction, and the moment of inertia, respectively. \(F_{e}\) (N), \(F_{l}\) (N), \(r\) (m), and \(G_{r}\) are the electrical thrust, load, radius of the wheel, and gearbox ratio, respectively.  
The source (battery), inverter, and motor are connected in the arrangement [36], as shown in Figure 18.  
The data are logged from the installed test setup [36], as shown in Figure 19, and used to validate the simulation model. The DC side of the three-phase inverter is connected to the battery, and the AC side is connected to the three-phase induction motor. DC and AC voltages and currents are measured using transducers. The Kistler RoaDyn wheel force transducer measures the 6-DOF forces and the wheel's speed and torque. The throttle device is connected to the inverter to adjust the throttle input. The electrical current and voltage are measured on the inverter's DC as well as AC sides using the three voltage probes (Tektronix P5200A) and the three zero-flux current transducers (LEM IN 1000-S) [36].  
The data acquisition has been made with the Siemens (SCADAS) mobile system at a different sample rate that depends on the bandwidth of examined quantities. Particularly for phase voltages, high-frequency measurement was needed. The square wave character of the PWM AC voltage refers to the presence of an inverter's 10 kHz switching frequency. Therefore, the electrical quantities such as voltages and currents are logged at a sample rate of 204.8 kHz. In addition to the 92 kHz cut-off frequency built-in anti-aliasing filter, an additional low pass filter (zero phase) of 5 kHz cut-off frequency has been fitted. These filters wash out switching harmonics from high-frequency Yokogawa measurements.  
Figure 18: Instrumental powertrain schematic view.