## 4 Experimental Results and Analysis  
The MRB test-bed shown in Figure 7 was used for the stability control experiment, where the data were collected by the torque speed sensor and data acquisition card, and the upper computer realized the automatic control of braking torque. Firstly, we adjusted the frequency of the frequency inverter to keep the rotating speed of the driving shaft at 400 r/min, and then, the target torque values were set in the interface of the upper computer platform and the output torques of the system under different target torques were recorded. Figure 15a-c show the braking torque of MRB when the rotation speed \(n\) was from 0 to 300, 400, and 500 r/min, and the target torque \(T\) was 60, 100 and 110 N\(\cdot\)m, respectively. The fast and stable output response of MRB is an important foundation for its application in the braking field. Stability control experiments of braking torque prove the stability of the MRB, that is, it can quickly reach the set output torque and keep it stable. The sooner the output torque reaches the target value, the better the torque response will be. Otherwise, the torque response performance will be worse. Moreover, the greater the fluctuation of the output torque value near the set torque value, the more stable the torque output is; on the contrary, the torque output becomes more unstable. In general, the output performance of the MRB is evaluated by static potential difference rate, fluctuation rate and response time [23]. Using the static potential difference rate to evaluate the stability of the system, the calculation formula can be expressed as follows:  
\[\delta_{1}=\frac{\Delta T}{T_{  
Figure 15: Comparison of the control effect for different target torques. (**a**) 0 to 300 r/min with a target torque of 60 N-m. (**b**) 0 to 400 r/min with a target torque of 100 N-m. (**c**) 0 to 500 r/min with a target torque of 110 N-m.  
Table 7 shows the MRB evaluation indexes of three different PID controllers under the target braking torque T1 (60 N-m), T2 (100 N-m) and T3 (110 N-m). It can be seen from the table that the maximum static potential difference rates of PID, GWO PID and EGWO PID controller were 9.85 %, 4.47% and 2.2%, respectively. Additionally, the fluctuation rate of the three modes was less than 9.91%, 4.49% and 2.20 %, respectively. When the target braking torque was adjusted from 0 to 200 N.m, the response time of EGWO PID controller was shorter than that of the GWO PID and PID controllers, ranging from 0.5 to 0.6 s. Therefore, compared with the conventional PID controller and GWO PID, the EGWO PID controller has a better effect of adjusting and controlling the output torque. Meanwhile, the output torque was more stable, the adjustment time was shorter, and the response speed was quicker. As shown in Figure 16, the performance of MRB torque tracking control with EGWO PID was evaluated. The target torque was set to 60, 100 and 110 N-m, and it was kept for 10 s in each stage. It was observed that the braking torque of the black line matched the expected braking torque of the red line well, and the system had good torque tracking control performance. The experimental results showed that the torque transmitted by the brake had good stability when the braking torque was constant. After adjusting the brake torque, the torque fluctuations of the PID controller optimized by the algorithm took less time than the conventional PID controller to restore to the stable state. The EGWOA PID controller not only takes less time, but also has more accurate adjustment results.