## 5 Experiments and Results  
### Pool Experiments  
The experiments were conducted in a round pool with a diameter of 45 m and a depth of 6 m at the Ocean College of Zhejiang University (Figure 10). There were two experiments carried out: a fixed-point experiment and a dynamic experiment. During the fixed-point experiment, the AUH received signals for depth and heading adjustments and maintained its position in the horizontal plane while translating vertically. In the dynamic experiment,  
Figure 9: Simulations of depth control with PID, LADRC, and LADRC-TD. (**a**) Long-span-step response; (**b**) multi-step response. the AUH moved back and forth between two points at a low speed, and the outcomes of PID and LADRC-TD were compared. In the tuning process, \(K_{p}\) should be first tuned by increasing it gradually until an oscillation is observed. Then, \(K_{d}\) will be increased until a small overshoot is achieved. Following this, \(K_{i}\) is tuned to reduce steady-state accuracy. Finally, subtle adjustments are made to the parameters to optimize the dynamic response and steady-state performance. The tuning process for LADRC and LADRC-TD is similar. The bandwidth \(w_{0}\) should be tuned first. In theory, a larger value of \(w_{0}\) would result in better performance. However, the appropriate value of \(w_{0}\) is dependent on factors such as the sampling frequency and the level of noise in the sensors. As the sampling frequency of the IMU and a depth altimeter are all set to 1 Hz, the optimal value of \(w_{0}\) may be smaller than anticipated. Then, \(K_{p}\) and \(K_{d}\) should be tuned until the system is stable, which is similar to PID and finally, \(b_{1}\) and \(r_{a}\) should be fine-tuned to optimize the performance. As exhibited in Figure 11a, for the heading control experiment, overshoot exits in all PID, LADRC, and LADRC-TD controllers, with overshoot amounts of \(12^{\circ}\), \(6^{\circ}\), and \(3^{\circ}\), respectively. The response time of LADRC is slightly shorter than that of LADRC-TD, conforming to the simulation results. However, the response time of PID is significantly longer than that of LADRC and LADRC-TD, which differs from what is observed in the simulation. In practice, to reduce the oscillations, the parameter \(K_{p}\) must be reduced, thus increasing the response time compared to the simulations. The steady-state accuracy of LADRC and LADRC-TD is about \(\pm 2.5^{\circ}\), and that of PID is \(\pm 3^{\circ}\). As for the depth control shown in Figure 11b, the overshoot of PID is 43 cm, and the steady-state accuracy is \(\pm 1.1\) m. The steady-state accuracy of LADRC is similar to that of LADRC-TD, namely approximately \(\pm 21\) cm. However, the overshoot of LADRC is 41 cm, and that of LADRC-TD is merely 20 cm around. Figure 11: Fixed-point experiment; (**a**) step response in heading control; (**b**) step response in the depth control. Figure 10: The pool experiment of the AUH. In the dynamic experiment, the AUH needs to go back and forth between two points by three times at 0.2 m/s, thereby simulating the docking process when the AUH is close to the SDS. As observed from the comparison of the heading tracking of LADRC-TD and PID (Figure 12a,b), LADRC-TD has a better tracking performance, shorter response time, and lower overshoot. It is worth noting that the heading angle range is from 0 to 360 degrees, and when the angle turns from 300 to 380 degrees, it appears to be discontinuous (Figure 12b) because it first turns from 300 to 0 degrees and then from 0 to 20 degrees Due to the excellent heading tracking performance of the LADRC-TD, the three trajectories of the AUH show high similarity, as presented in Figure 12c. On the contrary, the three trajectories under PID control (Figure 12d) are chaotic because PID cannot accurately track the heading change in a timely manner.