# Design and Depth Control of a Buoyancy-Driven Profiling Float
## 4 Results and Analysis
### Simulation Results and Analysis  
The proposed control method was compared in this simulation with PD control and SMC, which are currently most the commonly used methods in industrial processes. In order to simulate the actual process, the following comparison was adopted. First, the target depth of depth control was set to 20 m, which is relatively shallow. The parameters of the three methods were adjusted to ensure that the final depth control performance was good. In addition, it was necessary to ensure that the speed of the float during the diving process did not exceed 0.2 m/s. In this paper, the parameters of traditional PD control were set as \(K_{p}\) = 1 and \(K_{d}\) = 70. In the speed control process of segment PD control, the parameters were set as \(K_{p}\) = 1, \(K_{d}\)= 2, and in the depth control process, as \(K_{p}\) = 1, \(K_{d}\)= 150. For SMC, the sliding surface was set as \(s=k\cdot x1+x2\), where \(k\) is the sliding surface coefficient, which was taken as 0.1 in this paper, \(x1\) is the depth, and \(x2\) is the speed. The approach rate is \(\dot{s}=-\varepsilon\cdot\text{sgn}(s)\), where \(\varepsilon\) is a constant greater than zero, which was 0.2 in this paper. Figure 3: Schematic diagram of segment PD control. Then, without changing the parameters, simulations with target depths of 50 m and 80 m were carried out. The final simulation results using the three depth control methods are shown in Figure 4. The three graphs from left to right in Figure 5 show the speed curves of the three control algorithms during the depth control process t 20 m, 50 m, and 80 m, respectively. As can be seen in Figures 4 and 5, when the depth target was 20 m, since the parameters of each method were adjusted to the optimum, both segment PD control and SMC could dive at a speed not exceeding 0.2 m/s and successfully determine the depth. The SMC stabilized faster. For the traditional PD method, in order to control the diving speed and reduce the depth oscillation of the float in the fixed depth stage, the coefficient of the differential term was set to be very large. This also caused the traditional PD method to converge slowly when approaching the target depth. When the target depth was 50 m, the results of segment PD control and SMC control were similar to those obtained at  
Figure 4: Control performance of the three depth control methods at the target depths of 20 m, 50 m, and 80 m.  
Figure 5: Speed comparison of the three depth control methods in the processes of float diving and depth control. 20 m. While the traditional PD control did not change the parameters as the target depth increased, the proportional term played a leading role in the first half of the dive, resulting in a speed significantly greater than 0.2 m/s in 15-100 s. This is not acceptable for some ocean observation sensors. When the target depth was 80 m, the convergence time of segment PD control was significantly smaller than that of SMC. This is because, when the target depth was small for SMC, the initial state was closer to the sliding mode surface, so a small approach rate could meet the requirements of quickly reaching the sliding mode surface and converging. However, as the target depth increased, the initial state was farther and farther away from the sliding surface, and the convergence time increased significantly with the increase of the target depth, without changing the approach rate. However, the traditional PD method showed the shortest final convergence time due to the fast speed in the initial dive. In addition, since the float system was damped low and the linear actuator had a certain time delay, the float was not stable at the target depth but oscillated up and down, as shown in the enlarged areas in the lower parts of Figures 4 and 5. The control strategy of SMC was similar to the switch structure, vibrating back and forth at the sliding surface, so the final vibration amplitude was the smallest. However, this vibration had a significant impact on the actuator.