# Design and Depth Control of a Buoyancy-Driven Profiling Float
## 1 Introduction  
Typically, various materials in the upper ocean present significant vertical changes. In the mixed zone, the influence of ocean currents is more pronounced than in deep ocean. Therefore, the upper-middle layer of the ocean is the wealthiest region of physical and biological processes, where most of internal waves, thermocline, and vertical exchange of biological and chemical elements occur [1, 2]. Continuous observation of the upper and middle layers of the ocean over long periods is necessary to analyze these phenomena. Among the numerous upper ocean phenomena, the thermocline is worth studying and utilizing [3, 4, 5]. In the thermocline, seawater goes from top to bottom, with a sudden drop in temperature and a sudden increase in density. This particular property makes the thermocline region a natural sound barrier in the ocean [6]. At the same time, the huge physical differences between the water layers also limit the exchange of water bodies, so the influence of water flow in the vertical direction can be ignored. Therefore, the most important environmental impact is the highly variable density when tracking and maintaining depth in the thermocline. Most ocean-observing missions, including thermoclines, can be performed with floats [7, 8, 9]. Profiling floats equipped with sensors are a simple solution that allows water column monitoring for a long time and at a low cost. They are controlled generally by changing their buoyancy, which enables them to travel downwards or upwards. They can also be controlled so to reach and maintain a certain depth. They are normally simple systems that have no actuator for horizontal movement. However, floats also have a certain ability to track the horizontal current, which, to a certain extent, can reflect information on the current in deep water [7, 10]. According to the different tasks to be performed, a program can be preset to realize actions such as rising, diving, or depth-fixing in seawater. The shapeof the float is generally cylindrical [11; 12] or spherical [13] with a small cross-sectional area, making the vertical resistance coefficient small in water. Therefore, the float system has low damping and large inertia. The usual buoyancy control system of floats mainly relies on oil pumping or linear actuator movement to change the volume of floats [8; 12; 13; 14; 15]. The speed of this process is relatively slow, so it takes a specific time to reach the target drainage volume required by control, which gives the float system a certain time lag. In addition, the sampling rate of some oceanographic sensors on floats is relatively low. Therefore, to ensure the accuracy of data collection in the upper ocean where the environment changes rapidly, it is necessary to control the diving and floating speed of the float. It is also essential to develop a general control method suitable for floats with low damping and large time delay. The traditional PD method is independent of the float model and is simple and easy to implement [16]. However, this method is based on different parameters to achieve the best control effect in different environments or control tasks [8; 14] and avoid overshoot or even failure to reach the control target. At present, the most widely used control methods for the nonlinear float model are based on two approaches. One consists in linearizing a nonlinear system and then achieving control through state feedback [13; 14; 17] PID and other linear control methods. However, achieving a good control requires a relatively accurate modeling. The other approach is based on fuzzy control [18; 19], sliding mode control [20; 21], and active disturbance rejection control (ADRC) [22]. Among them, the sliding mode control is highly insensitive to model error, variation of controlled object parameters, and external interference, so it is often used in the motion control of underwater vehicles [20; 23]. However, chattering occurs when the state trajectory reaches the sliding mode surface.