# Dynamic Modeling and Simulation of a Cyclic Towing System for Underwater Vehicles
## 1 Introduction  
As the new century faces multiple challenges, such as resource constraints and environmental concerns, the ocean, with its abundant biological resources, is bound to attract increasing attention. As marine resources have been developed and utilized, related equipment and experimental devices have also rapidly evolved [1; 2]. The cyclic towing system proposed in this paper is a system established in an experimental water tank that enables the dynamic testing of underwater vehicles. The cyclic towing system mainly consists of a main base bracket, auxiliary base bracket, towing device, tensioning device, depth adjustment device, cable circuit, and electrical control system. The system can support underwater vehicle masses ranging from 100 kg to 1500 kg. The system is constructed based on an experimental water tank, using a lifting platform to submerge the towed underwater vehicle from the surface to the bottom of the tank, simulating the underwater navigation state of a submarine model. This provides a realistic environment for verification and research. During the towing experiments, an underwater vehicle is connected to the towing cable circuit, with two parallel guide ropes attached to the left and right ends of the model. The mechanical tensioning device tightens the cable circuit, ensuring that the upper and lower transverse cables are in a horizontally straight line. The depth adjustment device regulates the depth at which the lower section of the cable circuit submerges underwater, as well as the depth of the model. The towing device drives the cable circuit to rotate clockwise and counterclockwise through the towing wheel, thereby moving the tested vessel back and forth between the two ends of the tank in both reverse and forward directions. This setup enables the model to accelerate, maintain a constant speed, and decelerate at different submergence depths. The schematic diagram of the cyclic towing system is shown in Figure 1.  
The primary purpose of the experimental water tank is to conduct hydrodynamic experiments on underwater vehicles, using model testing methods to analyze and evaluate an underwater vehicle's speed, propulsion power, and other performance characteristics. In recent years, underwater vehicle towing systems have gradually improved in terms of structural complexity and operational stability. Based on different system structures, underwater vehicle towing systems can be categorized into single flexible cable towing systems, double flexible cable towing systems, and self-propelled towing systems [3,4]. The single flexible cable towing system, which is the type of towing system studied in this paper, typically consists of a motor and a pulley cable transmission loop, forming an overall closed-loop structure; the double flexible cable towing system usually consists of two hydraulic winches, one at the front and one at the rear, connected to the towed body through two independent pulley cable transmission loops, forming an open-type, multi-body series transmission system; the self-propelled towing system has a simple structure that uses a motor-driven device to provide power, a carriage to move the towed body laterally, and a corresponding lifting device to submerge the towed body to different depths underwater. In recent years, numerous scholars have conducted extensive research on underwater vehicle towing systems in experimental water tanks, with a focus on system modeling and the development of various advanced control techniques. [PERSON] et al. designed a double flexible cable towing-type catapult test carriage system built in a shallow water tank, developed dynamic models for both the carriage and the hydraulic mechanism, studied the dynamic characteristics of the towing system through simulations, and proposed a coordinated control strategy for double flexible cable towing and a multi-mode switching control strategy in response to the force coupling characteristics of dual-drive hydraulic winches [5,6]. [PERSON] et al.