Constant Depth and Constant Speed ​​Underwater Two-Stage Towing System and Its Control Method

Abstract

This invention relates to a two-stage underwater towing system for constant depth and speed and its control method, belonging to the field of underwater equipment technology. In this system, the towing mother vessel is connected to the ballast via a main towing cable, and the ballast is connected to the towed platform via a secondary towing cable. A sensing module collects signals from the towed system and platform in real time and transmits them to a host computer. The PID control module in the host computer performs PID calculations on the deviation between the actual and target signals based on the target depth and attitude, outputting closed-loop control commands to the actuators. By adjusting the angle of attack of the towed platform's tail fin, high-precision constant depth and speed control of the towed system is achieved in complex marine environments. The ballast reduces the interference of the mother vessel's motion and environmental factors such as waves on the stability of the towed platform. Combined with the dynamic correction capability of the PID control algorithm, the system's anti-interference ability and control accuracy are improved, achieving an attitude angle error of ≤±1°. This system is widely applicable in scenarios such as marine resource exploration, underwater environmental monitoring, and hydrological data acquisition.

Description

Technical Field

[0001] This invention relates to a constant-depth, constant-speed underwater two-stage towing system and its control method, which belongs to the field of underwater equipment technology. Background Technology

[0002] A marine towing system mainly consists of three parts: a towing mother vessel, a towing cable, and a towed body. Typically, it lacks its own propulsion function and relies on the mother vessel for movement. Traditional single-stage underwater towing systems depend on complex sensors, controllers, and actuators, frequently and coupledly adjusting the towing cable length, tugboat speed, and towed body attitude to counteract external environmental interference. These systems are structurally complex, energy-intensive, and have a high failure rate and maintenance costs during long-term operation. Furthermore, relying solely on the towing cable is insufficient to counteract the effects of the mother vessel's motion and flow field disturbances, resulting in poor towed body attitude stability.

[0003] Currently, due to the increasing precision requirements of marine operations, the demands for the accuracy and stability of the motion attitude of marine towed bodies have also increased. Roll and pitch are the two most important attitudes during the motion of marine towed bodies. When a towed body is towed by a mother ship in the water via a tow cable, it sometimes cannot maintain a stable motion attitude due to environmental factors such as ocean currents and the swaying of the towing mother ship. At the same time, the tow cable is prone to vibration underwater due to environmental factors such as ocean currents and waves, thus affecting the operational results. Therefore, developing an underwater towing system that is simple in structure, low in energy consumption, has a low failure rate, and can resist various environmental interferences has become an urgent need in the field of underwater equipment. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a constant-depth, constant-speed underwater two-stage towing system, aiming to solve the problems of complex system design, difficult-to-operate control programs, high energy consumption, and poor attitude stability of the towed body in traditional methods. Using the method of this invention, the towed platform can be modeled, and the Newton-Euler equations of motion composed of gravity, buoyancy, towing force, towed body hydrodynamics, and tail fin hydrodynamics can be derived. Then, based on a PID control algorithm, the tail fin angle of attack can be scientifically adjusted to achieve attitude control of the towed platform. Ballasts are installed to counteract the disturbances of the mother ship and waves on the tow cable and towed platform. Matlab software is used to simulate and analyze the motion attitude of the towing system under different sea conditions.

[0005] The technical solution adopted in this invention is a constant-depth, constant-speed underwater two-stage towing system. This system uses a towing mother ship connected to a towing platform via cables. The towing mother ship is equipped with a host computer, and the towing platform is equipped with a servo motor, a depth and speed sensor, a PID controller, and an attitude angle measuring instrument. The towing platform is equipped with a cross-shaped tail fin, namely a vertical tail fin and a horizontal tail fin. The vertical tail fin is fixed to the towing platform to resist the roll motion of the towing platform under the action of water current. The horizontal tail fin is controlled by a servo motor to adjust the angle of attack, providing lift for the towing platform.

[0006] Ballasters are installed on the cable via pulleys. The ballasts divide the cable into main towing cables and auxiliary towing cables. The main towing cable is the cable between the towing mother ship and the ballast, and the auxiliary towing cable is the cable between the ballast and the towing point of the towing body platform.

[0007] The towing mother ship is equipped with a host computer, which integrates the control method of the towing system. This method is used to construct the motion control equation of the towed platform, preset the current velocity and buoyancy parameters based on actual ocean data, and simulate the towing situation of the towed platform under different towing speeds and sea conditions. Based on the attitude angle input PID algorithm of the towed platform in the ballast state, the attitude of the towed platform is corrected through PID controller and servo motor.

[0008] Furthermore, the towed platform is configured as a slender, streamlined, symmetrical structure with a length-to-diameter ratio of 6:1, and the cross-shaped tail fin with an aspect ratio of 1.7 is installed at its tail; the horizontal tail fin can rotate less than ±20°; the center of gravity of the towed platform is located directly below the center of buoyancy, and the buoyancy is set to 5%.

[0009] Furthermore, the towed platform is equipped with multiple sensors and actuators, including an attitude sensing module, a depth sensing module, a velocity sensing module, a rotation angle limiting module, and a servo electric drive module. Among them, the attitude sensing module is used to measure its actual attitude angle underwater in real time, providing data input for the PID control algorithm; the depth sensing module and the velocity sensing module are used to measure the actual depth and towing speed of the towed platform; the rotation angle limiting module is used to limit the tail fin rotation angle within ±20°; and the servo electric drive module is used to receive the tail fin command after limiting and drive the tail fin of the towed platform to perform mechanical deflection.

[0010] The control method for a constant-depth, constant-speed underwater two-stage towing system includes the following steps:

[0011] S1. Using static modeling, establish the relationships between the towing force, gravity, buoyancy, hydrodynamic forces of the towed platform, and hydrodynamic forces of the tail fin, and construct the motion equations of the towed platform, including translational and rotational motion equations; obtain the actual attitude angles of the towed platform: pitch angle. Roll angle and yaw angle ;

[0012] S2. Construct the dynamic coupling of the translational and rotational nonlinear motions of the towing system. Multiply the total mass matrix by the generalized acceleration. Simultaneously, the system's translational velocity and angular velocity are coupled with the mass matrix through a cross product to generate a Coriolis-centrifugal force term. Finally, the resultant force of the product of the total mass matrix and the generalized acceleration plus the Coriolis-centrifugal force term is equal to the externally applied translational generalized force and rotational generalized torque. This yields the accelerations of the towed platform's six degrees of freedom: linear acceleration... and inertial acceleration ;

[0013] S3. Through PID control algorithm and actuator coupling control, the control loop adopts PID control strategy to ensure that it maintains a horizontal navigation attitude underwater, with an attitude deviation of no more than ±1°.

[0014] Furthermore, step S1 specifically includes:

[0015] S1.1. Define the body coordinate system and the inertial coordinate system. The body coordinate system is located at the center of buoyancy of the towed platform. b The axis points towards the bow, y b The axes reference a right-handed coordinate system; variable X I =[x,y,z] T It is the position of the towed platform relative to the inertial coordinate system, Φ I =[φ,θ,ψ] T Let V represent the Euler angles of the towed platform relative to the inertial coordinate system, where V = [u, v, w]. T It is the linear velocity represented in volume coordinates, Ω=[p,q,r] T It is the angular velocity of the towed platform relative to the inertial coordinate system;

[0016] S1.2 Construct the coordinate system transformation matrix, matrix R IB It is the rotation matrix from the volume coordinate system to the inertial coordinate system:

[0017]

[0018] S1.3 Construct the equations of motion. The state of the towed platform is represented as follows:

[0019]

[0020] The equation of translational motion for the towed platform is:

[0021]

[0022] Therefore, we can determine the forward velocity u, lateral velocity v, and vertical velocity w of the towed platform in the inertial coordinate system.

[0023] The equation of motion for the towed platform is:

[0024]

[0025] Therefore, the pitch angle of the towed platform in the inertial coordinate system can be determined. Roll angle and yaw angle .

[0026] Furthermore, step S2 specifically includes the following sub-steps:

[0027] S2.1 Establish the external force equations and moment equations for the towing force, gravity, buoyancy, hydrodynamic forces of the towing body and tail fin of the towed platform:

[0028] = + + + +

[0029] Among them, F ext : The external force acting on the towed fish and represented in body coordinates; F axial :F ext Along x b Components of the axis; F lateral :F ext Along y b Axial component; F normal :F ext Along z b Axial component; F body : Represents the fluid force acting on the hull surface in an inertial coordinate system; F tail : Represents the fluid force acting on the tail fin in the inertial coordinate system; F tow : Represents the drag force generated by the secondary cable on the towed platform in the body coordinate system; F weight : Gravity of the towed platform in the body coordinate system; F buoyancy : The buoyancy of the towed platform in the body coordinate system;

[0030] = + + + +

[0031] Among them, M ext M: The external torque acting on the towed fish in the body coordinate system. roll M ext Around x b Components of the axis; M pitch M ext Around y b Components of the axis; M yaw M ext Around z b Components of the axis; M body : Fluid torque acting on the outer surface of the hull in body coordinates; M tail : The fluid torque acting on the tail fin in the volume coordinate system; M tow The traction torque generated by the secondary cable in the body coordinate system: M damping : The damping moment of the towed platform in the body coordinate system; M weightThe torque generated in the body coordinate system due to the displacement of the center of mass;

[0032] S2.2 Construct the rigid body mass and additional mass matrix. Define the 3x3 matrix M as the rigid body mass and additional mass matrix, with the following expression:

[0033]

[0034] Where K1, K2, and K3 are the axial, lateral, and rotational additional mass coefficients, respectively, and their expressions are as follows:

[0035]

[0036] The towed platform is approximated as having a minor axis length of Db and a major axis length of l. b An oblate spheroid, where e is the eccentricity:

[0037]

[0038]

[0039] S2.3 Construct the rigid body inertia and additional inertia matrices, defining the 3x3 matrix J as the rigid body inertia and additional inertia matrices:

[0040]

[0041] in , , , , , It is the moment of inertia of the towing platform. Three-dimensional additional inertia coefficient, It is the pitch angular velocity plus the inertia coefficient. It is the yaw rate plus the inertia coefficient;

[0042] S2.4 Constructing the inertial coupling matrix: Matrix D represents the inertial coupling between translational and rotational motions, when the center of mass CG does not coincide with the origin of the towed platform coordinates:

[0043]

[0044] Where m is the mass of the towing platform. , , It represents the offset of the centroid CG relative to the origin of the volume coordinate system in the x, y, and z directions. It is the core parameter that causes inertial coupling when the centroid does not coincide with the origin. To add the derivative of the mass moment for pitch, Add the derivative of the mass moment to the yaw;

[0045] S2.5 Determine the overall mass matrix:

[0046]

[0047] S2.6 Calculate the Coriolis force and torque:

[0048]

[0049] in It is a linear velocity-mass coupling term used to describe the inertial effect of its own mass. It is the angular velocity-center of mass coupling term, used to describe the coupling between rotation and center of mass shift. The sum of the two and the cross product with the angular velocity give the inertial force caused by rotation, i.e., the Coriolis-centrifugal force.

[0050]

[0051] in It is an angular velocity-inertia coupling term used to describe the inertial effect of rotational inertia. This is the linear velocity-center-of-mass coupling term, used to describe the rotational coupling between linear velocity and center-of-mass offset. It is a rotational coupling torque. It is the linear velocity-angular velocity coupled torque, and the sum of the two gives the Coriolis-centrifugal torque;

[0052] S2.7 Calculate the acceleration of the six degrees of freedom, including linear acceleration. Equals the cross product of the inverse of the total mass matrix and the sum of the total external force and the Coriolis-centrifugal force; inertial acceleration It equals the cross product of the inverse of the total mass matrix and the sum of the total external torque and the Coriolis-centrifugal torque.

[0053] Furthermore, step S3 specifically includes the following sub-steps:

[0054] S3.1 Determine the coefficients of the PID controller. The proportional loop takes the attitude angle error as the direct input and outputs a control component proportional to the magnitude of the attitude angle error to achieve an immediate response to the current attitude deviation. The integral loop continuously captures the attitude angle deviation state, accumulates the historical attitude angle error, and outputs a control component proportional to the integral value. By tracking the duration and accumulation of the attitude angle error, it cancels the steady-state error and makes the attitude angle eventually stabilize at the desired value. The derivative loop takes the change of attitude angle, i.e., the rate of change of the actual attitude angle over time, as the core input.

[0055] S3.2, The position and attitude angles (roll angle) of the towed platform obtained in S1 Pitch angle ), PID coefficients, Euler angle derivatives in inertial coordinate system ( , That is, the differential terms of PID control are integrated into the state information vector, States.

[0056] The PID gain matrices of the pitch and roll channels are multiplied by the States vector to calculate the desired deflection commands (d2, d4) for tail fins 2 and 4 of the towed platform.

[0057] S3.4. Use a first-order inertial model to simulate the response characteristics of the physical servo motor, and let the actual tail fin deflection angle (z2, z4) gradually track the desired command at a rate of time constant.

[0058] S3.5 The actual tail fin deflection angle changes the resultant fluid force and resultant torque on the towed body. The real-time linear acceleration and inertial acceleration are calculated through S2. The linear acceleration integral updates the towed body position and linear velocity, and the inertial acceleration integral updates the towed body angular velocity and attitude angle. The new attitude and motion information will be updated in the state array X, forming a complete closed-loop feedback, and continuously realizing PID control of attitude.

[0059] The beneficial effects of this invention are as follows: By using a metal sphere of fixed mass as a ballast and installing it between the main and auxiliary towing cables of the secondary towing system, this invention helps reduce the vibration of the towing cables caused by water flow disturbance, thereby increasing the stability of the towing platform. Furthermore, it fully considers the impact of wave loads on the towing system under actual usage scenarios, and simulates the real environment by superimposing irregular waves, resulting in calculation results that are more consistent with reality.

[0060] This invention couples an irregular wave model, a ballast motion model, and a PID control model. By using the ballast motion parameters under the influence of waves as input to the PID control program, it achieves tail fin angle of attack control for towed platforms in complex environments, further enhancing the stability of the towed platform underwater, reducing the difference between the actual attitude angle and the desired attitude angle of the towed platform, and facilitating stable control of the towed platform. Attached Figure Description

[0061] To illustrate the technical solution more clearly, the following figure will briefly introduce the accompanying drawings used in the existing description.

[0062] Figure 1 This is a schematic diagram of a constant-depth, constant-speed underwater two-stage towing system;

[0063] Figure 2 This is a schematic diagram of the equipment layout of the towing platform;

[0064] Figure 3 This is a schematic diagram of an embodiment of PID control;

[0065] Figure 4 It is the differential unit of the cable during static analysis;

[0066] Figure 5 It is an irregular spectrum generated by simulation;

[0067] Figure 6 It is a drag platform Figure 5 Map showing changes in position under sea conditions;

[0068] Figure 7 It is a drag platform Figure 5 Diagram showing the change in attitude angle under sea conditions.

[0069] In the diagram: 1. Towing mother ship, 2. Host computer, 3. Winch, 4. Main towing cable, 5. Ballast, 6. Pulley, 7. Secondary towing cable, 8. Towing point, 9. Towing platform, 10. Vertical tail fin, 11. Horizontal tail fin, 12. Depth and velocity sensor, 13. PID controller, 14. Vertical gyroscope, 15. Power conversion unit, 16. Servo motor. Detailed Implementation

[0070] Example 1

[0071] To make the technical solution of the present invention clearer, a constant-depth, constant-speed underwater two-stage towing system of the present invention will be further described below with reference to specific examples. This embodiment is only used to illustrate the technical solution of the present invention, and is not intended to limit it.

[0072] This embodiment provides a constant depth and constant speed underwater two-stage towing system, which is used in marine exploration. By installing ballast and PID control, the towed platform can sail stably in a horizontal attitude with an attitude angle deviation of no more than ±1°.

[0073] like Figure 1 As shown, the underwater two-stage towing system with constant depth and speed in this embodiment mainly includes:

[0074] The towing mother ship consists of: 1. Host computer; 2. Winch; 3. Main towing cable; 4. Ballast; 5. Pulley; 6. Auxiliary towing cable; 7. Towing point; 8. Towing platform; 9. Vertical tail fin; 10. Horizontal tail fin; and 11. Sensors and actuators mounted on the towing platform, such as... Figure 2 As shown, it includes a depth and velocity sensor 12, a PID controller 13, a vertical gyroscope 14, a power conversion unit 15, and a servo motor 16.

[0075] The towing mother ship provides the power source for the towing system. It is equipped with an embedded processor (such as a DSP or microcontroller), integrating a main controller (PID controller) and a tail fin angle limiting module. It is responsible for receiving desired attitude commands, executing the control algorithm, and outputting the desired rudder angle command after limiting. .

[0076] Towing cables and ballast: Composed of main towing cables, auxiliary towing cables, and lead alloy ballast. The main towing cable connects the mother ship to the ballast, while the auxiliary towing cable connects the ballast to the towed platform. The ballast uses its own weight to counteract the heave, roll, and wave disturbances caused by the mother ship, reducing the shaking and drift of the towed platform. The auxiliary towing cable has a diameter of 0.02m, an underwater weight per unit length ζ=0.00014N / m, and a drag coefficient C. Dc =1.05.

[0077] The towed platform 9 consists of a slender, streamlined main body and a NACA0012 cross-shaped tail fin. The towed body has a hemispherical head, a cylindrical middle section, and a tapered tail, with a length-to-diameter ratio of 6:1, designed to reduce water flow resistance and vortex-induced vibration. The cross-shaped tail fin includes mutually perpendicular horizontal tail fins 11 and vertical tail fins 10, with an aspect ratio of 1.7 and an installation angle of 0°, used to generate stable hydrodynamic lift and resist pitch and roll disturbances. A vertical gyroscope 14 (VG) is installed at the center of gravity inside the towed platform to obtain the actual pitch angle of the towed body in the reference coordinate system in real time. And high-frequency sampling ensures the real-time nature of attitude feedback.

[0078] In this embodiment, the specific workflow of the system is as follows:

[0079] S1. Install the vertical tail fin 10, horizontal tail fin 11, depth and velocity sensor 12, vertical gyroscope 13, PID controller 14, power conversion unit 15, and servo motor 16 onto the towing platform.

[0080] S2. The main towing cable 4 and ballast 5, and ballast 5 and auxiliary towing cable 7 are connected by pulley 6 to counteract the interference transmitted to the towing cable and towed platform by the ship's motion and wave environment: Ballast 5 is made of lead alloy. When the mother ship 1 undergoes heave or roll motion, ballast 5 counteracts part of the disturbance energy by its own weight, reduces the pitch and roll of the towed platform 9, and ensures that its attitude remains stable.

[0081] S3. Obtain the real-time attitude angle of the towed platform 9 through the vertical gyroscope 13, and input the difference between the desired attitude angle and the actual attitude angle into the input. Figure 3 The PID algorithm flow shown is used to precisely control the rotation angle of the horizontal tail fin 11 through the servo motor 16 in order to adjust the attitude of the towed platform.

[0082] S4. Input the initial parameters for the mother ship, towline, and towed body. Key parameters for the towed body platform: towed body length 2.59m, diameter 0.43m, mass 252.93kg, volume 0.2529m³. 3 Initial velocity 3 m / s, tail fin area 0.27 m² 2 The fuselage cross-sectional area is 0.15m². 2Center of gravity position (x,y,z)=(0.0000,0.0000,0.0762)m, cable stiffness 100.00N / m, cable damping 325.18Ns / m.

[0083] S5. Construct the motion equations of the entire towing system (towing cable, ballast, towing platform), and establish the relationship between the towing force, gravity, buoyancy, hydrodynamic force of the towing body and the hydrodynamic force of the tail fin using static modeling. Simulate and analyze the attitude of the towing platform under different working conditions to ensure that the towing system can achieve dynamic balance.

[0084] S6. Quantitative analysis of the towed platform's navigation attitude through simulation: MATLAB software was used to simulate and analyze the towing behavior of the towed platform under different towing speeds and sea states. The simulation results are as follows: Figures 5-7 Irregular waves were constructed based on the JONSWAP wave spectrum to simulate the attitude changes of the towed body under real sea conditions; the attitude of the towed body was corrected based on the PID algorithm to ensure that it maintains a horizontal navigation attitude underwater with an attitude deviation of no more than ±1°.

[0085] S7. After the simulation is completed, a sea trial will be conducted for verification: the main towing cable will be connected to the mother ship, the towing speed will be set to 3 m / s, and the relevant physical parameters of the towed platform, such as pitch angle, roll angle, towing depth, and towing speed, will be monitored in real time and compared with the simulation results to determine the accuracy of the simulation results. At the same time, in response to the attitude fluctuations that occur during the test, the installation position of the cruciform tail fin and the weight of the ballast will be optimized to further improve the stability of the towed platform.

[0086] The above embodiments are only used to illustrate the present invention. Any equivalent transformations (such as adjusting the size of the towing platform, changing the type and material of the ballast, optimizing the tail fin airfoil parameters, etc.) and improvements made on the basis of the technical solution of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. A constant-depth, constant-speed underwater two-stage towing system, wherein the system employs a towing mother ship (1) connected to a towing platform (9) via cables, characterized in that: The towing mother ship (1) is equipped with a host computer (2), and the towing platform (9) is equipped with a servo motor (16), a depth and speed sensor (12), a PID controller (13) and an attitude angle measuring instrument (14). The tail of the towing platform (9) is equipped with a cross-shaped tail fin, namely a vertical tail fin (10) and a horizontal tail fin (11). The vertical tail fin (10) is fixed on the towing platform (9) to resist the rolling motion of the towing platform under the action of water flow. The horizontal tail fin (11) is controlled by the servo motor (16) to adjust the angle of attack and provide lift for the towing platform. Ballast (5) is installed on the cable via pulley (6). Ballast (5) divides the cable into main towing cable (4) and auxiliary towing cable (7). Main towing cable (4) is the cable between the towing mother ship (1) and ballast (5). Auxiliary towing cable (7) is the cable between ballast (5) and towing point (8) of towing platform (9). The towing mother ship (1) is equipped with a host computer (2), which integrates the control method of the towing system. It is used to construct the motion control equation of the towing platform, preset the current velocity and buoyancy parameters according to the actual ocean data, and simulate the towing situation of the towing platform under different towing speeds and different sea conditions. Based on the attitude angle input PID algorithm of the towing platform (9) in the ballast state, the attitude of the towing platform (9) is corrected by the PID controller (13) and the servo motor (16). The control method of this system includes the following steps: S1. Using static modeling, establish the relationships between the towing force, gravity, buoyancy, hydrodynamic forces of the towed platform, and hydrodynamic forces of the tail fin, and construct the motion equations of the towed platform, including translational and rotational motion equations; obtain the actual attitude angles of the towed platform: pitch angle. Roll angle and yaw angle ; S2. Construct the dynamic coupling of the translational and rotational nonlinear motions of the towing system. Multiply the total mass matrix by the generalized acceleration. Simultaneously, the system's translational velocity and angular velocity are coupled with the mass matrix through a cross product to generate a Coriolis-centrifugal force term. Finally, the resultant force of the product of the total mass matrix and the generalized acceleration plus the Coriolis-centrifugal force term is equal to the externally applied translational generalized force and rotational generalized torque. This yields the accelerations of the towed platform's six degrees of freedom: linear acceleration... and inertial acceleration ; S3. Through PID control algorithm and actuator coupling control, the control loop adopts PID control strategy to ensure that it maintains a horizontal navigation attitude underwater, with an attitude deviation of no more than ±1°.

2. The constant-depth, constant-speed underwater two-stage towing system according to claim 1, characterized in that: The towed platform (9) is configured as a slender streamlined symmetrical structure with a length-to-diameter ratio of 6:1, and the cross-shaped tail fin with an aspect ratio of 1.7 is installed at its tail; the horizontal tail fin (11) rotates less than ±20°; the center of gravity of the towed platform is located directly below the center of buoyancy, and the buoyancy is set to 5%.

3. The constant-depth, constant-speed underwater two-stage towing system according to claim 1, characterized in that: The towed platform is equipped with multiple sensors and actuators, including an attitude sensing module, a depth sensing module, a velocity sensing module, a rotation angle limiting module, and a servo electric drive module. Among them, the attitude sensing module is used to measure its actual attitude angle underwater in real time, providing data input for the PID control algorithm; the depth sensing module and the velocity sensing module are used to measure the actual depth and towing speed of the towed platform; the rotation angle limiting module is used to limit the tail fin rotation angle within ±20°; and the servo electric drive module is used to receive the tail fin command after limiting and drive the tail fin of the towed platform to perform mechanical deflection.

4. The constant-depth, constant-speed underwater two-stage towing system according to claim 1, characterized in that, Step S1 specifically involves: S1.

1. Define the body coordinate system and the inertial coordinate system. The body coordinate system is located at the center of buoyancy of the towed platform. b The axis points towards the bow, y b The axis references a right-handed coordinate system; variable X I =[x,y,z] T It is the position of the towed platform relative to the inertial coordinate system, Φ I =[φ,θ,ψ] T Let V represent the Euler angles of the towed platform relative to the inertial coordinate system, where V = [u, v, w]. T It is the linear velocity represented in volume coordinates, Ω=[p,q,r] T It is the angular velocity of the towed platform relative to the inertial coordinate system; S1.2 Construct the coordinate system transformation matrix, matrix R IB It is the rotation matrix from the volume coordinate system to the inertial coordinate system: ； S1.3 Construct the equations of motion. The state of the towed platform is represented as follows: ； The equation of translational motion for the towed platform is: ； Therefore, we can determine the forward velocity u, lateral velocity v, and vertical velocity w of the towed platform in the inertial coordinate system. The equation of motion for the towed platform is: ； Therefore, the pitch angle of the towed platform in the inertial coordinate system can be determined. Roll angle and yaw angle .

5. The constant-depth, constant-speed underwater two-stage towing system according to claim 1, characterized in that: Step S2 specifically includes the following sub-steps: S2.1 Establish the external force equations and moment equations for the towing force, gravity, buoyancy, hydrodynamic forces of the towing body and tail fin of the towed platform: = + + + + ； Among them, F ext : The external force acting on the towed fish and represented in body coordinates; F axial :F ext Along x b Components of the axis; F lateral :F ext Along y b Axial component; F normal :F ext Along z b Axial component; F body : Represents the fluid force acting on the hull surface in an inertial coordinate system; F tail : Represents the fluid force acting on the tail fin in the inertial coordinate system; F tow : Represents the drag force generated by the secondary cable on the towed platform in the body coordinate system; F weight : Gravity of the towed platform in the body coordinate system; F buoyancy : The buoyancy of the towed platform in the body coordinate system; = + + + + ； Among them, M ext M: The external torque acting on the towed fish in the body coordinate system. roll M ext Around x b Components of the axis; M pitch M ext Around y b Components of the axis; M yaw M ext Around z b Components of the axis; M body : Fluid torque acting on the outer surface of the hull in body coordinates; M tail : The fluid torque acting on the tail fin in the volume coordinate system; M tow The traction torque generated by the secondary cable in the body coordinate system: M damping : The damping moment of the towed platform in the body coordinate system; M weight The torque generated in the body coordinate system due to the displacement of the center of mass; S2.2 Construct the rigid body mass and additional mass matrix. Define the 3x3 matrix M as the rigid body mass and additional mass matrix, with the following expression: ； Where K1, K2, and K3 are the axial, lateral, and rotational additional mass coefficients, respectively, and their expressions are as follows: ； The towed platform is approximated as having a minor axis length of Db and a major axis length of l. b An oblate spheroid, where e is the eccentricity: ； ； S2.3 Construct the rigid body inertia and additional inertia matrices, defining the 3x3 matrix J as the rigid body inertia and additional inertia matrices: ； in , , , , , It is the moment of inertia of the towing platform. Three-dimensional additional inertia coefficient, It is the pitch angular velocity plus the inertia coefficient. It is the yaw rate plus the inertia coefficient; S2.4 Constructing the inertial coupling matrix: Matrix D represents the inertial coupling between translational and rotational motions, when the center of mass CG does not coincide with the origin of the towed platform coordinates: ； Where m is the mass of the towing platform. , , It represents the offset of the centroid CG relative to the origin of the volume coordinate system in the x, y, and z directions. It is the core parameter that causes inertial coupling when the centroid does not coincide with the origin. To add the derivative of the mass moment for pitch, Add the derivative of the mass moment to the yaw; S2.5 Determine the overall mass matrix: ； S2.6 Calculate the Coriolis force and torque: ； in It is a linear velocity-mass coupling term used to describe the inertial effect of its own mass. It is the angular velocity-center of mass coupling term, used to describe the coupling between rotation and center of mass shift. The sum of the two and the cross product with the angular velocity give the inertial force caused by rotation, i.e., the Coriolis-centrifugal force. ； in It is an angular velocity-inertia coupling term used to describe the inertial effect of rotational inertia. This is the linear velocity-center-of-mass coupling term, used to describe the rotational coupling between linear velocity and center-of-mass offset. It is a rotational coupling torque. It is the linear velocity-angular velocity coupled torque, and the sum of the two gives the Coriolis-centrifugal torque; S2.7 Calculate the acceleration of the six degrees of freedom, including linear acceleration. Equals the cross product of the inverse of the total mass matrix and the sum of the total external force and the Coriolis-centrifugal force; inertial acceleration It equals the cross product of the inverse of the total mass matrix and the sum of the total external torque and the Coriolis-centrifugal torque.

6. The constant-depth, constant-speed underwater two-stage towing system according to claim 1, characterized in that: Step S3 specifically includes the following sub-steps: S3.1 Determine the coefficients of each term in the PID controller. The proportional element takes the attitude angle error as the direct input and outputs a control component that is proportional to the magnitude of the attitude angle error, so as to realize the instantaneous response to the current attitude deviation. The integral stage continuously captures the deviation of the attitude angle, accumulates the historical attitude angle error, and outputs a control component that is proportional to the integral value. By tracking the duration and accumulation of the attitude angle error, it cancels the steady-state error and makes the attitude angle eventually stabilize at the desired value. The derivative stage takes the change of the attitude angle, that is, the rate of change of the actual attitude angle over time, as the core input. S3.2 Integrate the position, attitude angles, PID coefficients, Euler angle derivatives in the inertial coordinate system, i.e. the differential terms of PID control, of the towed platform obtained in S1 into a state information vector, States. The PID gain matrices of the S3.3 pitch and roll channels are multiplied with the States vector to calculate the desired deflection angle commands for tail fins 2 and 4 of the towed platform. S3.

4. Use a first-order inertial model to simulate the response characteristics of the physical servo motor, and let the actual deflection angle of the tail fin gradually track the desired command at a rate of time constant. S3.5 The actual tail fin deflection angle changes the resultant fluid force and resultant torque on the towed body. The real-time linear acceleration and inertial acceleration are calculated through S2. The linear acceleration integral updates the towed body position and linear velocity, and the inertial acceleration integral updates the towed body angular velocity and attitude angle. The new attitude and motion information will be updated in the state array X, forming a complete closed-loop feedback, and continuously realizing PID control of attitude.

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