A long-distance stable navigation control method for a supercavitation vehicle

Abstract

The application provides a supercavitation vehicle long-distance stable navigation control method, and belongs to the technical field of supercavitation vehicles.The control method is as follows: S1, obtaining the geometric shape and dynamic parameters of the supercavitation vehicle and control targets; S2, establishing a cruising supercavitation vehicle dynamic model; S3, establishing a water-entry supercavitation vehicle dynamic model; S4, designing an underwater turning and cruising stage control module, and controlling the supercavitation vehicle navigation through the underwater turning and cruising stage control module in combination with the cruising supercavitation vehicle dynamic model and the water-entry supercavitation vehicle dynamic model.The application solves the problem that the current supercavitation vehicle has not formed a whole process stable navigation control technology from water entry, turning to cruising, the dynamic characteristics and environmental configuration are not comprehensive enough, and a comprehensive whole process trajectory control strategy has not been formed, and has the advantage of comprehensive stable control.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of supercavitation vehicles, in particular to a supercavitation vehicle long-distance stable navigation control method. BACKGROUND

[0002] For underwater vehicles, high-speed navigation has always been of great significance, and the development of high-speed underwater vehicles has always been a popular direction for underwater vehicles. The speed of traditional underwater vehicles can only reach about 40 meters per second, and the reason is that underwater movement will be subject to particularly large fluid resistance. According to relevant theories and experimental data, the fluid resistance in water can be as much as 20 times the air resistance. Under the condition that the power and thrust of the vehicle are constant, how to reduce the resistance of the underwater movement of the vehicle as much as possible becomes the key to improving the underwater navigation speed of the vehicle.

[0003] Supercavitation technology is one of the key technologies for reducing the resistance of underwater vehicle movement. When the speed of the vehicle continues to increase, and the local pressure of the vehicle can be reduced below the minimum pressure of the fluid, a sharp corner can be installed at the front end to pierce the flowing liquid in front and produce a gas bubble behind it. The liquid will change from water to gas, and this phenomenon is called cavitation. When such a phenomenon continues to occur, the underwater vehicle may be surrounded by a low-density gas cavity, so that most of the surface area of the vehicle is separated from the liquid, which makes the vehicle have very small resistance when navigating, making it possible to further improve the underwater navigation speed and develop super-speed vehicles. The "long distance" of the supercavitation vehicle navigation is defined as: the supercavitation vehicle navigation can meet the stable navigation of more than 10km at a cruising speed of 200 knots after entering the water.

[0004] However, the current supercavitation vehicle has not yet formed a stable navigation control technology from entering the water, turning flat to cruising, the dynamic characteristics and environmental configuration are not comprehensive enough, and the overall whole-process trajectory control strategy has not been formed. SUMMARY

[0005] The technical problem solved by the present application is that the current supercavitation vehicle has not yet formed a stable navigation control technology from entering the water, turning flat to cruising, the dynamic characteristics and environmental configuration are not comprehensive enough, and the overall whole-process trajectory control strategy has not been formed.

[0006] To solve the above problems, the technical scheme of the present application is as follows:

[0007] A supercavitation vehicle long-distance stable navigation control method, comprising the following steps:

[0008] S1, obtain the geometric shape and dynamic parameters of the supercavitation vehicle, and the control target corresponding to the running stage of the supercavitation vehicle;

[0009] S2, establish a cruise supercavitation vehicle dynamics model:

[0010] Based on the geometric shape and dynamic parameters of the supercavitation vehicle, and the control target corresponding to the running stage of the supercavitation vehicle, the cruise supercavitation vehicle dynamics model corresponding to the cruise stage is obtained by the exact linearization method of Lie derivative;

[0011] S3, establish a water-entry supercavitation vehicle dynamics model:

[0012] Based on the full wet additional force, the water-entry supercavitation vehicle dynamics model is improved to the cruise supercavitation vehicle dynamics model, and the water-entry supercavitation vehicle dynamics model corresponding to the water-entry stage and the underwater turning stage is obtained;

[0013] S4, design an underwater turning and cruise stage control module, and control the supercavitation vehicle by the underwater turning and cruise stage control module combined with the cruise supercavitation vehicle dynamics model and the water-entry supercavitation vehicle dynamics model:

[0014] Based on the PID controller with time delay term and the sliding mode control method, the underwater turning and cruise stage control module corresponding to the supercavitation vehicle is designed, and the underwater turning and cruise stage control module is loaded on the cruise supercavitation vehicle dynamics model and the water-entry supercavitation vehicle dynamics model respectively. In the process of the supercavitation vehicle navigation, the rudder angle deflection of the supercavitation vehicle is calculated by selecting the supercavitation vehicle dynamics model corresponding to the stage where the supercavitation vehicle is located, and the rudder angle deflection is used to control the tail rudder to realize the navigation control of the supercavitation vehicle.

[0015] Further, the front end of the supercavitation vehicle is fixed with a disc-shaped cavitator, the outer surface of the tail of the vehicle is fixed with four tail rudders, the four tail rudders are composed of two pitch tail rudders and two yaw tail rudders, the two pitch tail rudders are fixed on the left and right sides of the tail of the supercavitation vehicle, the two yaw tail rudders are fixed on the upper and lower sides of the tail of the supercavitation vehicle, the inside of the supercavitation vehicle is provided with an engine, and the engine is electrically connected with the tail rudders.

[0016] Further, the geometric shape and dynamic parameters include: vehicle mass, vehicle total length, vehicle tail length, tail rudder to vehicle center of mass distance, vehicle thrust, vehicle tail rudder flow area, vehicle moment of inertia, vehicle cross section radius, fluid density, fluid resistance coefficient, vehicle cavitator radius, cavitator to vehicle center of mass distance, cavitator ideal cavitation number, and control target includes: vehicle water-entry speed, vehicle cruise depth, vehicle cruise speed.

[0017] Furthermore, the operation phases of a supercavitating vehicle include: the water entry phase, the underwater transition phase, and the cruise phase.

[0018] Further, step S2 includes the following steps:

[0019] S2-1. Analyze and calculate the geometric shape, dynamic parameters, and control objectives of the supercavitating vehicle to obtain the gravity, thrust, cavitation force, tail rudder force, and gliding force experienced by the vehicle during the cruise phase. Establish a dynamic model of the supercavitating vehicle through the center of mass motion equation and Euler rotation equation.

[0020] S2-2. Based on the assumption of satisfying the small angle approximation in engineering, the dynamic state variables of the supercavitating vehicle are extracted. The state equation of the supercavitating vehicle is obtained through the dynamic state variables. Then, the state equation is precisely linearized by the method based on Lie derivatives to obtain the cruise supercavitating vehicle dynamic model corresponding to the cruise phase.

[0021] Furthermore, step S2-1 includes the following steps:

[0022] S2-1-1. Analyze the motion pattern of the cavitation generated by the cavitation device, calculate the gravity and thrust of the supercavitating vehicle, calculate the cavitation force and torque of the vehicle, and project the cavitation force and torque onto the coordinates of the vehicle in the projectile coordinate system.

[0023] S2-1-2. Analyze the motion pattern of the cavitation bubble during the cruise phase to calculate the wetting situation of the vehicle body. Calculate the wetting coefficients of the tail rudder and yaw rudder respectively. Analyze the overall immersion of the supercavitating vehicle body. Calculate the tail rudder wetting force of the supercavitating vehicle body in the fully submerged and fully wetted area of ​​the vehicle body. The tail rudder wetting force is the tail rudder force.

[0024] S2-1-3. Treat the gliding of the supercavitating vehicle as the flow of free fluid on the surface of a cylinder, and then express the gliding force as a fluid force perpendicular to the longitudinal axis of the cylinder and calculate it. At the same time, calculate the gliding viscous drag on the supercavitating vehicle.

[0025] S2-1-4. Substitute the calculated results of gravity, thrust, cavitation force, tail rudder force, and gliding force into the equations of motion of the center of mass and the Euler rotation equations to output the dynamic model of the supercavitating vehicle. The model formula for the dynamic model of the supercavitating vehicle is as follows:

[0026]

[0027]

[0028] in, The forces acting on the aforementioned ship are... Let m be the torque acting on the vehicle, and m be the mass of the vehicle. Let be the angular momentum of the ship. The velocity vector of the aircraft. The angular velocity vector of the vehicle. Let be the relative derivative of the velocity of the vehicle. It is the relative derivative of the angular momentum of the ship.

[0029] Preferably, step S2-2 includes the following steps:

[0030] S2-2-1. To simplify the dynamic model of the supercavitating vehicle, the following assumptions are made: Assume the lateral velocity v of the supercavitating vehicle is v. x1 In a steady state, the engine thrust is balanced and remains constant, and the longitudinal velocity v of the supercavitating vehicle... y1 Since the ratio of the magnitude to the lateral velocity is less than 0.02, the velocity of the supercavitating vehicle is assumed to be constant during the cruise phase, and only the longitudinal velocity v is considered. y1 The magnitude of the change in angle of attack α of the supercavitating vehicle is approximated by a first order, i.e., sinα≈αcosα≈1 / arctanα≈α. By simplifying the dynamic equations through a small angle approximation, the dynamic state variables describing the supercavitating vehicle are selected as follows:

[0031] x = [y0 v] y1 θω] T ,

[0032] In the above formula, x is the dynamic state variable, y0 is the depth parameter of the vehicle body, and v y1 θ is the velocity of the vehicle in the y-direction, θ is the pitch angle of the vehicle, and ω is the pitch angular velocity of the vehicle.

[0033] S2-2-2 The equation of state of the supercavitating vehicle obtained through dynamic state variables is as follows:

[0034]

[0035] In the above formula, x is the dynamic state variable, x = [y0 v y1 θ ω] T y0 is the depth parameter of the vehicle body, v y1 Let θ be the velocity of the vehicle in the y-direction, θ be the pitch angle of the vehicle, ω be the pitch angular velocity of the vehicle, and u be the control variable, u = [δ]. c δ f / p ] T δ c δ is the cavitation control quantity for supercavitating vehicles. f / p This refers to the control amount of the tail rudder deflection angle for a supercavitating vehicle. for the derivative of the state variable, y is the observation, f(x) is the system function, b(x) is the control function, h(x) is the observation function,

[0036] Each row of the system function f(x) is composed of four scalar functions defined on the state vector x, so f(x) = [f1 f2 f3 f4] T The 4x2 control matrix can be written as composed of two vector field functions: b(x) = [b1(x) b2(x)] T The second-order observation function of the vehicle state equation of the supercavitating vehicle is:

[0037]

[0038] In the above formula, h(x) is the observation function, h1(x) is the first observation, and h1(x) = x1 = y0, h2(x) is the second observation, and h2(x) = x3 = θ, x1 is the depth parameter of the supercavitating vehicle, and x3 is the pitch angle of the supercavitating vehicle;

[0039] S2-2-3, the decoupling matrix of the simplified supercavitating vehicle dynamics model is calculated by the method of Lie derivative, the supercavitating vehicle dynamics model corresponding to the cruise stage is obtained by accurately linearizing the supercavitating vehicle dynamics model, and the decoupling matrix is:

[0040]

[0041] In the above formula, is the second-order Lie derivative of h1(x) with respect to f(x) and b1(x), is the second-order Lie derivative of h1(x) with respect to f(x) and b2(x), is the second-order Lie derivative of h2(x) with respect to f(x) and b1(x), is the second-order Lie derivative of h2(x) with respect to f(x) and b2(x), h1(x) is the first observation, h2(x) is the second observation, f(x) is the system function, b1(x) is the first vector field function, and b2(x) is the second vector field function,

[0042] The supercavitating vehicle dynamics model corresponding to the cruise stage is obtained by accurately linearizing the vehicle state equation through the decoupling matrix, and the supercavitating vehicle dynamics model corresponding to the cruise stage is as follows:

[0043]

[0044] In the above formula, u1 is the first control, u2 is the second control, is the second-order Lie derivative of h1(x) with respect to f(x), is the second order Lie derivative of h2(x) with respect to f(x), h1(x) is the first observation, h2(x) is the second observation, f(x) is the system function, y1 is the observed depth of the supercavitating vehicle, y2 is the observed vertical velocity of the supercavitating vehicle, is the second order derivative of y1, is the second order derivative of y2.

[0045] Preferably, step S3 comprises the following:

[0046] Based on the full wet added force of the water-entry supercavitating vehicle dynamics improvement, it is assumed that the kinetic energy of the water-entry supercavitating vehicle is converted into the kinetic energy and potential energy of the water, so that the motion state of the cavity in the water-entry process of the supercavitating vehicle is derived, and then the water-entry full wet condition of the vehicle is obtained. The cruise supercavitating vehicle dynamics model is added with the full wet buoyancy, the viscous resistance of the fluid and the tail pressure difference, and the water-entry supercavitating vehicle dynamics model corresponding to the water-entry stage and the underwater turning flat stage is obtained. The model formula of the water-entry supercavitating vehicle dynamics model is as follows:

[0047]

[0048] In the above formula, u1 is the first control quantity, u2 is the second control quantity, is the second order Lie derivative of h1(x) with respect to is the second order Lie derivative of h2(x) with respect to is the second order Lie derivative of h2(x) with respect to is the second order Lie derivative of h2(x) with respect to is the system function after the system is added with the full wet buoyancy, the viscous resistance of the fluid and the tail pressure difference, y1 is the observed depth of the supercavitating vehicle, y2 is the observed vertical velocity of the supercavitating vehicle, is the second order derivative of y1, is the second order derivative of y2.

[0049] Preferably, step S4 comprises the following steps:

[0050] S4-1, establish an underwater turning flat and cruise stage control module capable of simultaneously controlling the PID controller and the sliding mode controller with time delay term, and load the underwater turning flat and cruise stage control module on the cruise supercavitating vehicle dynamics model and the water-entry supercavitating vehicle dynamics model respectively;

[0051] S4-2, when the supercavitating vehicle is in the water entry stage and the underwater turning level stage, the underwater turning level and cruising stage control module outputs the control amount of the PID controller with time delay as the control amount of the rudder angle deflection amount of the supercavitating vehicle, inputs the water entry supercavitating vehicle dynamics model, obtains the rudder angle deflection amount of the supercavitating vehicle, controls the rudder through the rudder angle deflection amount, realizes the water entry and underwater turning level control of the supercavitating vehicle, and the calculation formula of the control amount of the PID controller with time delay is as follows:

[0052]

[0053] In the above formula, δ(t) is the control turning angle of the rudder at time t, θ c (t) is the deviation of the pitch angle at time t from the expectation, is the derivative of the deviation of the pitch angle at time t from the expectation, K p is the PID control proportional parameter, K d is the PID control differential parameter, K i is the PID control integral parameter, t is time, t0 is time delay, the time delay is the time from the cavitation birth to the movement to the tail of the supercavitating vehicle, that is:

[0054]

[0055] In the above formula, t0 is the time delay, L is the length of the supercavitating vehicle, and V is the speed of the supercavitating vehicle.

[0056] Further preferably, step S4 further comprises the following steps:

[0057] S4-3, the underwater turning level and cruising stage control module configures a sliding mode controller for each of the two observation values y1 and y2 of the cruising supercavitating vehicle dynamics model based on a sliding mode controller through a linear sliding mode method, and the linear sliding mode structure formula provided by the sliding mode controller is as follows:

[0058]

[0059] In the above formula, s(x) is a linear sliding mode structure, a i is a first parameter determined by Lyapunov's second stability theory, b i is a second parameter determined by Lyapunov's second stability theory, e i is the deviation of the observation value from the expected value, and the Lyapunov function determined by s(x) is:

[0060] and

[0061] In the above formula, Y is a Lyapunov function, s is the derivative of Lyapunov function, i (x) is the i th linear sliding mode structure, is the derivative of the i th linear sliding mode structure;

[0062] Configure the sliding mode approach rate of constant speed Wherein, v is the speed parameter of the control sliding mode rate, sgn is the sign function;

[0063] S4-4, define the improved sign function sgn*(x) function The sign function sgn is improved to improve the stability performance of the sliding mode controller, and the formula of the improved sign function is as follows:

[0064]

[0065] In the above formula, sgn*(x) is the improved sign function, x is the input parameter of the sign function, Q is the improved parameter of the sign function, and the value range is 0 -3 ;

[0066] S4-5, the sliding mode control quantity is compounded with the decoupling matrix, and the result of the compounding is input into the cruise supercavitating vehicle dynamics model as the control quantity of the supercavitating vehicle rudder deflection angle. The cruise supercavitating vehicle dynamics model is compounded by the second order Lie derivative coupling quantity part and the sliding mode control quantity part, and the rudder deflection angle of the supercavitating vehicle is obtained. The rudder deflection angle is controlled by the tail rudder to realize the cruise control of the supercavitating vehicle. The control quantity calculation formula of the supercavitating vehicle rudder deflection angle is as follows:

[0067]

[0068] In the above formula, u1 is the first control quantity, u2 is the second control quantity, the first control quantity is the cavitator control quantity of the supercavitating vehicle, and the second control quantity is the tail rudder deflection angle control quantity in the supercavitating cruise dynamics, v1 is the first control quantity of the sliding mode controller, v2 is the second control quantity of the sliding mode controller, A -1 is the compound decoupling matrix, is the second order Lie derivative of h1(x) to f(x), is the second order Lie derivative of h2(x) to f(x), h1(x) is the first observation, h2(x) is the second observation, and f(x) is the system function.

[0069] The beneficial effects of the present application are:

[0070] The application sets up the dynamics equation of the multi-degree-of-freedom supercavitation vehicle with time delay characteristics by considering the supercavity motion state and force condition of the supercavitation vehicle in the whole process stages of entering water, turning flat and cruising, and improves and designs the whole process control module of the supercavitation vehicle based on the Lie derivative accurate linearization and the Lyapunov stability theory, so that the long-distance stable navigation of the supercavitation vehicle in the whole process is realized, and the supercavitation vehicle can have a simple and reliable engineering stable navigation control method facing the needs of real engineering application. BRIEF DESCRIPTION OF DRAWINGS

[0071] Figure 1 is a flow chart of a long-distance stable navigation control method of a supercavitation vehicle in an embodiment;

[0072] Figure 2 is a whole structure diagram of a supercavitation vehicle in an embodiment;

[0073] Figure 3 is a tail rudder structure diagram of a supercavitation vehicle in an embodiment. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0075] The terms used in the embodiments of the present application are only for the purpose of describing the specific embodiments, and are not intended to limit the present application. The singular forms "a", "an" and "the" used in the embodiments of the present application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise. "Plural" generally includes at least two.

[0076] It should be understood that although the terms first, second, third, etc. may be used in the embodiments of the present application to describe …, these … should not be limited to these terms. These terms are only used to distinguish … from each other. For example, without departing from the scope of the embodiments of the present application, the first … can also be called the second …, and similarly, the second … can also be called the first ….

[0077] Noun explanation

[0078] Supercavitation vehicle: a kind of underwater vehicle using supercavitation technology, which uses the supercavity generated by cavitation technology to wrap the surface of the vehicle, realizes the isolation of the vehicle and underwater fluid, and greatly reduces the fluid resistance of the vehicle when navigating underwater.

[0079] PID controller: linear proportional-derivative-integral controller, the output control quantity of which at a certain time is the linear combination of the error quantity, the derivative of the error quantity and the integral of the error quantity at the current time.

[0080] Sliding mode controller: a controller designed based on the sliding mode control method.

[0081] Sliding mode control method: a variable structure control method, which designs different control modes according to the degree of system deviation from the set expectation, so that the system runs according to the specified rule, and belongs to the prior art.

[0082] Equation of motion of center of mass: one of the basic equations of rigid body motion, the translational equation established at the center of mass of the rigid body, used to represent the translation of the rigid body, and belongs to the prior art.

[0083] Euler rotation equation: one of the basic equations of rigid body motion, the rotation equation established at the center of mass of the rigid body, used to represent the rotation of the rigid body, and belongs to the prior art.

[0084] Embodiment

[0085] The embodiment is a long-distance stable navigation control method for a supercavitation vehicle, comprising the following steps:

[0086] S1, obtaining the geometric shape and dynamic parameters of the supercavitation vehicle, and the control target corresponding to the running stage of the supercavitation vehicle.

[0087] The most front end of the supercavitation vehicle is fixed with a disc-shaped cavitator, the outer surface of the tail of the vehicle is fixed with four tail rudders, the four tail rudders are composed of two pitch tail rudders and two yaw tail rudders, the two pitch tail rudders are fixed on the left and right sides of the tail of the supercavitation vehicle, the two yaw tail rudders are fixed on the upper and lower sides of the tail of the supercavitation vehicle, an engine is arranged in the interior of the supercavitation vehicle, and the engine is electrically connected with the tail rudders. The running stage of the supercavitation vehicle includes: water entry stage, underwater turning flat stage and cruising stage.

[0088] In the embodiment, the structure of the supercavitation vehicle is as shown in Figure 2 The center of mass of the supercavitation vehicle is slightly behind, and the distance from the most front end of the vehicle is l c , the distance from the center of mass to the tail rudder is l f / p , the full length of the vehicle is L, and the radius of the vehicle cylinder is R. As shown in Figure 3 The four tail rudders of the supercavitation vehicle are similar to a cone, so the projection of each tail rudder in the incoming flow direction is a triangle, where l is the length of a single tail rudder, and h represents the thickness of the tail rudder.

[0089] The geometric shape and dynamic parameters include: the mass of the vehicle, the total length of the vehicle, the tail length of the vehicle, the distance from the tail rudder to the center of mass of the vehicle, the thrust of the vehicle, the vehicle rudder inflow area, the vehicle rotational inertia, the vehicle cross-sectional radius, the fluid density, the fluid resistance coefficient, the vehicle cavitator radius, the distance from the cavitator to the center of mass of the vehicle, and the ideal cavitation number of the cavitator.

[0090] In this embodiment, the geometric shape and dynamic parameters of the supercavitating vehicle are shown in Table 1.

[0091] Table 1 Geometric shape and dynamic parameters of supercavitating vehicle

[0092]

[0093] The control targets include: the water entry speed of the vehicle, the cruising depth of the vehicle, and the cruising speed of the vehicle.

[0094] In this embodiment, the water entry speed of the supercavitating vehicle is 200 m / s, the cruising depth is 10 m, and the cruising speed is 100 m / s.

[0095] S2, a cruising supercavitating vehicle dynamics model is established:

[0096] Based on the geometric shape and dynamic parameters of the supercavitating vehicle and the control targets corresponding to the operation stage of the supercavitating vehicle, the cruising supercavitating vehicle dynamics model corresponding to the cruising stage is obtained by the exact linearization method of Lie derivative, including the following steps:

[0097] S2-1, the geometric shape and dynamic parameters of the supercavitating vehicle and the control targets are analyzed and calculated to obtain the gravity, thrust, cavitator force, tail rudder force and sliding force of the vehicle in the cruising stage, and the supercavitating vehicle dynamics model is established through the center of mass motion equation and the Euler rotation equation, including the following steps:

[0098] S2-1-1, the motion form of the cavitator generating a cavity is analyzed, the gravity and thrust of the supercavitating vehicle are calculated, the cavitator force and torque are calculated, and the cavitator force and torque are projected and calculated to the coordinates of the vehicle in the body coordinate system;

[0099] S2-1-2, the motion form of the cavity in the cruising stage is analyzed, so as to calculate the wetting condition of the vehicle, the wetting coefficients of the tail rudder and the yaw rudder are calculated respectively, the immersion condition of the supercavitating vehicle as a whole is analyzed, the tail rudder wetting force of the supercavitating vehicle is calculated in the fully immersed and fully wetted area of the vehicle, and the tail rudder wetting force is the tail rudder force;

[0100] S2-1-3, the sliding of the supercavitating vehicle is regarded as the flow of free fluid on the surface of a cylinder, so that the sliding force is represented as a vertical flow fluid force on the longitudinal axis of the cylinder and is calculated, and the sliding viscous drag force on the supercavitating vehicle is also calculated;

[0101] S2-1-4, the above gravity, thrust, cavitator force, and tail rudder force are substituted into the mass center motion equation and the Euler rotation equation, and the supercavitating vehicle dynamics model is output, and the model formula of the supercavitating vehicle dynamics model is:

[0102]

[0103]

[0104] wherein, is the force on the above vehicle, is the moment on the vehicle, m is the mass of the vehicle, is the moment of momentum of the vehicle, is the velocity vector of the vehicle, is the angular velocity vector of the vehicle, is the relative derivative of the velocity of the vehicle, is the relative derivative of the moment of momentum of the vehicle.

[0105] In this embodiment, the gravity F G1 of the vehicle and the thrust size F T1 are calculated, c1 the cavitating force F c of the vehicle and the moment size M f are calculated,

[0106] Then according to the motion process of the cavity, the ratio I f (t,τ) of the part of the rudder immersed in water to the whole, i.e. the wetness ratio of the vehicle, is calculated, and the tail rudder force and moment of the supercavitating vehicle are configured according to the wetness ratio:

[0107]

[0108] wherein p represents the density of the liquid, v represents the speed of the vehicle, S f is the surface area of the elevator, σ represents the cavitator cavitation number, and a f represents the attack angle of the elevator relative to the speed coordinate.

[0109] Secondly, the sliding force of the supercavitating vehicle is calculated, the sliding force is regarded as the flow of a cylinder free fluid surface, and the sliding force is a vertical flow fluid force on the longitudinal axis, which is defined by the immersion depth h0 and the immersion angle γ, so that the sliding force F h and the viscous drag force Fd .

[0110]

[0111]

[0112] where p is the density of the fluid, v is the magnitude of the vehicle's velocity, R c is the radius of the cavity at this time.

[0113] S2-2, on the basis of considering to meet the engineering small angle approximation case, refining the dynamic state variables of supercavitation vehicle, through the dynamic state variables to obtain the vehicle state equation of supercavitation vehicle, and then through the method based on Lie derivative to accurately linearize the state equation, obtain the cruise supercavitation vehicle dynamics model corresponding to the cruise stage, including the following steps:

[0114] S2-2-1, in order to simplify the supercavitation vehicle dynamics model, make the following assumptions: assume that the lateral velocity v x1 of the supercavitation vehicle is constant, and the ratio of the magnitude of the longitudinal velocity v y1 to the lateral velocity is less than 0.02, consider that the speed of the supercavitation vehicle in the cruise stage is constant and unchanged, only consider the change of the magnitude of the longitudinal velocity v y1 , take the first order approximation of the attack angle a of the supercavitation vehicle, that is, sin a ≈ a cos a ≈ 1 arctan a ≈ a, simplify the dynamic equation through small angle approximation, select the dynamic state variables of the supercavitation vehicle as follows:

[0115] x = [y 0 v y1 θ ω] T ,

[0116] In the above formula, x is the dynamic state variable, y 0 is the depth parameter of the vehicle, v y1 is the speed of the vehicle in the y direction, theta is the pitch angle of the vehicle, and omega is the pitch angle velocity of the vehicle;

[0117] S2-2-2, the vehicle state equation of the supercavitation vehicle obtained through the dynamic state variables is as follows:

[0118]

[0119] In the above formula, x is the dynamic state variable, x = [y 0 v y1 θ ω] T , y 0 is the depth parameter of the vehicle, v y1 is the speed of the vehicle in the y direction, theta is the pitch angle of the vehicle, and omega is the pitch angle velocity of the vehicle, u is the control quantity, u = [deltac δ f / p ] T , δ c is the cavitator control variable of the supercavitating vehicle, δ f / p is the rudder deflection angle control variable of the supercavitating vehicle, is the derivative of the state variable, y is the observation variable, f(x) is the system function, b(x) is the control function, h(x) is the observation function,

[0120] Each row of the system function f(x) is composed of four scalar functions defined on the state vector x, so f(x) = [f1 f2 f3 f4] T The 4x2 control matrix can be written as two vector field functions: b(x) = [b1(x) b2(x)] T The second-order observation function of the vehicle state equation of the supercavitating vehicle is:

[0121]

[0122] In the above formula, h(x) is the observation function, h1(x) is the first observation variable, and h1(x) = x1 = y0, h2(x) is the second observation variable, and h2(x) = x3 = θ, x1 is the depth parameter of the supercavitating vehicle, and x3 is the pitch angle of the supercavitating vehicle;

[0123] S2-2-3, the decoupling matrix of the simplified supercavitating vehicle dynamics model is calculated by the method of Lie derivative, the supercavitating vehicle dynamics model corresponding to the cruise stage is obtained by accurate linearization, and the decoupling matrix is:

[0124]

[0125] In the above formula, is the second-order Lie derivative of h1(x) with respect to f(x) and b1(x), is the second-order Lie derivative of h1(x) with respect to f(x) and b2(x), is the second-order Lie derivative of h2(x) with respect to f(x) and b1(x), is the second-order Lie derivative of h2(x) with respect to f(x) and b2(x), h1(x) is the first observation variable, h2(x) is the second observation variable, f(x) is the system function, b1(x) is the first vector field function, and b2(x) is the second vector field function,

[0126] The supercavitating vehicle dynamics model corresponding to the cruise stage is obtained by accurate linearization of the vehicle state equation through the decoupling matrix, as shown in the following formula:

[0127]

[0128] In the above formula, u1 is the first control quantity, u2 is the second control quantity, is the second order Lie derivative of h1(x) to f(x), is the second order Lie derivative of h2(x) to f(x), h1(x) is the first observation, h2(x) is the second observation, f(x) is the system function, y1 is the observed depth of the supercavitating vehicle, y2 is the observed vertical velocity of the supercavitating vehicle, is the second order derivative of y1, is the second order derivative of y2.

[0129] S3, a water-entry supercavitating vehicle dynamics model is established:

[0130] Based on the full wet additional force, the water-entry supercavitating vehicle dynamics is improved, and the cruise supercavitating vehicle dynamics model is improved. The water-entry supercavitating vehicle dynamics model corresponding to the water-entry stage and the underwater turning stage is obtained, including the following contents:

[0131] Based on the full wet additional force, the water-entry supercavitating vehicle dynamics is improved, and the cruise supercavitating vehicle dynamics model is improved. The water-entry supercavitating vehicle dynamics model corresponding to the water-entry stage and the underwater turning stage is obtained, including the following contents:

[0132]

[0133] In the above formula, u1 is the first control quantity, u2 is the second control quantity, is the second order Lie derivative of h1(x) to , is the second order Lie derivative of h2(x) to , is the system function after the system is added with the full wet buoyancy, the viscous resistance of fluid and the tail pressure difference, y1 is the observed depth of the supercavitating vehicle, y2 is the observed velocity of the supercavitating vehicle in the y direction, is the second order derivative of y1, is the second order derivative of y2.

[0134] In this embodiment, step S3 first theoretically deduces the motion state of the cavity in the water-entry process of the supercavitating vehicle, and calculates the cavity radius R c and the cavity change rate

[0135] The shape of the cavity in the water entry phase is generally not large, and the vehicle will have a full wet area, which is the biggest difference between the vehicle in the water entry phase and the running state under the action of the cavitation device in the cruising phase. The supercavitation of the water entry process needs to be configured with full-wet buoyancy F b , viscous resistance of fluid F T , and tail differential pressure ΔF p

[0136] F h = ρgV

[0137]

[0138]

[0139]

[0140] Here V represents the volume of the full-wet part of the tail of the vehicle, C l is the lift coefficient, S represents the maximum cross-sectional area of the force surface of the vehicle, v is the instantaneous speed of the vehicle, Re is the Reynolds number of the vehicle. μ is the efficiency coefficient, which should be between 0 and 1. The difference in pressure caused by this efficiency coefficient is due to the fact that the sliding force of the tail wrapped in the cavity and the fluid power received by the full-wet tail are changing all the time, and the length of the cavity wrapped in the vehicle during the maneuvering process cannot be determined and measured in real time. The experience coefficient is about 0.55.

[0141] S4, design underwater turning and cruising phase control module, control supercavitation vehicle through underwater turning and cruising phase control module combined with cruising supercavitation vehicle dynamics model, water entry supercavitation vehicle dynamics model:

[0142] Design underwater turning and cruising phase control module corresponding to supercavitation vehicle based on PID controller with time delay term and sliding mode control method, and load underwater turning and cruising phase control module on cruising supercavitation vehicle dynamics model, water entry supercavitation vehicle dynamics model, in the process of supercavitation vehicle navigation, through the stage of supercavitation vehicle navigation, select the corresponding supercavitation vehicle dynamics model of the stage, calculate the rudder deflection of supercavitation vehicle, control the tail rudder work through the rudder deflection, realize the navigation control of supercavitation vehicle, including the following steps:

[0143] S4-1, establish underwater turning and cruising phase control module capable of simultaneously controlling PID controller with time delay term and sliding mode controller, and load underwater turning and cruising phase control module on cruising supercavitation vehicle dynamics model, water entry supercavitation vehicle dynamics model.

[0144] S4-2, when the supercavitating vehicle is in the water-entry stage and the underwater turning level stage, the underwater turning level and cruising stage control module outputs the control amount of the PID controller with time delay as the control amount of the rudder angle deflection of the supercavitating vehicle, inputs the water-entry supercavitating vehicle dynamics model, obtains the rudder angle deflection of the supercavitating vehicle, controls the tail rudder through the rudder angle deflection, realizes the water-entry and underwater turning level control of the supercavitating vehicle, and the calculation formula of the control amount of the PID controller with time delay is as follows:

[0145]

[0146] In the above formula, δ(t) is the control turning angle of the tail rudder at t, θ c (t) is the deviation of the pitch angle at t from the expectation, is the derivative of the deviation of the pitch angle at t from the expectation, K p is the PID control proportional parameter, K d is the PID control differential parameter, K i is the PID control integral parameter, t is time, t0 is time delay, the time delay is the time from the cavitation birth to the movement to the tail of the supercavitating vehicle, that is:

[0147]

[0148] In the above formula, t0 is the time delay, L is the length of the supercavitating vehicle, and V is the speed of the supercavitating vehicle.

[0149] In the water-entry and underwater turning level stage in the embodiment, the following control amount is designed:

[0150]

[0151]

[0152] Where δ c , δ f / p are the deflection angles of the cavitator and the tail rudder.

[0153] S4-3, the underwater turning level and cruising stage control module is based on a sliding mode controller, and a configuration sliding mode controller is configured for each of two observation quantities y1 and y2 of the cruising supercavitating vehicle dynamics model through a linear sliding mode method, and the linear sliding mode structure formula provided by the sliding mode controller is as follows:

[0154]

[0155] In the above formula, s(x) is a linear sliding mode structure, a i is a first parameter determined by Lyapunov's second stability theory, and b iSecond parameter determined by Lyapunov's second stability theory, e i The Lyapunov function determined by s(x) is:

[0156] And

[0157] In the above formula, Y is the Lyapunov function, is the derivative of the Lyapunov function, and si(x) is the i-th linear sliding mode structure, is the derivative of the i-th linear sliding mode structure;

[0158] Configure a constant sliding mode approach rate Wherein, v is the speed parameter of the control sliding mode rate, and sgn is the sign function;

[0159] S4-4, define the improved sign function sgn*(x) The sign function sgn is improved to improve the stability performance of the sliding mode controller. The formula of the improved sign function is as follows:

[0160]

[0161] In the above formula, sgn*(x) is the improved sign function, x is the input parameter of the sign function, and Q is the improvement parameter of the sign function, which is in the range of 0 -3 ;

[0162] S4-5, the sliding mode control quantity is compounded with the decoupling matrix, and the result of the compound is input into the cruise supercavitating vehicle dynamics model as the control quantity of the supercavitating vehicle rudder deflection angle. The cruise supercavitating vehicle dynamics model is compounded by the second order Lie derivative coupling quantity part and the sliding mode control quantity part, and the rudder deflection angle of the supercavitating vehicle is obtained. The rudder deflection angle is controlled by the rudder to realize the cruise control of the supercavitating vehicle. The control quantity calculation formula of the supercavitating vehicle rudder deflection angle is as follows:

[0163]

[0164] In the above formula, u1 is the first control quantity, u2 is the second control quantity, the first control quantity is the cavitator control quantity of the supercavitating vehicle, and the second control quantity is the rudder deflection angle control quantity in the supercavitating cruise dynamics, v1 is the first control quantity of the sliding mode controller, v2 is the second control quantity of the sliding mode controller, A -1 is the compound decoupling matrix, is the second order Lie derivative of h1(x) to f(x), is the second order Lie derivative of h2(x) to f(x), h1(x) is the first observation, h2(x) is the second observation, and f(x) is the system function.

[0165] In this embodiment, the control center is arranged in the supercavitation vehicle, the cruise supercavitation vehicle dynamics model and the water-entry supercavitation vehicle dynamics model are arranged on the control center, the underwater turning and the cruise stage control module are arranged on the cruise supercavitation vehicle dynamics model and the water-entry supercavitation vehicle dynamics model respectively, and the control center is electrically connected with the tail rudder, so that the control center controls the work of the tail rudder based on the output results of the cruise supercavitation vehicle dynamics model and the water-entry supercavitation vehicle dynamics model, and the navigation control of the supercavitation vehicle is completed.

Claims

1. A method for long-range stable navigation control of a supercavitating vehicle, characterized in that, The method comprises the following steps: S1, obtaining the geometric shape and dynamic parameters of the supercavitation vehicle, and the control target corresponding to the operation stage of the supercavitation vehicle; S2, establishing a cruising supercavitation vehicle dynamics model: Based on the geometric shape and dynamic parameters of the supercavitation vehicle, and the control target corresponding to the operation stage of the supercavitation vehicle, the cruising supercavitation vehicle dynamics model corresponding to the cruising stage is obtained through the exact linearization method of Lie derivative; S3, establishing an entering water supercavitation vehicle dynamics model: Based on the full wet additional force, the entering water supercavitation vehicle dynamics model corresponding to the entering water stage and the underwater turning stage is obtained by improving the cruising supercavitation vehicle dynamics model; S4, designing an underwater turning and cruising stage control module, and controlling the supercavitation vehicle through the underwater turning and cruising stage control module combined with the cruising supercavitation vehicle dynamics model and the entering water supercavitation vehicle dynamics model: Based on the PID controller with time delay term and the sliding mode control method, the underwater turning and cruising stage control module corresponding to the supercavitation vehicle is designed, and the underwater turning and cruising stage control module is respectively loaded on the cruising supercavitation vehicle dynamics model and the entering water supercavitation vehicle dynamics model. In the process of the supercavitation vehicle navigation, the rudder angle deflection of the supercavitation vehicle is calculated by selecting the supercavitation vehicle dynamics model corresponding to the stage where the supercavitation vehicle is located, and the rudder angle deflection is used to control the tail rudder to realize the navigation control of the supercavitation vehicle.

2. The method for long-range stable navigation control of a supercavitating body according to claim 1, characterised in that The most front end of the supercavitation vehicle is fixed with a disc-shaped cavitator, the outer surface of the tail of the vehicle is fixed with four tail rudders, the four tail rudders are composed of two pitch tail rudders and two yaw tail rudders, the two pitch tail rudders are fixed on the left and right sides of the tail of the supercavitation vehicle, the two yaw tail rudders are fixed on the upper and lower sides of the tail of the supercavitation vehicle, the inside of the supercavitation vehicle is provided with an engine, and the engine is electrically connected with the tail rudder.

3. The method for long-range stable navigation control of a supercavitating body according to claim 1, characterised in that The geometric shape and dynamic parameters include: vehicle mass, vehicle total length, vehicle tail length, tail rudder to vehicle center of mass distance, vehicle thrust, vehicle tail rudder flow area, vehicle moment of inertia, vehicle cross section radius, fluid density, fluid resistance coefficient, vehicle cavitator radius, cavitator to vehicle center of mass distance, and cavitator ideal cavitation number. The control target includes: vehicle entering water speed, vehicle cruising depth, and vehicle cruising speed.

4. The method for long-range stable navigation control of a supercavitating body according to claim 1, characterised in that, The operation stage of the supercavitation vehicle includes: entering water stage, underwater turning stage, and cruising stage.

5. The method for long-range stable navigation control of a supercavitating body according to claim 1, characterised in that The step S2 comprises the following steps: S2-1, analyzing and calculating the geometric shape and dynamic parameters of the supercavitation vehicle and the control target to obtain the gravity, thrust, cavitator force, tail rudder force and sliding force received by the vehicle in the cruising stage, and establishing the supercavitation vehicle dynamics model through the center of mass motion equation and the Euler rotation equation; S2-2, on the basis of considering satisfying the engineering small angle approximation, refining the dynamic state variables of the supercavitation vehicle, obtaining the vehicle state equation of the supercavitation vehicle through the dynamic state variables, and then performing accurate linearization on the state equation through the method based on the Lie derivative, obtaining the cruise supercavitation vehicle dynamic model corresponding to the cruise stage.

6. The method for long-range stable navigation control of a supercavitating body according to claim 5, characterized in that The step S2-1 includes the following steps: S2-1-1, analyzing the motion form of the cavitation to generate the cavity, calculating the gravity and thrust of the supercavitation vehicle, calculating the force and torque of the cavitation to the vehicle, and projecting the force and torque of the cavitation to the coordinates of the vehicle in the body coordinate system; S2-1-2, analyzing the motion form of the cavity in the cruise stage, thereby calculating the wetting condition of the vehicle, respectively calculating the wetting coefficients of the tail rudder and the yaw rudder, analyzing the immersion condition of the supercavitation vehicle as a whole, and calculating the tail rudder wetting force of the supercavitation vehicle in the fully immersed and fully wetted area of the vehicle, the tail rudder wetting force being the tail rudder force; S2-1-3, regarding the sliding of the supercavitation vehicle as the flow of free fluid on the surface of a cylinder, thereby representing the sliding force as a vertical flow fluid force on the cylinder and calculating it, and simultaneously calculating the sliding viscous drag force on the supercavitation vehicle; S2-1-4, substituting the calculation results of the gravity, the thrust, the cavitation force, the tail rudder force and the sliding force into the mass center motion equation and the Euler rotation equation, and outputting the supercavitation vehicle dynamic model.

7. The method for long-range stable navigation control of a supercavitating body according to claim 5, characterized in that The step S2-2 includes the following steps: S2-2-1. To simplify the dynamic model of the supercavitating vehicle, the following assumptions are made: Assume the lateral velocity v of the supercavitating vehicle is v. x1 In a steady state, the longitudinal velocity v of the supercavitating vehicle is balanced with and remains constant with engine thrust. y1 Since the ratio of the magnitude to the lateral velocity is less than 0.02, the velocity of the supercavitating vehicle is assumed to be constant during the cruise phase, and only the longitudinal velocity v is considered. y1 The magnitude of the change in angle of attack α of the supercavitating vehicle is approximated by a first order, i.e., sinα≈αcosα≈1 / arctanα≈α. By simplifying the dynamic equations through a small angle approximation, the dynamic state variables describing the supercavitating vehicle are selected as follows: x = [y0 v y1 θ ω] T , In the above equation, x is a kinetic state variable, y0is a depth parameter of the vehicle, v y1 is the speed of the vehicle in the y direction, θ is the pitch angle of the vehicle, and ω is the pitch angular velocity of the vehicle. S2-2-2, the vehicle state equation of the supercavitation vehicle obtained through the dynamic state variables is as follows: In the above formula, x is a kinetic state variable, x = [y0 v y1 θ ω] T , y0 is the depth parameter of the vehicle, v y1 is the speed of the vehicle in the y direction, θ is the pitch angle of the vehicle, ω is the pitch angle velocity of the vehicle, u is the control quantity, u = [δ c δ f / p ] T , δ c is the control quantity of the supercavitating vehicle's cavitator, δ f / p is the control quantity of the supercavitating vehicle's rudder deflection angle, is the derivative of the state variable, y is the observation quantity, f(x) is the system function, b(x) is the control function, and h(x) is the observation function, Each row of the system function f(x) consists of four scalar functions defined on the state vector x, so f(x) = [f1f2 f3 f4] T The 4x2 control matrix can be written as consisting of two vector field functions: b(x) = [b1(x) b2(x)] T The second-order observation function of the supercavitation vehicle state equation is: In the above formula, h(x) is an observation function, h1(x) is a first observation, and h1(x)=x1=y0, h2(x) is a second observation, and h2(x)=x3=θ, x1 is a supercavitation vehicle depth parameter, and x3 is a supercavitation vehicle pitch angle; S2-2-3, calculating the decoupling matrix of the simplified supercavitation vehicle dynamic model by the Lie derivative method, accurately linearizing the supercavitation vehicle dynamic model, and obtaining the cruise supercavitation vehicle dynamic model corresponding to the cruise stage, the decoupling matrix being: In the above formulae, is the second-order Lie derivative of h1(x) with respect to f(x) and b1(x), is the second-order Lie derivative of h1(x) with respect to f(x) and b2(x), is the second-order Lie derivative of h2(x) with respect to f(x) and b1(x), is the second-order Lie derivative of h2(x) with respect to f(x) and b2(x), h1(x) is a first observation, h2(x) is a second observation, f(x) is a system function, b1(x) is a first vector field function, and b2(x) is a second vector field function. The cruise supercavitation vehicle dynamic model corresponding to the cruise stage obtained by accurately linearizing the vehicle state equation through the decoupling matrix is as follows: In the above formula, u1 is the first control quantity, u2 is the second control quantity, is the second order Lie derivative of h1(x) with respect to f(x), is the second order Lie derivative of h2(x) with respect to f(x), h1(x) is the first observation quantity, h2(x) is the second observation quantity, f(x) is the system function, y1 is the observed depth of the supercavitating vehicle, y2 is the observed vertical velocity of the supercavitating vehicle, is the second order derivative of y1, is the second order derivative of y2.

8. The method for long-range stable navigation control of a supercavitating body according to claim 1, characterised in that, The step S3 includes the following contents: Based on the improvement of the water-entry supercavitation vehicle dynamics of the full-wetting additional force, it is assumed that the kinetic energy of the supercavitation vehicle at the time of water entry is converted into the kinetic energy and potential energy of water, thereby deriving the motion state of the cavity in the water entry process of the supercavitation vehicle, and further obtaining the full-wetting condition of the vehicle at water entry, adding the full-wetting buoyancy, the viscous resistance of the fluid and the tail pressure difference to the cruise supercavitation vehicle dynamic model, and obtaining the water-entry supercavitation vehicle dynamic model corresponding to the water-entry stage and the underwater turning stage, the model formula of the water-entry supercavitation vehicle dynamic model being as follows: In the above formula, u1 is the first control variable, u2 is the second control variable, is the second-order Lie derivative of h1(x) with respect to , is the second-order Lie derivative of h2(x) with respect to , is the system function after the system is added with full wetting buoyancy, viscous resistance of fluid, and tail pressure difference, y1 is the observed depth of the supercavitating vehicle, y2 is the observed speed of the supercavitating vehicle in the y direction, is the second-order derivative of y1, is the second-order derivative of y2.

9. The method for long-range stable navigation control of a supercavitating body according to claim 1, characterised in that, The step S4 includes the following steps: S4-1, establish an underwater turning and cruising stage control module capable of simultaneously controlling a PID controller and a sliding mode controller with time delay terms, and load the underwater turning and cruising stage control module on a cruising supercavitating vehicle dynamics model and a water-entry supercavitating vehicle dynamics model, respectively; S4-2, when the supercavitating vehicle is in the water-entry stage and the underwater turning stage, the underwater turning and cruising stage control module outputs a control amount of a rudder angle deflection amount of the supercavitating vehicle by the PID controller with time delay terms, inputs the water-entry supercavitating vehicle dynamics model, obtains the rudder angle deflection amount of the supercavitating vehicle, controls the tail rudder to work through the rudder angle deflection amount, and realizes water-entry and underwater turning control of the supercavitating vehicle, and a calculation formula of the control amount of the PID controller with time delay terms is as follows: In the above formula, δ(t) is the control angle of the tail fin at time t, θ c (t) is the deviation of the pitch angle at time t from the expectation, is the derivative of the deviation of the pitch angle at time t from the expectation, K p is the PID control proportional parameter, K d is the PID control derivative parameter, K i is the PID control integral parameter, t is time, t0 is the time delay, which is the time from the birth of the cavity to the movement of the cavity to the tail of the supercavitating vehicle, i.e. In the above formula, t0 is a time delay, L is the length of the supercavitating vehicle, and V is the speed of the supercavitating vehicle.

10. The method for long-range stable navigation control of a supercavitating body according to claim 8, characterised in that The step S4 further comprises the following steps: S4-3, the underwater turning and cruising stage control module configures a sliding mode controller for each of two observation quantities y1 and y2 of the cruising supercavitating vehicle dynamics model based on the sliding mode controller through a linear sliding mode method, and a linear sliding mode structure formula provided by the sliding mode controller is as follows: In the above formula, s(x) is a linear sliding mode structure, a i is a first parameter determined by the second Lyapunov stability theory, b i is a second parameter determined by the second Lyapunov stability theory, e i is a deviation of an observation value from an expected value, and a Lyapunov function determined by s(x) is: and In the above equation, Y is a Lyapunov function, is the derivative of the Lyapunov function, s i (x) is the i-th linear sliding mode structure, is the derivative of the i-th linear sliding mode structure; Configuring a constant sliding mode approach rate where v is a velocity parameter that controls the sliding mode rate, and sgn is the sign function. S4-4, an improved sign function sgn*(x) is defined to improve the sign function sgn to improve the stability performance of the sliding mode controller, and a formula of the improved sign function is as follows: In the above equation, sgn*(x) is an improved sign function, x is an input parameter of the sign function, and Q is an improved parameter of the sign function, with a value range of 0 < Q < 10 -3 ; S4-5, the sliding mode control amount is compounded with a decoupling matrix, and the compounded result is input into the cruising supercavitating vehicle dynamics model as a control amount of a rudder angle deflection amount of the supercavitating vehicle, the cruising supercavitating vehicle dynamics model is compounded by a second-order Lie derivative coupling amount part and a sliding mode control amount part, a rudder angle deflection amount of the supercavitating vehicle is obtained, the tail rudder is controlled to work through the rudder angle deflection amount, and cruising control of the supercavitating vehicle is realized, and a calculation formula of the control amount of the rudder angle deflection amount of the supercavitating vehicle is as follows: In the above formula, u1 is the first control quantity, u2 is the second control quantity, the first control quantity is the cavitator control quantity of the supercavitating vehicle, the second control quantity is the rudder deflection angle control quantity in the supercavitating cruise dynamics, v1 is the first control quantity of the sliding mode controller, v2 is the second control quantity of the sliding mode controller, A -1 is a composite decoupling matrix, is the second-order Lie derivative of h1(x) with respect to f(x), is the second-order Lie derivative of h2(x) with respect to f(x), h1(x) is the first observation quantity, h2(x) is the second observation quantity, and f(x) is a system function.

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