Path tracking sliding mode control method based on preset performance function

Abstract

The invention discloses a path tracking sliding mode control method based on a preset performance function. The path tracking sliding mode control method based on the preset performance function comprises the following steps: defining an error value of a course angle; constructing a preset performance function, and obtaining an error value of the converted course angle based on the constructed preset performance mapping and the defined error value of the course angle; setting a sliding film surface; and obtaining control input parameters based on the error value of the converted course angle and the sliding mode surface through a backstepping method. Path tracking control is realized based on combination of sliding mode surface control and preset performance, and convergence speed and overshoot can be controlled.

Description

Technical Field

[0001] The present application relates to the field of ship motion control, and in particular to a path tracking sliding mode control method based on a preset performance function. Background Art

[0002] In the field of navigation, the path tracking control system consists of three subsystems: guidance, control and navigation. Figure 1 The guidance system can automatically construct a heading reference signal based on the positional relationship between the current attitude of the ship and the expected path; the control system can achieve effective convergence by stabilizing the error between the current attitude and the heading reference signal; the navigation system can transmit the position and attitude information of the controlled object to the guidance system and control system through sensors.

[0003] At present, there are problems such as underactuation, uncertainty of system internal dynamics and external disturbance, and control input saturation in the path tracking control of ships. Therefore, the prior art proposes a nonlinear dynamic model of underactuated ships. The nonlinear dynamic model of underactuated ships is shown in Equations (1) and (2).

[0004] (1) (2); in, x Indicates the abscissa value of the ship; Represents the time first derivative of the ship's abscissa value; y Indicates the vertical coordinate value of the ship, represents the time first derivative of the ordinate value of the ship; Ψ Indicates the heading angle of the ship; Represents the time first-order derivative of the ship's heading angle; ( x , y , Ψ ) represents the position coordinates and heading angle of the ship; u Indicates the vertical speed; represents the time first derivative of the surge velocity; v Indicates the sway speed; represents the time first derivative of the sway velocity; r represents the yaw angular velocity; It represents the time first derivative of the yaw angular velocity; m u represents the additional mass on the longitudinal freedom degree; m v represents the additional mass in the sway degree of freedom; m r represents the additional mass on the pitching degree of freedom; d wi Indicates the interference force of the external environment.i = u , v , r ;in, d wu It indicates the interference force on the longitudinal freedom degree of the external environment; d wv It represents the disturbance force on the lateral freedom degree of the external environment; d wr Indicates the disturbance force of the external environment on the yaw freedom; f u (v) Represents the nonlinear terms on the longitudinal degrees of freedom in the model; f v (v) Represents the nonlinear terms on the sway degrees of freedom in the model; f r (v) Represents the nonlinear term on the yaw degree of freedom in the model; represents the control input parameters of the propeller; Indicates the control input parameters of the servo.

[0005] Furthermore, the prior art proposes to solve the tracking control problem of real ships and virtual ships in marine engineering by using a robust neural damping adaptive control algorithm. The robust neural damping adaptive control algorithm is a control algorithm widely used in shipborne automatic pilots.

[0006] The robust neural damping adaptive control algorithm is mainly constructed by dynamic surface control (DSC), minimum parameter learning method and adaptive parameters.

[0007] DSC is a method applied to the first-order derivative of the error to prevent the problem of parameter explosion. Its principle is to pass the virtual control law through a filter instead of directly deriving the virtual control law, as shown in formula (3).

[0008] (3); in, ε u Represents the filter time constant, usually a positive number; α u represents the designed virtual control law, β u represents the virtual control law after filtering, which is used as the final output virtual control law; represents the time first-order derivative of the virtual control law after filtering; β u (0) represents the initial filtered virtual control law, that is, the filtered virtual control law at time 0;α u (0) represents the initial virtual control law, that is, the virtual control law at time 0. DSC technology solves the problem of complex parameters generated when deriving the virtual control law.

[0009] The minimum parameter learning method compresses multiple parameters and simplifies the remaining terms in the neural network function, making its form more concise, as shown in Equation (4) and Equation (5), which is conducive to the design of the controller under the introduction of the neural network function.

[0010] (4); (5); in, S u ( u ), A u 、β u is taken as the remainder of the three neural network functions, d u represents a constant related to the mass of the ship, express ε u The upper bound value of .

[0011] The design of adaptive parameters is to facilitate the definition of stability in the sense of Lyapunov. The adaptive parameters are not static during the control process, they will be updated in real time and are auxiliary adjustments and corrections made to the controller.

[0012] The main idea of ​​the existing robust neural damping adaptive technology is to calculate the control signal through the track deviation, guide the actual ship to follow the virtual ship through heading control and speed control, and indirectly guide the ship formation to sail along the planned reference path to achieve path tracking control. In recent years, domestic and foreign scholars have done a lot of research work on underactuated ship path tracking control.

[0013] However, the existing robust neural damping adaptive control algorithm has some defects. For example, for the transient convergence performance and steady-state performance of the system, the existing robust neural damping algorithm cannot ensure the requirements of performance indicators such as convergence speed, overshoot, and steady-state error in engineering; for another example, when designing the controller, the existing robust neural damping algorithm needs to stabilize the position error first, and then stabilize the speed error. The process is cumbersome and the calculation load is relatively large. The sliding surface defined in the sliding surface control includes both the speed error and the position error, but the traditional sliding mode control has a long time for the system state to reach the sliding surface, and a more obvious overshoot may occur when it just reaches the sliding surface.

[0014] Therefore, an optimized path tracking sliding mode control method is needed. Summary of the invention

[0015] An advantage of the present application is that it provides a path tracking sliding mode control method based on a preset performance function, wherein the path tracking sliding mode control method based on the preset performance function can control the convergence speed and overshoot.

[0016] Another advantage of the present application is that it provides a path tracking sliding mode control method based on a preset performance function, wherein the path tracking sliding mode control method based on the preset performance function simultaneously stabilizes the position error and the speed error through the logarithmic sliding surface, simplifies the control steps, and reduces the calculation load.

[0017] Another advantage of the present application is that it provides a path tracking sliding mode control method based on a preset performance function, wherein the path tracking sliding mode control based on the preset performance function specifies the transient convergence performance and steady-state performance of the system by introducing preset performance control, thereby ensuring the requirements for performance indicators such as convergence speed, overshoot, and steady-state error in the project.

[0018] According to one aspect of the present application, a path tracking sliding mode control method based on a preset performance function is provided, which comprises the steps of: Define the error value of the heading angle; Constructing a preset performance function, and obtaining a transformed heading angle error value based on the constructed preset performance map and the defined heading angle error value; Setting the synovial surface; and The control input parameters are obtained based on the error value of the transformed heading angle and the sliding membrane surface by backstepping method; in, ,in, E ѱ Indicates the error value of the transformed heading angle; ѱ e Indicates the error value of the defined heading angle; ρ ( t ) represents the preset performance function, ; ѱ 0，i represents the error of the initial preset performance function; ѱ 0，∞ represents the error of the final preset performance function; the constraint condition of the error value of the transformed heading angle is: ; The synovial surface is defined as: ;in, S ѱ Indicates synovial surface; k 1 is a set constant and a positive number; Indicates the value of the time first derivative of the error value of the transformed heading angle.

[0019] In one embodiment of the path tracking sliding mode control method based on a preset performance function according to the present application, in the process of defining the error value of the heading angle, Define the error value of the heading angle, where: ѱ e Indicates the error value of the defined heading angle; ѱ d Indicates the azimuth of the virtual ship relative to the actual ship; Ψ Indicates the heading angle of the ship.

[0020] In one embodiment of the path tracking sliding mode control method based on a preset performance function described in the present application, by The azimuth of the virtual ship relative to the actual ship is calculated; where: x e Indicates the coordinate error between the virtual ship and the actual ship in the longitudinal freedom degree; y e Indicates the coordinate error between the virtual ship and the actual ship in the swaying degree of freedom; ,in, x d Indicates the horizontal coordinate value of the virtual ship; x Indicates the abscissa value of the ship; ,in, y d Indicates the vertical coordinate value of the virtual ship; y Indicates the vertical coordinate value of the ship.

[0021] In one embodiment of the path tracking sliding mode control method based on a preset performance function according to the present application, the path tracking sliding mode control method based on a preset performance function further comprises the steps of: using a radial basis function neural network to approximate the nonlinear term; wherein, in the process of using the radial basis function neural network to approximate the nonlinear term, the nonlinear term on the yaw degree of freedom in the model is introduced into the neural network processing system, wherein, ;in, represents the nonlinear term on the yaw degree of freedom in the model; Represents the estimated weights of the neural network; S ( r ) represents the damping function of the neural network; ε ( r ) represents the random approximation error.

[0022] In one embodiment of the path tracking sliding mode control method based on a preset performance function according to the present application, the path tracking sliding mode control method based on a preset performance function further includes the step of filtering the time second-order derivative of the error value of the transformed heading angle through a first-order filter, wherein the first-order filter is designed as: ;in, t ѱ is the time constant; ε ѱ represents the value after first-order filtering of the time second-order derivative of the error value of the transformed heading angle; represents the time first-order derivative of the value obtained by first-order filtering the time second-order derivative of the error value of the transformed heading angle; Represents the time second derivative of the error value of the transformed heading angle; where, , ε ѱ (0) means ε ѱ The initial value of express The initial value of; the error produced by the first-order filter is defined as: ; Represents the error produced by a first-order filter.

[0023] In one embodiment of the path tracking sliding mode control method based on a preset performance function according to the present application, the path tracking sliding mode control method based on a preset performance function further includes the step of: setting a Lyapunov stability equation, wherein the Lyapunov stability equation is: ;in, V represents the function value of the Lyapunov stability equation.

[0024] In one embodiment of the path tracking sliding mode control method based on a preset performance function described in the present application, by Get the control input parameters; where, Indicates the control input parameters of the ship in the turning direction; m r represents the model parameters on the yaw degree of freedom; k 2 is a set control parameter, which is a constant and a positive number; d wr represents the environmental disturbance parameter on the yaw degree of freedom; where, ;in, k r is a set control parameter, a constant, and a positive number; σ r is a set control parameter, which is a constant; Represents the initial value of the neural network's weight estimate; Represents the time first derivative of the neural network's weight estimates.

[0025] In one embodiment of the path tracking sliding mode control method based on a preset performance function according to the present application, before constructing the preset performance function, the path tracking sliding mode control method based on the preset performance function further includes the steps of: setting parameters of the path tracking experiment; and constructing a mathematical model of the motion of an underactuated ship, wherein the mathematical model of the motion of an underactuated ship is: ; in, Ψ Indicates the heading angle of the ship; Represents the time first-order derivative of the ship's heading angle; r represents the yaw angular velocity; It represents the time first derivative of the yaw angular velocity; u Indicates the vertical speed; represents the time first derivative of the surge velocity; m u represents the additional mass on the longitudinal freedom degree; m r represents the additional mass on the pitching degree of freedom; d wu It indicates the interference force on the longitudinal freedom degree of the external environment; d wr Indicates the disturbance force of the external environment on the yaw freedom; represents the nonlinear term on the sway degrees of freedom in the model; represents the nonlinear term on the yaw degree of freedom in the model; Indicates the control input parameters of the ship in the forward direction; Indicates the input parameters for controlling the ship in the turning direction.

[0026] In one embodiment of the path tracking sliding mode control method based on a preset performance function according to the present application, the parameters of the path tracking experiment include a turning speed, and the turning speed is: ;in, r d ( t ) represents the turning speed.

[0027] Further objectives and advantages of the present application will be fully reflected through understanding of the following description and drawings.

[0028] These and other objects, features and advantages of the present application are fully reflected in the following detailed description, drawings and claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] By describing the embodiments of the present application in more detail in conjunction with the accompanying drawings, the above and other purposes, features and advantages of the present application will become more apparent. The accompanying drawings are used to provide a further understanding of the embodiments of the present application and constitute a part of the specification. Together with the embodiments of the present application, they are used to explain the present application and do not constitute a limitation of the present application. In the drawings, the same reference numerals generally represent the same components.

[0030] Figure 1 The figure shows a schematic block diagram of the composition structure of the path tracking control system.

[0031] Figure 2 A flowchart schematic diagram of a path tracking sliding mode control method based on a preset performance function according to an embodiment of the present application is illustrated.

[0032] Figure 3 A flowchart schematic diagram of a specific example of a path tracking sliding mode control method based on a preset performance function according to an embodiment of the present application is illustrated.

[0033] Figure 4 A schematic diagram of a two-dimensional view of environmental interference in a simulation environment is shown.

[0034] Figure 5 A schematic diagram showing a 3D view of irregular ocean waves in the simulation environment.

[0035] Figure 6 The figure shows a schematic diagram of a path tracking control effect diagram corresponding to a path tracking sliding mode control method based on a preset performance function according to an embodiment of the present application under simulation conditions.

[0036] Figure 7 The figure shows a schematic diagram of a control input parameter change diagram of a path tracking sliding mode control method based on a preset performance function according to an embodiment of the present application under simulation conditions.

[0037] Figure 8 The figure shows a schematic diagram of the error value change of the heading angle defined by the path tracking sliding mode control method based on a preset performance function according to an embodiment of the present application under simulation conditions. DETAILED DESCRIPTION

[0038] Below, the exemplary embodiments according to the present application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application, and it should be understood that the present application is not limited to the exemplary embodiments described here.

[0039] It is understood that the term "one" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "one" cannot be understood as a limitation on the number. "Multiple" means greater than or equal to two.

[0040] Although ordinals such as "first," "second," and the like will be used to describe various components, those components are not limited herein. The term is used only to distinguish one component from another. For example, a first component may be referred to as a second component, and likewise, a second component may be referred to as a first component without departing from the teachings of the present application. The term "and / or" as used herein includes any and all combinations of one or more associated listed items.

[0041] The terms used herein are only used for the purpose of describing various embodiments and are not intended to be limiting. As used herein, the singular form is intended to include the plural form, unless the context clearly indicates an exception. It will also be understood that the terms "including" and / or "having" when used in this specification specify the presence of the described features, numbers, operations, components, elements, or combinations thereof, without excluding the presence or addition of one or more other features, numbers, operations, components, elements, or combinations thereof.

[0042] Glossary Surge: The translational movement of a ship in the forward (bow) and aft (stern) directions.

[0043] Sway: The translation of a ship to the left (port side) or right (starboard side).

[0044] Yaw pitch: The left-right swaying of the bow of a ship.

[0045] Surge speed: the translational speed of a ship in the fore-and-aft direction.

[0046] Sway speed: the translation speed of the ship in the left and right directions.

[0047] Yaw speed: the angular velocity of the ship in the left and right directions.

[0048] Schematic diagram of a path-following sliding mode control method based on a preset performance function like Figures 2 to 8 As shown, the path tracking sliding mode control method based on the preset performance function according to the embodiment of the present application is explained. Taking into account the fact of "underactuated ships" in the practice of ship control engineering, the path tracking sliding mode control method based on the preset performance function proposes to realize path tracking control based on the combination of sliding surface control and preset performance, which can control the convergence speed and overshoot, and is suitable for unmanned ship heading keeping control tasks.

[0049] Accordingly, if Figure 2 As shown, the path tracking sliding mode control method based on a preset performance function according to an embodiment of the present application includes the following steps: S110, defining the error value of the heading angle; S120, constructing a preset performance function, and obtaining the error value of the transformed heading angle based on the constructed preset performance mapping and the defined error value of the heading angle; S130, setting the sliding film surface; S140, obtaining the control input parameters based on the error value of the transformed heading angle and the sliding film surface through the backstepping method.

[0050] In step S110, the error value of the heading angle is defined. Specifically, in the process of defining the error value of the heading angle, the error value of the heading angle is defined to be equal to the azimuth of the virtual ship relative to the actual ship. Accordingly, in the process of defining the error value of the heading angle, Define the error value of the heading angle, where: ѱ e Indicates the error value of the defined heading angle; ѱ d Indicates the azimuth of the virtual ship relative to the actual ship; Ψ Indicates the heading angle of the ship.

[0051] pass The azimuth of the virtual ship relative to the actual ship is calculated; where: x e Indicates the coordinate error between the virtual ship and the actual ship in the longitudinal freedom degree; y e Indicates the coordinate error between the virtual ship and the actual ship in the swaying degree of freedom. x e ) is about x e The sign function of . x e When greater than 0, sign( x e ) is equal to 1, when x e When equal to 0, sign( x e ) is equal to 0, when x e When less than 0, sign( x e ) is equal to -1. sign( y e ) is about y e The sign function of . y e When greater than 0, sign( y e ) is equal to 1, when ye When equal to 0, sign( y e ) is equal to 0, when y e When less than 0, sign( y e ) is equal to -1. is the inverse tangent function of , which represents the tangent value The corresponding angle. ,in, x d represents the horizontal coordinate value of the virtual ship, that is, the coordinate value of the virtual ship in the longitudinal freedom degree; x It represents the abscissa value of the ship, that is, the coordinate value of the ship in the longitudinal freedom degree; ,in, y d represents the ordinate value of the virtual ship, that is, the coordinate value of the virtual ship in the swaying degree of freedom; y It represents the longitudinal coordinate value of the ship, that is, the coordinate value of the ship in the heave degree of freedom.

[0052] like Figure 2 and Figure 3 As shown, before step S120, it is necessary to set the parameters of the path tracking experiment and construct the mathematical model of the motion of the underactuated ship. Accordingly, before constructing the preset performance function, the path tracking sliding mode control method based on the preset performance function also includes the steps of: S150, setting the parameters of the path tracking experiment; and S160, constructing the mathematical model of the motion of the underactuated ship.

[0053] Specifically, in an example of the present application, the parameters of the path tracking experiment include a turning speed, and the turning speed is: ; in, r d ( t ) indicates the turning speed. Timing is carried out from the start of the ship's movement. The turning speed is 0 degrees / s in the time period of 0 seconds or more and less than 50 seconds and in the time period of 130 seconds or more and less than 170 seconds; the turning speed is -0.06 degrees / s in the time period of 50 seconds or more and less than 90 seconds; and the turning speed is 0.06 degrees / s in the time period of 90 seconds or more and less than 130 seconds.

[0054] The mathematical model of underactuated ship motion is: ; in, Ψ Indicates the heading angle of the ship; Represents the time first-order derivative of the ship's heading angle; rrepresents the yaw angular velocity; It represents the time first derivative of the yaw angular velocity; u Indicates the vertical speed; represents the time first derivative of the surge velocity; m u represents the additional mass on the longitudinal freedom degree; m r represents the additional mass on the pitching degree of freedom; d wu It indicates the interference force on the longitudinal freedom degree of the external environment; d wr Indicates the disturbance force of the external environment on the yaw freedom; represents the nonlinear term on the sway degrees of freedom in the model; represents the nonlinear term on the yaw degree of freedom in the model; Indicates the control input parameters of the ship in the forward direction; Indicates the input parameters for controlling the ship in the turning direction.

[0055] In step S120, a preset performance function is constructed. Specifically, in order to simplify the controller design and ensure the transient stability of the system, the present invention introduces a preset performance control, which defines a smooth, bounded, strictly monotonically decreasing preset time-varying function with respect to time: ρ ( t ), as a preset performance function. ; ѱ 0，i The error representing the initial preset performance function is the angle value preset by the user; ѱ 0，∞ The error representing the final preset performance function is an angle value preset by the user.

[0056] The constraint condition of the error value of the transformed heading angle is: . ,in, E ѱ Indicates the error value of the transformed heading angle; ѱ e Indicates the error value of the defined heading angle.

[0057] This application specifies the transient convergence performance and steady-state performance of the system by introducing preset performance control, ensuring the requirements for performance indicators such as convergence speed, overshoot, and steady-state error in the project.

[0058] In step S130, a sliding surface is set. Specifically, for the existing robust neural damping algorithm, the present application proposes to replace the existing robust neural damping algorithm with a logarithmic sliding surface control algorithm to simultaneously stabilize the position error and the velocity error, simplify the control steps, and reduce the computational load. Furthermore, the present application improves the traditional sliding surface, and the defined logarithmic sliding surface simplifies the design of the controller while ensuring the dynamic quality of the system. The logarithmic sliding surface defined in the present application can ensure that when the error approaches 0, the sliding surface also approaches 0, while ensuring the convergence speed, the amplitude of the overshoot is limited.

[0059] More specifically, in this application, the synovial surface is defined as: ; is the logarithmic synovial surface, where S ѱ Represents the synovial surface, which is an angle value; k 1 is a set constant and a positive number; Indicates the value of the time first derivative of the error value of the transformed heading angle.

[0060] In the embodiment of the present application, before step S140, the path tracking sliding mode control method based on the preset performance function further includes step: S170, using a radial basis function neural network to approximate the nonlinear term. In the process of using the radial basis function neural network to approximate the nonlinear term, the nonlinear term on the yaw degree of freedom in the model is introduced into the neural network processing system, wherein: ;in, represents the nonlinear term on the yaw degree of freedom in the model; Represents the estimated weights of the neural network; S ( r ) represents the damping function of the neural network; ε ( r ) represents the random approximation error. In the process of using radial basis neural network to approximate nonlinear terms, the nonlinear terms on the swaying degrees of freedom in the model can also be Introducing the neural network processing system.

[0061] Taking the derivative of the sliding surface, we can get: ;in, represents the time first derivative of the synovial surface; The value of the time second derivative of the error value of the transformed heading angle.

[0062] In order to simplify the controller design, this application designs a first-order filter to reduce the calculation load.

[0063] Accordingly, the path tracking sliding mode control method based on the preset performance function further includes the step: S180, filtering the time second-order derivative of the error value of the transformed heading angle through a first-order filter, wherein the first-order filter is designed as: ;in, t ѱ is the time constant; ε ѱ represents the value after first-order filtering of the time second-order derivative of the error value of the transformed heading angle; represents the time first-order derivative of the value obtained by first-order filtering the time second-order derivative of the error value of the transformed heading angle; Represents the time second derivative of the error value of the transformed heading angle; where, , ε ѱ (0) means ε ѱ The initial value of express The initial value of; the error produced by the first-order filter is defined as: ; Represents the error produced by a first-order filter.

[0064] The path tracking sliding mode control method based on the preset performance function further includes the step: S190, setting the Lyapunov stability equation, wherein the Lyapunov stability equation is: ;in, V represents the function value of the Lyapunov stability equation.

[0065] In step S140, the control input parameter is obtained based on the error value of the transformed heading angle and the sliding membrane surface by backstepping. Get the control input parameters; where, Indicates the control input parameters of the ship in the turning direction; m r represents the model parameters on the yaw degree of freedom; k 2 is a set control parameter, which is a constant and a positive number; d wr represents the environmental disturbance parameter on the yaw degree of freedom; where, ;in, k r is a set control parameter, a constant, and a positive number; σ r is a set control parameter, which is a constant; Represents the initial value of the neural network's weight estimate; Represents the time first derivative of the neural network's weight estimates.

[0066] In order to verify the effectiveness of the path tracking sliding mode control method based on the preset performance function of the embodiment of the present application, a computer simulation experiment was performed using Matrix&laboratory (matlab). In the computer simulation experiment, an underactuated boat with a length of 38m and a displacement of 1.18*105kg was used as the controlled object. The initial motion state of the unmanned boat was set as: ,in, x (0) represents the initial abscissa value of the ship; y (0) represents the initial ordinate value of the ship; Ψ (0) represents the initial heading angle of the ship; r (0) represents the initial yaw angular velocity. The desired path tracking speed is set to u d =4.7m / s. The turning speed of the unmanned ship is set to: .

[0067] The level-four wind and wave mechanism model used in the simulation environment can be found in the book “Handbook of Marine Craft Hydrodynamics and Motion Control”, which was written by Thor I. Fossen and published on April 8, 2011.

[0068] Figures 4 to 8 The simulation structure of path tracking control under level 4 sea conditions simulated on the MATLAB simulation platform is demonstrated. Figure 4 A 2D view of the environmental disturbances in the simulation environment is shown. Figure 5 A 3D view showing irregular ocean waves in the simulation environment. Figure 6 The two-dimensional trajectory of the unmanned ship under the proposed preset performance sliding surface control is shown. Figure 6 It can be seen that under the proposed preset performance sliding surface control, the trajectory of the unmanned ship is basically consistent with the reference path of the unmanned ship, and the tracking effect is good. Figure 7 Display the control input parameters of the unmanned ship . Figure 8 The tracking error of the unmanned ship is shown, that is, the error value of the defined heading angle ѱ e .Depend on Figure 8 It can be seen that the convergence speed and overshoot are both within the proposed preset performance boundaries.

[0069] Combined with the above verification experiments, the path tracking sliding mode control method based on the preset performance function of the embodiment of the present application can control the convergence speed and overshoot, and realize path tracking more accurately.

[0070] The present application and its implementation methods are described above, and such description is not restrictive. The drawings show only one implementation method of the present application, and the actual structure is not limited thereto. In short, if ordinary technicians in the field are inspired by it and design structural methods and embodiments similar to the technical solution without creative design without departing from the inventive purpose of the present application, they should all fall within the protection scope of the present application.

Claims

1. A path tracking sliding mode control method based on a preset performance function, characterized in that: Includes steps: Define the error value of the heading angle; Constructing a preset performance function, and obtaining a transformed heading angle error value based on the constructed preset performance map and the defined heading angle error value; Set the synovial surface; as well as The control input parameters are obtained based on the error value of the transformed heading angle and the sliding membrane surface by backstepping method; in, ,in, E ѱ Indicates the error value of the transformed heading angle; ѱ e Indicates the error value of the defined heading angle; ρ ( t ) represents the preset performance function, ; ѱ 0，i represents the error of the initial preset performance function; ѱ 0，∞ represents the error of the final preset performance function; the constraint condition of the error value of the transformed heading angle is: ; The synovial surface is defined as: ;in, S ѱ Indicates synovial surface; k 1 is a set constant and a positive number; Indicates the value of the time first derivative of the error value of the transformed heading angle.

2. The path tracking sliding mode control method based on a preset performance function according to claim 1, characterized in that: In the process of defining the error value of the heading angle, Define the error value of the heading angle, where: ѱ e Indicates the error value of the defined heading angle; ѱ d Indicates the azimuth of the virtual ship relative to the actual ship; Ψ Indicates the heading angle of the ship.

3. The path tracking sliding mode control method based on a preset performance function according to claim 2, characterized in that: pass The azimuth of the virtual ship relative to the actual ship is calculated; where: x e Indicates the coordinate error between the virtual ship and the actual ship in the longitudinal freedom degree; y e Indicates the coordinate error between the virtual ship and the actual ship in the swaying degree of freedom; ,in, x d Indicates the horizontal coordinate value of the virtual ship; x Indicates the abscissa value of the ship; ,in, y d Indicates the vertical coordinate value of the virtual ship; y Indicates the vertical coordinate value of the ship.

4. The path tracking sliding mode control method based on a preset performance function according to claim 1, characterized in that: The path tracking sliding mode control method based on the preset performance function also includes the steps of: using a radial basis function neural network to approximate the nonlinear term; wherein, in the process of using the radial basis function neural network to approximate the nonlinear term, the nonlinear term on the yaw degree of freedom in the model is introduced into the neural network processing system, wherein, ;in, represents the nonlinear term on the yaw degree of freedom in the model; Represents the estimated weights of the neural network; S ( r ) represents the damping function of the neural network; ε ( r ) represents the random approximation error.

5. The path tracking sliding mode control method based on a preset performance function according to claim 4, characterized in that: The path tracking sliding mode control method based on the preset performance function also includes the step of filtering the time second-order derivative of the error value of the transformed heading angle through a first-order filter, wherein the first-order filter is designed as follows: ;in, t ѱ is the time constant; ε ѱ represents the value after first-order filtering of the time second-order derivative of the error value of the transformed heading angle; represents the time first-order derivative of the value obtained by first-order filtering the time second-order derivative of the error value of the transformed heading angle; Represents the time second derivative of the error value of the transformed heading angle; where, , ε ѱ (0) means ε ѱ The initial value of express The initial value of; the error produced by the first-order filter is defined as: ; Represents the error produced by a first-order filter.

6. The path tracking sliding mode control method based on a preset performance function according to claim 5, characterized in that: The path tracking sliding mode control method based on the preset performance function also includes the step of setting a Lyapunov stability equation, wherein the Lyapunov stability equation is: ;in, V represents the function value of the Lyapunov stability equation.

7. The path tracking sliding mode control method based on a preset performance function according to claim 6, characterized in that: pass Get the control input parameters; where, Indicates the control input parameters of the ship in the turning direction; m r represents the model parameters on the yaw degree of freedom; k 2 is a set control parameter, which is a constant and a positive number; d wr represents the environmental disturbance parameter on the bow pitch degree of freedom; where, ;in, k r is a set control parameter, a constant, and a positive number; σ r is a set control parameter, which is a constant; Represents the initial value of the neural network's weight estimate; Represents the time first derivative of the neural network's weight estimates.

8. The path tracking sliding mode control method based on a preset performance function according to claim 1, characterized in that: Before constructing the preset performance function, the path tracking sliding mode control method based on the preset performance function further includes the steps of: Set the parameters of the path tracking experiment; and The mathematical model of the motion of an underactuated ship is constructed, wherein the mathematical model of the motion of an underactuated ship is: ； in, Ψ Indicates the heading angle of the ship; Represents the time first-order derivative of the ship's heading angle; r represents the yaw angular velocity; It represents the time first derivative of the yaw angular velocity; u Indicates the vertical speed; represents the time first derivative of the surge velocity; m u represents the additional mass on the longitudinal freedom degree; m r represents the additional mass on the pitching degree of freedom; d wu It indicates the interference force on the longitudinal freedom degree of the external environment; d wr Indicates the disturbance force of the external environment on the yaw freedom; represents the nonlinear term on the sway degrees of freedom in the model; represents the nonlinear term on the yaw degree of freedom in the model; Indicates the control input parameters of the ship in the forward direction; Indicates the input parameters for controlling the ship in the turning direction.

9. The path tracking sliding mode control method based on a preset performance function according to claim 8, characterized in that: The parameters of the path tracking experiment include the turning speed, which is: ； in, r d ( t ) represents the turning speed.

Images