CN110989628A - CFD-based under-actuated surface ship course control method - Google Patents
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Abstract
The invention belongs to the field of ship hydrodynamic force and ship control, and particularly relates to a CFD-based under-actuated surface ship course control method. The method comprises four parts of CFD numerical analysis, hydrodynamic calculation, mathematical modeling and stabilization control design, wherein a three-degree-of-freedom mathematical model of the under-actuated ship is established through hydrodynamic equation analysis and hydrodynamic derivative calculation, so that a propulsion moment matrix control law and a steering force matrix control law are obtained, and the course angle of the under-actuated ship is controlled by adopting a stabilization control method. The invention provides a simple and effective solution to the problem of course control of an under-actuated ship with an unknown model, and can observe the state change of the under-actuated ship in the control process to realize rapid and stable course control.
Description
Technical Field
The invention belongs to the field of ship hydrodynamic force and ship control, and particularly relates to a CFD-based under-actuated surface ship course control method.
Background
In recent years, with the continuous development of the fields of machinery, control, electricity and the like, the ship industry has also been developed at a high speed, and high-technology smart ships have become the main direction of development in the ship field. The intelligent ship controls the navigation process of the ship by technical methods such as a sensor, shore-based communication, GPS positioning and the like and combining technologies such as a computer, automatic control and the like, so that the ship is safer and more reliable, and most of the existing intelligent ships are under-actuated ships.
The under-actuated ship is a ship with the input dimension of a control system smaller than the degree of freedom, and is reflected in the practical application that the under-actuated ship only has a longitudinal propulsion device and a rudder, lacks a lateral propulsion device and needs to utilize two independent control inputs to simultaneously control the motion of three degrees of freedom.
The motion control of the under-actuated ship is a hotspot and a difficulty in the field of ship control, and the realization of the motion control of the under-actuated ship is beneficial to deepening the understanding of a nonlinear under-actuated system. For an under-actuated ship, currently, the commonly used control methods are point stabilization control, model prediction control, adaptive control method and the like, but the establishment of a ship mathematical model cannot be separated in the control methods.
The water surface ship is a complex control system, and the main control difficulty of the water surface ship is that an accurate and effective mathematical model of the water surface ship is difficult to establish. Before a controller of a ship is designed, a mathematical model of ship motion needs to be obtained through calculation and analysis, and establishment of an accurate mathematical model is a premise for researching ship motion characteristics and a premise for designing a control system.
In the field of ships, most modeling methods are maneuverability experimental methods, namely a method for obtaining K, T parameters of a ship through rotation and Z-shaped maneuvering experiments of a real ship, further obtaining a transfer function of the K, T parameters and finally obtaining a ship mathematical model.
Computational Fluid Dynamics (CFD) is a method of simulating a motion process of a target object by a computer numerical simulation method to obtain various numerical values in the motion process. The simulation method has the advantages of good simulation effect and low calculation cost, and has good application prospect, so that the simulation method is widely applied to simulation research in the field of ship kinematics in recent years. Similar patents are not found through the search of the existing method. Therefore, the CFD-based course control method of the under-actuated surface craft has certain prospect.
Disclosure of Invention
The invention aims to provide a CFD-based under-actuated surface ship course control method for solving the problem of unknown under-actuated ship course control of a mathematical model.
The purpose of the invention is realized by the following technical scheme: the method comprises the following steps:
step 1: establishing a three-degree-of-freedom motion model of the under-actuated surface ship;
the following assumed conditions are adopted for the under-actuated surface ship: ignoring the pitch, roll and heave motions of the surface vessel, i.e. z is 0, ω is 0, Φ is 0, p is 0, θ is 0, q is 0; the gravity center of the ship is assumed to be coincident with the origin of the follow-up coordinate system, and the mass distribution of the ship body is uniform; the vessel being symmetrical about a longitudinal vertical plane x-o-z and a lateral vertical plane y-o-z, i.e. the moment of inertia Ixy＝Iyz＝0；
The three-degree-of-freedom motion model of the under-actuated surface ship can be expressed as follows:
wherein η ═ x y ψ]TRespectively representing the longitudinal position, the transverse position and the heading angle of the ship; v ═ u v r]TRespectively representing the longitudinal speed, the transverse speed and the heading angular speed of the ship; τ ═ τ [ τ ]10 τ3]TRepresenting the input to the control system, τ1For propulsion moment matrix control law, tau3Is a steering force matrix control law;
m represents an inertia parameter matrix;
c (v) denotes the Coriolis and centripetal force matrix, C13＝-m22v，C23＝m11u；
D (v) represents a damping parameter matrix; xu、
Yv、
NrAnd
representing the hydrodynamic derivative of the vessel;
step 2: calculating a hydrodynamic derivative of the ship to obtain a mathematical model of the three-degree-of-freedom motion of the under-actuated surface ship;
and step 3: according to a mathematical model of three-degree-of-freedom motion of the under-actuated surface ship, a stabilizing control method is adopted to control the course angle of the under-actuated surface ship; wherein the propulsion matrix control law1And steering force matrix control law3Comprises the following steps:
the present invention may further comprise:
the method for calculating the hydrodynamic derivative of the ship in the step 2 specifically comprises the following steps:
step 2.1: inputting a closed solid model of the under-actuated surface ship, setting and calculating a background domain according to the size of a ship body, and carrying out grid division according to the background domain;
step 2.2: configuring a solver, and initializing parameters and iteration times;
step 2.3: respectively carrying out simulation experiments on the straight voyage motion, the pure swaying motion and the pure yawing motion of the ship;
the hydrodynamic equation of the ship direct navigation motion is as follows:
the hydrodynamic equation of the pure swaying motion of the ship is as follows:
the hydrodynamic equation of the pure bow motion of the ship is as follows:
step 2.4: for a direct navigation motion simulation experiment of a ship, the relationship between longitudinal force and longitudinal speed at different navigation speeds is obtained through CFD simulation, curve fitting is carried out on the relationship, and dimensionless hydrodynamic derivative X is obtained through calculationu' and
step 2.5: for the pure swaying motion simulation experiment of the ship, according to the motion rule of the pure swaying motion of the ship:
make the ship move in a pure swaying waySubstituting the motion law into a hydrodynamic equation of pure ship swaying motion to perform curve fitting to obtain a hydrodynamic derivative YvAnd
step 2.6: for the pure bow motion simulation experiment of the ship, according to the motion rule of the pure bow motion of the ship:
substituting the motion rule of the pure ship swaying motion into the hydrodynamic equation of the pure ship swaying motion, performing curve fitting to obtain dimensionless hydrodynamic derivative at each frequency, and finally performing linear regression to obtain the dimensionless hydrodynamic derivative N at zero frequencyrAnd
the invention has the beneficial effects that:
the invention provides a simple and effective solution to the problem of course control of an under-actuated ship with an unknown model, and can observe the state change of the under-actuated ship in the control process to realize rapid and stable course control.
Drawings
Fig. 1 is a schematic diagram of the coordinates of a ship used in the present invention in the ocean.
FIG. 2 is an overall grid diagram in an embodiment of the invention.
FIG. 3 is a partial grid diagram in an embodiment of the invention.
Fig. 4 is a diagram of a ship surface grid in an embodiment of the present invention.
Fig. 5 is a schematic diagram of the straight-ahead motion of the ship in the embodiment of the invention.
FIG. 6 is a schematic diagram of a pure swaying motion of a ship according to an embodiment of the invention.
Fig. 7 is a schematic diagram of pure yawing motion of a ship in an embodiment of the invention.
FIG. 8 is a diagram illustrating the simulation effect of the ship heading angle in the embodiment of the invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
A CFD-based under-actuated surface vessel course control method is characterized by comprising the following steps:
step 1: establishing a three-degree-of-freedom motion model of the under-actuated surface ship;
the following assumed conditions are adopted for the under-actuated surface ship: ignoring the pitch, roll and heave motions of the surface vessel, i.e. z is 0, ω is 0, Φ is 0, p is 0, θ is 0, q is 0; the gravity center of the ship is assumed to be coincident with the origin of the follow-up coordinate system, and the mass distribution of the ship body is uniform; the vessel being symmetrical about a longitudinal vertical plane x-o-z and a lateral vertical plane y-o-z, i.e. the moment of inertia Ixy＝Iyz＝0；
The three-degree-of-freedom motion model of the under-actuated surface ship can be expressed as follows:
wherein η ═ x y ψ]TRespectively, the longitudinal position and the transverse position of the shipSetting and heading angle; v ═ u v r]TRespectively representing the longitudinal speed, the transverse speed and the heading angular speed of the ship; τ ═ τ [ τ ]10 τ3]TRepresenting the input to the control system, τ1For propulsion moment matrix control law, tau3Is a steering force matrix control law;
m represents an inertia parameter matrix;
c (v) denotes the Coriolis and centripetal force matrix, C13＝-m22v，C23＝m11u；
D (v) represents a damping parameter matrix; xu、
Yv、
NrAnd
representing the hydrodynamic derivative of the vessel;
step 2: calculating a hydrodynamic derivative of the ship to obtain a mathematical model of the three-degree-of-freedom motion of the under-actuated surface ship;
the method for calculating the hydrodynamic derivative of the ship specifically comprises the following steps:
step 2.1: inputting a closed solid model of the under-actuated surface ship, setting and calculating a background domain according to the size of a ship body, and carrying out grid division according to the background domain;
step 2.2: configuring a solver, and initializing parameters and iteration times;
step 2.3: respectively carrying out simulation experiments on the straight voyage motion, the pure swaying motion and the pure yawing motion of the ship;
the hydrodynamic equation of the ship direct navigation motion is as follows:
the hydrodynamic equation of the pure swaying motion of the ship is as follows:
the hydrodynamic equation of the pure bow motion of the ship is as follows:
step 2.4: for a direct navigation motion simulation experiment of a ship, the relationship between longitudinal force and longitudinal speed at different navigation speeds is obtained through CFD simulation, curve fitting is carried out on the relationship, and dimensionless hydrodynamic derivative X is obtained through calculationu' and
step 2.5: for the pure swaying motion simulation experiment of the ship, according to the motion rule of the pure swaying motion of the ship:
substituting the motion rule of the pure ship swaying motion into the hydrodynamic equation of the pure ship swaying motion to perform curve fitting to obtain the hydrodynamic derivative YvAnd
step 2.6: for the pure bow motion simulation experiment of the ship, according to the motion rule of the pure bow motion of the ship:
substituting the motion rule of the pure ship swaying motion into the hydrodynamic equation of the pure ship swaying motion, performing curve fitting to obtain dimensionless hydrodynamic derivative at each frequency, and finally performing linear regression to obtain the dimensionless hydrodynamic derivative N at zero frequencyrAnd
and step 3: according to a mathematical model of three-degree-of-freedom motion of the under-actuated surface ship, a stabilizing control method is adopted to control the course angle of the under-actuated surface ship; wherein the propulsion matrix control law1And steering force matrix control law3Comprises the following steps:
example 1:
the invention provides a CFD-based course control method for an under-actuated ship surface ship. The CFD numerical analysis comprises a pretreatment process, a solver setting process and a post-treatment process; the hydrodynamic calculation comprises hydrodynamic equation analysis and hydrodynamic derivative calculation; the calm control includes controller design and simulation. And solving the required hydrodynamic derivative to establish a three-degree-of-freedom mathematical model of the under-actuated ship, and finally verifying the control effect of the controller through simulation. The invention provides a simple and effective solution to the problem of course control of an under-actuated ship with an unknown model, can observe the state change of the under-actuated ship in the control process, and realizes quick and stable course control
A CFD-based under-actuated ship surface ship course control method comprises the following steps: a pretreatment part for numerical modeling and grid division, a solver part for calculation and solution, a post-treatment part for result analysis and a design and simulation part for a controller; the pre-processing comprises two parts of establishing a geometric model and dividing a computational grid: for the division of the computational grid, the adopted strategies are: firstly, determining a calculation background domain containing a ship body, dividing the whole background domain by adopting thicker grids, and then encrypting the grids near the surface of the ship body; and finally, setting boundary conditions for each surface to generate a grid file, namely finishing all the work of pretreatment.
The solver adopts STAR CCM + software, which specifically comprises the following steps: firstly, setting a model, including setting implicit unsteady Euler multiphase flow, selecting a K-Epsilon turbulence model and selecting the volume of a fluid domain; then setting parameters, including setting multiphase fluid and initial conditions; after the model and the parameters are set, selecting a solver, setting an under-relaxation factor and setting the time step length to 0.01 second; next, rigid motion conditions are set, and the motion form of the ship is limited by adopting a plane motion mechanism; and finally, finishing calculation initialization and iterative solution calculation.
The post-processing is to obtain a relation curve of longitudinal force, transverse force and yawing moment along with time change under different working conditions according to CFD simulation; and performing curve fitting through MATLAB, and calculating the result to finally obtain the required dimensionless hydrodynamic derivative and obtain a mathematical model of the three-degree-of-freedom motion of the under-actuated ship. The mathematical model is as follows:
the course angle of the under-actuated ship is controlled by using a stabilizing control method, and the control law of the course controller of the under-actuated ship is as follows:
the invention provides a three-degree-of-freedom motion modeling and stabilizing control method for an under-actuated surface ship based on computational fluid dynamics simulation, which is used for solving the problem of unknown course control of the under-actuated surface ship based on a mathematical model.
The method for establishing the ship motion model is realized by commercial computational fluid dynamics simulation software STAR CCM + and commercial mathematical software MATLAB. In this section, the technical scheme adopted by the invention is divided into the following steps:
s1, importing a geometric model of the target ship;
s2, selecting a background calculation domain, dividing grids and setting boundary conditions;
s3, carrying out motion setting and calculation solving;
s4, carrying out post-processing of simulation result analysis to obtain simulation data of ship motion;
s5, performing curve fitting and calculation on the simulation data through MATLAB, and performing dimensionless processing on the result;
and S6, substituting the obtained dimensionless hydrodynamic derivative result into the three-degree-of-freedom motion model of the under-actuated ship, and then establishing the mathematical model of the three-degree-of-freedom motion of the under-actuated ship.
And S7, designing the controller by using the obtained mathematical model, and realizing by MATLAB simulation.
The ship geometric model introduced into the STAR CCM + is a standard KCS (KRISO Container ship) model and is a closed solid model.
The background calculation domain is selected from a cuboid calculation domain which takes the gravity center of a ship as a central point, the length of the cuboid calculation domain is 5 times of the ship length, the width of the cuboid calculation domain is 3 times of the ship length, and the height of the cuboid calculation domain is 1.5 times of the ship length.
The grid division adopts unstructured grids, and the grid type is a cutting body grid. And (4) encrypting the grids near the ship body, wherein the mass of all the grids is greater than 0.01.
The boundary conditions are set as follows: the boundary of the ship body is set as a wall surface boundary, the background domain surface close to the tail of the ship body is set as a pressure outlet, and the rest is set as a speed inlet.
The motion configuration comprises three motions of straight sailing, pure swaying and pure yawing.
The calculation solution uses the following physical model: implicit unsteady, euler multiphase flow, fluid domain Volume (VOF), and K-Epsilon turbulence models.
The post-processing process is a process of extracting transverse force, longitudinal force and moment required in the whole motion process from a flow field to obtain a relation curve of the transverse force, the longitudinal force and the moment changing along with time.
The curve fitting is a process of fitting the relation curve through commercial mathematical software MATLAB. The required factorial hydrodynamic derivative can be obtained by curve fitting and calculation.
After the hydrodynamic derivative is obtained through calculation, dimensionless processing needs to be carried out on the hydrodynamic derivative, and a mathematical model of the ship motion can be obtained after the dimensionless processing is carried out.
The course controller adopts a global progressive point stabilization control method, can realize relatively accurate and stable control on the under-actuated surface boat, can meet the global progressive stability of the under-actuated surface boat control system, and enables the course angle index of the surface boat to be converged.
In order to better show the technical scheme and advantages of the invention, the following clearly and completely explains the specific implementation mode of the invention with reference to the attached drawings.
When describing the motion of a ship in the ocean, two orthogonal coordinate systems are generally adopted, one is a fixed coordinate system, and the other is a follow-up coordinate system. The six-degree-of-freedom motion of the ship on the sea and the coordinate system thereof are shown in figure 1.
The surface ship has 6 degrees of freedom movement in the sea, and the movement form is complex. Therefore, the controller needs to be modeled according to actual needs, which is beneficial to the design of the controller.
The following assumed conditions are adopted for the surface ship: the pitching, rolling and heaving motions of the surface vessel are ignored. When z is 0, ω is 0, Φ is 0, p is 0, θ is 0, and q is 0; the gravity center of the ship is assumed to be coincident with the origin of the follow-up coordinate system, and the mass distribution of the ship body is uniform; the ship is symmetrical about a vertical plane x-o-z and a side vertical plane y-o-z, and the moment of inertia Ixy＝Iyz＝0。
The three-degree-of-freedom motion model of the under-actuated surface ship can be expressed as follows:
wherein η ═ x y ψ]T,v＝[u v r]T,τ＝[τ 10 τ3]T，
Wherein C is13＝-m22v，C23＝m11u。
[x y ψ]TThe medium physical quantities respectively represent the longitudinal position, the lateral position and the heading angle of the ship. [ u v r]TThe medium physical quantities respectively represent the longitudinal speed, the lateral speed and the heading angular speed of the ship. τ ═ τ [ τ ]10 τ3]TRepresenting the input to the control system. M represents an inertial parameter matrix. C (v) represents the coriolis and centripetal force matrices. D (v) represents a damping parameter matrix. Xu，
Yv，
NrAnd
representing the hydrodynamic derivative of the vessel.
Therefore, the mathematical model of the three-degree-of-freedom motion of the under-actuated ship can be established by obtaining the value of each required hydrodynamic derivative.
For solving the ship hydrodynamic derivative, the three-degree-of-freedom model of the target under-actuated ship is calculated and solved by adopting a planar execution mechanism (PMM) method and through various motion forms of CFD simulation PMM experiments.
Firstly, a closed entity model of a target ship is led into STAR CCM + software, a calculation background domain is set according to the size of a ship body, the selection of the background calculation domain is a cuboid calculation domain which takes the gravity center of the ship as a central point, the length of the cuboid calculation domain is 5 times the ship length, the width of the cuboid calculation domain is 3 times the ship length, and the height of the cuboid calculation domain is 1.5 times the ship length, then grid division is carried out according to the background domain, the grid division adopts unstructured grids, the specific type of the grids is cut body grids, and the grids near the ship body are encrypted. The grid partitioning process cannot generate negative grids and all the grid qualities are greater than 0.01, and the global grid effect is shown in fig. 2.
Then, configuring a solver, and firstly setting a calculation model, wherein the setting comprises setting of implicit unsteady, Euler multiphase flow, selection of a K-Epsilon turbulence model, selection of fluid domain volume and the like; then setting parameters, including specific parameters such as multiphase fluid, boundary conditions, initial conditions and the like; after the model and the parameters are set, selecting a solver, setting an under-relaxation factor and setting the time step length to 0.01 second; setting the motion conditions of the rigid body, and limiting the motion form of the ship by adopting a plane motion mechanism so that the ship can only carry out specific motion in an x-o-y plane; and finally, initializing the calculation and performing iterative solution calculation.
The simulation experiment was performed according to the following three motion patterns: straight-ahead motion, pure sway motion and pure yawing motion of the ship.
The schematic diagram of the straight-through motion of the ship is shown in fig. 3, and the hydrodynamic equation can be expressed as follows:
obtaining the relation between the longitudinal force and the longitudinal speed under different speeds through CFD simulation, substituting the relation into MATLAB for curve fitting, and finally obtaining dimensionless X through calculationu' and
for pure swaying motion of the ship, the motion diagram is shown in fig. 4, and the hydrodynamic equation can be expressed as:
the motion rule of the pure swaying motion of the ship is as follows:
substituting formula (5) for formula (4) to obtain:
and (3) taking the equations (6) and (7) as the equation of the force and the moment changing along with time, setting the fitting formula in the MATLAB into the form of the equation, and carrying out curve fitting to obtain the required hydrodynamic derivative.
For pure yawing motion of a ship, the motion diagram is shown in fig. 5, and the hydrodynamic equation can be expressed as:
the motion rule of the pure bow rolling motion of the ship is as follows:
in the formula (8), the formulae (9) and (10) are substituted by:
similarly, by adopting a curve fitting and calculating method used in pure swaying motion, the dimensionless hydrodynamic derivative under each frequency can be obtained, and finally linear regression is carried out on the dimensionless hydrodynamic derivative under each frequency to obtain the dimensionless hydrodynamic derivative under zero frequency, and finally the three-degree-of-freedom motion model of the under-actuated ship is obtained.
Expanding the matrix equation system of the formula (1) and the formula (2) can obtain the following under-actuated surface boat horizontal plane motion equation expressed in an expanded form:
the following control laws are designed so that the control system meets global gradual stabilization:
wherein A ═ m11/m22,B＝d22/m22，
Carrying out simulation verification on the designed controller in MATLAB, wherein the model parameters of the ship in the simulation are as follows: m is11＝0.00364，m22＝0.00774，m33＝0.000222，d11＝0.000342，d22＝0.000140，d330.000033, the target heading angle is set to be 0 degrees, the change curve of the heading angle along with time is shown in fig. 8, and the control effect of the designed controller is good, and the convergence of the heading angle can be realized.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. A CFD-based under-actuated surface vessel course control method is characterized by comprising the following steps:
step 1: establishing a three-degree-of-freedom motion model of the under-actuated surface ship;
to under-actuated waterThe following assumptions were adopted for the surface vessel: ignoring the pitch, roll and heave motions of the surface vessel, i.e. z is 0, ω is 0, Φ is 0, p is 0, θ is 0, q is 0; the gravity center of the ship is assumed to be coincident with the origin of the follow-up coordinate system, and the mass distribution of the ship body is uniform; the vessel being symmetrical about a longitudinal vertical plane x-o-z and a lateral vertical plane y-o-z, i.e. the moment of inertia Ixy＝Iyz＝0；
The three-degree-of-freedom motion model of the under-actuated surface ship can be expressed as follows:
wherein η ═ x y ψ]TRespectively representing the longitudinal position, the transverse position and the heading angle of the ship; v ═ u v r]TRespectively representing the longitudinal speed, the transverse speed and the heading angular speed of the ship; τ ═ τ [ τ ]10 τ3]TRepresenting the input to the control system, τ1For propulsion moment matrix control law, tau3Is a steering force matrix control law;
m represents an inertia parameter matrix;
c (v) denotes the Coriolis and centripetal force matrix, C13＝-m22v，C23＝m11u；
D (v) represents a damping parameter matrix; xu、
Yv、
NrAnd
representing the hydrodynamic derivative of the vessel;
step 2: calculating a hydrodynamic derivative of the ship to obtain a mathematical model of the three-degree-of-freedom motion of the under-actuated surface ship;
and step 3: according to a mathematical model of three-degree-of-freedom motion of the under-actuated surface ship, a stabilizing control method is adopted to control the course angle of the under-actuated surface ship; wherein the propulsion matrix control law1And steering force matrix control law3Comprises the following steps:
2. the CFD-based under-actuated surface vessel heading control method as claimed in claim 1, wherein: the method for calculating the hydrodynamic derivative of the ship in the step 2 specifically comprises the following steps:
step 2.1: inputting a closed solid model of the under-actuated surface ship, setting and calculating a background domain according to the size of a ship body, and carrying out grid division according to the background domain;
step 2.2: configuring a solver, and initializing parameters and iteration times;
step 2.3: respectively carrying out simulation experiments on the straight voyage motion, the pure swaying motion and the pure yawing motion of the ship;
the hydrodynamic equation of the ship direct navigation motion is as follows:
the hydrodynamic equation of the pure swaying motion of the ship is as follows:
the hydrodynamic equation of the pure bow motion of the ship is as follows:
step 2.4: for a direct navigation motion simulation experiment of a ship, the relationship between longitudinal force and longitudinal speed at different navigation speeds is obtained through CFD simulation, curve fitting is carried out on the relationship, and dimensionless hydrodynamic derivative X is obtained through calculationu' and
step 2.5: for the pure swaying motion simulation experiment of the ship, according to the motion rule of the pure swaying motion of the ship:
substituting the motion rule of the pure ship swaying motion into the hydrodynamic equation of the pure ship swaying motion to perform curve fitting to obtain the hydrodynamic derivative YvAnd
step 2.6: for the pure bow motion simulation experiment of the ship, according to the motion rule of the pure bow motion of the ship:
substituting the motion rule of the pure ship swaying motion into the hydrodynamic equation of the pure ship swaying motion, performing curve fitting to obtain dimensionless hydrodynamic derivative at each frequency, and finally performing linear regression to obtain the dimensionless hydrodynamic derivative N at zero frequencyrAnd
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| CN111611650A (en) * | 2020-05-18 | 2020-09-01 | 智慧航海（青岛）科技有限公司 | Method, computer-readable storage medium, and apparatus for determining hydrodynamic derivative |
| CN112180915A (en) * | 2020-09-16 | 2021-01-05 | 哈尔滨工业大学（威海） | ROS-based double-thrust unmanned ship motion control system and control method |
| CN112327635A (en) * | 2020-11-27 | 2021-02-05 | 哈尔滨工程大学 | Control method of underactuated surface ship based on robust stabilizing controller |
| CN112596393A (en) * | 2020-12-24 | 2021-04-02 | 武汉理工大学 | Control method, system and storage medium for ship path tracking |
| CN113341718A (en) * | 2021-06-10 | 2021-09-03 | 浙江大学 | Hydrodynamic coefficient hybrid adaptive estimation method of under-actuated water surface robot |
| CN113656894A (en) * | 2021-08-20 | 2021-11-16 | 大连海事大学 | Direct simulation calculation method for maneuverability rotation and Z-shaped motion of trimaran |
| CN113779698A (en) * | 2021-09-14 | 2021-12-10 | 浙江数智交院科技股份有限公司 | Simplified design method of ship mooring system under water flow action |
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Cited By (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111611650A (en) * | 2020-05-18 | 2020-09-01 | 智慧航海（青岛）科技有限公司 | Method, computer-readable storage medium, and apparatus for determining hydrodynamic derivative |
| CN112180915A (en) * | 2020-09-16 | 2021-01-05 | 哈尔滨工业大学（威海） | ROS-based double-thrust unmanned ship motion control system and control method |
| CN112327635A (en) * | 2020-11-27 | 2021-02-05 | 哈尔滨工程大学 | Control method of underactuated surface ship based on robust stabilizing controller |
| CN112596393B (en) * | 2020-12-24 | 2022-02-22 | 武汉理工大学 | Control method, system and storage medium for ship path tracking |
| CN112596393A (en) * | 2020-12-24 | 2021-04-02 | 武汉理工大学 | Control method, system and storage medium for ship path tracking |
| CN113341718A (en) * | 2021-06-10 | 2021-09-03 | 浙江大学 | Hydrodynamic coefficient hybrid adaptive estimation method of under-actuated water surface robot |
| CN113341718B (en) * | 2021-06-10 | 2022-07-08 | 浙江大学 | Hydrodynamic coefficient hybrid adaptive estimation method of under-actuated water surface robot |
| CN113656894B (en) * | 2021-08-20 | 2022-09-02 | 大连海事大学 | Direct simulation calculation method for maneuverability rotation and Z-shaped motion of trimaran |
| CN113656894A (en) * | 2021-08-20 | 2021-11-16 | 大连海事大学 | Direct simulation calculation method for maneuverability rotation and Z-shaped motion of trimaran |
| CN113779698A (en) * | 2021-09-14 | 2021-12-10 | 浙江数智交院科技股份有限公司 | Simplified design method of ship mooring system under water flow action |
| CN113779698B (en) * | 2021-09-14 | 2023-07-14 | 浙江数智交院科技股份有限公司 | Simplified design method of ship mooring system under action of water flow |
| CN116482984A (en) * | 2023-06-20 | 2023-07-25 | 中国船舶集团有限公司第七〇七研究所 | Model self-adaptive optimal control method and system based on ship towing rope tension monitoring |
| CN116482984B (en) * | 2023-06-20 | 2023-09-05 | 中国船舶集团有限公司第七〇七研究所 | Model self-adaptive optimal control method and system based on ship towing rope tension monitoring |
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