A finite-time synchronous convergence control method for a dynamically positioned vessel

Abstract

The present invention discloses a finite-time synchronous convergence control method for a dynamic positioning vessel. The method comprises: establishing kinematic and dynamic models of the vessel; establishing error dynamic equations based on the kinematic and dynamic models and a desired position; designing a sign function, and designing a synchronous convergence sliding surface based on the sign function; and designing a finite-time convergence synchronous controller based on the sliding surface and Lypunov stability. The control method of the present invention can achieve synchronous convergence of the errors of each degree of freedom of the dynamic positioning vessel, has a relatively small number of control parameters, and can effectively simplify the controller form and the workload of parameter adjustment.

Description

Technical Field

[0001] The present invention relates to the technical field of ship control, and in particular to a synchronous convergence control method for a dynamic positioning ship based on finite time. Background Art

[0002] In recent years, with the continuous development of the marine resource economy, countries have increasingly attached importance to marine resources. Ships, as maritime transportation vehicles, have been widely used. Dynamic positioning vessels, with full-drive configurations, can perform civil and military applications such as pipe laying, offshore oil and gas drilling, and mine hunting and sweeping.

[0003] Among existing dynamic positioning control technologies, control methods based on backstepping suffer from characteristics such as differential explosion and complex controller structure, making them difficult to apply in engineering practice. Control methods based on neural networks and fuzzy control also suffer from problems such as numerous parameters and a large workload for parameter adjustment. In addition, there is little research on the finite-time synchronous convergence control of dynamic positioning vessels. Existing research results can only guarantee the finite-time stability of the controller, and there are few studies that can simultaneously converge the lateral position error, longitudinal position error, and heading angle error to the equilibrium point. In summary, there is a need to invent a control method that can solve the problem of synchronous convergence of the position and attitude of dynamic positioning vessels. Summary of the Invention

[0004] The purpose of the present invention is to propose a finite time synchronous convergence control method for a ship dynamic positioning control system to solve the problems of synchronous convergence of errors in each degree of freedom and excessive parameters in the controller during the ship dynamic positioning control process.

[0005] The technical solution for achieving the purpose of the present invention is as follows: In a first aspect, the present invention provides a method for synchronous convergence control of a dynamic positioning vessel based on finite time, comprising the following steps:

[0006] Step 1: Establish a mathematical model of the dynamic positioning vessel, collect the current speed information, position information and heading information of the dynamic positioning vessel through speed sensors, position sensors and platform compass, and transmit them in real time;

[0007] Step 2: Calculate the relative error based on the dynamic positioning vessel's desired positioning position and heading information, and establish the error dynamic equation;

[0008] Step 3: Establish a finite-time synchronously convergent sliding surface and derive the sliding surface;

[0009] Step 4: Design a finite-time synchronous convergence formation control scheme for dynamically positioned vessels.

[0010] Furthermore, the kinematic and mathematical models of the dynamic positioning vessel are as follows:

[0011]

[0012]

[0013] Where: η = [x, y, ψ] T represents the position and heading angle of the dynamic positioning vessel; v = [u, v, r] T represents the longitudinal velocity, lateral velocity and angular velocity of the dynamic positioning vessel; M represents the mass and moment of inertia of the vessel; τ = [τ u ,τ v ,τ r ] T Represents control force and control torque; τ w =[τ wu τ wv τ wr ] T represents the component force of external disturbance on the three degrees of freedom; C(ν) represents the Coriolis centripetal force matrix, D(ν) represents the damping coefficient matrix and J(η) represents the coordinate system transformation matrix.

[0014] Furthermore, the relative error equation is as follows:

[0015] e=η-η d

[0016] Among them, η d is the desired position and heading.

[0017] Furthermore, the error dynamic equation is in the following form:

[0018]

[0019]

[0020] Where x1 = e,

[0021] Furthermore, the finite-time synchronous convergence sliding mode surface formula and the finite-time synchronous convergence dynamic positioning controller of the power ship are as follows:

[0022] s=x²+sig n (e) α

[0023] in,

[0024] The synchronous convergence controller of the dynamic positioning vessel based on finite time is designed as follows:

[0025]

[0026] Furthermore, the stability verification process of the dynamic positioning vessel synchronous convergence controller based on finite time is as follows:

[0027] Through the Lyapunov function:

[0028] V=s T s

[0029] Taking the derivative of V we get:

[0030]

[0031] The convergence time is calculated as follows:

[0032] Where s0 is the initial value of s at time t=0, and V(s0) is the initial value of V at time t=0.

[0033] In a second aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method described in the first aspect when executing the program.

[0034] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0035] In a fourth aspect, the present invention provides a computer program product, comprising a computer program, which implements the steps of the method described in the first aspect when executed by a processor.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] (1) The present invention provides a finite-time synchronous convergence control method for ship dynamic positioning, which can achieve synchronous convergence of errors in each degree of freedom of a dynamic positioning ship;

[0038] (2) The finite time-based ship dynamic positioning synchronous convergence control method designed by the present invention has fewer control parameters and can effectively simplify the form of the controller and the workload of parameter adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Flow chart of the steps of the present invention.

[0040] Figure 2 It is a structural diagram of the control system of the present invention.

[0041] Figure 3 This is a trajectory curve diagram of the dynamic positioning vessel under the present invention.

[0042] Figure 4This is a graph of the error of the dynamic positioning vessel obtained by the control method of the present invention. DETAILED DESCRIPTION

[0043] The present invention will be described in further detail below with reference to the embodiments and accompanying drawings. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification.

[0044] like Figure 1 As shown, a finite time-based synchronous convergence control method for a dynamic positioning vessel comprises the following steps:

[0045] Step 1: Establish a mathematical model of the dynamic positioning vessel, collect the speed information of the dynamic positioning vessel, and collect the actual position information and heading information of the dynamic positioning vessel;

[0046] Step 2: Determine the error between the dynamic positioning vessel and the desired position based on the desired position and heading and the information in step 1, and establish the error dynamic equation;

[0047] Step 3: Based on step 2, a finite-time sliding surface is designed to ensure that the longitudinal error, lateral error, and heading error of the ship converge to zero quickly and synchronously.

[0048] Step 4: Select the global Lyapunov function based on the ship model and the sliding surface in step 3;

[0049] Step 5: Based on Lyapunov stability, design the synchronous convergence control law of the dynamic positioning vessel;

[0050] Step 6: Dynamic positioning control simulation of dynamic positioning vessel.

[0051] Figure 2 The structural block diagram of the control system is shown in Figure 2. The detailed implementation process of this method is as follows:

[0052] Step 1: Establish a three-degree-of-freedom mathematical model of the dynamic positioning vessel:

[0053]

[0054]

[0055] Where: η = [x, y, ψ] T represents the position and heading angle of the dynamic positioning vessel; ν = [u, v, r] T represents the longitudinal velocity, lateral velocity and angular velocity of the dynamic positioning vessel; M represents the mass and moment of inertia of the vessel; τ = [τ u ,τ v ,τ r ] T represents the control force and control torque; τ w =[τ wu τwv τ wr ] T represents the component force of external interference on the three degrees of freedom; C(v) represents the Coriolis centripetal force matrix, D(v) represents the damping coefficient matrix, and J(η) represents the coordinate system transformation matrix; the speed and position information are obtained through sensors.

[0056] Step 2: Define the error variable of the dynamic positioning vessel as the difference between the actual position and the expected position η d Error:

[0057] e=η-η d

[0058] Furthermore, in order to facilitate the design of the control law, let Establish the mathematical expression of the dynamic model of power ship error:

[0059]

[0060]

[0061] Step 3. Define a new sliding surface:

[0062] s=x²+sig n (e) α

[0063] in, x represents variables, such as error, state, etc.; α is an adjustable parameter, and

[0064] Find the first-order derivative with respect to s:

[0065]

[0066] Step 4. Further, the global Lyapunov function is selected as follows:

[0067] V=s T s

[0068] Taking the derivative of V we get:

[0069]

[0070] Step 5: Based on Lyapunov stability theory, the control law that satisfies the dynamic positioning of the ship is designed as follows:

[0071]

[0072] Step 6: Based on the above implementation method, the simulation results of the three-dimensional attitude synchronization convergence and stabilization control of the dynamic positioning ship can be obtained as follows: Figure 3 and Figure 4The simulation process of given expected position and heading is as follows:

[0073] First, the expected position and heading η in the simulation process are given d =[35,30,0].

[0074] Then, a finite time based synchronous convergence controller for dynamic positioning vessel is used to simulate the dynamic positioning vessel as the control object. Figure 3 As shown, it shows the running curve of the dynamic positioning vessel from the starting point to the desired point, where the solid line represents the actual route, and * represents the starting point and the desired end point of the vessel for dynamic positioning operation. Figure 4 The real-time curves of the longitudinal error, lateral error and heading error are shown in Figure 2. Although the initial errors of each degree of freedom are different, they all converge to 0 at the same time, which proves that the method proposed in the present invention can well realize the control of the errors of each degree of freedom of the dynamic positioning vessel in the dynamic positioning operation to converge to the equilibrium point at the same time.

[0075] The above description is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited thereto. d When it is a time-related variable, it can be used as a reference trajectory to implement trajectory tracking control of second-order nonlinear systems such as dynamic positioning vessels, unmanned boats, and robotic arms using the method proposed in this article. Therefore, according to the concept of the present invention, equivalent replacement or transformation of the control object should be covered within the scope of protection of the present invention.

Claims

1. A finite time based synchronous convergence control method for a dynamic positioning vessel, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of the dynamic positioning vessel, collect the current speed information, position information and heading information of the dynamic positioning vessel through speed sensors, position sensors and platform compass, and transmit them in real time; Step 2: Calculate the relative error based on the dynamic positioning vessel's desired positioning position and heading information, and establish the error dynamic equation; Step 3: Establish a finite-time synchronously convergent sliding surface and derive the sliding surface; Step 4: Design a finite time synchronous convergence formation control scheme for dynamic positioning vessels; the finite time synchronous convergence controller for dynamic positioning vessels is as follows: where η = [x, y, ψ] T represents the position and heading angle of the dynamic positioning vessel, ν=[u,v,r] T represents the longitudinal velocity, lateral velocity and angular velocity of the dynamic positioning vessel; M represents the mass and moment of inertia of the vessel; τ = [τ u ,τ v ,τ r ] T Represents control force and control torque; τ w =[τ wu τ wv τ wr ] T represents the component force of external interference on the three degrees of freedom; C(ν) represents the Coriolis centripetal force matrix, D(ν) represents the damping coefficient matrix, J(η) represents the coordinate system transformation matrix; e represents the relative error, x1 = e, sig n (s) α represents the conformity function, and α is an adjustable parameter.

2. The method for synchronous convergence control of a dynamic positioning vessel based on finite time according to claim 1, characterized in that: The kinematic and dynamic mathematical models of the dynamic positioning vessel are as follows:

3. The method for synchronous convergence control of a dynamic positioning vessel based on finite time according to claim 2, characterized in that: The relative error is established as follows: e=η-η d Among them, η d is the desired position and heading; The error dynamic equation is established based on the relative error, which is as follows: Where x1 = e, 4. The method for synchronous convergence control of a dynamic positioning vessel based on finite time according to claim 3, characterized in that: The symbolic function form of the sliding surface is as follows: Among them, x represents a variable, α is an adjustable parameter, and The finite-time synchronous convergence sliding mode surface and the finite-time synchronous convergence controller of the error between the actual posture and the desired posture of the dynamic positioning vessel are as follows: s=x2+sig n (And) α The derivative of the above formula is as follows:

5. The method for synchronous convergence control of a dynamic positioning vessel based on finite time according to claim 4, characterized in that: The stability verification process of the synchronous convergence controller of the dynamic positioning vessel based on finite time is as follows: Through the Lyapunov function: V=s T s Taking the derivative of V we get: The convergence time is calculated as follows: Where s0 is the initial value of s at time t=0, and V(s0) is the initial value of V at time t=0.

6. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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