Ship predefined time stipulation performance tracking control method based on hyperbolic sine function

Abstract

The invention provides a hyperbolic sine function-based ship predefined time stipulation performance tracking control method, which comprises the following steps of: inputting an expected trajectory eta d, and taking a difference value between the expected trajectory eta d and an actual trajectory eta of a ship as a tracking error eta e; inputting the tracking error eta e into a preset performance constraint module to carry out rule constraint processing constructed by using a hyperbolic sine function, and then converting the tracking error eta e into a constraint on a specified performance function rho; further converting the specified performance function rho into a form of mapping l through an unconstrained transformation module; on the basis, a control input tau is finally formed by processing a sliding mode function and a control rate in a predefined time control module and acts on the ship; and the ship is influenced by the disturbance tau d to form a ship actual track eta, and the ship actual track eta is used as an input quantity of closed-loop feedback to form closed-loop control.

Description

Technical Field

[0001] The invention belongs to the technical field of ship tracking control, and in particular relates to a ship predefined time specified performance tracking control method based on a hyperbolic sine function. Background Art

[0002] Contemporary maritime operations are becoming increasingly complex and sophisticated, requiring ships to efficiently perform trajectory tracking control tasks. Tracking control is a fundamental issue in the field of ship control and has always been a research hotspot. It is crucial to ensure that the steady-state tracking error converges quickly to the residual set and prevent excessive overshoot of the transient tracking error. This dual goal requires that the steady-state and transient response values ​​of the ship tracking error are strictly maintained within a predefined safety range. These measures are crucial to mitigate collision accidents and improve operational safety. The design of a trajectory tracking control scheme that can ensure that the tracking error is constrained has important practical value for the safe operation of ships.

[0003] Real-world engineering systems often require high-performance control systems, which require a predefined time due to the response time of the ship controller, complex nonlinear dynamics, and interaction with the dynamic environment. Simply achieving stability does not necessarily mean that the system can meet the requirements of practical applications. Systems for practical applications often need to be able to achieve fast convergence and high accuracy. In some systems that require high control accuracy, the control system must be stable within a predetermined time range. In order to achieve fast performance indicators in automatic control and ensure that indicators such as convergence time are within the predefined standard range, prescribed performance control has emerged. With the increasing complexity of tasks, higher and higher requirements for control systems, and the continuous development of various new intelligent algorithms, the research on control methods based on prescribed performance control still has broad development prospects. Finite-time stability cannot avoid the constraints of initial conditions, while fixed-time stability users still cannot specify the convergence time themselves. In actual industrial processes, it is usually difficult to measure the initial state of most actual systems. Therefore, it is necessary to ensure that the system can remain stable within a predefined time.

[0004] Predefined-time control has been used in networked marine surface vehicles. However, there is still no comprehensive general theory available for predefined-time convergence. Only a limited number of criteria exist. Considering the need to achieve better control performance of the system, it is worthwhile to further investigate and explore the various factors that exist in the design process of predefined-time controllers.

[0005] Therefore, in a complex marine environment, the control action under the preset performance requirements still faces many unresolved problems. In order to meet the needs of future tasks and taking into account the defects of the preset performance control method itself, it is still necessary to preset the problems and research directions of the performance control method. Summary of the invention

[0006] In view of the defects and shortcomings of the existing technology, considering how to accurately process and obtain good transient performance in a short time is a key factor of the system. The present invention proposes a ship predefined time prescribed performance tracking control method based on a hyperbolic sine function, and uses a hyperbolic sine function to construct a prescribed performance function that converges in a predefined time. A predefined standard for time convergence evaluation based on a gamma function and a Riemann zeta function is introduced. By integrating performance indicators such as speed, stability and efficiency into the design of the prescribed performance function, the performance framework ensures the realization of the establishment of a comprehensive performance optimization model. The present invention improves the upper limit of the settling time, establishes sufficient conditions for achieving convergence in the predetermined time, and is verified through experiments on unmanned surface ships.

[0007] The technical solution specifically adopted by the present invention to solve the technical problem is:

[0008] A ship predefined time specified performance tracking control method based on hyperbolic sine function: the input is the expected trajectory η d , and the difference between the actual trajectory η of the ship is the tracking error η e ; The tracking error η e After the input of the preset performance constraint module is processed by the rule constraint constructed by the hyperbolic sine function, it is converted into a constraint on the specified performance function ρ; the specified performance function ρ is further converted into the form of mapping l through the unconstrained transformation module; on this basis, the control input τ is finally formed through the processing of the synovial function and the control rate in the predefined time control module, and acts on the ship; the ship is disturbed by τ d The actual trajectory η of the ship is formed as the input of the closed-loop feedback to constitute a closed-loop control.

[0009] Furthermore, the mathematical model of ship motion is specifically:

[0010] Let η represent the position vector corresponding to the actual trajectory of the ship, v represent the lateral velocity, u represent the forward velocity, ψ represent the yaw angle, r represent the yaw angular velocity, y represent the lateral position, x represent the forward position, υ represent the velocity vector, τ d represents disturbance and τ represents control input:

[0011]

[0012] η=[x,y,ψ] T (3)

[0013] υ=[u,v,r] T (4)

[0014]

[0015] where M is the inertia matrix, C is the Coriolis matrix, and D is the damping matrix;

[0016] Substituting (1) into (2) gives:

[0017]

[0018] Furthermore, the tracking error η e =[η e1 , η e2 , η e3 T , which means that in the case of disturbances in the x, y, and ψ directions, it converges to 0 within the preset time T:

[0019] η e =η - η d (7).

[0020] Furthermore, the preset performance constraint module is specifically:

[0021] Construct a prescribed performance function for the performance constraints and bounds of the tracking error For all cases where t ≥ 0, ρ is smooth, positive definite, and decreasing; ρ0 > 0 is the upper bound;

[0022]

[0023] where 0 < δ < 1 is a constant used to reduce overshoot; ρ = [ρ1, ρ2, ρ3] T , i = 1, 2, 3;

[0024] The derivative of ρ is:

[0025]

[0026] where 0 < p < 1; k1 is used to control the convergence rate of the preset performance function; ρ ∞ =[ρ 1∞ , ρ 2∞ , ρ 3∞ T is the boundary value of the preset performance function; ρ ∞i > 0, i = 1, 2, 3; sgn(.) is the sign function.

[0027] Furthermore, the unconstrained transformation module is specifically:

[0028] Define the mapping function for converting the constrained error η ei into the unconstrained variable θ i :

[0029]

[0030] Where θ=[θ1,θ2,θ3] T for:

[0031]

[0032] The derivative of l is:

[0033]

[0034] remember:

[0035]

[0036] Thus, equation (13) is converted into:

[0037]

[0038] Furthermore, the sliding mode function is:

[0039]

[0040] In the formula, parameter k>0.

[0041] Furthermore, the control law is:

[0042]

[0043] Where ||Λ||≥||τ d ||, parameter k e >0, parameter k s >0.

[0044] And, a ship predefined time specified performance tracking controller based on a hyperbolic sine function, comprising: a preset performance constraint module, an unconstrained transformation module and a predefined time control module; the input is the expected trajectory η d , and the difference between the actual trajectory η of the ship is the tracking error η e ; The tracking error η e After the input of the preset performance constraint module is processed by the rule constraint constructed by the hyperbolic sine function, it is converted into a constraint on the specified performance function ρ; the specified performance function ρ is further converted into the form of mapping l through the unconstrained transformation module; on this basis, the control input τ is finally formed through the processing of the synovial function and the control rate in the predefined time control module, and acts on the ship; the ship is disturbed by τ d The actual trajectory η of the ship is formed as the input of the closed-loop feedback to constitute a closed-loop control.

[0045] An electronic device comprises 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 ship predefined time specified performance tracking control method based on the hyperbolic sine function as described above are implemented.

[0046] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the ship predefined time specified performance tracking control method based on a hyperbolic sine function as described above.

[0047] Compared with the prior art, the present invention and its preferred embodiment utilize hyperbolic sine function to construct a prescribed performance function that converges in a predefined time. Predefined criteria for evaluating time convergence based on gamma function and Riemann zeta function are introduced. By integrating performance indicators such as speed, stability and efficiency into the design of the prescribed performance function, the performance framework ensures the realization of establishing a comprehensive performance optimization model. The present invention improves the upper limit of the settling time, establishes sufficient conditions for achieving convergence in a predetermined time, and verifies it through experiments on unmanned surface vessels. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0049] Figure 1 This is a control flow chart of an embodiment of the present invention;

[0050] Figure 2-Figure 7 They are respectively the trajectory, position and posture, speed, input control, tracking error, and tracking result diagram of the specified performance function in the embodiment of the present invention. DETAILED DESCRIPTION

[0051] In order to make the features and advantages of this patent more obvious and easy to understand, the following embodiments are specifically described in detail as follows:

[0052] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0053] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0054] The design of the specified performance controller includes three important steps: the selection of the performance function, the transformation of the unconstrained space and the design of the stable controller. The control objective is to ensure that all closed-loop variables in the tracking error system are bounded for the initial conditions, that is, to make the ship state meet the specified performance constraints within the predetermined time. The controller structure and the corresponding control closed loop are designed as follows: Figure 1 shown.

[0055] The input of the system is the expected trajectory η d , the difference between it and the actual trajectory η of the ship is the tracking error η e , as shown in formula (7).

[0056] The tracking error η e After inputting the preset performance constraint module (Prescribed Performance Constraint) and performing rule constraint processing as shown in equations (8) and (9), it is converted into a constraint on the prescribed performance function ρ;

[0057] The prescribed performance function ρ is further converted into the form of mapping l through the unconstrained transformation module, and the process is shown in equations (10)-(17).

[0058] On this basis, the control input τ is finally formed through the processing of the sliding film function and the control rate in the predefined-time control module and acts on the ship.

[0059] And through the perturbation τ d The actual trajectory η of the ship is formed by the influence of the surrounding environment (such as wind, waves, water currents, etc.), which serves as the input of the closed-loop feedback to form a closed-loop control.

[0060] The specific design process of the controller of the embodiment of the present invention is provided below:

[0061] Step 1: Establish a mathematical model of ship motion.

[0062] Let η represent the position vector corresponding to the actual trajectory of the ship, v represent the lateral velocity, u represent the forward velocity, ψ represent the yaw angle, r represent the yaw angular velocity, y represent the lateral position, x represent the forward position, υ represent the velocity vector, τ d represents disturbance and τ represents control input.

[0063]

[0064] η=[x,y,ψ] T (3)

[0065] υ=[u,v,r] T (4)

[0066]

[0067] where M is the inertia matrix, C is the Coriolis matrix, and D is the damping matrix;

[0068] Substituting (1) into (2) gives:

[0069]

[0070] The tracking error η e =[η e1 , η e2 , η e3 T , which means that in the case of disturbances in the x, y, and ψ directions, it converges to 0 within the preset time T:

[0071] η e =η - η d (7)

[0072] where η d is the desired trajectory.

[0073] Step 2: Design a preset performance function. For the performance constraints and bounds of the tracking error, construct a prescribed performance function For all cases of t ≥ 0, ρ is smooth, positive definite, and decreasing. ρ0 > 0 is the upper bound.

[0074]

[0075] where 0 < δ < 1 is a constant used to reduce overshoot. ρ = [ρ1, ρ2, ρ3] T , i = 1, 2, 3.

[0076] The derivative of ρ is:

[0077]

[0078] where 0 < p < 1. k1 is used to control the convergence rate of the preset performance function. ρ ∞ =[ρ 1∞ , ρ 2∞ , ρ 3∞ T is the boundary value of the preset performance function. ρ ∞i > 0, i = 1, 2, 3.

[0079] Define the mapping function for converting the constrained error η ei to the unconstrained variable θ i :

[0080] ​​

[0081] Where θ=[θ1,θ2,θ3] T for:

[0082]

[0083] The derivative of l is:

[0084]

[0085] remember:

[0086]

[0087] Formula (13) can be written as:

[0088]

[0089] The prescribed performance function satisfying (8) and (9) is a predefined temporal performance function.

[0090] Step 3: Construct the sliding mode function as follows:

[0091]

[0092] In the formula, parameter k>0.

[0093] Step 4: Design the control law as follows:

[0094]

[0095] Where ||Λ||≥||τ d ||, parameter k e >0, parameter k s >0. sgn(.) is the sign function:

[0096]

[0097] The initial condition satisfies |η ei (0)|<ρ i (0),k i >max|H i (t)|, the system tracking error converges within the predefined time. The results verified by the unmanned surface ship experiment are as follows Figure 2-Figure 7As shown. Based on the same inventive concept, the present invention also provides a computer device, which includes: one or more processors, and a memory for storing one or more computer programs; the program includes program instructions, and the processor is used to execute the program instructions stored in the memory. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is used to implement one or more instructions, specifically for loading and executing one or more instructions in a computer storage medium to implement the above method.

[0098] It needs to be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium, on which a computer program is stored, and the computer program is executed by a processor to execute the above method. The storage medium can adopt any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electrical, magnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples (non-exhaustive list) of computer-readable storage media include: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program, which can be used by an instruction execution system, device or device or used in combination with it.

[0099] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0100] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0101] This patent is not limited to the above-mentioned optimal implementation mode. Anyone can derive other various forms of ship tracking control methods with predefined time specification performance under the inspiration of this patent. All equal changes and modifications made according to the scope of the patent application of the present invention should be covered by this patent.

Claims

1. A ship predefined time specified performance tracking control method based on hyperbolic sine function, characterized in that: The input is the expected trajectory η d , and the difference between the actual trajectory η of the ship is the tracking error η e ; The tracking error η e After the input of the preset performance constraint module is processed by the rule constraint constructed by the hyperbolic sine function, it is converted into a constraint on the specified performance function ρ; the specified performance function ρ is further converted into the form of mapping l through the unconstrained transformation module; on this basis, the control input τ is finally formed through the processing of the synovial function and the control rate in the predefined time control module, and acts on the ship; the ship is disturbed by τ d The actual trajectory η of the ship is formed as the input of the closed-loop feedback to constitute a closed-loop control.

2. The method for tracking and controlling the ship's predefined time specified performance based on the hyperbolic sine function according to claim 1 is characterized in that: The mathematical model of ship motion is as follows: Let η represent the position vector corresponding to the actual trajectory of the ship, v represent the lateral velocity, u represent the forward velocity, ψ represent the yaw angle, r represent the yaw angular velocity, y represent the lateral position, x represent the forward position, υ represent the velocity vector, τ d represents disturbance and τ represents control input: η=[x,y,ψ] T (3) υ=[u,v,r] T (4) Among them, M is the inertia matrix, C is the Coriolis matrix, and D is the damping matrix; Substituting (1) into (2) we obtain:

3. The method for tracking and controlling the ship's predefined time specified performance based on the hyperbolic sine function according to claim 2 is characterized in that: The tracking error η e =[η e1 ,η e2 ,η e3 ] T , which means that the three directions x, y, and ψ converge to 0 within the preset time T under disturbance: or e =th-th d (7)。 4. The method for tracking and controlling the ship's predefined time specified performance based on the hyperbolic sine function according to claim 3 is characterized in that: The preset performance constraint module is specifically: Construct a prescribed performance function for the performance constraints and bounds of the tracking error For all t ≥ 0, ρ is smooth, positive definite, and decreasing; ρ0>0 is an upper bound; Where 0<δ<1 is a constant used to reduce overshoot; ρ=[ρ1,ρ2,ρ3] T ,i=1,2,3; The derivative of ρ is: where 0 < p < 1; k1 is used to control the convergence rate of the preset performance function; ρ ∞ = [ρ 1∞ , ρ 2∞ , ρ 3∞ T are the boundary values of the preset performance function; ρ ∞i > 0, i = 1, 2, 3; sgn(.) is the sign function.​ 5. The method for tracking and controlling the ship's predefined time specified performance based on the hyperbolic sine function according to claim 4 is characterized in that: The unconstrained transformation module is specifically: Defining the mapping function Used to constrain the error η ei Convert to unconstrained variable θ i : In the formula, θ=[θ1,θ2,θ3] T for: The derivative of l is: remember: Thus, equation (13) is converted into:

6. The method for tracking and controlling the ship's predefined time specified performance based on the hyperbolic sine function according to claim 5 is characterized in that: The sliding mode function is: In the formula, parameter k>0.

7. The method for tracking and controlling the ship's predefined time specified performance based on the hyperbolic sine function according to claim 6 is characterized in that: The control law is: Where ||Λ||≥||τ d ||, parameter k e >0, parameter k s >0, G is the gain matrix.

8. A ship predefined time specified performance tracking controller based on hyperbolic sine function, characterized in that: include: Preset performance constraint module, unconstrained transformation module and predefined time control module; The input is the expected trajectory η d , and the difference between the actual trajectory η of the ship is the tracking error η e ; The tracking error η e After the input of the preset performance constraint module is processed by the rule constraint constructed by the hyperbolic sine function, it is converted into a constraint on the specified performance function ρ; the specified performance function ρ is further converted into the form of mapping l through the unconstrained transformation module; on this basis, the control input τ is finally formed through the processing of the synovial function and the control rate in the predefined time control module, and acts on the ship; the ship is disturbed by τ d The actual trajectory η of the ship is formed as the input of the closed-loop feedback to constitute a closed-loop control.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the ship predefined time specified performance tracking control method based on the hyperbolic sine function as described in any one of claims 1-7 are implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the ship predefined time specified performance tracking control method based on a hyperbolic sine function as described in any one of claims 1 to 7 are implemented.

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