Full-drive ship trajectory tracking method based on predictive optimization control

Abstract

The invention provides a full-drive ship trajectory tracking method based on predictive optimization control, and belongs to the technical field of ocean technology and intelligent navigation. The method comprises the following steps: constructing a basic dynamic nonlinear model based on three degrees of freedom of a ship; converting the basic dynamic nonlinear model into a linear steady-state system through a parameterization design method; constructing an enhanced error system and an internal model compensator by utilizing a linear steady-state system; determining a controller form in combination with an enhanced error system and an internal model compensator; and introducing a predictive item to obtain an optimal controller. According to the method, the calculation process of control input is optimized, the calculation burden of real-time control is reduced, and the control strategy is optimized; moreover, the controller can respond to the change of the dynamic trajectory more quickly, thereby shortening the adjustment time of the system, improving the adaptability to the complex trajectory, and achieving the quick response.

Description

Technical Field

[0001] The invention relates to the fields of marine technology and intelligent navigation technology, and in particular to a full-drive ship trajectory tracking method based on predictive optimization control. Background Art

[0002] Trajectory tracking control technology is widely used in the field of ship navigation and control, especially in unmanned surface vessels (USVs), floating wind farm maintenance vessels, and marine engineering. Traditional ship navigation systems mostly use proportional integral differential (PID) control and robust control methods. These methods have the advantages of simple implementation and low computational burden, and are widely used in path tracking control of small ships. However, traditional methods are difficult to cope with nonlinear disturbances in complex marine environments, and the control accuracy and response speed are insufficient in scenarios with rapid trajectory changes or turns. With the improvement of computing power, model predictive control technology has gradually been applied to ship trajectory tracking control. By optimizing the control input within the prediction window, model predictive control can balance tracking error and energy consumption to a certain extent. However, the linear modeling assumption of the system by model predictive control limits its application to nonlinear ship systems, and large-scale calculations lead to limited real-time performance, especially in complex environments.

[0003] In the field of ship trajectory tracking control, the prior art proposes predictive control as a feedforward control strategy, which uses the future information of the reference trajectory to improve the dynamic response and tracking accuracy of the system. However, traditional predictive control methods are mainly designed for linear systems. They are difficult to apply directly to ship models with nonlinear characteristics, resulting in reduced control performance. In addition, disturbance factors such as wind, waves, and currents in the marine environment have a significant impact on ship motion, and existing predictive control methods are insufficient in dealing with these uncertainties. Complex predictive control algorithms increase the computational burden and affect the real-time performance of the system, especially when faced with multi-variable and strongly coupled ship systems, where the control accuracy and real-time response performance are limited.

[0004] Therefore, a trajectory tracking method for a fully driven ship based on predictive optimization control is needed. Summary of the invention

[0005] In view of this, the present invention provides a full-drive ship trajectory tracking method based on predictive optimization control, which combines dynamic linearization and predictive control technology to improve control accuracy and adapt to real-time requirements.

[0006] To this end, the present invention provides the following technical solutions:

[0007] A trajectory tracking method for a fully driven ship based on foresight optimization control, comprising:

[0008] Construct a basic dynamic nonlinear model based on the three degrees of freedom of the ship;

[0009] The basic dynamic nonlinear model is transformed into a linear steady-state system by a parametric design method;

[0010] constructing an enhanced error system and an internal model compensator using the linear steady-state system;

[0011] Determine the optimal controller form by combining the enhanced error system and the internal model compensator;

[0012] Based on the optimization controller, a foresight term is introduced to obtain the optimal controller with the foresight term.

[0013] Furthermore, the basic dynamic nonlinear model:

[0014]

[0015] in: The position and yaw angle of the ship; v = [u, ν, r] T : velocity vector, including forward velocity, lateral velocity and yaw velocity; τ = [τ1, τ2, τ3] T control inputs, including thrust, sway, and yaw moments; The ship attitude transformation matrix maps the velocity vector to the geographic coordinate system; M, C(v) and D(v) represent the ship's inertia matrix, Coriolis force matrix and damping matrix respectively.

[0016] Furthermore, the linear steady-state system:

[0017]

[0018] Among them, the status Output y = η; state matrix Control Matrix Output matrix C c =[I 0]; virtual output is

[0019] Furthermore, the internal model compensator eliminates the influence of reference trajectory disturbance and external disturbance:

[0020]

[0021] Among them, ξ represents the internal compensation state variable; G1 and G2 represent the compensation gain matrix, and e represents the tracking error.

[0022] Furthermore, the enhanced error system:

[0023]

[0024] Among them, η dis the reference trajectory; is the enhanced state vector;

[0025] They are the state matrix, input matrix and reference compensation matrix of the system respectively; is the state matrix of the open loop system.

[0026] Further, the introduction of the foresight term to obtain the optimal controller includes:

[0027] Balance tracking accuracy and control energy consumption through cost function;

[0028] Solve the optimal feedback gain matrix through the algebraic Riccati equation;

[0029] Based on the optimization controller, a foresight term is introduced to obtain the optimal controller with the foresight term.

[0030] Furthermore, the cost function:

[0031]

[0032] Among them, Q represents the trade-off state error; R represents the trade-off control energy consumption; Represents an optimization controller.

[0033] Furthermore, the algebraic Riccati equation:

[0034]

[0035] The optimal feedback gain matrix: K = -R -1 B T P.

[0036] Furthermore, the optimization controller introduces a foresight term:

[0037]

[0038] Where: Lyapunov function positive definite matrix P = [P x P ξ P e ]; l r Represents the look-ahead length parameter, which is used to adjust the response to future trajectories.

[0039] Furthermore, the input of the optimal controller is:

[0040]

[0041] Among them, the feedback gain Feedback gain

[0042] Virtual Input:

[0043] Foreseeable items:

[0044] Weight matrix:

[0045] Generate a reference trajectory by referring to the dynamic model:

[0046]

[0047] η d =C d x d

[0048] Where: x d is the tracking status signal, (A d ,C d ) is a known matrix;

[0049] Inertia matrix:

[0050] Coriolis and Centrifugal Matrices

[0051] Damping Matrix

[0052] Advantages and positive effects of the present invention:

[0053] The present invention utilizes foresight information and obtains future information of the reference trajectory in advance, which significantly improves the dynamic response performance of the system and achieves higher trajectory tracking accuracy. It also adopts a parametric design method to transform the complex nonlinear ship dynamic model into a linear steady-state form, thereby improving the applicability of the control algorithm in the nonlinear system and achieving precise control of the nonlinear system.

[0054] The present invention designs an internal model compensator and an error enhancement system to effectively resist marine environmental disturbances such as wind, waves, and currents, and ensure the stability of trajectory tracking; and designs an efficient decoupling control method for the movement of the ship in three degrees of freedom: forward, lateral, and yaw, to achieve multi-degree-of-freedom decoupling control.

[0055] The present invention optimizes the calculation process of control input by combining algebraic Riccati equations and predictive control design, reduces the calculation burden of real-time control, and realizes optimized control strategy; and the predictive controller can respond to dynamic trajectory changes more quickly, shorten the adjustment time of the system, improve adaptability to complex trajectories, and achieve rapid response.

[0056] Combined with the above advantages, the present invention can improve trajectory tracking accuracy, enhance system robustness and improve the real-time performance of the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0058] Figure 1 is the dynamic response trajectory in the longitudinal direction in the embodiment of the present invention;

[0059] Figure 2 is the dynamic response trajectory in the lateral direction in the embodiment of the present invention;

[0060] Figure 3 is the dynamic response trajectory in the yaw direction in the embodiment of the present invention;

[0061] Figure 4 Flow chart of the method in the embodiment of the present invention. DETAILED DESCRIPTION

[0062] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0063] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0064] The present invention provides a trajectory tracking method for a full-drive ship based on predictive optimization control. By introducing predictive terms and strictly designing controllability and observability, an efficient, robust and practical trajectory tracking control method is provided, which is suitable for ship control tasks in complex dynamic environments.

[0065] S1. Nonlinear ship system modeling;

[0066] S11. Construct a basic dynamic nonlinear model based on the three degrees of freedom (DOF) of the ship:

[0067]

[0068] in: The position and yaw angle of the ship; v = [u, ν, r] T : velocity vector, including forward velocity, lateral velocity and yaw velocity; τ = [τ1, τ2, τ3] T control inputs, including thrust, sway, and yaw moments; The ship attitude transformation matrix maps the velocity vector to the geographic coordinate system; M, C(v) and D(v) represent the ship's inertia matrix, Coriolis force matrix and damping matrix respectively.

[0069] S12. Transform the nonlinear model into a linear steady-state system through parametric design method:

[0070]

[0071] Among them: Status Output y = η; state matrix Control Matrix Output matrix C c =[I 0]; virtual output is

[0072] S13, generating a reference trajectory by referring to the dynamic model:

[0073]

[0074] η d =C d x d

[0075] Where: (A d ,C d ) is a known matrix; trajectory signal η d is piecewise continuously differentiable.

[0076] S2, obtain the optimal controller;

[0077] S21. Define tracking error: e = y - η d ; The tracking error dynamic equation is:

[0078] S22, introduce an internal model compensator to eliminate the influence of reference trajectory disturbance and external disturbance;

[0079] Internal Model Compensator:

[0080] Where: ξ represents the internal compensation state variable; G1 and G2 represent the compensation gain matrix, which is used to ensure the dynamic compensation capability of the system.

[0081] S23. Constructing enhanced error system:

[0082]

[0083] in: is the enhanced state vector;

[0084] They are the state matrix, input matrix and reference compensation matrix of the system respectively; is the state matrix of the open loop system.

[0085] S3. Verify the controllability and observability of linear systems;

[0086] S31. The controllability of a linear system is defined by the control matrix:

[0087]

[0088] If (G1, G2) is stabilizable, then the row rank of the matrix is ​​full, and the system is completely controllable, that is, all state variables can be controlled by input.

[0089] S32. The observability of a linear system is defined by the output matrix:

[0090]

[0091] If the state weight submatrix (C ξ , C e ) is positive definite, then the matrix is ​​of full rank, and all states of the system can be accurately estimated through the output variables.

[0092] Through design, the system's enhanced error system and internal model compensator are theoretically fully controllable and observable.

[0093] S4, determining the optimal controller;

[0094] S41. Design a cost function to balance tracking accuracy and control energy consumption;

[0095] Design cost function:

[0096]

[0097] Where: Q represents the trade-off state error; R represents the trade-off control energy consumption; Represents an optimization controller.

[0098] pass Verify the detectability of the system;

[0099] S42. Through the algebraic Riccati equation:

[0100]

[0101] Solve the optimal feedback gain matrix K = -R -1 B T P, optimize system performance.

[0102] S43. Add a foresight term to the controller design and optimize the control input by introducing future reference trajectory information:

[0103]

[0104] Where: P = [P x P ξ P e ]; l r Represents the look-ahead length parameter, which is used to adjust the response to future trajectories.

[0105] S44, the final input item of the unmanned ship trajectory tracking controller is:

[0106]

[0107] Where: Feedback gain Feedback gain

[0108] Virtual Input:

[0109] Foreseeable items:

[0110] Weight matrix:

[0111] Where: x d is the tracking status signal, (A d ,C d ) is a known matrix;

[0112] Inertia matrix:

[0113] Coriolis and Centrifugal Matrices

[0114] Damping Matrix

[0115] The method of the present invention is further described with the following specific examples:

[0116] 1. Nonlinear ship system modeling;

[0117] 1.1. Establish a three-degree-of-freedom full-drive ship dynamics model, including position (η x ,η y )and

[0118] Yaw angle The dynamic equation of:

[0119]

[0120] in: The position and yaw angle of the ship; v = [u, ν, r] T : velocity vector, including forward velocity, lateral velocity and yaw velocity; τ = [τ1, τ2, τ3] T Control input.

[0121] 1.2. Eliminate nonlinear terms through parametric design and obtain a linearized dynamic model for controller design.

[0122] 2. Controller design;

[0123] 2.1. Construct an enhanced error system;

[0124] Definition of tracking error: e = y-η d ;

[0125] Among them, η d is the reference trajectory;

[0126] 2.2. Design an internal model compensator to eliminate the interference effect of the reference trajectory on the control system: enhance the combination of the error system and the internal model compensator to construct a complete mathematical model of the predictive controller.

[0127] 2.3 Optimal Controller Design

[0128] Optimize the control input, use the algebraic Riccati equation to design the optimal feedback gain matrix and internal model compensator gain, and optimize the trajectory tracking performance; according to the future information of the reference trajectory, add the foresight compensation term to improve the control accuracy.

[0129] 3. The classic Cybership II ship model is used as the test object, and its dynamic parameters are as follows: ship mass: 23.8kg; damping coefficient:

[0130] Verify the dynamic sinusoidal trajectory tracking task: Initial state: η(0) = [0.1m, 0.5m, 0rad], velocity v(0) = [0, 0, 0] T ; Forecast length: l r =5.

[0131] Prediction length l r= 5, the trajectory error converges to zero quickly; when the foresight length increases, the system response time is significantly shortened, for example, r =5, the adjustment time is 8.1s, l r =0 is 73.5s. The amplitude of the control input gradually decreases, and the system becomes more stable. The simulation test results for the sinusoidal trajectory verify the effectiveness of the preview optimization control method.

[0132] In summary, the method of the present invention significantly improves the tracking accuracy of the system under dynamic complex trajectories, optimizes the response time, and enhances the smoothness of the control input and the anti-disturbance ability of the system, showing wide applicability in complex dynamic environments. The present invention shows excellent performance in trajectory tracking of complex nonlinear ship systems, which not only significantly improves the control accuracy and system stability, but also demonstrates wide engineering application potential.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A trajectory tracking method for a fully driven ship based on predictive optimization control, characterized in that: include: Construct a basic dynamic nonlinear model based on the three degrees of freedom of the ship; The basic dynamic nonlinear model is transformed into a linear steady-state system by a parametric design method; constructing an enhanced error system and an internal model compensator using the linear steady-state system; Determine the optimal controller form by combining the enhanced error system and the internal model compensator; Based on the optimization controller, a foresight term is introduced to obtain the optimal controller with the foresight term.

2. According to claim 1, a method for tracking the trajectory of an all-drive ship based on predictive optimization control is characterized in that: The basic dynamic nonlinear model: in: The position and yaw angle of the ship; v = [u, ν, r] T : velocity vector, including forward velocity, lateral velocity and yaw velocity; τ = [τ1, τ2, τ3] T control inputs, including thrust, sway, and yaw moments; The ship attitude transformation matrix maps the velocity vector to the geographic coordinate system; M, C(v) and D(v) represent the ship's inertia matrix, Coriolis force matrix and damping matrix respectively.

3. According to claim 1, a method for tracking the trajectory of an all-drive ship based on predictive optimization control is characterized in that: The linear steady-state system: Among them, the status Output y = η; state matrix Control Matrix Output matrix C c =[I 0]; virtual output is 4. According to claim 1, a method for tracking the trajectory of a fully driven ship based on predictive optimization control is characterized in that: The internal model compensator eliminates the influence of reference trajectory disturbance and external disturbance: Where ξ represents the internal compensation state variable; G1 and G2 represent the compensation gain matrices, and e represents the tracking error.

5. According to claim 4, a method for tracking the trajectory of an all-drive ship based on predictive optimization control is characterized in that: The enhanced error system: Among them, η d is the reference trajectory; is the enhanced state vector; They are the state matrix, input matrix and reference compensation matrix of the system respectively; is the state matrix of the open loop system.

6. According to claim 1, a method for tracking trajectory of a fully driven ship based on predictive optimization control is characterized in that: The introducing of the foresight term to obtain the optimal controller comprises: Balance tracking accuracy and control energy consumption through cost function; Solve the optimal feedback gain matrix through the algebraic Riccati equation; Based on the optimization controller, a foresight term is introduced to obtain the optimal controller with the foresight term.

7. The method for tracking the trajectory of an all-drive ship based on predictive optimization control according to claim 6, characterized in that: The cost function: Among them, Q represents the trade-off state error; R represents the trade-off control energy consumption; Represents an optimization controller.

8. The method for tracking the trajectory of an all-drive ship based on predictive optimization control according to claim 6, characterized in that: The algebraic Riccati equation: The optimal feedback gain matrix: K = -R -1 B T P.

9. The method for tracking the trajectory of an all-drive ship based on predictive optimization control according to claim 6, characterized in that: The optimization controller introduces the foresight term: Where: Lyapunov function positive definite matrix P = [P x P ξ P e ]; l r Represents the look-ahead length parameter, which is used to adjust the response to future trajectories.

10. The method for tracking trajectory of a fully driven ship based on predictive optimization control according to claim 6, characterized in that: The input of the optimal controller is: Among them, the feedback gain Feedback gain Virtual Input: Foreseeable items: Weight matrix: Generate a reference trajectory by referring to the dynamic model: or d =C d x d Where: x d is the tracking status signal, (A d ,C d ) is a known matrix; Inertia matrix: Coriolis and Centrifugal Matrices Damping Matrix

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