Under-actuated ship path tracking model predictive control method and system based on adaptive event triggering

Abstract

The application discloses a kind of underactuated ship path tracking model prediction control method and system based on adaptive event triggering, first, the path point of path tracking is set, and three degrees of freedom nonlinear model of ship is established;Second, according to the path point information and its path point switching mechanism of preset, in the process of ship navigation, the expected heading angle is obtained, the heading error and vertical error are calculated;Finite time extended state observer is used to estimate the ship sway speed, yaw angle velocity, roll angle velocity and disturbance;Then, a robust model predictive controller is designed, and input constraints, roll constraints and performance index constraints are included in the optimization objective;Finally, set adaptive trigger condition and update according to whether the heading error and vertical error meet the trigger condition, effectively reduce the steering frequency, improve the stability and control efficiency of the system.

Description

Technical Field

[0001] This invention belongs to the field of ship motion control technology, specifically relating to a model predictive control method and system for underactuated ship path tracking based on adaptive event triggering. Background Technology

[0002] When underactuated vessels navigate at sea, sudden turns and strong winds, waves, and currents can cause significant rolling motions, affecting their stability. Excessive rolling angles during navigation can impact system performance and stability, necessitating the inclusion of rolling constraints in controller design. Conventional model predictive control, heavily reliant on the model, does not incorporate rolling constraints into its optimization, leading to performance degradation when faced with model uncertainties and external environmental disturbances.

[0003] In recent years, time-triggered mechanisms have been widely used in the design of ship path tracking control systems, where control signals are updated according to a fixed time period. While this mechanism is simple and easy to implement, it has significant shortcomings in practical applications:

[0004] Waste of communication resources: Frequent updates at fixed time intervals can lead to unnecessary consumption of computing and communication resources.

[0005] The control efficiency is low, and it is impossible to adjust the update frequency according to the real-time status of the system. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a model predictive control method and system for underactuated ship path tracking based on adaptive event triggering, which solves the problem that the underactuated ship controller in the prior art does not consider the effects of roll constraints and dynamic errors.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] The model predictive control method for underactuated ship path tracking based on adaptive event triggering includes the following steps:

[0009] Step 1: Set the waypoints for path tracking Establish a three-degree-of-freedom nonlinear model of the ship;

[0010] Step 2: Based on the preset waypoint information and its waypoint switching mechanism, obtain the desired heading angle during the ship's navigation. ;

[0011] Step 3: Calculate the heading error and vertical error ;

[0012] Step 4: Based on the roll angle measured by the ship Bow roll A finite-time extended state observer is used to study the ship's sway velocity. Bow roll rate Roll angular velocity and disturbance Make an estimate;

[0013] Step 5: Design a model predictive controller, incorporating input constraints, roll constraints, and performance index constraints into the optimization objective;

[0014] Step 6: Set adaptive trigger conditions and determine whether the heading error and vertical error meet the trigger conditions. If "yes", update the control law; if "no", update the state and proceed to step 3.

[0015] In step 5, the model predictive controller transforms the optimization problem into a mini-max optimization problem, considering an underactuated ship traveling at a constant speed. Moving forward, when designing a heading controller, the sway speed is usually much greater than the roll speed, so the sway speed is approximately equal to a constant speed.

[0016] In step 6, the deviation from the desired heading and the deviation from the lateral distance are considered as two constraints used to set the criteria for event triggering. The event can only be triggered when the following conditions are met:

[0017]

[0018] The adaptive trigger thresholds are as follows:

[0019]

[0020] in: and It is the initial threshold. and It is the rate at which the control threshold adjusts as the error changes.

[0021] An adaptive event triggering mechanism is predefined. During the ship's path tracking phase, the model prediction controller only updates when a triggering event occurs. The triggering event is defined as follows:

[0022]

[0023] The event triggering mechanism dynamically adjusts the update frequency of control signals according to the actual needs of the system.

[0024] The adaptive event triggering mechanism is expressed by the following formula:

[0025]

[0026] In the formula: and These are the heading error and the vertical error, respectively. and It is an adaptive trigger threshold.

[0027] When the control signal is updated, there is a loss in the actuator. A servo motor loss index is designed to measure the impact of the control signal update on the actuator. The specific servo motor loss index is as follows:

[0028]

[0029] In the formula, and The loss weight coefficient is greater than 0. It is the number of times it is triggered. It is the first The rudder angle input at the next trigger.

[0030] An adaptive event-triggered underactuated ship path tracking model prediction and control system includes a ship controller. When the ship controller is in operation, it applies the method to perform real-time dynamic prediction and optimization of the ship's motion path.

[0031] A computer-readable storage medium storing computer-readable instructions that, when executed by a processor, invoke the steps of the method.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. The controller designed in this invention can significantly reduce the ship's roll angle while ensuring tracking performance, thus realizing multi-objective control of robust model predictive control (RMPC).

[0034] 2. This invention designs a dynamic threshold adjustment strategy that automatically adjusts the threshold according to the system state and error change rate, making the triggering mechanism more reasonable.

[0035] 3. The servo motor loss index designed in this invention, compared with the traditional average servo angle energy loss index, can more comprehensively reflect the two key factors of "trigger frequency + control load", and is more targeted and practical.

[0036] 4. This method effectively reduces the frequency of control signal updates, reduces the wear and tear on actuators such as rudder motors, and suppresses ship rolling motion while ensuring path tracking accuracy, thereby improving system stability and control efficiency. Attached Figure Description

[0037] Figure 1 This is a flowchart of the underactuated ship path tracking control of the present invention.

[0038] Figure 2This is a schematic diagram of the coordinate system for underactuated ship path tracking control according to the present invention.

[0039] Figure 3 This is a schematic diagram of the trigger interval of the actuator of the present invention based on the adaptive trigger threshold.

[0040] Figure 4 This is a schematic diagram comparing the event triggering of the present invention.

[0041] Figure 5 This is a schematic diagram illustrating the effect of the present invention on reducing roll in underactuated ships.

[0042] Figure 6 This is a schematic diagram illustrating the underactuated ship path tracking effect of the present invention. Detailed Implementation

[0043] The structure and working process of the present invention will be further described below with reference to the accompanying drawings.

[0044] The purpose of this invention is to propose an adaptive event-triggered control mechanism to ensure the safety and economy of ships navigating at sea. An adaptive trigger threshold is set based on vertical and heading errors, and the designed controller updates only when the trigger conditions are met, effectively reducing the frequency of rudder turns. A quantitative index is also designed to evaluate rudder angle loss.

[0045] This solution primarily addresses the following technical issues:

[0046] 1. Existing research has not fully considered dynamic roll constraints: Some control methods do not incorporate the ship's roll constraints into the optimization design, which may cause large roll movements during path tracking, thus affecting the ship's navigation stability and the safety of personnel and equipment. This invention studies how to effectively suppress roll during path tracking of underactuated ships. To this end, robust model predictive control (RMPC) is used to achieve multi-objective coordinated control of path tracking and roll reduction for underactuated ships, ensuring stable navigation attitude.

[0047] 2. Conventional event-triggered control strategies often employ static fixed thresholds, but in real-world systems, error changes are often dynamic. This invention constructs an adaptive event-triggered mechanism that reduces the controller's update frequency, the actuator's operating frequency, and the intensity of mechanical wear by dynamically triggering thresholds.

[0048] 3. In order to better quantify the servo motor loss, a servo angle loss index is introduced into the control target, so that the controller can automatically balance the relationship between performance and resource consumption.

[0049] The model predictive control method for underactuated ship path tracking based on adaptive event triggering includes the following steps:

[0050] Step 1: Set the waypoints for path tracking Establish a three-degree-of-freedom nonlinear model of the ship;

[0051] Step 2: Based on the preset waypoint information and its waypoint switching mechanism, obtain the desired heading angle during the ship's navigation. ;

[0052] Step 3: Calculate the heading error and vertical error ;

[0053] Step 4: Based on the roll angle measured by the ship Bow roll A finite-time extended state observer is used to study the ship's sway velocity. Bow roll rate Roll angular velocity and disturbance Make an estimate;

[0054] Step 5: Design a model predictive controller, incorporating input constraints, roll constraints, and performance index constraints into the optimization objective;

[0055] Step 6: Set adaptive trigger conditions and determine whether the heading error and vertical error meet the trigger conditions. If "yes", update the control law; if "no", update the state and proceed to step 3.

[0056] Specific embodiments, such as Figures 1 to 6 As shown:

[0057] The model predictive control method for underactuated ship path tracking based on adaptive event triggering includes the following steps:

[0058] Step 1: Set the waypoints for path tracking Taking into account the ship's roll, bow roll, and sway motions, and neglecting the heave and pitch dynamics, a three-degree-of-freedom nonlinear model of the ship is established, expressed as follows:

[0059] (1)

[0060] in: For oscillation speed, Indicates the mass of the ship; and for and Additional mass in the direction; and For the moments of inertia in the roll and bow directions; and Additional moments of inertia in the roll and bow directions; for exist The center coordinates on the axis; , and These represent the swaying hydrodynamics, rolling hydrodynamics, and bowing hydrodynamics, respectively. For the weight of the ship, It is the acceleration due to gravity; It has high lateral stability; This refers to the roll angle; and for and exist The center coordinates on the axis; Indicates the center of gravity is Position on the axis.

[0061] Step 2, according to Figure 2 Schematic diagram, desired heading angle The calculation formula is:

[0062] (2)

[0063] In the formula: For Let the radius of the circle formed by the center be 2L (where L is the length of the ship). For vertical error, .

[0064] During ship navigation, the preset waypoints need to be switched. When it is found that the ship enters a circle centered on the current waypoint, When the radius is a circle, the path will switch to the next path point. The switching conditions are as follows:

[0065] (3)

[0066] General selection , usually take =2, Captain.

[0067] Step 3: Calculate the heading error and vertical error The calculation formula is:

[0068] (4)

[0069] In the formula: For the ship's position, The path point at the current moment, .

[0070] Step 4: Use the Finite Time Extended State Observer (FTESO) to estimate the system state and compound disturbances. The model for the underactuated surface vessel during design can be expressed as:

[0071] (5)

[0072] In the formula: , , Usually, these are unknown items. , For the control coefficient vector, This is the system output.

[0073] Let FTESO be designed as follows:

[0074] (6)

[0075] In the formula: and These are parameters to be determined. , and Represents state observations; .

[0076] Step 5: Design a robust model predictive controller, incorporating input constraints, roll constraints, and performance index constraints into the optimization objective; the robust model predictive controller model is as follows:

[0077] (7)

[0078] In the formula: For heading error, For sway speed, The bow roll rate is angular velocity. The angular velocity of the roll is... The roll angle, Let be the perturbation vector. For ocean interference in the roll direction, bow direction Wave interference, This is a control law.

[0079] The formula for calculating the control law is designed as follows:

[0080] (8)

[0081] In the formula: For the feedback gain matrix, .

[0082] The robust predictive controller model described above is rewritten as follows:

[0083] (9)

[0084] In the formula: For state vectors, For the system matrix, To control the input matrix, For the output matrix, For the output vector, This is the perturbation vector.

[0085] Taking a sampling time of 0.1s, the above equation is discretized into the following form using the zero-order hold method:

[0086] (10)

[0087] The performance index of an infinite-time quadratic form can be written as:

[0088] (11)

[0089] In the formula: and It is a positive definite symmetric matrix.

[0090] This can be transformed into the following minimum-maximum optimization problem:

[0091] (12)

[0092] Excessive roll angles during navigation can affect system performance and stability; roll constraints must be considered.

[0093] (13)

[0094] In the formula: This represents the maximum value of the roll angle.

[0095] because ,in Rewrite the above equation as follows:

[0096] (14)

[0097] In the formula: To satisfy the control law The control gain matrix, and .

[0098] According to Schur complement theory, the above equation can be rewritten as follows:

[0099] (15)

[0100] By processing the infinite time-domain performance index and input constraints, and using Schur's complement lemma, the following linear matrix inequality (LMI) is obtained:

[0101] (16)

[0102] In the formula: To define a matrix and , To define a scalar and , It is a positive definite matrix.

[0103] (17)

[0104] In the formula, "This is a symmetrical block where the corresponding element is symmetrical and equal to the element in the bottom left corner." It is an identity matrix.

[0105] (18)

[0106] In the formula, This represents the maximum value of the rudder angle.

[0107] RMPC transforms the optimization problem from (12) into the following optimization problem:

[0108] Equations (15), (16), (17), (18), and (19)

[0109] Consider an underactuated vessel at a constant speed Forward movement, therefore only a heading controller needs to be designed. Typically, the pitch speed is much greater than the sway speed, thus... .

[0110] Step 6: Determine whether the adaptive triggering conditions are met.

[0111] To reflect control performance, deviations from the desired heading and lateral distance are considered as two constraints used to set the criteria for event triggering. An event can only be triggered when the following conditions are met:

[0112] (20)

[0113] Design an adaptive trigger threshold:

[0114] (twenty one)

[0115] In the formula: and It is the initial threshold. and It is the rate at which the control threshold adjusts as the error changes.

[0116] If the heading error and vertical error satisfy equation (20), then the event occurs, the optimization problem (19) will be solved, and a new control input sequence will be obtained. Assume... This is the initial trigger time; the time corresponding to the previous trigger event is... For the triggering time interval rudder angle of the control system It will remain unchanged.

[0117] The triggering mechanism for ships during the path tracking phase is defined as follows:

[0118] (twenty two)

[0119] In the formula, and To adapt the trigger threshold, determine when to update the control input; and These are the heading error and the vertical error, respectively.

[0120] The trigger threshold can be dynamically adjusted based on the heading error, vertical error, and their rate of change. Event-triggered robust model predictive control (ET-RMPC) is updated only when the trigger event occurs.

[0121] The triggering event is defined as follows:

[0122] (twenty three)

[0123] With this design, the event-triggered mechanism can dynamically adjust the update frequency of the control signal according to the actual needs of the system, thereby reducing the consumption of communication resources and the wear and tear of the actuator while ensuring control accuracy.

[0124] To quantify this loss, a servo motor loss index is introduced to measure the impact of control signal updates on the actuator. The design of the servo motor loss index considers not only the update frequency of the control signal but also the loss to the actuator with each update. The servo motor loss index is designed as follows:

[0125] (twenty four)

[0126] In the formula, and The loss weight coefficient is greater than 0. It is the number of times it is triggered. It is the first The rudder angle input at the next trigger.

[0127] To further illustrate the effects of the technical solution of this invention, a specific data example will be used for detailed explanation below.

[0128] Using the S-175 container ship as the controlled object, computer numerical simulation was performed using MATLAB. Key parameters of the S-175: Length: Width: First draft: Tail draft: Average draft: Drainage volume: Horizontal coordinates of the epicenter and vertical coordinates: Height of center of buoyancy: Square coefficient: Rudder area: Rudder aspect ratio: Propeller diameter: fin area .

[0129] Initial value settings: m / s, , , , , , , The controller model parameters are as follows: , , , , , , , , , , , , , , , , , , Preset waypoints: , , , , , .

[0130] Adaptive event triggering related parameter settings: , , , .

[0131] Parameter settings for the finite-time state observer:

[0132] , , , , , , , , , Servo loss parameters: , .

[0133] Figure 3 The simulation results show the trigger interval under the event-triggered mechanism. The maximum trigger interval is 70.1s, and the time interval between any two triggers is greater than zero. This indicates that the system effectively suppresses the Zeno phenomenon, ensuring a good balance between stability and controllability, and avoiding system instability due to excessive control frequency or wasted resources due to frequent calculations.

[0134] Figure 4 The diagram illustrates the comparison of event-triggered control. Compared with time-triggered control, the proposed control method based on adaptive event-triggered mechanism can significantly reduce the number of communications, samplings, and control executions.

[0135] Figure 5 and Figure 6 This indicates that adding roll constraints achieves a good roll reduction effect while ensuring the path tracking performance of the underactuated ship.

[0136] The introduction of servo motor loss index enables explicit modeling of the impact of system update mechanism on execution resources, which is applicable to embedded controllers, low-power platforms or control scenarios with limited actuator resources.

[0137] It should be understood that this solution is not limited to the specific embodiments described above. Devices and structures not described in detail herein should be understood as being implemented in a manner common to the art. Any person skilled in the art can make many possible variations and modifications to this solution, or modify it into equivalent embodiments, without departing from the scope of this solution, using the methods and techniques disclosed above. This does not affect the substantive content of this solution. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of this solution, without departing from its scope, still fall within the protection scope of this solution.

[0138] To further realize the beneficial effects of the above method, a robust model predictive control system for underactuated ship path tracking based on adaptive event triggering is also disclosed, including a ship controller. When the ship controller is working, it applies the method to perform real-time dynamic prediction and optimization of the ship's motion path.

[0139] A computer-readable storage medium storing computer-readable instructions that, when executed by a processor, invoke the steps of the method.

[0140] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A model predictive control method for underactuated ship path tracking based on adaptive event triggering, characterized in that: Includes the following steps: Step 1: Set the waypoints for path tracking Establish a three-degree-of-freedom nonlinear model of the ship; Step 2: Based on the preset waypoint information and its waypoint switching mechanism, obtain the desired heading angle during the ship's navigation. ; Step 3: Calculate the heading error and vertical error ; Step 4: Based on the roll angle measured by the ship Bow roll A finite-time extended state observer is used to study the ship's sway velocity. Bow roll rate Roll angular velocity and disturbance Make an estimate; Step 5: Design a model predictive controller, incorporating input constraints, roll constraints, and performance index constraints into the optimization objective; Step 6: Set adaptive trigger conditions and determine whether the heading error and vertical error meet the trigger conditions. If "yes", update the control law; if "no", update the state and proceed to step 3.

2. The model predictive control method for underactuated ship path tracking based on adaptive event triggering according to claim 1, characterized in that: In step 5, the model predictive controller transforms the optimization problem into a mini-max optimization problem, considering an underactuated ship traveling at a constant speed. Moving forward, when designing a heading controller, the sway speed is usually much greater than the roll speed, so the sway speed is approximately equal to a constant speed.

3. The model predictive control method for underactuated ship path tracking based on adaptive event triggering according to claim 1, characterized in that: In step 6, the deviation from the desired heading and the deviation from the lateral distance are considered as two constraints used to set the criteria for event triggering. The event can only be triggered when the following conditions are met: The adaptive trigger thresholds are as follows: in: and It is the initial threshold. and It is the rate at which the control threshold adjusts as the error changes.

4. The model predictive control method for underactuated ship path tracking based on adaptive event triggering according to claim 3, characterized in that: An adaptive event triggering mechanism is predefined. During the ship's path tracking phase, the model prediction controller only updates when a triggering event occurs. The triggering event is defined as follows: The event triggering mechanism dynamically adjusts the update frequency of control signals according to the actual needs of the system.

5. The model predictive control method for underactuated ship path tracking based on adaptive event triggering according to claim 4, characterized in that: The adaptive event triggering mechanism is expressed by the following formula: In the formula: and These are the heading error and the vertical error, respectively. and It is an adaptive trigger threshold.

6. The model predictive control method for underactuated ship path tracking based on adaptive event triggering according to claim 5, characterized in that: When the control signal is updated, there is a loss in the actuator. A servo motor loss index is designed to measure the impact of the control signal update on the actuator. The specific servo motor loss index is as follows: In the formula, and The loss weight coefficient is greater than 0. It is the number of times it is triggered. It is the first The rudder angle input at the next trigger.

7. A model predictive control system for underactuated ship path tracking based on adaptive event triggering, characterized in that: The system includes a ship controller, which, when in operation, applies the method described in any one of claims 1 to 6 to perform real-time dynamic prediction and optimization of the ship's motion path.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-readable instructions that, when executed by a processor, invoke the steps of the method according to any one of claims 1 to 6.

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