A ship dynamic positioning output feedback control method based on hamilton theory

Abstract

The embodiment discloses a ship power positioning output feedback control method based on Hamilton theory, obtains state error interconnection and damping distribution passivity control law based on a three-degree-of-freedom port controlled Hamilton model of a ship horizontal plane, obtains auxiliary state variables and disturbance estimation values by constructing a reduced-order extended state observer, estimates and compensates total disturbance in real time, constructs a non-convex constraint operator of a propeller control input, establishes a dynamic auxiliary system to obtain a dynamic auxiliary system state vector, compensates input saturation error by using the dynamic auxiliary system, obtains actual application control instructions after non-convex projection based on an adaptive event triggering mechanism, finally obtains unconstrained ideal control instructions, and obtains actual control input based on the adaptive event triggering mechanism, so that high-precision trajectory tracking and propeller service life extension are realized.

Description

Technical Field

[0001] This invention relates to the field of ship motion control technology, and in particular to a ship dynamic positioning output feedback control method based on Hamiltonian theory. Background Technology

[0002] Crane vessels are core equipment in marine engineering, widely used in offshore wind power installation, large structure hoisting, and underwater construction. Unlike conventional dynamically positioned vessels, crane vessels are not only subject to disturbances from complex marine environments such as wind, waves, and currents during operation, but also face highly nonlinear dynamics such as load changes caused by the swing of the load and large hull movements. Simultaneously, the propulsion system suffers from physical saturation constraints, and the output capabilities of the thrusters in different degrees of freedom are coupled (e.g., thrust and torque cannot reach their maximum values ​​simultaneously). This coupling effect results in a non-convex shape for the input feasible region. Traditional "independent limiting for each channel" methods may overestimate the actual available control capability, leading to control commands exceeding limits or actuators failing to respond.

[0003] On the other hand, traditional continuous control strategies lead to frequent thruster movements, accelerating mechanical wear and increasing energy consumption. To reduce the execution frequency, event-triggered control has been introduced, but fixed-threshold event triggering struggles to balance control performance and energy-saving requirements. Furthermore, actual ship model parameters are difficult to obtain accurately, and external environmental disturbances are unknown; traditional controllers often rely on precise models, resulting in insufficient robustness.

[0004] Currently, there are ship motion control methods based on passive control (PBC) or interconnected and damped distributed passive control (IDA-PBC), but most of them do not consider non-convex input constraints, do not introduce event triggering mechanisms, and fail to effectively combine disturbance observers to handle model uncertainties. Summary of the Invention

[0005] This invention discloses a ship dynamic positioning output feedback control method based on Hamiltonian theory to overcome the above-mentioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A ship dynamic positioning output feedback control method based on Hamiltonian theory includes the following steps: S1: Establish a three-degree-of-freedom port-controlled Hamiltonian model of the ship in the horizontal plane to obtain the passive control law for state error interconnection and damping distribution; S2: Construct a reduced-order extended state observer to obtain auxiliary state variables and perturbation estimates; S3: Construct a non-convex constraint operator for the thruster control input based on the auxiliary state variables; S4: Based on the non-convex constraint operator of the thruster control input, establish a dynamic auxiliary system to obtain the dynamic auxiliary system state vector; and based on the adaptive event triggering mechanism, obtain the actual application control command after non-convex projection; S5: Based on the passive control law of state error interconnection and damping allocation, the actual application control command after non-convex projection, the dynamic auxiliary system state vector and the disturbance estimate, obtain the unconstrained ideal control command, and obtain the actual control input based on the adaptive event triggering mechanism to realize the control of the ship.

[0007] Furthermore, the passive control law for the interconnection of state errors and damping distribution is expressed as follows:

[0008] In the formula: Assign passive control laws to interconnect and damping state errors; For the controller gain matrix used for energy shaping, ; For position tracking error, , This is the desired reference trajectory for the ship's position and heading in the northeast coordinate system; To match the reference momentum corresponding to the desired trajectory, , for The derivative with respect to time; The controller gain matrix is ​​used for damping injection. , and It is a symmetric positive definite matrix; For the system momentum tracking error, .

[0009] Furthermore, the reduced-order extended state observer is represented as follows:

[0010]

[0011] In the formula: As auxiliary state variables, This is the observation gain diagonal matrix of the reduced-order extended state observer. , These are the observation gain coefficients for the ship's pitch channel, sway channel, and bow channel, respectively. This is the derivative with respect to time; It is a diagonal matrix; Given the lumped dynamics function terms of the ship system, This is the velocity vector in the ship's coordinate system; This is the estimated value of the disturbance; For the velocity domain Coriolis matrix; The damping matrix is ​​in the velocity domain. This is the actual control input.

[0012] Furthermore, the non-convex constraint operator for the thruster control input is represented as follows:

[0013]

[0014]

[0015] In the formula: Non-convex constraint operators for thruster control input; The input vector is an unconstrained ideal control vector. The Euclidean 2-norm operator for vectors; To control the input vector The maximum feasible scaling factor that satisfies the non-convex constraint in the direction; For supremum mathematical operators; This is the mathematical division operator; To describe the non-convex constraint set for multi-degree-of-freedom direction-amplitude coupling constraints of a thruster, ; Let be the set of the real number space consisting of all real numbers; It is a continuous and non-convex constraint function; The parameters for traversing the line segments in the interval [0,1] are used. in,

[0016]

[0017] In the formula: For projection operator The supremum constant of the norm on the constraint set Ω; For infimal mathematical operators; For projection operator The infimum constant of the norm on the constraint set Ω.

[0018] Furthermore, the dynamic assistance system is established as follows:

[0019]

[0020] In the formula: This represents the state vector of the dynamic auxiliary system. State vector of dynamic auxiliary system rate of change over time; Design matrix for damping configuration of auxiliary system, ; This refers to the system's momentum tracking error. To control input saturation error; The actual application control commands are obtained after non-convex projection; This is an unconstrained ideal control command; To assist the system in segmented switching threshold constant, ; It is a zero vector with 3 rows and 1 column;

[0021]

[0022] In the formula: This is an unconstrained ideal control command; These are intermediate calculation parameters; in, , for The lower bound of the global normal number is the minimum conservative threshold constant.

[0023] Furthermore, the adaptive event triggering mechanism is expressed as follows:

[0024] In the formula: To adapt to dynamic event triggering thresholds, , , These are the upper and lower bounds of the preset threshold; for The derivative with respect to time; Let be the threshold decay constant, and ; Let be the threshold adaptive learning gain constant, and ; The actual control command from the previous moment; The actual application control command after non-convex projection at the current moment; The triggering condition is as follows:

[0025] ,

[0026] In the formula: To control the triggering error of commands; The actual application control command after non-convex projection at the current moment; A fixed offset constant is used for trigger margin.

[0027] Furthermore, the formula used to obtain the unconstrained ideal control command is as follows:

[0028] In the formula: This is an unconstrained ideal control command; This represents the state vector of the dynamic auxiliary system. This is the estimated value of the disturbance; This is the gain matrix of the auxiliary system; Passive control laws are assigned to the interconnection and damping of state errors.

[0029] Furthermore, the three-degree-of-freedom port-controlled Hamiltonian model of the ship in the horizontal plane is as follows:

[0030] In the formula: Let be the ship's position and heading vector in the northeast coordinate system. , This indicates the ship's northward position. This indicates the ship's eastward position. The bow angle of the ship. This is the matrix transpose operator; for The derivative with respect to time; For ship momentum, , It is a positive definite inertial matrix. This is the velocity vector in the ship's coordinate system. , For the longitudinal speed of the ship, For the ship's lateral speed, The bow roll rate of the ship; for The derivative with respect to time; It is a rotation matrix; The momentum space Coriolis matrix; Here is the momentum space damping matrix; For open-loop Hamiltonian functions right The gradient of, where ; For open-loop Hamiltonian functions right gradient, ; for The identity matrix; For actual control input; It is an open-loop Hamiltonian function.

[0031] Beneficial Effects: This invention provides a ship dynamic positioning output feedback control method based on Hamiltonian theory. Based on a three-degree-of-freedom port-controlled Hamiltonian model of the ship's horizontal plane, it obtains a passive control law for state error interconnection and damping allocation. By constructing a reduced-order extended state observer, it obtains auxiliary state variables and disturbance estimates, and estimates and compensates for the total disturbance in real time. Furthermore, it constructs a non-convex constraint operator for the thruster control input, establishes a dynamic auxiliary system, obtains the dynamic auxiliary system state vector, and uses the dynamic auxiliary system to compensate for input saturation errors. Based on an adaptive event triggering mechanism, it obtains the actual application control command after non-convex projection, and finally obtains the unconstrained ideal control command. Based on the adaptive event triggering mechanism, it obtains the actual control input, achieving high-precision trajectory tracking and extending the thruster's service life. This invention is a ship trajectory tracking control method capable of simultaneously handling strong nonlinear disturbances, non-convex input saturation, reducing execution frequency, and possessing strict stability guarantees. By employing a nonlinear extended state observer to compensate for unknown disturbances in real time and designing an adaptive event triggering mechanism, a ship IDA-PBC trajectory tracking control method is formed. This invention achieves high-precision, low-energy trajectory tracking control under complex sea conditions by designing a non-convex projection operator to process the thruster direction-amplitude coupling constraint, introducing a dynamic auxiliary system to compensate for saturation error, and adopting an adaptive event triggering mechanism to reduce the execution frequency. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a flowchart of the ship dynamic positioning output feedback control method based on Hamiltonian theory according to the present invention. Figure 2 This is a block diagram of the ship control system structure in an embodiment of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] This embodiment introduces a ship dynamic positioning output feedback control method based on Hamiltonian theory, including the following steps: Figure 1 and Figure 2 As shown: S1: Establish a three-degree-of-freedom port-controlled Hamiltonian model of the ship in the horizontal plane to obtain the passive control law for state error interconnection and damping distribution (IDA-PBC).

[0036] Preferably, the three-degree-of-freedom port-controlled Hamiltonian model of the ship in the horizontal plane is as follows: (1) In the formula: Let be the ship's position and heading vector in the northeast coordinate system. , This indicates the ship's northward position. This indicates the ship's eastward position. The bow angle of the ship. This is the matrix transpose operator; for The derivative with respect to time; For ship momentum, , It is a positive definite inertial matrix. This is the velocity vector in the ship's coordinate system. , For the longitudinal speed of the ship, For the ship's lateral speed, The bow roll rate of the ship; for The derivative with respect to time; It is a rotation matrix; The momentum space Coriolis matrix; Here is the momentum space damping matrix; For open-loop Hamiltonian functions right The gradient of, where ; For open-loop Hamiltonian functions right gradient, ; for The identity matrix; For actual control input; It is an open-loop Hamiltonian function.

[0037] Preferably, the passive control law for the state error interconnection and damping distribution is expressed as follows: (2) In the formula: Assign passive control laws to interconnect and damping state errors; For the controller gain matrix used for energy shaping, ; For position tracking error, , This is the desired reference trajectory for the ship's position and heading in the northeast coordinate system; To match the reference momentum corresponding to the desired trajectory, , for The derivative with respect to time; The controller gain matrix is ​​used for damping injection. , and It is a symmetric positive definite matrix; For the system momentum tracking error, ; Specifically, the core difference between the State Error IDA-PBC method and traditional "signal processing" control strategies (such as sliding mode control and backstepping) lies in its completely energy-centric controller design. Traditional methods focus on directly eliminating time-domain error signals, typically requiring accurate models and employing a mechanical approach to handling system nonlinear characteristics. In contrast, the State Error IDA-PBC in this embodiment utilizes "potential energy shaping" and "damped injection" techniques to directly construct an energy function within the port-controlled Hamiltonian (PCH) framework, transforming the control objective into a desired energy curve. This allows the controller to profoundly reveal the intrinsic physical relationship between system energy and dynamic characteristics, possessing clear physical meaning and a modular design approach.

[0038] S2: Construct a reduced-order extended state observer to obtain auxiliary state variables and disturbance estimates. Use the ship's position and heading measurements to estimate the total composite disturbance consisting of model parameter uncertainties, unknown environmental disturbances, and measurement noise in real time, and use the estimates for feedforward compensation. Preferably, the reduced-order extended state observer is represented as follows: (3)

[0039] In the formula: As auxiliary state variables, This is the observation gain diagonal matrix of the reduced-order extended state observer. , These are the observation gain coefficients for the ship's pitch channel, sway channel, and bow channel, respectively. This is the derivative with respect to time; It is a diagonal matrix; Given the lumped dynamics function terms of the ship system, This is the velocity vector in the ship's coordinate system; This is the estimated value of the disturbance; For the velocity domain Coriolis matrix; The damping matrix is ​​in the velocity domain. This is the actual control input.

[0040] S3: Construct a non-convex constraint operator for the thruster control input based on the auxiliary state variables; Specifically, for the input saturation characteristics formed by the multi-degree-of-freedom direction-amplitude coupling of the thruster, a non-convex constraint operator is defined to project the design control command along the original direction to the boundary of the feasible set.

[0041] Specifically, a non-convex constraint set describing the direction-amplitude coupling constraints of the thruster's multi-degree-of-freedom mode is introduced. And define nonconvex constraint operators. The design control commands are projected along the original direction to the boundary of the feasible set. Preferably, the non-convex constraint operator for the thruster control input is represented as follows: (4)

[0042]

[0043] In the formula: Non-convex constraint operators for thruster control input; The input vector is an unconstrained ideal control vector. The Euclidean 2-norm operator for vectors; To control the input vector The maximum feasible scaling factor that satisfies the non-convex constraint in the direction; For supremum mathematical operators; This is the mathematical division operator; To describe the non-convex constraint set for multi-degree-of-freedom direction-amplitude coupling constraints of a thruster, It is a nonempty bounded closed nonconvex constrained set and , Let be the set of the real number space consisting of all real numbers; It is a continuous and non-convex constraint function; The parameters for traversing the line segments in the interval [0,1] are used. in,

[0044]

[0045] In the formula: For projection operator The supremum constant of the norm on the constraint set Ω; For infimal mathematical operators; For projection operator The infimum constant of the norm on the constraint set Ω.

[0046] Specifically, unlike the traditional "independent amplitude limiting for each channel" anti-saturation method, the anti-saturation design based on non-convex constraint operators proposed in this embodiment fully considers the inherent "direction-amplitude" coupling physical constraints of ship propellers in multiple degrees of freedom. Traditional methods not only ignore the power and steering coupling relationship between different degrees of freedom of the propeller, but also cause distortion of the direction of the desired control force, reducing positioning accuracy and even causing closed-loop instability. In contrast, this embodiment introduces a non-convex constraint operator to accurately project the desired control command along the original direction to the boundary of the real non-convex feasible set, ensuring that the force / torque direction of the output command is strictly consistent with the desired direction, and only reasonably compressing the amplitude. This design fundamentally avoids energy waste and control deviation caused by directional deflection, significantly improving the actual response efficiency and control quality of the propulsion system. At the same time, this operator does not require an additional auxiliary system to compensate for saturation errors, simplifies the controller structure, and has a unified processing capability for both convex and non-convex constraints, possessing stronger engineering universality and robustness.

[0047] S4: Based on the non-convex constraint operator of the thruster control input, a dynamic auxiliary system is established to obtain the dynamic auxiliary system state vector; this is used to compensate for the saturation error caused by the anti-saturation mapping and correct the tracking error. Based on an adaptive event triggering mechanism, the actual application control command after non-convex projection is obtained. Preferably, the dynamic assistance system is established as follows: (5)

[0048] In the formula: This represents the state vector of the dynamic auxiliary system. State vector of dynamic auxiliary system rate of change over time; Design matrix for damping configuration of auxiliary system, ; This refers to the system's momentum tracking error. To control input saturation error; The actual application control commands are obtained after non-convex projection; This is an unconstrained ideal control command; To assist the system in segmented switching threshold constant, This indicates that the threshold value of this segment is a positive real number, which serves as the boundary for the start and stop of the auxiliary system. It is a zero vector with 3 rows and 1 column.

[0049] Specifically, due to and Having the same direction, the current application control command with non-convex constraints, i.e., the actual application control command after non-convex projection, is expressed as: (6) (7) In the formula: This is an unconstrained ideal control command; These are intermediate calculation parameters; in, , for The lower bound of the global normal number is the minimum conservative threshold constant.

[0050] Preferably, in the adaptive event triggering mechanism, the trigger threshold The system dynamically adjusts according to its state to determine whether to update control commands; the adaptive event triggering mechanism is described as follows: (1) In the formula: To adapt to dynamic event triggering thresholds, , , These are the upper and lower bounds of the preset threshold; for The derivative with respect to time; Let be the threshold decay constant, and ; Let be the threshold adaptive learning gain constant, and ; The actual control command from the previous moment; The actual application control command after non-convex projection at the current moment; The triggering condition is as follows: (8) ,

[0051] In the formula: To control the triggering error of commands; The actual application control command after non-convex projection at the current moment; A fixed offset constant is used for trigger margin.

[0052] Specifically, compared with the traditional fixed threshold event triggering mechanism, the adaptive event triggering mechanism proposed in this embodiment can dynamically adjust the triggering threshold according to the system state, overcoming the fundamental defect of fixed thresholds that make it difficult to balance control performance and resource efficiency. In traditional methods, if the threshold is set too high, although it can significantly reduce the start-stop frequency of the thrusters and reduce mechanical wear, it can easily lead to a lag in control command updates, resulting in an inability to respond in time when the ship encounters strong winds, waves, or ice loads, causing increased positioning deviations. If the threshold is set too low, the controller updates almost continuously, and energy consumption and actuator wear problems remain prominent. This embodiment designs a threshold adaptive law so that the triggering threshold is adjusted in real time according to the rate of change of control commands or tracking errors: when the ship's dynamics are drastic and the control signal changes significantly, the threshold automatically decreases to increase the control update frequency to ensure positioning accuracy; when the system tends to be steady and the control signal changes gradually, the threshold automatically increases to reduce the update frequency to save energy and extend the service life of the thrusters. This mechanism achieves a dynamic trade-off between control performance and execution frequency, and is especially suitable for ships that operate in harsh environments such as polar regions for extended periods. It can significantly reduce communication and computing burdens and improve system economy and reliability.

[0053] S5: Based on the passive control law of state error interconnection and damping allocation, the actual application control command after non-convex projection, the dynamic auxiliary system state vector and the disturbance estimate, obtain the unconstrained ideal control command, and obtain the actual control input based on the adaptive event triggering mechanism to realize the control of the ship.

[0054] Specifically, the control command for the current moment is obtained by combining the state error IDA-PBC control law, the state of the dynamic auxiliary system, and the disturbance estimate. After being mapped by the non-convex constraint operator, it is applied to the propulsion system, and the event triggering conditions are checked periodically.

[0055] Preferably, the formula used to obtain the unconstrained ideal control command is as follows: (9) In the formula: This is an unconstrained ideal control command; This represents the state vector of the dynamic auxiliary system. This is the estimated value of the disturbance; This is the gain matrix of the auxiliary system; Passive control laws are assigned to the interconnection and damping of state errors.

[0056] Implementation method: S1: Establishing the PCH model and IDA-PBC control law: First, establish the ship's position and bow vector in the northeast coordinate system. velocity vector in the ship's coordinate system Define momentum ,in, The system has a positive definite inertia matrix (including added mass). The open-loop Hamiltonian function of the system is... (No potential energy). According to ship kinematics and dynamics, the horizontal motion of a ship can be expressed in the following port-controlled Hamiltonian (PCH) form:

[0057] in,

[0058]

[0059] , .

[0060] Set the desired trajectory It is smooth and bounded, and its second derivative is bounded. The tracking error is defined. , ,

[0061] According to the IDA-PBC principle, we expect the closed-loop system to have the following desired Hamiltonian function through the control law: (10) In the formula: Let Hamiltonian be the desired Hamiltonian function; The potential energy shaping matrix to be designed.

[0062] To obtain the corresponding control law, we assume the actual control input. Take as nominal form And derive its expression, Substitute into an open-loop system and utilize as well as , can be obtained .

[0063] Dynamics

[0064] because , Substituting, we get: (11) In a closed-loop system: (12) in, Let the damping injection matrix be the one to be designed. The IDA-PBC control law can then be solved: (13) S2: Design a reduced-order extended state observer (ESO): Actual ships are subject to disturbances from unknown environments and uncertainties in model parameters; all these uncertainties are collectively referred to as the total disturbance. The actual dynamic equation is then: (14) For ease of observer design, the known dynamics are denoted as: Then the original equation simplifies to: (15) set up for From the estimated values, construct auxiliary state variables: (16) in, This is the observation gain diagonal matrix.

[0065] In order to make Able to asymptotically track , For the total composite disturbance, design the following first-order filter form for error dynamics: (17) Differentiating both sides of (16) and substituting equations (17) and (15) into the equation, we get: (18) Finally, the reduced-order extended state observer is constructed using formulas (18) and (16): (19) The observer only needs to be known. , and It can output disturbance estimates online in real time without requiring velocity derivatives. It is used for feedforward compensation in control laws.

[0066] S3: Thruster anti-saturation design method based on non-convex constraint operators: To mathematically encompass both "independent saturation (convex)" and "coupled saturation (non-convex)" scenarios while preserving the generality of subsequent controller design, we abstract the thruster saturation constraint coupling problem into a unified three-dimensional input constraint problem with non-convex boundaries, i.e., a non-convex input constraint problem. Specifically, taking the actual control input of the hull... Define the feasible set as the control input vector: (20) in, A continuous and non-convex constraint function To handle non-convex input constraint problems, the following non-convex constraint operator is defined: Non-convex constraint operators satisfy (twenty one) in, , It is a nonempty bounded closed nonconvex constrained set and ,also, , .

[0067] because and Having the same direction, the application control command at the current moment with non-convex constraints can be expressed as: (twenty two) in, Indicates the control commands for the design. It can be obtained through the following formula: (twenty three) in, .

[0068] S4: Establishment of Dynamic Assist System: To compensate for the saturation error caused by the mapping of non-convex constraint operators, this invention designs a dynamic auxiliary system. This system uses the saturation error... Input, output compensation term The feedback is sent to the output of the state error IDA-PBC controller to correct the tracking error, thereby mitigating the adverse effects of saturation on system performance. The dynamic auxiliary system is designed as follows: (twenty four) in, , Design matrix for damping configuration of auxiliary system, This is the threshold constant for segmented switching in the auxiliary system. Where, in the formula... At this time, the system is in an active state, and its dynamics consist of three parts: first, the linear damping term. First, it is used to stabilize the auxiliary state; second, it is a nonlinear energy absorption term. The first is used to dissipate the energy of saturation error; the second is the direct driving term. The saturation error is injected into the auxiliary system. When When this happens, the auxiliary system state is set to zero to avoid unnecessary compensation triggered by minor numerical disturbances.

[0069] S5: Adaptive event triggering mechanism: To reduce the controller update frequency, an adaptive event triggering mechanism is introduced. Let the previous trigger time be... At present Define the trigger error: (25) The triggering condition is: (26) in, To fix a small threshold, The adaptive parameters are updated by the following adaptive law: (27) In the formula, , For design parameters, , , Preset upper and lower bounds.

[0070] The event is triggered when the triggering condition is not met: Update control commands and reset. Between two triggers, the control command remains at the value of the previous trigger.

[0071] S6: Synthesis of General Control Commands: By combining the state error IDA-PBC control law, the auxiliary system state, and the disturbance estimate, we obtain the unconstrained ideal control command at the current moment: (28) In the formula: This is the gain matrix for the auxiliary system. The actual control commands after non-convex projection.

[0072] Then, based on the decision of the event triggering mechanism, the actual control input is determined. Finally, The output is sent to the ship's propulsion system to drive the ship's movement.

[0073] This embodiment is based on a three-degree-of-freedom port-controlled Hamiltonian model of the ship's horizontal plane, obtaining a passive control law for state error interconnection and damping allocation. By constructing a reduced-order extended state observer, auxiliary state variables and disturbance estimates are obtained, and the total disturbance is estimated and compensated in real time. A non-convex constraint operator for the propeller control input is constructed, establishing a dynamic auxiliary system to obtain the dynamic auxiliary system state vector, which is then used to compensate for input saturation errors. Based on an adaptive event triggering mechanism, the actual application control command after non-convex projection is obtained, and finally, an unconstrained ideal control command is obtained. Based on the adaptive event triggering mechanism, the actual control input is obtained, achieving high-precision trajectory tracking and extending propeller lifespan. This invention is a ship trajectory tracking control method capable of simultaneously handling strong nonlinear disturbances, non-convex input saturation, reducing execution frequency, and possessing strict stability guarantees. By employing a nonlinear extended state observer to compensate for unknown disturbances in real time, and designing an anti-saturation projection operator and an adaptive event triggering mechanism, a ship IDA-PBC trajectory tracking control method is formed. This invention achieves high-precision, low-energy trajectory tracking control under complex sea conditions by designing a non-convex projection operator to process the thruster direction-amplitude coupling constraint, introducing a dynamic auxiliary system to compensate for saturation error, and adopting an adaptive event triggering mechanism to reduce the execution frequency.

[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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 ship dynamic positioning output feedback control method based on Hamiltonian theory, characterized in that, Includes the following steps: S1: Establish a three-degree-of-freedom port-controlled Hamiltonian model of the ship in the horizontal plane to obtain the passive control law for state error interconnection and damping distribution; S2: Construct a reduced-order extended state observer to obtain auxiliary state variables and perturbation estimates; S3: Construct a non-convex constraint operator for the thruster control input based on the auxiliary state variables; S4: Based on the non-convex constraint operator of the thruster control input, establish a dynamic auxiliary system to obtain the dynamic auxiliary system state vector; and based on the adaptive event triggering mechanism, obtain the actual application control command after non-convex projection; S5: Based on the passive control law of state error interconnection and damping allocation, the actual application control command after non-convex projection, the dynamic auxiliary system state vector and the disturbance estimate, obtain the unconstrained ideal control command, and obtain the actual control input based on the adaptive event triggering mechanism to realize the control of the ship.

2. The ship dynamic positioning output feedback control method based on Hamiltonian theory according to claim 1, characterized in that, The passive control law for the interconnection of state errors and damping distribution is expressed as follows: In the formula: Assign passive control laws to interconnect and damping state errors; For the controller gain matrix used for energy shaping, ; For position tracking error, , This is the desired reference trajectory for the ship's position and heading in the northeast coordinate system; To match the reference momentum corresponding to the desired trajectory, , for The derivative with respect to time; The controller gain matrix is ​​used for damping injection. , and It is a symmetric positive definite matrix; For the system momentum tracking error, .

3. The ship dynamic positioning output feedback control method based on Hamiltonian theory according to claim 1, characterized in that, The reduced-order extended state observer is represented as follows: In the formula: As auxiliary state variables, This is the observation gain diagonal matrix of the reduced-order extended state observer. , These are the observation gain coefficients for the ship's pitch channel, sway channel, and bow channel, respectively. This is the derivative with respect to time; It is a diagonal matrix; Given the lumped dynamics function terms of the ship system, This is the velocity vector in the ship's coordinate system; This is the estimated value of the disturbance; For the velocity domain Coriolis matrix; The damping matrix is ​​in the velocity domain. This is the actual control input.

4. The ship dynamic positioning output feedback control method based on Hamiltonian theory according to claim 1, characterized in that, The non-convex constraint operator for the thruster control input is represented as follows: In the formula: Non-convex constraint operators for thruster control input; The input vector is an unconstrained ideal control vector. The Euclidean 2-norm operator for vectors; To control the input vector The maximum feasible scaling factor that satisfies the non-convex constraint in the direction; For supremum mathematical operators; This is the mathematical division operator; To describe the non-convex constraint set for multi-degree-of-freedom direction-amplitude coupling constraints of a thruster, ; Let be the set of the real number space consisting of all real numbers; It is a continuous and non-convex constraint function; The parameters for traversing the line segments in the interval [0,1] are used. in, In the formula: For projection operator The supremum constant of the norm on the constraint set Ω; The infimum mathematical operator; For projection operator The infimum constant of the norm on the constraint set Ω.

5. The ship dynamic positioning output feedback control method based on Hamiltonian theory according to claim 1, characterized in that, The dynamic assistance system is established as follows: In the formula: This represents the state vector of the dynamic auxiliary system. State vector of dynamic auxiliary system rate of change over time; Design matrix for damping configuration of auxiliary system, ; This refers to the system's momentum tracking error. To control input saturation error; The actual application control commands are obtained after non-convex projection; This is an unconstrained ideal control command; To assist the system in segmented switching threshold constant, ; It is a zero vector with 3 rows and 1 column; In the formula: This is an unconstrained ideal control command; These are intermediate calculation parameters; in, , for The lower bound of the global normal number is the minimum conservative threshold constant.

6. The ship dynamic positioning output feedback control method based on Hamiltonian theory according to claim 1, characterized in that, The adaptive event triggering mechanism is described as follows: In the formula: To adapt to dynamic event triggering thresholds, , , These are the upper and lower bounds of the preset threshold; for The derivative with respect to time; Let be the threshold decay constant, and ; Let be the threshold adaptive learning gain constant, and ; The actual control command from the previous moment; The actual application control command after non-convex projection at the current moment; The triggering condition is as follows: ， In the formula: To control the triggering error of commands; The actual application control command after non-convex projection at the current moment; A fixed offset constant is used for trigger margin.

7. The ship dynamic positioning output feedback control method based on Hamiltonian theory according to claim 1, characterized in that, The formula used to obtain the unconstrained ideal control command is as follows: In the formula: This is an unconstrained ideal control command; This represents the state vector of the dynamic auxiliary system. This is the estimated value of the disturbance; This is the gain matrix of the auxiliary system; Passive control laws are assigned to the interconnection and damping of state errors.

8. The ship dynamic positioning output feedback control method based on Hamiltonian theory according to claim 1, characterized in that, The controlled Hamiltonian model of the ship's horizontal plane three-degree-of-freedom port is as follows: In the formula: Let be the ship's position and heading vector in the northeast coordinate system. , This indicates the ship's northward position. This indicates the ship's eastward position. The bow angle of the ship. This is the matrix transpose operator; for The derivative with respect to time; For ship momentum, , It is a positive definite inertial matrix. This is the velocity vector in the ship's coordinate system. , For the longitudinal speed of the ship, For the ship's lateral speed, The bow roll rate of the ship; for The derivative with respect to time; It is a rotation matrix; The momentum space Coriolis matrix; Here is the momentum space damping matrix; For open-loop Hamiltonian functions right The gradient of, where ; For open-loop Hamiltonian functions right gradient, ; for The identity matrix; For actual control input; It is an open-loop Hamiltonian function.

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