An ESO-based cooperative active disturbance rejection heading control method for unmanned sailboat

Abstract

The application belongs to the technical field of ship course control, and discloses an unmanned sailboat rudder and sail collaborative self-disturbance rejection course control method based on ESO, which comprises the following steps: establishing a nonlinear course motion mathematical model; designing an adaptive tracking differentiator to smooth the expected course; using ESO to observe the course, yaw angular velocity, sail aerodynamic moment and comprehensive disturbance in real time; based on a nonlinear state error feedback control law, combining the output of the tracking differentiator and the observation value of the ESO, generating a rudder moment control quantity, outputting a rudder angle instruction after constraint processing of the rudder moment control quantity; according to the lift-drag ratio parameter of the sail aerodynamic model after real-time correction, the apparent wind speed and the relative wind angle, deciding a dynamic optimal sail angle, combining the course deviation to compensate and constrain the dynamic optimal sail angle, and generating a sail angle instruction. The application enhances the adaptability to time-varying wind field and model uncertainty, and improves the anti-disturbance performance and energy efficiency of the system through dynamic optimization and compensation of the sail angle.

Description

An ESO-based method for sail and rudder cooperative active disturbance rejection heading control of unmanned sailboats Technical Field

[0001] This invention relates to the technical field of ship heading control, and specifically to an ESO-based unmanned sailboat sailboat sail-rudder cooperative self-disturbance heading control method. Background Technology

[0002] Unmanned sailboats are a type of autonomous marine vehicle that utilizes wind energy as its primary propulsion, offering advantages such as green energy consumption, environmental friendliness, and long endurance. Compared to traditionally powered unmanned vessels, unmanned sailboats demonstrate superior economy and environmental adaptability in long-duration ocean observation and resource monitoring missions. However, the course control process of unmanned sailboats is complex, especially when subjected to multi-source disturbances such as gusts, random winds, waves, and currents. Their motion exhibits strong nonlinearity, time-varying parameters, and coupling characteristics, posing significant challenges to precise control.

[0003] Currently, the heading control of unmanned sailboats often uses control methods based on simplified dynamic models. However, these methods often suffer from response hysteresis and large steady-state errors when dealing with complex sea conditions. The aerodynamic model of a sailboat is greatly affected by apparent wind speed and relative wind angle, and the model parameters are not easy to obtain accurately. When external disturbances are superimposed with model uncertainties, the heading deviation increases significantly, the rudder moves frequently, increasing energy consumption and reducing component life.

[0004] For example, the traditional Proportional-Integral-Derivative (PID) control method compares the instantaneous position and heading of the unmanned sailboat with the desired values ​​and outputs control commands to adjust the rudder angle. This method is simple in structure, easy to implement, and has good steady-state performance. However, because PID ignores the nonlinear dynamics of the sailboat and the time-varying nature of the wind field, its control accuracy is low under large disturbances and rapid parameter changes, and it is prone to overshoot and low-frequency rolling. Furthermore, PID cannot effectively separate the critical driving torque (generated by the sail) from other environmental disturbances, resulting in compensation lag and affecting heading stability.

[0005] In summary, there is a need to design an ESO-based unmanned sailboat sail-rudder cooperative active disturbance rejection heading control method to solve the problems in the existing technology. Summary of the Invention

[0006] To address the problems in the prior art, this invention provides an ESO-based unmanned sailboat sail-rudder cooperative self-disturbance heading control method, which solves the problems of low heading control accuracy and weak wind disturbance resistance of unmanned sailboats under complex wind field and hydrodynamic interference conditions.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] An ESO-based method for sail and rudder cooperative active disturbance rejection heading control of an unmanned sailboat includes the following steps:

[0009] A nonlinear heading motion mathematical model incorporating sail aerodynamic characteristics is established, and an apparent wind calculation module is simultaneously constructed to obtain environmental input.

[0010] Design an adaptive tracking differentiator to smooth the desired heading;

[0011] ESO was used to monitor heading, bow roll rate, sail aerodynamic torque, and overall disturbances in real time.

[0012] Based on the nonlinear state error feedback control law, the output of the tracking differentiator and the observed value of the ESO are combined to generate the rudder torque control quantity. After constraining the rudder torque control quantity, the rudder angle command is output.

[0013] Based on the lift-to-drag ratio parameters, apparent wind speed and relative wind angle of the real-time corrected sail aerodynamic model, the dynamic optimal sail angle is determined. After compensating and constraining the dynamic optimal sail angle in combination with the heading deviation, the sail angle command is generated.

[0014] The sail angle command and rudder angle command work together on the sailboat dynamics model to achieve course tracking and disturbance suppression through a closed-loop system.

[0015] In some embodiments of the present invention, establishing a nonlinear heading motion mathematical model incorporating sail aerodynamic characteristics includes:

[0016] Based on the MMG (Main Force, Gauge, and Radius) separation modeling concept for ships, the motion loads of the unmanned sailboat are decomposed into the hull, sail, and rudder for force analysis, and a nonlinear heading motion mathematical model is established, as follows:

[0017] ;

[0018] Among them, I Z Let N be the moment of inertia of the bow roll, φ be the heading angle, and r be the angular velocity of the bow roll. R The desired rudder torque; N S For sail torque; N H denoted as , where is the hydrodynamic moment of the hull; f is the combined disturbance.

[0019] In some embodiments of the present invention, the adaptive tracking differentiator is used to dynamically adjust the velocity factor, and the velocity factor is calculated using the following formula:

[0020] ;

[0021] Where, r n The velocity factor of the adaptive tracking differentiator, where v is the ship's speed, vapp For apparent wind speed, r0 is the basic velocity factor, and k1 and k2 are adaptive coefficients.

[0022] In some embodiments of the present invention, the state update law of the ESO is:

[0023] ;

[0024] Where φ is the measured heading angle, z1, z2, z3, and z4 are the observed values ​​of heading angle, bow roll rate, sail aerodynamic torque, and combined disturbance, respectively, ε represents the observation bias, which is the difference between the system's observed output and the actual output, and N R β is the rudder torque, b0 is the compensation coefficient, and β is the rudder torque. 01 β 02 β 03 β 04 denoted as the observer gain coefficient, h as the system discretization sampling period, fal as the nonlinear observation function, and δ, α1, α2, α3, and α4 as the control parameters of the nonlinear observation function fal.

[0025] In some embodiments of the present invention, the bandwidth of the ESO is dynamically adjusted according to the navigation state using the following formula:

[0026] ;

[0027] Where v is the ship's speed. v is the rate of change of wind speed. app For apparent wind speed, k v k dv k α This is for adjusting the coefficient.

[0028] In some embodiments of the present invention, the process of generating the rudder angle command includes:

[0029] Calculate the error between the expected heading angle and the measured heading angle, as well as the error between the expected bow roll rate and the measured bow roll rate;

[0030] The desired rudder torque is calculated using a nonlinear state error feedback control law.

[0031] Substitute the desired rudder torque into the pre-calibrated rudder torque-rudder angle conversion model to convert it into the initial rudder angle;

[0032] The initial rudder angle is limited in amplitude and rate and filtered to generate the rudder angle command.

[0033] In some embodiments of the present invention, the formula for calculating the desired rudder torque is as follows:

[0034] ;

[0035] Where, N R Let u0 be the desired steering torque, and u0 be the initial control input of NLSEF; I Z Let the moment of inertia be the bow roll of the ship. For the observed sail torque, This is a composite of disturbance observations.

[0036] In some embodiments of the present invention, the process of generating the sail angle command is as follows:

[0037] Based on the deviation between the observed sail torque output by ESO and the theoretical sail torque, the lift-to-drag ratio parameter of the sail aerodynamic model is corrected in real time.

[0038] A decision model for the dynamic optimal sail angle is constructed based on real-time apparent wind speed and relative wind angle;

[0039] Using the sail moment observation value output by ESO and the heading deviation threshold as dual benchmarks, the dynamic optimal sail angle is compensated in real time.

[0040] The optimal sail angle is superimposed with the compensation amount, and then amplitude and rate limits are applied to generate the sail angle command.

[0041] In some embodiments of the present invention, the lift-to-drag ratio parameter of the sail aerodynamic model is corrected in real time using the following formula:

[0042] ;

[0043] Where, k c C is the correction factor. L (α), C D (α) represents the initial lift-to-drag ratio curve obtained from the wind tunnel test, N S The theoretical sail torque calculated for the sail aerodynamic model. C represents the observed sail moment. Lc (α), C Dc (α) represents the corrected lift coefficient and drag coefficient, used to replace the initial lift-to-drag ratio curve and recalculate the actual sail torque.

[0044] In some embodiments of the present invention, the real-time compensation for the dynamically optimal sail angle includes:

[0045] Let θ0 be a preset heading deviation threshold. If the heading deviation... Then, combined with the observed sail moment values Real-time size superposition compensation amount:

[0046] .

[0047] in, This is the threshold for sudden increase in sail torque, used to determine whether the sail torque is in a state of sudden increase; φ ref k1 is the reference heading; k2 is the heading deviation compensation coefficient; k2 is the sail moment auxiliary compensation coefficient.

[0048] The advantages of this invention over the prior art are:

[0049] This invention introduces an active disturbance rejection control architecture combined with a sail-rudder cooperative strategy, achieving separate sensing and compensation of sail dynamics and external disturbances based on traditional state observation. This method not only enhances adaptability to time-varying wind fields and model uncertainties but also further improves the system's disturbance rejection performance and energy efficiency through dynamic optimization and compensation of the sail angle. Simulation results show that this invention maintains high-precision, low-overshoot heading tracking performance even under random wind and gust disturbances, demonstrating promising engineering application prospects. Attached Figure Description

[0050] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 is a flowchart of the unmanned sailboat self-disturbance rejection heading control method in an embodiment of the present invention;

[0052] Figure 2 is a schematic diagram of the time-varying wind field of random wind and gust wind in an embodiment of the present invention;

[0053] Figure 3 is a schematic diagram of the unmanned sailboat heading tracking effect in an embodiment of the present invention;

[0054] Figure 4 is a schematic diagram of the real-time change curve of absolute wind angle (wind direction) under dynamic wind field in an embodiment of the present invention.

[0055] Figure 5 is a schematic diagram comparing the actual value of sail torque with the observed value of sail torque in an embodiment of the present invention;

[0056] Figure 6 is a schematic diagram of the rudder angle output in an embodiment of the present invention.

[0057] Figure 7 is a schematic diagram of the dynamic optimal angle and sail angle output in an embodiment of the present invention. Detailed Implementation

[0058] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0059] The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed.

[0060] Unmanned sailboats need to perform tasks such as observation and cruising in complex sea conditions. Traditional heading control methods suffer from low tracking accuracy and insufficient robustness due to model uncertainties and time-varying wind field interference. This invention proposes an ESO-based sail-rudder cooperative active disturbance rejection heading control method for unmanned sailboats. It combines active disturbance rejection control technology with the ship's MMG (Main Mode and Gauge) separation modeling concept. It obtains accurate actual rudder torque by constructing a rudder torque-rudder angle pre-calibration conversion model, uses ESO to separate the observation of sail aerodynamic torque and environmental disturbances, combines an adaptive tracking differentiator and nonlinear state error feedback to optimize the control logic, and then uses dynamic sail angle decision-making driven by "real-time apparent wind speed + relative wind angle + ESO estimated sail torque" to form a cooperative mechanism of "sail angle-assisted disturbance rejection and rudder angle-precise heading control." This effectively improves the shortcomings of traditional methods, such as susceptibility to interference and weak robustness. The specific implementation is as follows:

[0061] Example 1: As shown in Figure 1, an ESO-based unmanned sailboat sail-rudder cooperative active disturbance rejection heading control method includes the following steps:

[0062] S1. Establish a nonlinear heading motion mathematical model that includes the aerodynamic characteristics of the sail, and simultaneously construct an apparent wind calculation module to obtain environmental input.

[0063] S11. Decompose the motion load of the unmanned sailboat into the hull, sail, and rudder for force analysis, and establish a nonlinear heading motion mathematical model, as follows:

[0064] ;

[0065] Among them, I Z Let N be the moment of inertia of the bow roll, φ be the heading angle, and r be the angular velocity of the bow roll. R The desired rudder torque; N S For sail torque; NH denoted as , where is the hydrodynamic moment of the hull; f is the combined disturbance.

[0066] 1. Hull hydrodynamic moment model

[0067] The hydrodynamic moment of the hull consists of linear hydrodynamics, nonlinear hydrodynamics, and coupling terms, and is expressed as follows:

[0068]

[0069] Where v is the ship's speed, r is the bow roll rate, and N... v 、Nr、N ∣v∣v N ∣r∣r N vvr and N vrr This is the hydrodynamic torque coefficient.

[0070] 2. Sail Aerodynamic Model

[0071] The lift coefficient C of the sail is calculated using the relative wind angle. L With drag coefficient C D Then obtain the lift F of the sail. L Resistance F D This is ultimately converted into sail moment in the ship's coordinate system:

[0072] , , ;

[0073] ;

[0074] Among them, v app Let α be the apparent wind speed, α be the relative wind angle, S be the sail area, ρ be the air density, and C be the apparent wind speed. L and C D These are the lift coefficient and drag coefficient, respectively; F L and F D These represent sail lift and sail drag, respectively. S and Y S These are the heading thrust and the lateral thrust perpendicular to the sailboat's heading, respectively. S and y S The coordinates are from the point of action of the sail to the center of gravity of the ship.

[0075] 3. Rudder torque model and pre-calibration conversion

[0076] The rudder torque is output by a nonlinear state error feedback control law to determine the desired rudder torque. Together with ESO perturbation compensation, the following decision was made:

[0077] ;

[0078] Where u0 is the initial control quantity output by the nonlinear state error feedback control law. The sail torque observation value is obtained from step S3. This is a composite of disturbance observations.

[0079] The conversion between rudder torque and rudder angle is achieved by pre-calibrating the rudder torque-rudder angle model:

[0080] The formula for reverse conversion (desired rudder torque → initial rudder angle) is: ;

[0081] The formula for the forward conversion (actual rudder angle → actual rudder torque) is: ;

[0082] Where, k R The rudder angle-torque proportionality coefficient was obtained from bench tests for pre-calibration; N Rf The friction torque of the servo motor is obtained from the servo motor start-up test; k V This is the water flow resistance coefficient, obtained from sea trials.

[0083] During simulation verification, N can be ignored. Rf With k V At this point, the model simplifies to N. r =k R ∙δ r This is equivalent to the rudder torque-rudder angle conversion coefficient in the simulation.

[0084] S12, the calculation of apparent wind, relies on the nonlinear hydrodynamics and sail aerodynamics model of the unmanned sailboat. It takes longitudinal wind speed, lateral wind speed and gust disturbance term as input, and outputs apparent wind speed and relative wind angle, providing environmental parameters for the calculation of sail moment and hydrodynamic moment.

[0085] Specifically, integrating longitudinal wind speed v wx Crosswind speed v wy Gust disturbance item g x (t), through wind field synthesis, apparent wind speed calculation, and relative wind angle derivation, real-time apparent wind speed and relative wind angle are obtained, providing environmental parameters for the calculation of sail moment and hydrodynamic moment:

[0086] ;

[0087] Among them, v wx,avg v wy,avg For the average wind speed, n x (t), n y (t) represents random wind noise; v app Let α be the apparent wind speed, α be the relative wind angle, and v be the relative wind angle. wx v wy Let v be the longitudinal and lateral components of the ambient wind speed, v be the ship speed, φ be the heading angle, and δ be the yaw rate.S For sails.

[0088] Figure 2 is a schematic diagram of the time-varying wind field of random wind and gusts in this embodiment of the invention. The longitudinal and transverse wind speeds exhibit non-stationary random fluctuations and gust pulse changes over time, providing a realistic disturbance environment input for the control algorithm. The real-time change of the absolute wind angle (wind direction) under the dynamic wind field is shown in Figure 4, which provides a typical complex wind field input scenario for this embodiment.

[0089] S2. Design an adaptive tracking differentiator to smooth the desired heading.

[0090] Referring again to Figure 1, to avoid large servo movements and system oscillations caused by sudden changes in the heading reference signal, this invention employs an adaptive tracking differentiator (TD) to smooth the desired heading. Simultaneously, its differential signal is extracted, as follows:

[0091] S21. Initialize tracking parameters.

[0092] An adaptive tracking differentiator is used to dynamically adjust the velocity factor, which is calculated using the following formula:

[0093] ;

[0094] Where, r n The velocity factor of the adaptive tracking differentiator, where v is the ship's speed, v app For apparent wind speed, r0 is the basic velocity factor, and k1 and k2 are adaptive coefficients.

[0095] S22, Initial tracking state x1(0)=y d (0) (y) d (where x is the desired initial heading value), the initial differential state is x2(0)=0, and the control step size is h.

[0096] In step k, calculate the tracking error: y = x1(k) + h∙x2(k) - y d ;

[0097] The differential control quantity is generated using the steepest synthesis function (denoted as the fhan function), and its calculation process is as follows:

[0098] ;

[0099] S23, Status Update and Signal Output.

[0100] Update the tracking status based on the above results:

[0101]

[0102] The smoothed heading signal x1(k) and its approximate differential signal x2(k) (corresponding to the TD tracking heading in Figure 3) are output as the reference heading and reference bow roll rate for subsequent control, respectively.

[0103] The tracking differentiator adaptively adjusts the velocity factor r. n This allows the transition process to match the real-time navigation status of the unmanned sailboat, effectively suppressing system lag and oscillation caused by sudden command changes, and providing the controller with a smooth reference trajectory.

[0104] S3. Utilize ESO to monitor heading, bow roll rate, sail aerodynamic torque, and overall disturbances in real time.

[0105] The fourth-order discretized ESO, or extended state observer, used in this embodiment expands both sail aerodynamic torque and environmental disturbances into new state variables of the system. Simultaneously, it uses the actual heading angle, bow roll rate, and the actual rudder torque calculated by the pre-calibrated rudder torque-rudder angle model as inputs and the actual heading angle as output to reconstruct the state. This allows for the simultaneous observation of the original state variables (heading angle, bow roll rate) and the newly added extended disturbance variables (sail aerodynamic torque, environmental disturbances), achieving independent and separate perception of sail aerodynamic torque and environmental disturbances.

[0106] S31, Adaptively adjust the bandwidth of ESO.

[0107] ESO bandwidth ω0 is dynamically adjusted according to navigation status:

[0108] ;

[0109] Where v is the ship's speed. v is the rate of change of wind speed. app For apparent wind speed, k v k dv k α This is for adjusting the coefficient.

[0110] S32, The state update law of the ESO is:

[0111] ;

[0112] Where φ is the measured heading angle, z1, z2, z3, and z4 are the observed values ​​of heading angle, bow roll rate, sail aerodynamic torque, and combined disturbance, respectively, ε represents the observation bias, which is the difference between the system's observed output and the actual output, and N R β is the rudder torque, b0 is the compensation coefficient, and β is the rudder torque. 01 β 02 β 03 β 04denoted as the observer gain coefficient, h as the system discretization sampling period, fal as the nonlinear observation function, and δ, α1, α2, α3, and α4 as the control parameters of the nonlinear observation function fal.

[0113] Figure 5 is a schematic diagram comparing the actual value of the sail torque with the observed value of the sail torque in an embodiment of the present invention. During the gust interference period shown in Figure 2, the observation error of the sail torque by ESO is less than 5%, which can accurately capture the load fluctuation caused by the gust.

[0114] S4. Based on the Nonlinear State Error Feedback (NLSEF) control law, and combining the output of the tracking differentiator with the observed value of the ESO, a rudder torque control quantity is generated. After constraining the rudder torque control quantity, a rudder angle command is output. Specifically, this includes the following steps:

[0115] S41. Calculate the error between the desired heading angle and the measured heading angle, and the error between the desired bow roll rate and the measured bow roll rate; the calculation formulas are as follows:

[0116] e1 = x1 - z1; e2 = x2 - z2;

[0117] Where z1 is the heading estimate, z2 is the bow roll rate estimate, e1 is the error signal, and e2 is the error differential signal.

[0118] S42. Calculate the desired rudder torque using a nonlinear state error feedback control law;

[0119] The formula for calculating the desired rudder torque is:

[0120] ;

[0121] Where, N R Let u0 be the desired steering torque, and u0 be the initial control input of NLSEF; I Z Let the moment of inertia be the bow roll of the ship. For the observed sail torque, This is a composite of disturbance observations.

[0122] The formula for calculating the initial control quantity u0 is: u0=β1∙fal(e1,α1,δ)+β2∙fal(e2,α2,δ);

[0123] Where β1 is the proportional control coefficient of the system and β2 is the differential control coefficient of the system.

[0124] The aforementioned nonlinear state error feedback control law is an optimized control strategy adapted to the nonlinear characteristics of unmanned sailboats. By tracking the smoothed reference signal output by the differentiator and combining it with the state estimate obtained from the extended state observer, error signals for heading and yaw rates are constructed. This, combined with the fal nonlinear function, achieves nonlinear weighting of the errors, avoiding the response lag problem of linear control under large disturbances.

[0125] S43. Substitute the desired rudder torque into the pre-calibrated rudder torque-rudder angle conversion model to convert it into the initial rudder angle.

[0126] The formula for reverse conversion (desired rudder torque → initial rudder angle) is: ;

[0127] Where, k R The rudder angle-torque proportionality coefficient was obtained from bench tests for pre-calibration; N Rf The friction torque of the servo motor is obtained from the servo motor start-up test; k V This is the water flow resistance coefficient, obtained from sea trials.

[0128] S44. The initial rudder angle is limited in amplitude and rate and filtered to generate the rudder angle command. Specifically, soft limiting is achieved using a hyperbolic tangent function (to avoid signal abrupt changes caused by hard limiting). Then, the rate of change of the rudder angle is limited to prevent servo overload. Finally, high-frequency fluctuations in the command are smoothed by filtering to ensure the stability of the rudder angle command.

[0129] ;

[0130] Among them, K δ δ is the rudder torque-rudder angle conversion coefficient. r (1) The rudder angle is the median value after soft saturation treatment, δ r,max The maximum rudder angle is limited. Δδ is the maximum rate of change of the rudder angle. r τ represents the allowable change in rudder angle at the current moment, clip is the rudder angle rate limit function, and τ is the rudder angle change rate limit function. δ δ is the rudder angle filtering time constant, h is the control step size; r (k) is the final rudder angle command output.

[0131] Figure 6 is a schematic diagram of the rudder angle output in an embodiment of the present invention. The rudder angle change rate never exceeds 30° / s, the curve is smooth and there is no overshoot, which is in line with the physical characteristics of the servo motor.

[0132] S45. After generating the actual rudder angle command, in order to provide accurate control input information to the State Observer (ESO), the actual rudder angle needs to be converted into the actual rudder torque. The conversion formula is as follows:

[0133]

[0134] This actual rudder torque will serve as one of the core input parameters of the ESO. Together with information such as the actual heading angle and bow roll rate, it will support the ESO in independently and separately observing the sail aerodynamic torque and the comprehensive environmental disturbances. This is a key link in achieving accurate perception of the system state and disturbances.

[0135] S5, sail angle control and rudder angle control operate in parallel, using the actual sail torque estimated by ESO. Based on the core benchmark, a collaborative control mechanism of "sail-assisted disturbance rejection and rudder-driven heading control" is formed. Its core idea is: the sail angle, based on the dynamically optimal angle, is compensated for by feedforward in conjunction with heading deviation to generate an auxiliary turning moment to counteract wind disturbance; the rudder angle, based on the active disturbance rejection controller, provides precise state feedback and comprehensive disturbance compensation to achieve steady-state tracking and fine-tuning of the heading; the commands for both are generated synchronously and output in parallel, working together on the ship's dynamics model. The specific implementation steps are as follows:

[0136] S51. Based on the deviation between the observed sail torque output by ESO and the theoretical sail torque, the lift-to-drag ratio parameter of the sail aerodynamic model is corrected in real time.

[0137] The lift coefficient C in the aerodynamic model of the sail in step S11 above L Drag coefficient C D And the calculated theoretical sail torque N S All parameters are determined based on ideal uniform wind field conditions from wind tunnel tests, adapting to aerodynamic characteristic analysis under theoretical scenarios. However, during actual navigation, complex airflow disturbances such as gusts and turbulence in sea conditions can cause deviations between the actual aerodynamic characteristics of the sail and the initial model, leading to a drift between the theoretical and actual sail torque. To adapt to actual sea conditions, in practical applications, the lift-to-drag ratio parameter can be corrected in real time based on the actual sail torque observed by a fourth-order extended state observer (ESO). The corresponding correction formula is:

[0138] ;

[0139] Where, k c C is the correction factor. L (α), C D (α) represents the initial lift-to-drag ratio curve obtained from the wind tunnel test, N S The theoretical sail torque calculated for the sail aerodynamic model. C represents the observed sail moment. Lc (α), C Dc (α) represents the corrected lift coefficient and drag coefficient, used to replace the initial lift-to-drag ratio curve and recalculate the actual sail torque.

[0140] In this embodiment, the above correction can reduce the calculation error of the sail torque; the corrected lift-to-drag ratio parameter will be used simultaneously for dynamic optimal sail angle decision-making, providing an accurate aerodynamic parameter benchmark for sail angle compensation.

[0141] S52, Based on real-time apparent wind speed v app Using the relative wind angle α (the angle between the apparent wind direction and the longitudinal direction of the hull), a dynamically optimal sail angle δ is constructed through "wind zone adaptation reference sail angle + linear transition of wind speed range". S * The decision-making model is adapted to the aerodynamic characteristics of sails and sailing stability under different wind conditions:

[0142]

[0143] Where, δ w-up (α), δ w-mid (α), δ w-low (α) is the wind zone adaptation reference sail angle, δ w-up (α) corresponds to the windward region (α<60°), adapting to headwind stall characteristics; δ w-mid (α) corresponds to the crosswind region (α≤60°≤120°), matching the optimal angle of attack for the sail-shaped airfoil; δ w-low (α) corresponds to the downwind region (α>120°), and the wind speed is used to balance the thrust and heading stability; k is the transition coefficient, which is used to achieve a smooth transition of the sail angle without abrupt changes in different wind speed ranges, and avoid sudden changes in the aerodynamic characteristics of the sail surface.

[0144] Figure 7 is a schematic diagram of the dynamic optimal sail angle and sail angle output in an embodiment of the present invention, which shows the smooth transition of the sail angle and the output characteristics after constraint under different wind speed ranges and wind zones.

[0145] S53. To achieve active auxiliary disturbance rejection of the sail relative to the heading, the observed sail moment value output by ESO and the heading deviation threshold are used as dual benchmarks to perform real-time compensation for the dynamically optimal sail angle:

[0146] Let θ0 be a preset heading deviation threshold. If the heading deviation... Then, combined with the observed sail moment values Real-time size superposition compensation amount:

[0147] .

[0148] in, This is the threshold for sudden increase in sail torque, used to determine whether the sail torque is in a state of sudden increase; φ ref k1 is the reference heading; k2 is the heading deviation compensation coefficient; k2 is the sail moment auxiliary compensation coefficient.

[0149] S54. After superimposing the optimal sail angle and the compensation amount, amplitude and rate limits are applied to generate the sail angle command. Specifically, this includes:

[0150] S541. The compensation amount is superimposed on the dynamically optimal sail angle to obtain the compensated target sail angle: ;

[0151] S542. To prevent the sail angle from exceeding the mechanical travel range or causing aerodynamic stall of the sail surface, the amplitude and rate of the sail angle command must be constrained:

[0152] (1) Amplitude limit: The sail angle command must meet the following requirements:

[0153] Where, δ S,min and δ S,max These are the minimum and maximum allowable sail angles, respectively (determined by the mast rotation stroke and the aerodynamic stall critical angle); if the target sail angle exceeds the range, it will be clamped to δ. S,min or δ S,max The target sail angle after amplitude constraint is obtained. .

[0154] (2) Rate limit:

[0155] To avoid sail attitude fluctuations caused by sudden changes in sail angle, the adjustment rate of sail angle commands must meet the following requirements:

[0156]

[0157] Among them, R max is the maximum rate of change of the sail angle, and T is the control period.

[0158] To achieve this constraint, the target sail angle after amplitude constraint is... Perform rate limiting processing and define the saturation function sat(x,L)=max(-L,min(x,L)).

[0159] The allowable change in sail angle is:

[0160] Final sail angle command: δ S (k)=δ S (k-1)+Δδ S .

[0161] S6, sail angle command, and rudder angle command work together on the sailboat dynamics model to achieve course tracking and disturbance suppression through a closed-loop system.

[0162] To verify the heading control performance of this embodiment, a simulation test was conducted on the tracking process between the desired heading and the actual heading. Figure 3 is a schematic diagram of the heading tracking effect of the unmanned sailboat in this embodiment of the invention. It can be seen that under the random wind and gust disturbances shown in Figure 2, the actual heading always closely follows the desired heading, the tracking error is stably controlled within ±1°, the overshoot during the turning process is less than 3%, and there is no obvious steady-state deviation. Even during the sudden change of wind direction shown in Figure 4, the fluctuation range of the actual heading can still be controlled within a very small range, and the heading stability is not significantly disturbed. This fully demonstrates the adaptability of the "sail-assisted anti-disturbance and rudder-controlled heading" collaborative mechanism to complex wind fields and its high-precision heading tracking effect.

[0163] The sail-rudder coordinated control mechanism proposed in this invention combines feedforward disturbance rejection of the sail angle with feedback fine-tuning of the rudder angle, achieving torque complementarity and energy efficiency optimization in time-varying wind fields. This strategy significantly reduces the amplitude and frequency of servo motor movements under gusts and large deviations, improving the overall robustness and navigation efficiency of the system while ensuring high-precision heading tracking. In the description of the above embodiments, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0164] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for sail-rudder cooperative active disturbance rejection heading control of an unmanned sailboat based on ESO, characterized in that, Includes the following steps: A nonlinear heading motion mathematical model incorporating sail aerodynamic characteristics is established, and an apparent wind calculation module is simultaneously constructed to obtain environmental input. The establishment of a nonlinear heading motion mathematical model incorporating sail aerodynamic characteristics includes: based on the ship MMG separation modeling concept, the motion load of the unmanned sailboat is decomposed into the hull, sail, and rudder for force analysis, and a nonlinear heading motion mathematical model is established, as follows: Among them, I Z Let N be the moment of inertia of the bow roll, φ be the heading angle, and r be the angular velocity of the bow roll. R The desired rudder torque; N S For sail torque; N H Let f be the hydrodynamic moment of the hull; f be the overall disturbance; an adaptive tracking differentiator is designed to smooth the desired course; the course, bow roll rate, sail aerodynamic moment, and overall disturbance are observed in real time using an ESO; based on a nonlinear state error feedback control law, combined with the output of the tracking differentiator and the observations of the ESO, a rudder torque control quantity is generated, and the rudder torque control quantity is constrained before outputting a rudder angle command; the dynamically optimal sail angle is determined based on the lift-to-drag ratio parameters, apparent wind speed, and relative wind angle of the real-time corrected sail aerodynamic model, and the dynamically optimal sail angle is compensated and constrained by the course deviation before generating a sail angle command; the sail angle command and the rudder angle command work together on the sail dynamics model to achieve course tracking and disturbance suppression through a closed-loop system; wherein, the state update law of the ESO is: Where φ is the measured heading angle, z1, z2, z3, and z4 are the observed values ​​of heading angle, bow roll rate, sail aerodynamic torque, and combined disturbance, respectively, ε represents the observation bias, which is the difference between the system's observed output and the actual output, and N R β is the rudder torque, b0 is the compensation coefficient, and β is the rudder torque. 01 β 02 β 03 β 04 denoted as the observer gain coefficient, h as the system discretization sampling period, fal as the nonlinear observation function, and δ, α1, α2, α3, and α4 as the control parameters of the nonlinear observation function fal.

2. The unmanned sailboat sail-rudder cooperative self-disturbance rejection heading control method according to claim 1, characterized in that, The adaptive tracking differentiator is used to dynamically adjust the velocity factor, and the formula for calculating the velocity factor is: ; where r n The velocity factor of the adaptive tracking differentiator, where v is the ship's speed, v app For apparent wind speed, r0 is the basic velocity factor, and k1 and k2 are adaptive coefficients.

3. The unmanned sailboat sail-rudder cooperative autonomous disturbance rejection heading control method according to claim 1, characterized in that, The bandwidth of the ESO is dynamically adjusted according to the navigation status using the following formula: Where v is the ship's speed, v is the rate of change of wind speed. app For apparent wind speed, k v k dv k α This is for adjusting the coefficient.

4. The unmanned sailboat sail-rudder cooperative self-disturbance rejection heading control method according to claim 1, characterized in that, The process of generating the rudder angle command includes: calculating the error between the desired heading angle and the measured heading angle, as well as the error between the desired yaw rate and the measured yaw rate; calculating the desired rudder torque using a nonlinear state error feedback control law; substituting the desired rudder torque into a pre-calibrated rudder torque-rudder angle conversion model to convert it into an initial rudder angle; and performing amplitude and rate limiting and filtering on the initial rudder angle to generate the rudder angle command.

5. The unmanned sailboat sail-rudder cooperative self-disturbance rejection heading control method according to claim 4, characterized in that, The formula for calculating the desired rudder torque is: ; where N R Let u0 be the desired steering torque, and u0 be the initial control input of the nonlinear state error feedback control law; I Z Let the moment of inertia be the bow roll of the ship. For the observed sail torque, This is a composite of disturbance observations.

6. The unmanned sailboat sail-rudder cooperative self-disturbance rejection heading control method according to claim 5, characterized in that, The process of generating the sail angle command is as follows: based on the deviation between the observed sail torque value output by ESO and the theoretical sail torque, the lift-to-drag ratio parameter of the sail aerodynamic model is corrected in real time; a decision model for the dynamic optimal sail angle is constructed based on the real-time apparent wind speed and relative wind angle; the dynamic optimal sail angle is compensated in real time using the observed sail torque value output by ESO and the heading deviation threshold as dual benchmarks; the optimal sail angle and the compensation amount are superimposed and then subjected to amplitude and rate limits to generate the sail angle command.

7. The unmanned sailboat sail-rudder cooperative self-disturbance rejection heading control method according to claim 6, characterized in that, The lift-to-drag ratio parameter of the sail aerodynamic model is corrected in real time using the following formula: ; where k c C is the correction factor. L (α), C D (α) represents the initial lift-to-drag ratio curve obtained from the wind tunnel test, N S The theoretical sail torque calculated for the sail aerodynamic model. C represents the observed sail moment. Lc (α), C Dc (α) represents the corrected lift coefficient and drag coefficient, used to replace the initial lift-to-drag ratio curve and recalculate the actual sail torque.

8. The unmanned sailboat sail-rudder cooperative active disturbance rejection heading control method according to claim 6, characterized in that, The real-time compensation for the dynamically optimal sail angle includes: setting θ0 as a preset heading deviation threshold, if the heading deviation... Then, combined with the observed sail moment values Real-time size superposition compensation amount: ;in, This is the threshold for sudden increase in sail torque, used to determine whether the sail torque is in a state of sudden increase; φ ref k1 is the reference heading; k2 is the heading deviation compensation coefficient; k2 is the sail moment auxiliary compensation coefficient.

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