Unmanned ship course adaptive specified performance fault-tolerant control method with sideslip angle compensation

Abstract

The invention discloses an unmanned ship course adaptive regulation performance fault-tolerant control method with sideslip angle compensation, which comprises the following steps: analyzing the influence of a sideslip angle on the course stability of an unmanned ship, establishing a sideslip angle observation and compensation model, realizing real-time estimation of the sideslip angle, and dynamically adjusting a control gain in combination with an adaptive control strategy, thereby realizing the course adaptive regulation of the unmanned ship. A simulation result shows that under the action of energy unbounded disturbance and external environment disturbance, the course angle of the system can be quickly converged to an expected value, the sideslip angle is always controlled within a reasonable range, the course error is kept within specified performance constraints, overshoot and error accumulation do not occur, and compared with a traditional method, the method has the advantages that the method is simple and convenient to operate, and the cost is low. According to the method, the robustness, adaptability and precision of course keeping are remarkably improved, stable operation of the unmanned ship in a complex marine environment is ensured, and reliable technical support is provided for autonomous navigation of the unmanned ship.

Description

Technical Field

[0001] The present invention relates to the technical field of fault-tolerant control, and in particular to a heading adaptive control method for an unmanned vehicle (USV) system with uncertain internal parameters. Background Art

[0002] The sideslip angle is the angle between the actual direction of motion of an unmanned vessel and its longitudinal axis. Its variations are affected by external disturbances such as wind, waves, and ocean currents, and are directly related to heading stability and control accuracy. Excessively large sideslip angles can lead to deviations from the vessel's course, potentially compromising mission safety. Because the sideslip angle of an unmanned vessel is nonlinear and random, and fluctuates with environmental changes, traditional control methods struggle to provide sufficient robustness and accuracy in complex sea conditions. During USV system operation, various faults are inevitable, potentially impacting normal operation and even exposing it to unknown risks. In actual operating systems, some faults often exhibit the following probability distribution characteristics: Actuators generally experience only minor faults, with a very low probability of major failures. This characteristic can be used to segment faults into different intervals based on the fault distribution for further research, thereby more closely resembling the actual operating conditions of the actuators.

[0003] Among existing control strategies for sideslip angle compensation, fuzzy control is combined with adaptive control. This approach uses fuzzy reasoning to evaluate external disturbances and incorporates adaptive adjustment mechanisms, enabling the system to dynamically adjust compensation parameters based on environmental changes, thereby improving heading stability. Robust control employs multi-model systems and sideslip angle estimation techniques to select the optimal control strategy based on varying sea conditions, enhancing the system's anti-interference capabilities. Data-driven approaches utilize machine learning to train predictive models for real-time sideslip angle compensation, effectively improving heading control accuracy when sufficient data is available. Furthermore, event-triggered control (ETC) reduces computational and communication burdens through intelligently triggering control signals, improving navigation efficiency and enabling unmanned vessels to maintain high endurance during long missions. However, these approaches still have limitations, such as a strong reliance on pre-set models and data, and limited adaptability in complex environments. Summary of the Invention

[0004] The object of the present invention is to provide a method for self-adaptive fault-tolerant control of an unmanned ship with sideslip angle compensation, so as to solve the problems raised in the above background technology.

[0005] In order to solve the above technical problems, the present invention provides the following technical solution: a method for self-adaptive regulation performance fault-tolerant control of an unmanned ship with sideslip angle compensation, comprising the following steps:

[0006] Step S1: Establishing a heading keeping system;

[0007] The heading keeping system includes the following modules: an adaptive controller, a steering gear, and an unmanned vessel. The system outputs the deviation signal between the desired heading and the actual heading to the adaptive controller, generating a control signal u(t). The control signal acts on the steering gear to generate an actual rudder angle δ(t), so that the actual heading is consistent with the desired heading.

[0008] Step S2: establishing a USV model with internal parameter uncertainty, wherein the USV model is an unmanned ship model;

[0009] The hull of the unmanned ship is defined as completely symmetrical, and the origin of the coordinate system is set at the center of gravity of the USV. The mathematical model of the three-degree-of-freedom motion of the USV is:

[0010]

[0011] In formula (1), is the impact acceleration, To affect acceleration, is the yaw acceleration, I zz is the inertia of the ship along the Z axis, J zz is the additional inertia, m, m x 、m y Represent the mass, longitudinal and transverse additional mass of the ship respectively, X H 、Y H 、N H are the forces and moments acting on the ship, and the variables with subscripts “P” and “R” are the forces and moments acting on the propeller and steering gear.

[0012] Step S3: Using the servo characteristics, establish a rudder angle dynamic model;

[0013] The servo characteristics are described by a second-order underdamped system, and the rudder angle dynamic model is:

[0014]

[0015] Among them, T7 is the controller gain, T5 and T6 are time constants, u F (t) represents the actual control input due to actuator failure and can be expressed as: u F (t)=λ(u(t)-p(t)),0<λ≤1, in which P represents offset fault, λ represents partial failure fault, and parameter T i (i=1,...,6) represents different time constants;

[0016] Rudder angle δ(t) and rudder angle rate Subject to the following physical constraints: |δ(t)|≤35°,

[0017] The second-order steering system dynamics model of the unmanned ship is integrated with the heading control model to form the following equation:

[0018]

[0019] The rudder angle dynamic model is used to describe the dynamic characteristics of the heading of the unmanned ship.

[0020] Step S4: Construct an adaptive controller with partial failure of the servo.

[0021] Preferably, the adaptive controller includes: introducing an adaptive estimation method to perform online identification and compensation of the sideslip angle, and defining the estimated value of the sideslip angle as Based on adaptive control theory, design corresponding estimation algorithms and dynamically adjust The adaptive law for estimating the ship's sideslip angle is designed as follows:

[0022]

[0023] Design an adaptive controller with partial failure of the servo, and design the control law u F (t) is as follows:

[0024]

[0025] Among them, k1 is the control gain, τ1 is a negative constant, p represents an unknown actuator offset fault, λ represents a partial failure fault, is the estimated value of the actuator offset fault, Represents the estimated value of partial failure fault, design Obey the following adaptive update law:

[0026]

[0027] Among them, K2 and K3 are control gains.

[0028] For a heading keeping system with control law and adaptive law, when there is ρ(0), such that -σ min ρ(0)<e(0)<σ max ρ(0), then all signals in the resulting closed-loop system are ultimately semi-globally uniformly bounded, and the transformed tracking error is bounded within the specified performance bound for all t ≥ 0;

[0029] Finally, formula (3) can be rewritten as:

[0030]

[0031] Among them, Δβ' maxRepresents the upper bound of the sideslip angle disturbance, which comes from the influence of external environmental factors such as wind, waves, and ocean currents on the motion state of the unmanned ship;

[0032] The Lyapunov function related to the rudder angle error is defined as:

[0033]

[0034] Then the time derivative of V3 along formula (8) is:

[0035]

[0036] In summary, the above formula can be expressed as:

[0037]

[0038] Substituting the control law u(t) into the equation, we can obtain:

[0039]

[0040] Further we can get:

[0041]

[0042] Among them, k0=0.2758,τ1 is a positive constant, Available, Substituting the adaptive law of sideslip angle estimation into the equation, we can obtain:

[0043]

[0044] Substituting the adaptive law of ship's sideslip angle estimation into the formula, we can get:

[0045]

[0046] Depend on We can get:

[0047]

[0048] Substituting the adaptive update law into formula (15) yields:

[0049]

[0050] Depend on We can get:

[0051]

[0052] Substituting the adaptive law into formula (17) we can obtain:

[0053] because We can get:

[0054]

[0055] Depend on We can get:

[0056]

[0057] Depend on We can get:

[0058]

[0059] in

[0060] make We can get:

[0061]

[0062] Further we can get: Then multiply both sides by the integration factor e 2at :

[0063]

[0064] Integrating both sides of the inequality gives:

[0065]

[0066] From the above inequality we can get: Therefore, all variables are semi-globally uniformly ultimately bounded, and the tracking error satisfies all specified performance constraints, completing the proof.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] (1) The present invention reconstructs the mathematical model of the unmanned vessel based on sideslip angle compensation, taking into account external disturbances, partial failure of the steering gear, and offset failure, and accurately reflects the dynamic behavior of the unmanned vessel in a complex marine environment;

[0069] (2) By introducing a prescribed performance function and an adaptive control strategy, the present invention can ensure that the unmanned vessel maintains good control accuracy and stability when facing sideslip angle disturbances and system changes;

[0070] (3) By proposing the corresponding Lyapunov function, the present invention proves that all signals in the closed-loop system are semi-globally uniformly bounded, and the transformed tracking error is limited to the specified performance bound, ensuring the robustness and adjustability of the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0072] Figure 1 Schematic diagram of the structural composition of a heading keeping system provided by an embodiment of the present invention;

[0073] Figure 2 This is a schematic diagram of a MATLAB simulation environment experimental scenario provided by an embodiment of the present invention;

[0074] Figure 3 Schematic diagram of the heading angle of the "Qingshan" provided by an embodiment of the present invention;

[0075] Figure 4 is a schematic diagram of the dynamic change of the sideslip angle provided by an embodiment of the present invention;

[0076] Figure 5 1 is a schematic diagram comparing the heading angle output and the desired heading angle of the unmanned vessel under sideslip compensation control provided by an embodiment of the present invention;

[0077] Figure 6 Schematic diagram of the change in heading angle error of the system provided by an embodiment of the present invention under the sideslip compensation control strategy. DETAILED DESCRIPTION

[0078] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0079] The embodiment of the present invention is combined with Figures 1-6 , provides the following technical solution: a method for self-adaptive regulation performance fault-tolerant control of an unmanned ship with sideslip angle compensation, comprising the following steps:

[0080] Step S1: Establishing a heading keeping system;

[0081] In this embodiment, combined Figure 1 As shown in the figure, the heading keeping system includes the following modules: an adaptive controller, a steering gear, and an unmanned vessel. The system outputs the deviation signal generated by the desired heading and the actual heading to the adaptive controller, generating a control signal u(t). The control signal acts on the steering gear to generate an actual rudder angle δ(t), so that the actual heading is consistent with the desired heading.

[0082] Step S2: Establish a USV model with internal parameter uncertainty;

[0083] In this embodiment, the hull of the unmanned vessel is defined as completely symmetrical, and the origin of the coordinate system is set at the center of gravity of the USV. The mathematical model of the USV three-degree-of-freedom motion is:

[0084]

[0085] In formula (1), is the impact acceleration; To affect acceleration; is the yaw acceleration; I zz is the inertia of the ship along the Z axis; J zz is the additional inertia, m, m x 、m y Represent the mass, longitudinal and transverse additional mass of the ship respectively, X H 、Y H 、N H are the forces and moments acting on the ship, and the variables with subscripts “P” and “R” are the forces and moments acting on the propeller and steering gear.

[0086] For example, during heading control, the drift angle is very small, and equation (1) can be linearized as:

[0087]

[0088] In formula (2), r(t) is the angular velocity of the unmanned ship, u0 is the initial motion velocity, Δu is the motion velocity deviation, is the average rate of change of Δu, X u is the fluid force along the X axis, Y (*) is the hydrodynamic coefficient of the rocking motion, N (*) is the hydrodynamic coefficient of yaw motion. The first equation is decoupled from the second and third equations, indicating that the linear motion of the unmanned vessel can be controlled separately from the steering motion. In practical applications, engineers are usually more concerned with the angular velocity r(t) of the unmanned vessel than with the lateral drift motion. Therefore, in the process of heading control, it is usually assumed that the longitudinal velocity change is small, that is, Δu = u s (t)-u0≈0, then the transfer function H(s) of the rudder angle δ(s) and the yaw angular velocity r(s) can be described as:

[0089]

[0090] In formula (3), T1, T2, T3, and T4 are constants. Since the USV motion has low-frequency characteristics, the transfer function H(s) can be reduced to the following first-order model at low frequency:

[0091]

[0092] In formula (4), T is the ship time constant, T = T1 + T2 - T3. Formula (4) can be expressed in the time domain as follows:

[0093]

[0094] Further define the yaw rate When there are internal parameter uncertainties and external disturbances, Equation (5) can be rewritten as follows:

[0095]

[0096] In formula (6), ω(t) represents the environmental disturbance, and δ(t) is the rudder angle input.

[0097] Step S3: Using the servo characteristics, establish a rudder angle dynamic model;

[0098] In this embodiment, during the actual unmanned vessel's heading control process, there is usually an inevitable time lag between the rudder angle input signal and the actual rudder angle response. This time lag is mainly due to the mechanical characteristics of the steering gear actuator. On large ships, the dynamic characteristics of the rudder can usually be approximated by a first-order inertia link. However, since the unmanned vessel's steering gear usually has higher efficiency and faster response speed, the first-order inertia link cannot fully describe its dynamic behavior. Instead, a second-order underdamped system can more accurately describe the steering gear characteristics. Therefore, the mathematical expression of the rudder angle dynamic model is as follows:

[0099]

[0100] Among them, T7 is the controller gain, T5 and T6 are time constants, u F (t) represents the actual control input due to actuator failure and can be expressed as: u F (t)=λ(u(t)-p(t)),0<λ≤1, in which P represents offset fault, λ represents partial failure fault, and parameter T i (i=1,...,6) represents different time constants.

[0101] System constraints: In actual operation, the rudder angle δ(t) and the rudder angle rate Subject to the following physical constraints: |δ(t)|≤35°,

[0102] Finally, the second-order steering system dynamics model of the unmanned ship can be integrated with the heading control model to form the following equation:

[0103]

[0104] The model accurately describes the dynamic characteristics of the unmanned ship's heading and provides a theoretical basis for the subsequent control system design.

[0105] For example, unmanned vessels are not only affected by external disturbances (such as wind, waves, and currents), but also by the dynamic characteristics of the hull (such as the sideslip effect). In particular, the sideslip angle β, which is the deviation between the hull's motion direction and the actual heading angle, usually has a significant impact on the heading control system. The dynamic equation of the sideslip angle can be expressed as:

[0106]

[0107] Among them, c1 and c2 are the damping coefficient of the sideslip angle and the influence coefficient of the yaw rate on the sideslip angle, respectively. Parameter c1 reflects the natural attenuation effect of the sideslip angle and generally ranges from 0.2 to 0.8. A larger c1 indicates a stronger sideslip angle attenuation. Meanwhile, c2 reflects the influence coefficient of the yaw rate on the sideslip angle, indicating the coupling effect of the yaw angle on the sideslip angle and ranging from 0.1 to 0.3. The values of these coefficients are closely related to the hydrodynamic characteristics, hull structure, navigation speed, and external environmental factors of the unmanned vessel. Δβ(t) is the sideslip angle disturbance term, which is usually caused by the nonlinear effects of fluid dynamics and external disturbances (such as crosswind and waves).

[0108] Furthermore, in order to simplify the controller design and improve the real-time performance of the system, the present invention ignores the direct influence of the external disturbance ω(t) in the heading control and only performs compensation control on the sideslip angle disturbance Δβ(t). Since the influence of external disturbances ω(t) such as wind, waves, and currents usually manifests as low-frequency changes, their influence on the system dynamics can be indirectly suppressed by the robustness of the controller. Therefore, this item is not considered separately in the control design, but the main focus is on the compensation of the sideslip angle disturbance Δβ(t), that is:

[0109] Δβ'(t)=Δβ(t)+ω(t) (10)

[0110] Among them, Δβ(t) represents the deviation angle caused by the lateral external force during the navigation of the unmanned ship, and ω(t) can be suppressed by the inherent robustness of the controller due to its slowly changing characteristics. Therefore, when designing the control system, it is assumed that Δβ(t) is the main factor affecting the heading deviation, and control compensation is performed around it. This simplified processing not only reduces the complexity of system modeling and makes the controller design more intuitive, but also reduces the dependence on environmental disturbance modeling and improves the feasibility of the control algorithm.

[0111] In addition, ignoring the direct effect of the external disturbance ω(t) makes the control system more efficient. Compared with the complex method of modeling external disturbances and sideslip angle disturbances separately, directly compensating Δβ(t) can improve the computational efficiency and real-time performance of the controller without significantly reducing system performance. In practical applications, by appropriately adjusting the rudder angle and effectively compensating Δβ(t), the stable navigation of the unmanned ship and the desired heading accuracy can be ensured without relying on accurate modeling of external disturbances.

[0112] In this embodiment, according to the above derivation process, the second-order underdamped system can be further expressed as:

[0113]

[0114] Lemma 1: Let ξ>0 and Then the following inequality holds:

[0115]

[0116] Among them, k0 satisfies The constant is k0=0.2758.

[0117] Assumption 1: The external time-varying disturbance is bounded, that is, it satisfies |ω|≤ω max , where ω max is an unknown positive constant;

[0118] Assumption 2: The required heading angle and its derivative are bounded, i.e., ψ d and They are all bounded;

[0119] Definition 1: The performance function ρ(t) always maintains a positive value in the defined time domain and has a monotonically decreasing characteristic, that is, as time goes by, the limit of the error allowed gradually shrinks. When time tends to infinity, the lower bound of the performance function ρ(t) is not zero, that is:

[0120] For example, a typical performance function expression that satisfies the above conditions is as follows:

[0121] ρ(t)=(ρ0-ρ ∞ )e -γt +ρ ∞ (12)

[0122] Among them, ρ0 is the initial performance boundary, ρ ∞is the steady-state performance limit, and γ is the rate parameter for controlling error convergence. Its value should be selected reasonably to ensure that the error can converge to the stable range within an appropriate time. The larger γ is, the faster the convergence rate is, but it may cause the overshoot of the system response to increase. If γ is too small, it may lead to too slow convergence speed, affecting the dynamic performance of the system. Then, the performance function ρ(t) is further used to construct the following error constraint boundary function:

[0123] σ min ρ(t)<z(t)<σ max ρ(t), t>0 (13)

[0124] where z(t) represents the tracking error subject to performance constraints, σ min and σ max is the system overshoot constraint parameter, satisfying 0<σ min ≤1,0<σ max ≤ 1. This constraint ensures that the error is always under control, so that the system response can be kept within the expected range and avoid excessive overshoot or oscillation.

[0125] In order to make the error z(t) meet the above constraints, the following error transformation method is adopted:

[0126] z(t)=ρ(t)S(ε(t)) (14)

[0127] Where S(ε) is a strictly monotonically increasing and smooth nonlinear transformation function, defined as follows:

[0128]

[0129] In addition, the error transformation function S(ε) is monotonically reversible, and its inverse transformation expression is as follows:

[0130]

[0131] The mapping relationship is:

[0132] S -1 :(-σ min, σ max )→(-∞,+∞) (17)

[0133] In this embodiment, in the heading keeping task of an unmanned surface vehicle (USV), the main goal is to make the actual heading angle ψ of the vessel accurately track the desired heading ψ d Since the sideslip angle β(t) will change with the movement of the hull, external environmental disturbances and changes in steering control, its influence on the heading error cannot be ignored. The sideslip angle of the unmanned ship reflects the deviation between the longitudinal axis of the hull and the actual direction of movement. Therefore, the heading angle deviation is not only affected by the heading error ψ-ψ dThe impact of the heading error is also affected by the sideslip angle. In order to more accurately describe the dynamic behavior of the system, the sideslip angle β(t) is added to the definition of the heading error. The heading error is corrected as follows:

[0134] e3(t)=ψ3(t)-ψ d +β(t) (18)

[0135] Therefore, the heading error not only considers the deviation in the heading angle but also incorporates the effect of the sideslip angle on heading control. The sideslip angle β(t) is primarily determined by the ship's steering control, external environmental disturbances (such as wind, waves, and currents), and the hydrodynamic characteristics of the ship itself. This modification can effectively improve the accuracy of the control system, especially when the sideslip angle of the unmanned vessel is large. If the sideslip angle is not considered, the control system will not be able to effectively compensate for the heading error caused by the sideslip angle of the unmanned vessel, resulting in a decrease in heading accuracy. By incorporating the sideslip angle of the unmanned vessel into the heading error definition, we can more accurately describe the dynamic behavior of the vessel under different navigation conditions and design a more robust control system. Furthermore, the inclusion of the sideslip angle can reduce errors caused by model simplification and improve the reliability of the system in practical applications. Through appropriate control inputs (such as rudder angle adjustment), we can effectively compensate for the influence of the sideslip angle and ensure that the ship always moves on the desired course.

[0136] In this embodiment, in order to avoid the singularity problem in the error transformation and ensure that the variables are always within the valid definition domain, a buffer offset C>0 is introduced to ensure that the numerator and denominator are always positive. As mentioned above, the error after transformation can be defined as follows:

[0137]

[0138] in:

[0139] Then, the derivative of the transformed error can be obtained:

[0140]

[0141] in,

[0142] Taking the derivative of ε3, we can get:

[0143]

[0144] According to formula (11), we can get:

[0145]

[0146]

[0147] Combining the above three formulas, we can get:

[0148]

[0149] make Then we can get:

[0150]

[0151] In this embodiment, in the heading keeping control system, the sideslip angle β(t) is affected by the external environmental factors (such as wind, waves, currents, etc.) and the dynamic characteristics of the hull, forming a disturbance with dynamic change characteristics, which has a significant impact on the heading stability and control performance of the unmanned ship. If it is not effectively compensated, it may lead to the accumulation of heading deviations, thereby reducing the control accuracy of the system. Therefore, real-time estimation and compensation of the sideslip angle β(t) is an important means to ensure the robustness of the system. To this end, an adaptive estimation method is introduced to perform online identification and compensation of the sideslip angle, and the estimated value of the sideslip angle is defined as Based on adaptive control theory, the corresponding estimation algorithm is designed to dynamically adjust In order to accurately track the actual sideslip angle β(t), the influence of the sideslip angle on the heading control is effectively weakened, and the stability and control accuracy of the system are improved. The adaptive law for estimating the sideslip angle of the unmanned ship is designed as follows:

[0152]

[0153] Step S4: constructing an adaptive controller with partial failure of the servo;

[0154] In this embodiment, the control law u is designed as follows: F (t) can be obtained:

[0155]

[0156] Among them, k1 is the control gain, τ1 is a negative constant, p represents an unknown actuator offset fault, λ represents a partial failure fault, is the estimated value of the actuator offset fault, Denotes the estimated value of partial failure, and the following adaptive update law is designed:

[0157]

[0158] Among them, K2 and K3 are control gains;

[0159] For example, for a heading keeping system with a control law and an adaptive law, if there is ρ(0), such that -σ min ρ(0)<e(0)<σ maxρ(0), then all signals in the resulting closed-loop system are ultimately semiglobally uniformly bounded, and the transformed tracking errors are confined to the specified performance bounds for all t ≥ 0.

[0160] prove:

[0161] Select the Lyapunov function as:

[0162]

[0163] Then the time derivative of V3 is:

[0164]

[0165] Assume that Δβ(t) is a bounded quantity, that is, in the actual operation process, its maximum value will not exceed a preset limit, and use Δβ max to represent the upper bound of the sideslip angle disturbance. This disturbance term comes from the influence of external environmental factors such as wind, waves, and ocean currents on the motion state of the unmanned ship. This assumption ensures that the controller can effectively compensate for the sideslip angle changes under the most unfavorable conditions during design without the need for real-time estimation or observation of the specific disturbance value. Through this assumption, the system can optimize the control strategy under the premise of known disturbance boundaries, improve the stability and anti-interference ability of heading maintenance, thereby ensuring that the unmanned ship can still maintain precise heading control in complex marine environments.

[0166] In summary, the above formula can be expressed as:

[0167]

[0168] Substituting formula (31) into the equation, we can obtain:

[0169]

[0170] Further we can get:

[0171]

[0172] Where k0 = 0.2758, τ1 is a positive constant. Substituting the adaptive law of sideslip angle estimation into the equation, we can obtain:

[0173]

[0174] Substituting the adaptive law for estimating the sideslip angle of the ship into the equation, we can obtain:

[0175]

[0176] Depend on We can get:

[0177]

[0178] Substituting the adaptive update law into formula (36) yields:

[0179] Depend on We can get:

[0180]

[0181] Substituting the adaptive law into formula (38) yields:

[0182]

[0183] because We can get:

[0184]

[0185] Depend on We can get:

[0186]

[0187] Depend on We can get:

[0188]

[0189] in

[0190] make We can get:

[0191]

[0192] Further we can get:

[0193] Then multiply both sides by the integration factor e 2at :

[0194]

[0195] Integrating both sides of the inequality gives:

[0196]

[0197] From the above inequality we can get: Therefore, all variables are semi-globally uniformly ultimately bounded, and the tracking error satisfies all specified performance constraints, completing the proof.

[0198] In this embodiment, the effectiveness of the design method is verified through a digital simulation example:

[0199] Exemplary combinations Figure 2The experimental scenario shown in the figure is carried out in the MATLAB simulation environment. The main purpose is to verify the influence of the sideslip angle and its observation and compensation capabilities in the energy unbounded disturbance environment. The mathematical model with the sideslip angle information is added to re-carry out the model matching experiment. The model matching experiment is located in the Qiantang River in Hangzhou. The heading angle change of the "Qingshan" unmanned experimental ship with sideslip compensation and in the heading holding state is recorded. The MATLAB tool can be used to perform model identification on the "Qingshan" unmanned experimental ship. The model parameters of the "Qingshan" obtained after identification can be determined as: T4=0.0370, T=23.9912, and the model parameters of the servo system are T4=0.1267, T=1.9493, T E1 =0.19,T E2 =0.3446,T E3 = 0.28. The heading angle of the Qingshan is obtained as Figure 3 shown.

[0200] The control parameters are selected as follows:

[0201] k1=1.503,k2=0.269,k3=2.259,k β =1.972,τ1=-9.57,

[0202]

[0203] For the performance function, the parameters are chosen as follows:

[0204] ρ0=28,ρ ∞ =2,γ=0.1,σ min =0.18,σ max =0.98,C=0.05,c1=0.5,c2=0.5

[0205] In this embodiment, combined with Figure 4 The figure shows the dynamic variation of the sideslip angle, where the blue curve represents the actual sideslip angle and the red curve represents the observed estimated sideslip angle. As can be seen from the figure, in the initial stage (t < 20s), the actual sideslip angle fluctuates significantly. This is mainly due to the influence of complex external disturbances such as wind, waves, and ocean currents during the unmanned vessel's startup process, causing the sideslip angle to deviate from its stable value. Furthermore, there is a certain initial deviation between the estimated sideslip angle and the actual sideslip angle. This is because the control parameters have not yet fully converged during the system's initial adjustment phase, which limits the observer's ability to track the sideslip angle. However, over time, the observer gradually converges and improves its accuracy. After t > 40s, the actual sideslip angle is essentially consistent with the estimated value, demonstrating that the proposed sideslip angle observation and compensation strategy can accurately estimate the dynamic characteristics of the sideslip angle and perform real-time compensation, effectively suppressing the impact of the sideslip angle.

[0206] For example, further observation of the trend in the figure shows that although the sideslip angle is still affected by periodic disturbances throughout the entire navigation process, its fluctuation range is always limited to within ±4°, and there is no obvious cumulative error or divergence. This shows that the adaptive control method based on sideslip compensation can effectively adjust the control gain during long-term navigation, dynamically adapt to environmental changes, and thus suppress the adverse effects of the sideslip angle. In addition, although the sideslip angle exhibits large short-term fluctuations at certain moments, such as around t = 60s and t = 100s, the observed value can still accurately follow the changing trend of the actual sideslip angle and quickly adjust, allowing the system to return to a stable state in a relatively short period of time.

[0207] Overall, the experimental results fully verify the applicability and robustness of the control method proposed in this paper in complex marine environments. It can maintain a good compensation effect when the sideslip angle changes greatly, ensure the heading control accuracy and stability of the unmanned ship, and improve its autonomous navigation capability under uncertain disturbance conditions.

[0208] In this embodiment, combined with Figure 5 The figure shows a comparison between the heading angle output and the desired heading angle of the unmanned vessel under sideslip compensation control. In the figure, the red box indicates the command heading change, the blue dashed line represents the desired heading angle, and the purple dashed line is the actual heading angle. As can be seen from the figure, when the heading command changes, the actual heading angle can quickly approach and track the desired value and reach stability in a relatively short time. In particular, at t = 60s and t = 100s, the heading angle changes significantly, and the actual heading angle can be quickly adjusted and stabilized at the target value, indicating that the control strategy has good responsiveness to dynamic changes. At the same time, there is no obvious oscillation or error expansion in the heading angle, verifying that this control method has strong robustness and adaptability.

[0209] In this embodiment, combined with Figure 6 The figure shows the change in the system's heading error under the sideslip compensation control strategy. In the figure, the green dashed line represents the error range set by the prescribed performance function (PPF), and the blue curve represents the actual heading error. It can be seen that in the initial stage of the system, the heading error fluctuated slightly due to external disturbances and the sideslip angle. However, over time, the heading error quickly converged and remained within the error range set by the PPF, without exceeding the predetermined boundary. The figure shows that although the system's heading error experienced significant fluctuations in a short period of time, after approximately 60 seconds, the error gradually stabilized and remained within the specified performance limits. This demonstrates that the sideslip compensation control strategy can effectively control the heading error, ensuring heading accuracy and system stability. No significant overshoot or sustained oscillation occurred throughout the entire process, demonstrating the effectiveness of the control method in the face of complex disturbances.

[0210] Overall experimental results demonstrate that the proposed adaptive prescribed performance control method based on sideslip compensation effectively compensates for the effects of sideslip angle while maintaining heading accuracy, ensuring that the unmanned vessel maintains precise heading even in complex disturbance environments. Compared to traditional methods, this control strategy outperforms in terms of error convergence speed, stability, and disturbance resistance, providing more reliable technical support for autonomous navigation of unmanned vessels.

[0211] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0212] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for self-adaptive, specified-performance, fault-tolerant control of an unmanned vessel with sideslip angle compensation, characterized by: The following steps are involved: Step S1: Establishing a heading keeping system; Step S2: establishing a USV model with internal parameter uncertainty, wherein the USV model is an unmanned ship model; Step S3: Using the servo characteristics, establish a rudder angle dynamic model; Step S4: Construct an adaptive controller with partial failure of the servo.

2. The method for controlling the heading of an unmanned vessel with adaptive specified performance and fault-tolerant control with sideslip angle compensation according to claim 1, characterized in that: The heading keeping system includes the following modules: The adaptive controller, steering gear, and unmanned vessel generate a control signal u(t) by outputting the deviation signal generated by the desired heading and the actual heading to the adaptive controller. The control signal acts on the steering gear to generate an actual rudder angle δ(t) to make the actual heading consistent with the desired heading.

3. The method for controlling the unmanned vessel's heading with adaptive specified performance and fault-tolerant control with sideslip angle compensation according to claim 2, characterized in that: The established USV model specifically includes: defining the unmanned ship hull as completely symmetrical, setting the origin of the coordinate system at the center of gravity of the USV, and the USV three-degree-of-freedom motion mathematical model is: In formula (1), is the impact acceleration, To affect acceleration, is the yaw acceleration, I zz is the inertia of the ship along the Z axis, J zz is the additional inertia, m, m x 、m y Represent the mass, longitudinal and transverse additional mass of the ship respectively, X H 、Y H 、N H are the forces and moments acting on the ship, and the variables with subscripts "P" and "R" are the forces and moments acting on the propeller and steering gear.

4. The method for controlling the unmanned vessel's heading with adaptive specified performance and fault-tolerant control with sideslip angle compensation according to claim 3, characterized in that: The USV model also includes: during heading control, the drift angle is very small, and equation (1) can be linearized as: In formula (2), r(t) is the angular velocity of the unmanned ship, u0 is the initial motion speed, Δu is the motion speed deviation, is the average rate of change of Δu, X u is the fluid force along the X axis, Y (*) is the hydrodynamic coefficient of the rocking motion, N (*) is the hydrodynamic coefficient of yaw motion. The first equation is decoupled from the second and third equations, indicating that the linear motion of the unmanned ship can be controlled separately from the steering motion. In the course control process, the longitudinal velocity change is defined to be small, that is, Δu=u s (t)-u0≈0, then the transfer function H(s) of the rudder angle δ(s) and the yaw angular velocity r(s) is described as: In formula (3), T1, T2, T3, and T4 are constants. Since the USV motion has low-frequency characteristics, the transfer function H(s) can be reduced to the following first-order model at low frequency: In formula (4), T is the ship time constant, T = T1 + T2 - T3. Formula (4) can be expressed in the time domain as follows: Further define the yaw rate When there are internal parameter uncertainties and external disturbances, Equation (5) can be rewritten as follows: In formula (6), ω(t) represents the environmental disturbance, and δ(t) is the rudder angle input.

5. The method for controlling the unmanned vessel's heading with adaptive specified performance and fault-tolerant control with sideslip angle compensation according to claim 1, characterized in that: The servo characteristics are described by a second-order underdamped system, and the rudder angle dynamic model is: Among them, T7 is the controller gain, T5 and T6 are time constants, u F (t) represents the actual control input due to actuator failure and can be expressed as: u F (t)=λ(u(t)-p(t)),0<λ≤1, in which P represents offset fault, λ represents partial failure fault, and parameter T i (i=1,...,6) represents different time constants; Rudder angle δ(t) and rudder angle rate Subject to the following physical constraints: |δ(t)|≤35°, The second-order steering system dynamics model of the unmanned ship is integrated with the heading control model to form the following equation: The rudder angle dynamic model is used to describe the dynamic characteristics of the heading of the unmanned ship.

6. The method for controlling the unmanned vessel's heading with adaptive specified performance and fault-tolerant control with sideslip angle compensation according to claim 5, characterized in that: The rudder angle dynamic model also includes: analyzing the dynamic characteristics of the disturbance generated by the unmanned ship, including the sideslip effect. The sideslip angle β is the deviation between the hull motion direction and the actual heading angle. The dynamic equation of the sideslip angle β is expressed as: In formula (9), c1 and c2 are the damping coefficient of the sideslip angle and the influence coefficient of the yaw rate on the sideslip angle, respectively. The parameter c1 reflects the natural attenuation effect of the sideslip angle, and is usually in the range of 0.2 to 0.

8. A larger c1 indicates a stronger sideslip angle attenuation. C2 reflects the influence coefficient of the yaw rate on the sideslip angle, indicating the coupling effect of the yaw angle on the sideslip angle, and is in the range of 0.1 to 0.

3. Δβ(t) is the sideslip angle disturbance term. In heading control, the direct influence of the external disturbance ω(t) is ignored, and only the sideslip angle disturbance Δβ(t) is compensated. The compensation of the sideslip angle disturbance Δβ(t) is: Δβ'(t)=Δβ(t)+ω(t) (10) In formula (10), Δβ(t) represents the deviation angle caused by the lateral external force during the navigation of the unmanned ship, and ω(t) can be suppressed by the inherent robustness of the controller due to its slow changing characteristics. Therefore, when designing the control system, Δβ(t) is defined as the main factor affecting the heading deviation, and control compensation is performed around it.

7. The method for controlling the unmanned vessel's heading with adaptive specified performance and fault-tolerant control with sideslip angle compensation according to claim 6, characterized in that: The second-order underdamped system is further expressed as: Lemma 1: Let ξ>0 and Then the following inequality holds: Among them, k0 satisfies The constant is k0=0.2758; Assumption 1: The external time-varying disturbance is bounded, that is, it satisfies |ω|≤ω max , where ω max is an unknown positive constant; Assumption 2: The required heading angle and its derivative are bounded, i.e., ψ d and They are all bounded; Definition 1: The performance function ρ(t) always maintains a positive value in the defined time domain and has a monotonically decreasing characteristic, that is, as time goes by, the limit of the error allowed gradually shrinks. When time tends to infinity, the lower bound of the performance function ρ(t) is not zero, that is: A typical performance function expression that meets the above conditions is as follows: ρ(t)=(ρ0-ρ ∞ )e -γt +r ∞ (12) In formula (12), ρ0 is the initial performance boundary, ρ ∞ is the steady-state performance limit, γ is the rate parameter for the control error convergence. The larger γ is, the faster the convergence rate is, but it will cause the overshoot of the system response to increase. If γ is too small, the convergence speed will be too slow, affecting the dynamic performance of the system. The following error constraint boundary function is further constructed from the performance function ρ(t): s min ρ(t)<z(t)<σ max p(t), t>0 (13) In Equation (13), z(t) represents the tracking error subject to performance constraints, σ min and σ max is the system overshoot constraint parameter, satisfying 0<σ min ≤1,0<σ max ≤1, this constraint ensures that the error is always under control so that the system response can remain within the expected range; In order to make the error z(t) meet the above constraints, the following error transformation method is adopted: z(t)=ρ(t)S(ε(t)) (14) In formula (14), S(ε) is a strictly monotonically increasing and smooth nonlinear transformation function, which is defined as follows: In addition, the error transformation function S(ε) is monotonically reversible, and its inverse transformation expression is as follows: The mapping relationship is: S -1 :(-s min, s max )→(-∞,+∞) (17).

8. The method for controlling the unmanned vessel's heading with adaptive specified performance and fault-tolerant control with sideslip angle compensation according to claim 7, characterized in that: The sideslip angle β compensation further includes: adding the sideslip angle β(t) to the definition of the heading error, and the heading error is corrected to: in: Derivative of the transformed error yields: in, Taking the derivative of ε3, we can get: According to formula (11), we can get: Combining the above three formulas, we can get: make Then we can get:

9. The method for controlling the heading of an unmanned vessel with adaptive specified performance and fault-tolerant control with sideslip angle compensation according to claim 1, characterized in that: The adaptive controller includes: introducing an adaptive estimation method to perform online identification and compensation of the sideslip angle, and defining the estimated value of the sideslip angle as Based on adaptive control theory, design corresponding estimation algorithms and dynamically adjust The adaptive law for estimating the ship's sideslip angle is designed as follows: Design an adaptive controller with partial failure of the servo, and design the control law u F (t) is as follows: Among them, k1 is the control gain, τ1 is a negative constant, p represents an unknown actuator offset fault, λ represents a partial failure fault, is the estimated value of the actuator offset fault, Represents the estimated value of partial failure fault, design Obey the following adaptive update law: Among them, K2 and K3 are control gains. For a heading keeping system with control law and adaptive law, when there is ρ(0), such that -σ min ρ(0)<e(0)<σ max ρ(0), then all signals in the resulting closed-loop system are ultimately semi-globally uniformly bounded, and the transformed tracking error is bounded within the specified performance bound for all t ≥ 0; Finally, formula (11) can be rewritten as: Among them, Δβ' max Represents the upper bound of the sideslip angle disturbance, which comes from the influence of external environmental factors such as wind, waves, and ocean currents on the motion state of the unmanned ship; The Lyapunov function related to the rudder angle error is defined as: Then the time derivative of V3 along formula (20) is: In summary, the above formula can be expressed as: Substituting the control law u(t) into formula (31) yields: Further we can get: Among them, k0=0.2758,τ1 is a positive constant, from 0<λ<1, Available, Substituting the adaptive law of sideslip angle estimation into the equation, we can obtain: Substituting the adaptive law for ship sideslip angle estimation into formula (34), we can obtain: Depend on We can get: Substituting the adaptive update law into formula (36) yields: Depend on We can get: Substituting the adaptive law into formula (38) yields: Since 0<λ<1, We can get: Depend on We can get: Depend on We can get: in make We can get: Further we can get: Then multiply both sides by the integration factor e 2at : Integrating both sides of the inequality gives: From the above inequality we can get: Therefore, all variables are semi-globally uniformly ultimately bounded, and the tracking error satisfies all specified performance constraints, completing the proof.

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