Course tracking control method for unmanned surface vehicle with signal quantization based on double-expansion observer

Abstract

The invention provides an unmanned surface vehicle course tracking control method with signal quantization based on a double-expansion observer, and the method comprises the steps: building a third-order response type unmanned surface vehicle course control mathematical model according to the characteristics of a ship and the sea condition information of a surrounding environment; designing a double-expansion observer model for simultaneously estimating matched interference and non-matched interference in the ship course tracking control system and observing uncertain items and external interference in the ship control system; based on a backstepping method and a dynamic surface control algorithm, a course controller of the unmanned surface vehicle is designed, and the calculation complexity brought by a virtual control law is reduced; based on the Lyapunov stability theory, the stability of the designed unmanned surface vehicle course tracking control system with state quantization and input quantization is proved, all signals in a closed-loop system are consistent and bounded in a semi-global mode, and the tracking error is arbitrarily small by adjusting parameters of a controller.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and more particularly to a heading tracking control method for an unmanned surface vehicle based on dual extended observers with signal quantization. Background Technology

[0002] With the rise of intelligent maritime shipping, unmanned surface vehicles (USVs) have become an important part of global maritime operations. Their powerful maneuverability, advanced autonomous navigation capabilities, ability to carry multi-functional payloads, and ability to perform monitoring, rescue, and remotely hazardous missions in vast ocean areas have secured their crucial position in maritime transport. Maintaining vessel stability and precisely controlling its course in the complex and ever-changing marine environment is one of the main challenges for USVs to achieve autonomous navigation.

[0003] Currently, most unmanned surface vessels (USVs) rely on traditional control methods for course control, such as PID controllers, adaptive controllers, and model-based controllers. While these methods can achieve course tracking to some extent, they are often hampered by limited communication bandwidth and external interference in complex marine environments. To address these challenges, some research has begun to introduce state quantization and input quantization techniques to reduce the communication rate within the signal transmission bandwidth, thereby lowering the control execution frequency. Furthermore, some studies have considered the characteristics of ship steering servo systems to improve the performance of the control system.

[0004] However, existing technologies still have some shortcomings in solving the heading control problem of unmanned surface vessels (USVs). First, traditional control strategies often fail to effectively handle the quantization characteristics of signal transmission when communication bandwidth is limited, leading to decreased control performance. Second, most existing methods neglect the dynamic characteristics of the ship's steering servo system, which may result in insufficient control accuracy in practical applications. Finally, existing technologies typically employ linear analytical models when processing quantized signals, making it difficult to handle complex scenarios with time-varying parameters in real-world engineering. Therefore, a new control method is needed that can effectively process quantized signals under limited communication bandwidth and consider the dynamic characteristics of the steering servo system to improve the heading control accuracy and stability of USVs. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a heading tracking control method for unmanned surface vehicles (USVs) based on dual extended observers and signal quantization. By combining dual extended observers, state quantization, and input quantization techniques with advanced control algorithms, this method solves the problem of achieving stable and precise heading control for USVs in complex marine environments. This method not only improves the robustness and adaptability of the control system but also reduces communication bandwidth and actuator load, demonstrating significant practical application value.

[0006] The technical means employed in this invention are as follows:

[0007] A heading tracking control method for an unmanned surface vehicle based on dual extended observers with signal quantization includes:

[0008] S1. Based on the characteristics of the ship and the sea state information of the surrounding environment, establish a mathematical model for the heading control of a third-order response unmanned surface vehicle.

[0009] S2. Design a double-extended observer model to observe uncertainties and external disturbances in the ship control system;

[0010] S3. Design a heading controller for an unmanned surface vehicle based on backstepping and dynamic surface control algorithms;

[0011] S4. Based on Lyapunov stability theory, prove the stability of the designed unmanned surface vehicle heading tracking control system with state quantization and input quantization, and that all signals in the closed-loop system are semi-globally consistent and bounded, and the tracking error can be made arbitrarily small by adjusting the controller parameters.

[0012] Further, step S1 includes:

[0013] S11. The following is a known nonlinear Nomoto model of a ship:

[0014]

[0015] Where ψ is the ship's bow angle, δ is the rudder angle, K and T are the ship's maneuverability indices, and a1 and a2 are nonlinear parameters;

[0016] S12. The following is a known model of the dynamic characteristics of a ship with a steering gear:

[0017]

[0018] Where, δ E K is the rudder angle command issued by the servo motor. E For servo control gain, T E The servo time constant;

[0019] S13. Introducing state quantization and input quantization, a third-order response mathematical model of the unmanned surface vehicle is established as follows:

[0020]

[0021] Where x1 represents the ship's heading angle; x2 represents the ship's heading angular velocity; x3 represents the ship's rudder angle or a variable related to the rudder angle; ω1 and ω2 represent unknown disturbances caused by wind, current, and waves; and f(x2,t) represents a nonlinear function related to the heading angular velocity. Where a1 and a2 represent nonlinear parameters, T represents the ship's maneuverability index, and g(x3,t) represents a function related to the rudder angle. Where T E c represents the servo time constant; c represents the system parameters. Where K E is the servo control gain; Q(u) represents the quantization of the control input u.

[0022] Further, step S2 includes:

[0023] S21. Design the first observer model as follows:

[0024]

[0025] in, Represents the quantized state variables; This represents the estimated values ​​of state variables x1 and x2 in the first observer model; β1, β2, and β3 represent the estimated value of the matching disturbance term σ1 in the first observer model; β1, β2, and β3 represent the design parameters of the first observer model; ∈1 represents the gain coefficient of the first observer model.

[0026] S22. Design the second observer model as follows:

[0027]

[0028] S23, This represents the estimated value of the unmatched disturbance term σ2 in the second observer model; β4 and β5 represent the quantized control input; β5 and β4 represent the design parameters of the second observer model; ∈2 represents the gain coefficient of the second observer model. This represents the estimated value of the state variable x3 in the second observer model;

[0029] S24. Define the observation error as follows:

[0030]

[0031] Where e1 represents the observation error of the heading angle; e2 represents the observation error of the heading angular velocity; e3 represents the observation error of the matched disturbance; v1 represents the observation error of the rudder angle or a variable related to the rudder angle; and v2 represents the observation error of the unmatched disturbance.

[0032] S25. Differentiating the defined observation error, we get:

[0033]

[0034] Where s1 and s3 represent quantization errors;

[0035] S26. To facilitate stability analysis, the scaling error is defined as follows:

[0036]

[0037] Where θ and ξ both represent the scaling error vector; A1 and A2 represent the system matrices of the first observer model and the second observer model, respectively. D1 and D2 represent the perturbation terms of the first observer model and the second observer model, respectively.

[0038] Further, in step S26, the characteristic equations of the system matrices A1 and A2 of the first observer model and the second observer model are respectively:

[0039] A1: λ 3 +β1λ 2 +β2λ+β3=0

[0040] A2: λ 2 +β4λ+β5=0

[0041] As can be seen from the characteristic equation, when the parameters are chosen as β1=3, β2=3, β3=1, β4=2, β5=1, matrices A1 and A2 are Hurwitz matrices.

[0042] Further, step S3 includes:

[0043] S31. Define heading error as follows:

[0044]

[0045] Where z1 represents the heading angle error; ψ d z1 represents the desired heading angle; z2 represents the heading angular velocity error; α 1f α 2f Both represent virtual control law; z3 represents rudder angle error;

[0046] S32. Differentiating the defined heading error, we get:

[0047]

[0048] Where d1 represents the estimated value of the matched disturbance, that is, the disturbance term related to the heading angular velocity in the system; d2 represents the estimated value of the unmatched disturbance, that is, the disturbance term related to the rudder angle in the system.

[0049] S33. Define a first-order low-pass filter as follows:

[0050]

[0051] Where, τ f1 , τ f2 The filter's time constant is represented by α1 and α2, respectively, which are the designed virtual control laws.

[0052] S34. Design unquantized control inputs as follows:

[0053]

[0054] Where k3 represents the control gain.

[0055] Further, step S4 includes:

[0056] S41. Analyze the filter error and define the filter error as follows:

[0057] η1=α 1f -α1

[0058] η2=α 2f -α2

[0059] S42. Define the Lyapunov function as follows:

[0060]

[0061] And by differentiating the defined Lyapunov function, we get:

[0062]

[0063] Where M1 represents a constant upper bound used to limit The absolute value;

[0064] S43. Apply Young's inequality and substitute... get:

[0065]

[0066] in, Represents the Lyapunov function related to the filter error η1;

[0067] S44. Solving the inequality in step S43, we get:

[0068]

[0069] As time approaches infinity |η1(t)|≤τ f1 M1, meaning the filtering error is bounded;

[0070] S45. From step S26, we know that matrices A1 and A2 are Hurwitz matrices, therefore there exists a positive definite matrix P1 > 0.

[0071] Q1>0 and P2>0, Q2>0 satisfies:

[0072] A1 T P1+P1A1=-Q1

[0073] A2 T P² + P²A² = -Q²

[0074] Matrices D1 and D2 satisfy:

[0075] ||D1||≤ρ1(∈1)

[0076] ||D2||≤ρ2(∈2)

[0077] in, N1 represents the maximum external disturbance or unmodeled dynamic that may exist in the heading angular velocity dynamic; N2 represents the maximum external disturbance or unmodeled dynamic that may exist in the rudder angle dynamics;

[0078] S46. Analyze the observation error of the designed double-extended observer, and define the Lyapunov function V2 as follows:

[0079] V2=θ T P1θ+ξ T P2ξ

[0080] Taking the derivative of the defined Lyapunov function V2, we get:

[0081]

[0082] S47. Using matrix properties and the Cauchy-Schwarz inequality, we obtain:

[0083]

[0084] S48. Based on the Lyapunov function designed above, for the convenience of stability analysis, it is defined as follows:

[0085]

[0086] Applying Young's inequality, we obtain:

[0087]

[0088] therefore, in, Therefore, when |θ| or |ξ| is sufficiently large, ∈ i Small enough, then That is, the systematic error shrinks to a compact set. The observation errors θ(t) and ξ(t) are globally consistent and eventually bounded.

[0089] S49. Analyze the stability of the closed-loop system. Differentiate the heading error defined in step S31 to obtain:

[0090]

[0091] S410. Define the Lyapunov function V3 as follows:

[0092]

[0093] And by differentiating the defined Lyapunov function V3, we obtain:

[0094]

[0095] S411. Applying Young's inequality, we obtain:

[0096]

[0097] Substitute into From:

[0098]

[0099] S412. According to the Lyapunov function V3, let Then we have:

[0100]

[0101] Where Γ is a nonnegative constant, representing the upper bound of the influence of various disturbances and uncertainties in the system on the derivative of the Lyapunov function. If the controller parameters satisfy k1>1, k2>b 2 +1, Then G is a positive definite matrix, and it has a minimum eigenvalue (λ). min (G)>0) makes Let (h=2λ) min (G)), obtained Solving the differential inequality yields:

[0102]

[0103] When time approaches positive infinity, V3(t)≤Γ / h, where h is a positive constant representing the rate at which the error energy decays;

[0104] S413. Considering the Lyapunov function of the closed-loop system, V = V² + V³, the derivative is:

[0105]

[0106] When ∈ is sufficiently small, and under the condition that parameters k1, k2, k3 compensate for the influence of coupling terms and filtering errors, it is guaranteed that Therefore, the error signal of the closed-loop system is globally consistent and eventually bounded.

[0107] Compared with the prior art, the present invention has the following advantages:

[0108] 1. The heading tracking control method for unmanned surface vessels based on dual extended observers with signal quantization provided by this invention, compared with existing unmanned surface vessel heading control methods that focus more on ideal communication effects, takes into account the quantization characteristics of signal transmission in engineering practice and innovatively incorporates state quantization and input quantization into the research scope, which not only reduces the signal transmission burden, but also better fits the actual situation of marine engineering.

[0109] 2. The heading tracking control method for unmanned surface vessels based on dual extended observers with signal quantization provided by this invention, compared with the existing heading control models for unmanned surface vessels that often ignore the dynamic characteristics of the steering device, fully considers the characteristics of the steering device servo system and performs integrated control law design. By integrating the dynamic characteristics of the steering device into the control architecture, the theoretical design is better matched with the execution logic of the ship hardware.

[0110] 3. The heading tracking control method for unmanned surface vessels based on dual extended observers with signal quantization provided by this invention, compared with most existing unmanned surface vessel quantization control methods that use linear analytical models to describe the input quantization process, introduces dual extended state observers to estimate and compensate for unknown disturbances caused by quantization in real time, enabling the system to cope with quantization problems through its own feedback, and is more suitable for engineering scenarios with time-varying parameters.

[0111] Based on the above reasons, this invention can be widely promoted in fields such as artificial intelligence navigation practice. Attached Figure Description

[0112] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0113] Figure 1 This is a flowchart of the method of the present invention.

[0114] Figure 2 This is a simplified block diagram of the heading tracking control system for an unmanned surface vehicle based on dual extended observers and signal quantization proposed in this invention.

[0115] Figure 3 The tracking results of USV heading angle, USV bow roll rate and USV rudder angle provided in the embodiments of the present invention are shown in the figure.

[0116] Figure 4 The following diagram shows the tracking error results of USV heading angle, USV bow roll rate, and USV rudder angle provided for embodiments of the present invention.

[0117] Figure 5 The embodiments of the present invention provide control input diagrams that are quantized and unquantized.

[0118] Figure 6 The image shows the observation results provided by the observer in an embodiment of the present invention. Detailed Implementation

[0119] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0120] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0121] like Figure 1 As shown, this invention provides a heading tracking control method for an unmanned surface vehicle based on dual extended observers with signal quantization, comprising:

[0122] S1. Based on the characteristics of the ship and the sea state information of the surrounding environment, establish a mathematical model for the heading control of a third-order response unmanned surface vehicle.

[0123] S2. Design a double-extended observer model to observe uncertainties and external disturbances in the ship control system;

[0124] S3. Design a heading controller for an unmanned surface vehicle based on backstepping and dynamic surface control algorithms;

[0125] S4. Based on Lyapunov stability theory, prove the stability of the designed unmanned surface vehicle heading tracking control system with state quantization and input quantization, and that all signals in the closed-loop system are semi-globally consistent and bounded, and the tracking error can be made arbitrarily small by adjusting the controller parameters.

[0126] In a specific implementation, as a preferred embodiment of the present invention, step S1 includes:

[0127] S11. The following is a known nonlinear Nomoto model of a ship:

[0128]

[0129] Where ψ is the ship's bow angle, δ is the rudder angle, K and T are the ship's maneuverability indices, and a1 and a2 are nonlinear parameters;

[0130] S12. The following is a known model of the dynamic characteristics of a ship with a steering gear:

[0131]

[0132] Where, δ E K is the rudder angle command issued by the servo motor.E For servo control gain, T E The servo time constant;

[0133] S13. Introducing state quantization and input quantization, a third-order response mathematical model of the unmanned surface vehicle is established as follows:

[0134]

[0135] Where x1 represents the ship's heading angle; x2 represents the ship's heading angular velocity; x3 represents the ship's rudder angle or a variable related to the rudder angle; ω1 and ω2 represent unknown disturbances caused by wind, current, and waves; and f(x2,t) represents a nonlinear function related to the heading angular velocity. Where a1 and a2 represent nonlinear parameters, T represents the ship's maneuverability index, and g(x3,t) represents a function related to the rudder angle. Where T E c represents the servo time constant; c represents the system parameters. Where K E Here, Q(u) represents the servo control gain; Q(u) represents the quantization of the control input u. For example... Figure 2 The diagram shown is a simplified block diagram of a heading tracking control system for an unmanned surface vehicle based on dual extended observers with signal quantization.

[0136] In a specific implementation, as a preferred embodiment of the present invention, step S2 includes:

[0137] S21. Design the first observer model as follows:

[0138]

[0139] in, Represents the quantized state variables; This represents the estimated values ​​of state variables x1 and x2 in the first observer model; β1, β2, and β3 represent the estimated value of the matching disturbance term σ1 in the first observer model; β1, β2, and β3 represent the design parameters of the first observer model; ∈1 represents the gain coefficient of the first observer model.

[0140] S22. Design the second observer model as follows:

[0141]

[0142] S23, This represents the estimated value of the unmatched disturbance term σ2 in the second observer model; β4 and β5 represent the quantized control input; β5 and β4 represent the design parameters of the second observer model; ∈2 represents the gain coefficient of the second observer model. This represents the estimated value of the state variable x3 in the second observer model;

[0143] S24. Define the observation error as follows:

[0144]

[0145] Where e1 represents the observation error of the heading angle; e2 represents the observation error of the heading angular velocity; e3 represents the observation error of the matched disturbance; v1 represents the observation error of the rudder angle or a variable related to the rudder angle; and v2 represents the observation error of the unmatched disturbance.

[0146] S25. Differentiating the defined observation error, we get:

[0147]

[0148] Where s1 and s3 represent quantization errors;

[0149] S26. To facilitate stability analysis, the scaling error is defined as follows:

[0150]

[0151] Where θ and ξ both represent the scaling error vector; A1 and A2 represent the system matrices of the first observer model and the second observer model, respectively. D1 and D2 represent the perturbation terms of the first observer model and the second observer model, respectively.

[0152] In a specific implementation, as a preferred embodiment of the present invention, in step S26, the characteristic equations of the system matrices A1 and A2 of the first observer model and the second observer model are respectively:

[0153] A1: λ 3 +β1λ 2 +β2λ+β3=0

[0154] A2: λ 2 +β4λ+β5=0

[0155] As can be seen from the characteristic equation, when the parameters are chosen as β1 = 3, β2 = 3, β3 = 1, β4 = 2, and β5 = 1, matrices A1 and A2 are Hurwitz matrices.

[0156] In a specific implementation, as a preferred embodiment of the present invention, step S3 includes:

[0157] S31. Define heading error as follows:

[0158]

[0159] Where z1 represents the heading angle error; ψ d z1 represents the desired heading angle; z2 represents the heading angular velocity error; α 1f α 2f Both represent virtual control law; z3 represents rudder angle error;

[0160] S32. Differentiating the defined heading error, we get:

[0161]

[0162]

[0163] Where d1 represents the estimated value of the matched disturbance, that is, the disturbance term related to the heading angular velocity in the system; d2 represents the estimated value of the unmatched disturbance, that is, the disturbance term related to the rudder angle in the system.

[0164] S33. Define a first-order low-pass filter as follows:

[0165]

[0166] Where, τ f1 , τ f2 The filter's time constant is represented by α1 and α2, respectively, which are the designed virtual control laws.

[0167] S34. Design unquantized control inputs as follows:

[0168]

[0169] Where k3 represents the control gain.

[0170] In a specific implementation, as a preferred embodiment of the present invention, step S4 includes:

[0171] S41. Analyze the filter error and define the filter error as follows:

[0172] η1=α 1f -α1

[0173] η2=α 2f -α2

[0174] S42. Define the Lyapunov function as follows:

[0175]

[0176] And by differentiating the defined Lyapunov function, we get:

[0177]

[0178] Where M1 represents a constant upper bound used to limit The absolute value;

[0179] S43. Apply Young's inequality and substitute... get:

[0180]

[0181] in, Represents the Lyapunov function related to the filter error η1;

[0182] S44. Solving the inequality in step S43, we get:

[0183]

[0184] As time approaches infinity |η1(t)|≤τ f1 M1, meaning the filtering error is bounded;

[0185] S45. From step S26, we know that matrices A1 and A2 are Hurwitz matrices, therefore there exists a positive definite matrix P1 > 0.

[0186] Q1>0 and P2>0, Q2>0 satisfies:

[0187] A1 T P1+P1A1=-Q1

[0188] A2 T P² + P²A² = -Q²

[0189] Matrices D1 and D2 satisfy:

[0190] ||D1||≤ρ1(∈1)

[0191] ||D2||≤ρ2(∈2)

[0192] in, N1 represents the maximum external disturbance or unmodeled dynamic that may exist in the heading angular velocity dynamic; N2 represents the maximum external disturbance or unmodeled dynamic that may exist in the rudder angle dynamics;

[0193] S46. Analyze the observation error of the designed double-extended observer, and define the Lyapunov function V2 as follows:

[0194] V2=θ T P1θ+ξ T P2ξ

[0195] Taking the derivative of the defined Lyapunov function V2, we get:

[0196]

[0197] S47. Using matrix properties and the Cauchy-Schwarz inequality, we obtain:

[0198]

[0199] S48. Based on the Lyapunov function designed above, for the convenience of stability analysis, it is defined as follows:

[0200]

[0201] Applying Young's inequality, we obtain:

[0202]

[0203] therefore, in, Therefore, when |θ| or |ξ| is sufficiently large, ∈ i Small enough, then That is, the systematic error shrinks to a compact set. The observation errors θ(t) and ξ(t) are globally consistent and eventually bounded.

[0204] S49. Analyze the stability of the closed-loop system. Differentiate the heading error defined in step S31 to obtain:

[0205]

[0206] S410. Define the Lyapunov function V3 as follows:

[0207]

[0208] And by differentiating the defined Lyapunov function V3, we obtain:

[0209]

[0210] S411. Applying Young's inequality, we obtain:

[0211]

[0212] Substitute into From:

[0213]

[0214] S412. According to the Lyapunov function V3, let Then we have:

[0215]

[0216] Where Γ is a nonnegative constant, representing the upper bound of the influence of various disturbances and uncertainties in the system on the derivative of the Lyapunov function. If the controller parameters satisfy k1>1, k2>b 2 +1, Then G is a positive definite matrix, and it has a minimum eigenvalue (λ). min (G)>0) makes Let (h=2λ) min (G)), obtained Solving the differential inequality yields:

[0217]

[0218] When time approaches positive infinity, V3(t)≤Γ / h, where h is a positive constant representing the rate at which the error energy decays;

[0219] S413. Considering the Lyapunov function of the closed-loop system, V = V² + V³, the derivative is:

[0220]

[0221] When ∈ is sufficiently small, and under the condition that parameters k1, k2, k3 compensate for the influence of coupling terms and filtering errors, it is guaranteed that Therefore, the error signal of the closed-loop system is globally consistent and eventually bounded.

[0222] Example

[0223] To verify the effectiveness of the present invention, this embodiment uses MATLAB for computer simulation research, with the parameters set as follows:

[0224] The simulation object is the "Lanxin" unmanned surface vessel from Dalian Maritime University. The parameters of this unmanned vessel are: length 7.02m, beam 2.6m, full-load draft 0.32m, and full-load displacement 2.73m. 3 The square coefficient is 0.6976. The Norrbin motion model is adopted, with model parameters K = 0.71, T = 0.32, and nonlinear coefficients a1 = 1 and a2 = 0.001.

[0225] Let the ideal course of the unmanned vessel be ψ d=sin(0.5t)+cos(0.5)t, the controller designed in step S3 is used to control the unmanned surface vehicle. The design parameters are as follows: b=2.2, state quantization parameters χ1=χ2=χ3=0.002, input quantization parameters χ4=2; dual extended observer parameters β1=3, β2=3, β3=1, β4=2, β5=1.

[0226] Experimental results are shown in 3- Figure 6 As shown, Figure 3 The tracking results of the unmanned surface vehicle's heading angle, bow roll rate, and rudder angle are shown, demonstrating that the controller designed in this invention has good control performance and can quickly achieve ship heading tracking. Figure 4 The tracking errors for ship heading angle, ship bow roll rate, and ship rudder angle are shown to converge quickly to a small residual set, further verifying the effectiveness of the designed controller. Figure 5 To account for control input curves with and without input quantization, the figure shows that the input quantization process reduces signal transmission burden, lowers actuator execution frequency, and makes the process closer to the control law of multi-level servo systems in nautical practice. Figure 6 The observation results of the designed dual extended observer show that the designed extended state observer (ESO) can effectively estimate model uncertainties and external disturbances.

[0227] Simulation results verified the effectiveness of the proposed method for course tracking control. This control system effectively responds to changes and disturbances in the external environment, ensuring the stability of course control. By introducing quantization technology, not only is the communication burden on the unmanned surface vehicle reduced, but the execution frequency of the actuators is also lowered. In practical applications, to achieve good course control performance, the characteristics of a ship's steering servo system are also considered. Finally, the effectiveness of the proposed course tracking control method for unmanned surface vehicles based on dual extended observers and signal quantization is further verified.

[0228] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A heading tracking control method for an unmanned surface vehicle based on dual extended observers with signal quantization, characterized in that, include: S1. Based on the characteristics of the ship and the sea state information of the surrounding environment, establish a mathematical model for the heading control of a third-order response unmanned surface vehicle. S2. Design a double-extended observer model to observe uncertainties and external disturbances in the ship control system; S3. Design a heading controller for an unmanned surface vehicle based on backstepping and dynamic surface control algorithms; S4. Based on Lyapunov stability theory, prove the stability of the designed unmanned surface vehicle heading tracking control system with state quantization and input quantization, and that all signals in the closed-loop system are semi-globally consistent and bounded, and the tracking error can be made arbitrarily small by adjusting the controller parameters.

2. The heading tracking control method for an unmanned surface vehicle based on dual extended observers with signal quantization according to claim 1, characterized in that, Step S1 includes: S11. The following is a known nonlinear Nomoto model of a ship: Where ψ is the ship's bow angle, δ is the rudder angle, K and T are the ship's maneuverability indices, and a1 and a2 are nonlinear parameters; S12. The following is a known model of the dynamic characteristics of a ship with a steering gear: Where, δ E K is the rudder angle command issued by the servo motor. E For servo control gain, T E The servo time constant; S13. Introducing state quantization and input quantization, a third-order response mathematical model of the unmanned surface vehicle is established as follows: Where x1 represents the ship's heading angle; x2 represents the ship's heading angular velocity; x3 represents the ship's rudder angle or a variable related to the rudder angle; ω1 and ω2 represent unknown disturbances caused by wind, current, and waves; and f(x2,t) represents a nonlinear function related to the heading angular velocity. Where a1 and a2 represent nonlinear parameters, T represents the ship's maneuverability index, and g(x3,t) represents a function related to the rudder angle. Where T E c represents the servo time constant; c represents the system parameters. Where K E is the servo control gain; Q(u) represents the quantization of the control input u.

3. The heading tracking control method for an unmanned surface vehicle based on dual extended observers with signal quantization according to claim 1, characterized in that, Step S2 includes: S21. Design the first observer model as follows: in, Represents the quantized state variables; This represents the estimated values ​​of state variables x1 and x2 in the first observer model; β1, β2, and β3 represent the estimated value of the matching disturbance term σ1 in the first observer model; β1, β2, and β3 represent the design parameters of the first observer model; ∈1 represents the gain coefficient of the first observer model. S22. Design the second observer model as follows: S23, This represents the estimated value of the unmatched disturbance term σ2 in the second observer model; β4 and β5 represent the quantized control input; β5 and β4 represent the design parameters of the second observer model; ∈2 represents the gain coefficient of the second observer model. This represents the estimated value of the state variable x3 in the second observer model; S24. Define the observation error as follows: Where e1 represents the observation error of the heading angle; e2 represents the observation error of the heading angular velocity; e3 represents the observation error of the matched disturbance; v1 represents the observation error of the rudder angle or a variable related to the rudder angle; and v2 represents the observation error of the unmatched disturbance. S25. Differentiating the defined observation error, we get: Where s1 and s3 represent quantization errors; S26. Define scaling error as follows: Where θ and ξ both represent the scaling error vector; A1 and A2 represent the system matrices of the first observer model and the second observer model, respectively. D1 and D2 represent the perturbation terms of the first observer model and the second observer model, respectively.

4. The heading tracking control method for an unmanned surface vehicle based on dual extended observers with signal quantization according to claim 3, characterized in that, In step S26, the characteristic equations of the system matrices A1 and A2 of the first observer model and the second observer model are respectively: A1: l 3 +β1λ 2 +β2λ+β3=0 A2: l 2 +β4λ+β5=0 As can be seen from the characteristic equation, when the parameters are chosen as β1=3, β2=3, β3=1, β4=2, β5=1, matrices A1 and A2 are Hurwitz matrices.

5. The heading tracking control method for an unmanned surface vehicle based on dual extended observers with signal quantization according to claim 1, characterized in that, Step S3 includes: S31. Define heading error as follows: Where z1 represents the heading angle error; ψ d z1 represents the desired heading angle; z2 represents the heading angular velocity error; α 1f α 2f Both represent virtual control law; z3 represents rudder angle error; S32. Differentiating the defined heading error, we get: Where d1 represents the estimated value of the matched disturbance, that is, the disturbance term related to the heading angular velocity in the system; d2 represents the estimated value of the unmatched disturbance, that is, the disturbance term related to the rudder angle in the system. S33. Define a first-order low-pass filter as follows: α 1f (0)＝α1(0) α 2f (0)＝α2(0) Where, τ f1 , τ f2 The filter's time constant is represented by α1 and α2, respectively, which are the designed virtual control laws. S34. Design unquantized control inputs as follows: Where k3 represents the control gain.

6. The heading tracking control method for an unmanned surface vehicle based on dual extended observers with signal quantization according to claim 1, characterized in that, Step S4 includes: S41. Analyze the filter error and define the filter error as follows: η1=a 1f -a1 η2=a 2f -a2 S42. Define the Lyapunov function as follows: And by differentiating the defined Lyapunov function, we get: Where M1 represents a constant upper bound used to limit The absolute value; S43. Apply Young's inequality and substitute... get: in, Represents the Lyapunov function related to the filter error η1; S44. Solving the inequality in step S43, we get: As time approaches infinity |η1(t)|≤τ f1 M1, meaning the filtering error is bounded; S45. From step S26, we know that matrices A1 and A2 are Hurwitz matrices, therefore there exists a positive definite matrix P1 > 0. Q1>0 and P2>0, Q2>0 satisfies: A1 T P1+P1A1=-Q1 A2 T P2+P2A2=-Q2 Matrices D1 and D2 satisfy: ||D1||≤ρ1(∈1) ||D2||≤ρ2(∈2) in, N1 represents the maximum external disturbance or unmodeled dynamic that may exist in the heading angular velocity dynamic; N2 represents the maximum external disturbance or unmodeled dynamic that may exist in the rudder angle dynamics; S46. Analyze the observation error of the designed double-extended observer, and define the Lyapunov function V2 as follows: V2=θ T P1θ+ξ T P2ξ Taking the derivative of the defined Lyapunov function V2, we get: S47. Using matrix properties and the Cauchy-Schwarz inequality, we obtain: S48. Based on the Lyapunov function designed above, for the convenience of stability analysis, it is defined as follows: Applying Young's inequality, we obtain: therefore, in, Therefore, when |θ| or |ξ| is sufficiently large, ∈ i Small enough, then That is, the systematic error shrinks to a compact set. The observation errors θ(t) and ξ(t) are globally consistent and eventually bounded. S49. Analyze the stability of the closed-loop system. Differentiate the heading error defined in step S31 to obtain: S410. Define the Lyapunov function V3 as follows: And by differentiating the defined Lyapunov function V3, we obtain: S411. Applying Young's inequality, we obtain: Substitute into From: S412. According to the Lyapunov function V3, let Then we have: Where Γ is a nonnegative constant, representing the upper bound of the influence of various disturbances and uncertainties in the system on the derivative of the Lyapunov function. If the controller parameters satisfy k1>1, k2>b 2 +1, Then G is a positive definite matrix, and it has a minimum eigenvalue (λ). min (G)>0) makes Let (h=2λ) min (G)), obtained Solving the differential inequality yields: When time approaches positive infinity, V3(t)≤Γ / h, where h is a positive constant representing the rate at which the error energy decays; S413. Considering the Lyapunov function of the closed-loop system, V = V² + V³, the derivative is: When ∈ is sufficiently small, and under the condition that parameters k1, k2, k3 compensate for the influence of coupling terms and filtering errors, it is guaranteed that Therefore, the error signal of the closed-loop system is globally consistent and eventually bounded.

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