Underwater vehicle anti-saturation attitude control method based on dynamic event triggering

Abstract

The invention discloses an underwater vehicle anti-saturation attitude control method based on dynamic event triggering, belongs to the technical field of underwater vehicle control, and solves the problem that an AUV (Autonomous Underwater Vehicle) faces multiple challenges of strong nonlinear hydrodynamic characteristics, time-varying environment interference, actuator saturation constraint and model parameter uncertainty during underwater operation in the prior art. The method comprises the following steps: establishing a linearized state space model of a pitching channel of the autonomous underwater vehicle, designing a model reference adaptive PID control law based on dynamic event triggering, integrating a modern anti-integral saturation AW compensator into the model reference adaptive PID control law, and designing an event triggering strategy combining an index and a static threshold component; according to the invention, PID control, a modern integral saturation resisting AW compensator and an event triggering adaptive mechanism are integrated in an MRAC structure, the problems of parameter uncertainty and actuator saturation can be solved at the same time, adaptive parameters are updated only at the triggering moment, and the communication efficiency is effectively maintained.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater vehicle control, and in particular relates to an underwater vehicle anti-saturation attitude control method based on dynamic event triggering. Background Art

[0002] With the continuous growth of global demand for marine resource development, deep-sea exploration, and protection of marine rights and interests, autonomous underwater vehicles (AUVs), as core equipment for marine exploration and operations, have become a research hotspot in the field of marine engineering due to their intelligent and high-precision control technology. AUVs need to complete tasks such as trajectory tracking, target observation, and terrain mapping in complex underwater environments. Their attitude control (including pitch, roll, and yaw angle control) directly affects navigation stability, sensor data accuracy, and mission execution efficiency. However, AUV attitude control faces many technical challenges, mainly including the following aspects:

[0003] Parameter uncertainty in the hydrodynamic model: AUV dynamic models typically exhibit complex nonlinear characteristics, and their hydrodynamic coefficients can introduce uncertainties due to variations in operating conditions (such as speed, depth, and current). These uncertainties adversely affect the accuracy and robustness of attitude control, increasing the difficulty of controller design. Furthermore, variations in the AUV's geometry and flow conditions can lead to time-varying model parameters, further complicating control.

[0004] Actuator saturation: AUV actuators (such as elevators and thrusters) are subject to physical constraints. When control inputs exceed the actuator's saturation limit, they can lead to problems such as integral saturation, degrading control performance and even causing system instability, making it difficult to achieve desired attitude tracking. Actuator saturation is a common practical issue in AUV control systems, especially during large-scale attitude adjustments or in complex sea conditions.

[0005] Communication efficiency: In modern networked control systems, AUV attitude control requires the transmission of data and control commands over communication networks. Traditional continuous transmission architectures consume significant computing and bandwidth resources, especially in complex marine environments where limited communication resources are particularly prominent. Therefore, improving communication efficiency and reducing resource consumption while ensuring control performance is a pressing issue.

[0006] In recent years, researchers have made some progress in AUV attitude control. For example, anti-windup implementations for low-order linear systems, MRAC-AW compensation for actuator anomalies, and adaptive anti-windup methods for Euler-Lagrangian systems have been developed. However, most of these approaches focus on solving a single problem, lacking a comprehensive control scheme that can simultaneously address parameter uncertainty, actuator saturation, and communication efficiency. To address these issues, we propose an anti-windup attitude control method for underwater vehicles based on dynamic event triggering. Summary of the Invention

[0007] The purpose of the present invention is to address the shortcomings of the existing technology and provide an anti-saturation attitude control method for underwater vehicles based on dynamic event triggering, which solves the multiple challenges faced by existing AUVs when operating underwater, such as strong nonlinear hydrodynamic characteristics, time-varying environmental interference, actuator saturation constraints and model parameter uncertainty.

[0008] The present invention is implemented as follows: an anti-saturation attitude control method for underwater vehicles based on dynamic event triggering, the method comprising:

[0009] S10, constructing a six-degree-of-freedom nonlinear dynamic model of the underwater vehicle, and establishing a linearized state space model of the pitch channel of the autonomous underwater vehicle based on the six-degree-of-freedom nonlinear dynamic model;

[0010] S20, designing a model reference adaptive PID control law based on dynamic event triggering based on the linearized state space model of the pitch channel of the autonomous underwater vehicle;

[0011] S30, integrating a modern anti-windup AW compensator into a model-referenced adaptive PID control law based on dynamic event triggering;

[0012] S40, design an event triggering strategy that combines exponential and static threshold components, coordinate the event triggering strategy that combines exponential and static threshold components with the model reference adaptive PID control law based on dynamic event triggering, update the adaptive parameters at the triggering moment, and realize the control of the pitch attitude of the autonomous underwater vehicle.

[0013] Preferably, the linearized state space model of the pitch channel of the autonomous underwater vehicle is expressed as:

[0014]

[0015] Preferably, the model reference adaptive PID control law based on dynamic event triggering is as follows:

[0016]

[0017] The closed-loop equation of the model reference adaptive PID control law based on dynamic event triggering is expressed as:

[0018]

[0019] in, u=δ e .

[0020] Preferably, the reference model of the model reference adaptive PID control law based on dynamic event triggering is expressed as:

[0021]

[0022] The reference model is constructed based on the selected second-order transfer function, which is defined as:

[0023]

[0024] After substituting formula (2) into the system dynamic equation formula (3), the closed-loop system expression of the model reference adaptive PID control law based on dynamic event triggering is obtained:

[0025]

[0026] in, represents the parameter estimation error, the ideal gain K p , K i and K d Matching conditions:

[0027]

[0028] The tracking error dynamics is given by formula (7):

[0029]

[0030] Among them, e x (t) = x(t) - x m (t) and e(t) = x q (t)-x(t) represent the tracking error and trigger error respectively.

[0031] Preferably, the modern anti-integral windup AW compensator is integrated into a model reference adaptive PID control law based on dynamic event triggering to ensure signal boundedness while achieving bounded state tracking error. When integrating the modern anti-integral windup AW compensator, the model reference adaptive PID control law based on dynamic event triggering is combined with the following saturation function:

[0032] δ e_ac =sat(δ e (t),δmax ) (8)

[0033] In formula (8), δ e_ac represents the saturated output signal of the actuator, where δ max The saturation amplitude threshold is defined. Based on the saturation amplitude threshold, the mathematical abstraction of the actuator saturation nonlinearity is:

[0034]

[0035] The implementation of the AW compensator produces a corrected control input expressed as:

[0036]

[0037] Preferably, the modern anti-integral windup AW compensator is integrated into the model reference adaptive PID control law based on dynamic event triggering. The model reference adaptive PID control law based on dynamic event triggering for the modern anti-integral windup AW compensator is formulated as follows:

[0038]

[0039] According to formula (16), the tracking error at this time is expressed as follows:

[0040]

[0041] Its expanded form is:

[0042]

[0043] Preferably, the adaptive parameters are updated at the triggering moment, and the adaptive control law is established as:

[0044]

[0045] where Γ d ∈R n*n And Γ p ∈R + are all positive definite matrices, and P is the positive definite matrix used to construct the Lyapunov function;

[0046] Define the following formula:

[0047]

[0048] Then, for each j=1,2,3,…,n, the projection term Q d =[q d,1 ,…,q d,n ] T and q p It is clearly defined as:

[0049]

[0050] When designing an event triggering strategy that combines exponential and static threshold components, for the time interval t∈[t q , t q+1 )’s adaptive trigger mechanism is designed as follows:

[0051]

[0052] where Φ>0, σ>0, c1>0, and σ 2,q,t is a time-varying positive scalar given by:

[0053]

[0054] Here, χ>0 satisfies ||P||≤χ, and

[0055] Preferably, when designing an event-triggered strategy combining exponential and static threshold components, the tracking error is verified to converge asymptotically to zero using a Lyapunov function;

[0056] Among them, the Lyapunov function is expressed as:

[0057]

[0058] Trigger interval [t q , t q+1 ], the time derivative of the Lyapunov function is expressed as:

[0059]

[0060] The Lyapunov function is guaranteed to be asymptotically stable by the negative definite condition, which is expressed as:

[0061]

[0062] in,

[0063] Compared with the prior art, the embodiments of the present application have the following beneficial effects:

[0064] In this embodiment of the present invention, PID control, a modern anti-windup AW compensator, and an event-triggered adaptive mechanism are integrated into the MRAC structure. This can simultaneously address parameter uncertainty and actuator saturation problems, and the adaptive parameters are updated only at the trigger moment. Compared with traditional continuous adaptive methods, this significantly reduces the computational burden. At the same time, by updating the control parameters only at discrete trigger moments, communication efficiency is effectively maintained.

[0065] This paper combines the model reference adaptive control (MRAC) framework with PID control, a modern anti-windup AW compensator, and a dynamic event triggering mechanism, allowing the system to update time-varying control parameters only at the trigger moment, while simultaneously addressing parameter uncertainty and actuator constraints. An innovative control scheme is proposed, featuring an anti-windup compensator with adaptive control gain and time-varying adaptive parameters. Theoretical analysis shows that this approach not only ensures asymptotic stability and resolves the input saturation problem, but also effectively avoids Zeno behavior. Comprehensive simulation studies verify the effectiveness of the proposed scheme, demonstrating its applicability and performance advantages in practical engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 A schematic diagram of an autonomous underwater vehicle provided in an embodiment of the present invention is shown.

[0067] Figure 2 The block diagram shows the integration of a modern anti-windup AW compensator into a model reference adaptive PID control law based on dynamic event triggering.

[0068] Figure 3 The diagram shows the test results of event triggering interval in the simulation test of the present invention.

[0069] Figure 4 The figure shows the tracking error test result based on event triggering in the simulation test of the present invention.

[0070] Figure 5 The adaptive parameter estimation K in the simulation test of the present invention is shown. d Convergence test results.

[0071] Figure 6 The adaptive parameter estimation K in the simulation test of the present invention is shown. p Convergence test results.

[0072] Figure 7 The adaptive parameter estimation K in the simulation test of the present invention is shown. i Convergence test results.

[0073] Figure 8 shows the corrected control signal (δ e_ac ) and the uncorrected control signal (δ e ) comparison test chart. DETAILED DESCRIPTION

[0074] Unless otherwise defined, all technical and scientific terms used herein have the same meanings as commonly understood by those skilled in the art to which this application belongs. The terms used in the specification of the application are only for the purpose of describing specific embodiments and are not intended to limit this application. The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above-mentioned drawings are intended to cover non-exclusive inclusions. The terms "first", "second", etc. in the specification and claims of this application or the above-mentioned drawings are used to distinguish different objects, not to describe a specific order.

[0075] In the existing technology, AUVs face multiple challenges when operating underwater, such as strong nonlinear hydrodynamic characteristics, time-varying environmental interference, actuator saturation constraints, and model parameter uncertainty. To address the above problems, we propose an anti-saturation attitude control method for underwater vehicles based on dynamic event triggering. In short, when implementing the method, a six-degree-of-freedom nonlinear dynamic model of the underwater vehicle is first constructed, and a linearized state-space model of the pitch channel of the autonomous underwater vehicle is established based on the six-degree-of-freedom nonlinear dynamic model. A model reference adaptive PID control law based on dynamic event triggering is designed, and a modern anti-integral windup AW compensator is integrated into the model reference adaptive PID control law based on dynamic event triggering. An event triggering strategy combining exponential and static threshold components is designed. The event triggering strategy combining exponential and static threshold components is coordinated with the model reference adaptive PID control law based on dynamic event triggering to update the adaptive parameters at the triggering moment, ultimately achieving control of the pitch attitude of the autonomous underwater vehicle. In this embodiment of the present invention, PID control, a modern anti-windup AW compensator, and an event-triggered adaptive mechanism are integrated into the MRAC structure. This can simultaneously address parameter uncertainty and actuator saturation problems, and the adaptive parameters are updated only at the trigger moment. Compared with traditional continuous adaptive methods, this significantly reduces the computational burden. At the same time, by updating the control parameters only at discrete trigger moments, communication efficiency is effectively maintained.

[0076] An embodiment of the present invention provides an underwater vehicle anti-saturation attitude control method based on dynamic event triggering. The underwater vehicle anti-saturation attitude control method based on dynamic event triggering specifically includes:

[0077] S10, constructing a six-degree-of-freedom nonlinear dynamic model of the underwater vehicle, and establishing a linearized state space model of the pitch channel of the autonomous underwater vehicle based on the six-degree-of-freedom nonlinear dynamic model;

[0078] It should be noted that the linearized state space model of the pitch channel of the autonomous underwater vehicle is implemented in a verified six-degree-of-freedom (DOF) nonlinear model. Figure 1FIG. 1 shows a schematic diagram of an autonomous underwater vehicle provided in an embodiment of the present invention. The kinematic vector of the autonomous underwater vehicle is expressed as:

[0079]

[0080] in, Represents the position / Euler angle in the inertial coordinate system, represents the speed of the ship in the fixed coordinate system, Contains the control forces / torques. The kinematic relationship between the coordinate systems is described by the following equations:

[0081]

[0082] Use the transformation matrix:

[0083]

[0084] Where c(·)=cos(·), s(·)=sin(·) and t(·)=tan(·).

[0085] It should be noted that the above equations are necessary to introduce the coordinate axes and establish the governing relationships that represent the kinematic equations of motion. However, to fully describe the motion, the dynamic equations must also be included. For a rigid body with six degrees of freedom, its dynamic equations of motion are expressed as follows:

[0086]

[0087] The terms on the right side of the above equations summarize the hydrostatic / hydrodynamic forces, propulsion effects, and control inputs—a complex interaction that depends on the AUV’s geometry and flow conditions. Detailed calculation of the hydrodynamic coefficients is beyond the scope of this example, so we use a proven practical model.

[0088] Considering that the roll motion is bounded and the yaw dynamics are decoupled, the pitch channel dynamics involving the variables q (pitch velocity) and θ (pitch angle) can be simplified to:

[0089]

[0090] Among them I x , I y , I z represents the moment of inertia, (W, B) represents weight / buoyancy, x G 、z G 、x B 、y B are the coordinates of the center of buoyancy and center of mass in the body coordinate system, and M is the hydrodynamic coefficient. e Satisfy |δ e |≤20.

[0091] By linearizing the working point (ν, w, p, r, ψ ≈ 0), the linearized state space model of the pitch channel of the autonomous underwater vehicle is expressed as:

[0092]

[0093] Among them, the state space model introduces parameter uncertainty due to the change of the operating point and the linearization residual, which significantly increases the complexity of the controller design. This requires strict comparison and verification with the original six-degree-of-freedom nonlinear model. Although the traditional linear model can partially deal with computational uncertainty, adaptive control has become a more effective solution for such parameter time-varying constrained systems. This application constructs a systematic framework to design an adaptive controller with anti-saturation compensation to simultaneously deal with the input saturation (|δ e |≤20) and model uncertainty issues.

[0094] S20, designing a model reference adaptive PID control law based on dynamic event triggering based on the linearized state space model of the pitch channel of the autonomous underwater vehicle;

[0095] It should be noted that the model-reference adaptive PID control law based on dynamic event triggering can be an event-triggered model reference adaptive (EMRAC) framework with anti-windup compensation. In autonomous systems, PID control is known for its high reliability. This application provides a method for integrating an event-triggered mechanism into an adaptive PID control framework. The proposed control strategy intermittently updates the control signal and adaptive parameters each time an event is triggered.

[0096] Among them, for the time interval t∈[t q , t q+1 ), a model reference adaptive PID control law based on dynamic event triggering is designed as follows:

[0097]

[0098] The closed-loop equation of the model reference adaptive PID control law based on dynamic event triggering is expressed as:

[0099]

[0100] in, u=δ e .

[0101] The reference model of the model reference adaptive PID control law based on dynamic event triggering is expressed as:

[0102]

[0103] The reference model is constructed based on the selected second-order transfer function, which is defined as:

[0104]

[0105] This gives the system matrix and Its specific form is determined according to formula (4). In this embodiment, the damping ratio ξ=0.7, the natural frequency ω n =3 was selected as the reference model parameter.

[0106] After substituting formula (2) into the system dynamic equation formula (3), the closed-loop system expression of the model reference adaptive PID control law based on dynamic event triggering is obtained:

[0107]

[0108] in, represents the parameter estimation error, the ideal gain K p , K i and K d Matching conditions:

[0109]

[0110] The tracking error dynamics is given by formula (7):

[0111]

[0112] Among them, e x (t) = x(t) - x m (t) and e(t) = x q (t)-x(t) represent the tracking error and trigger error respectively.

[0113] S30, integrating a modern anti-windup AW compensator into a model-referenced adaptive PID control law based on dynamic event triggering;

[0114] In this embodiment, a modern anti-integral windup AW compensator is integrated into a model reference adaptive PID control law based on dynamic event triggering (MRAC-PID) to enhance its ability to handle saturation problems. The method provided in this embodiment systematically integrates the AW compensator into the extended model reference adaptive control (EMRAC) architecture and combines it with PID structural components. Figure 2 The block diagram shows the integration of a modern anti-windup AW compensator into a model reference adaptive PID control law based on dynamic event triggering. Figure 2The block diagram shows the architecture and operation of the proposed framework. An anti-windup compensator is proposed to be integrated as part of the adaptive control law to achieve a bounded state tracking error while ensuring signal boundedness.

[0115] The modern anti-integral windup AW compensator is integrated into the dynamic event-triggered model reference adaptive PID control law to ensure signal boundedness while achieving a bounded state tracking error. When integrating the modern anti-integral windup AW compensator, the dynamic event-triggered model reference adaptive PID control law is combined with the following saturation function:

[0116] δ e_ac =sat(δ e (t),δ max ) (8)

[0117] In formula (8), δ e_ac represents the saturated output signal of the actuator, where δ max The saturation amplitude threshold is defined. Based on the saturation amplitude threshold, the mathematical abstraction of the actuator saturation nonlinearity is:

[0118]

[0119] The implementation of the AW compensator produces a corrected control input expressed as:

[0120]

[0121] Among them, the anti-saturation compensator problem needs to be transformed into finding the following state feedback:

[0122]

[0123] Where △u=δ e -δ e_ac represents the control deviation, and the feedback gain F is synthesized by solving the Riccati equation:

[0124]

[0125] Where P, ρ, and ∈ represent the anti-saturation compensator design parameters.

[0126] The measurable error term is defined as:

[0127]

[0128] Therefore, we get the augmented error:

[0129]

[0130] At this point, we define the augmented control error as eaw =△u=δ e -δ e_ac , after substituting into this definition, we can deduce:

[0131] δ e_ac =δ e -e aw (14)

[0132] Taking the time derivative of both sides of formula (13), we get:

[0133]

[0134] The modern anti-integral windup AW compensator is integrated into the model reference adaptive PID control law based on dynamic event triggering. The model reference adaptive PID control law based on dynamic event triggering for the modern anti-integral windup AW compensator is formulated as follows:

[0135]

[0136] According to formula (16), the tracking error at this time is expressed as follows:

[0137]

[0138] Its expanded form is:

[0139]

[0140] S40, design an event triggering strategy that combines exponential and static threshold components, coordinate the event triggering strategy that combines exponential and static threshold components with the model reference adaptive PID control law based on dynamic event triggering, update the adaptive parameters at the triggering moment, and realize the control of the pitch attitude of the autonomous underwater vehicle.

[0141] For the adaptive gain, the following assumptions commonly used in model reference adaptive control are proposed.

[0142] Assumption: K p The sign of sgn[K p ]=1). In addition, there is a predefined boundary k d,j and k N Make and in k N ≠0(for K d =[k d,1 ,…,k d,n ] T ).

[0143] At the triggering moment, the adaptive parameters are updated and the adaptive control law is established as:

[0144]

[0145] where Γ d ∈R n*n And Γ p ∈R + are all positive definite matrices, and P is the positive definite matrix used to construct the Lyapunov function;

[0146] Define the following formula:

[0147]

[0148] Then, for each j=1,2,3,…,n, the projection term Q d =[q d,1 ,…,q d,n ] T and q p It is clearly defined as:

[0149]

[0150] The initial parameter estimates must satisfy the following conditions: for all j = 1, 2, 3, ..., n, the derivative gain k d,j Limited to a predefined range Within, and the proportional gain K p Limited to a range By initializing the condition and The continuity of parameter estimation at the triggering moment can be guaranteed.

[0151] It should be noted that the projection operator embedded in Equations (23) and (24) constitutes the key mechanism to ensure that the estimated system parameters are constrained to their predefined tight set. This methodological implementation effectively mitigates parameter drift while ensuring the boundedness of the estimation error throughout the system operation.

[0152] Then, for the time interval t∈[t q , t q+1 ) and an adaptive trigger mechanism. When designing an event trigger strategy that combines exponential and static threshold components, the adaptive trigger mechanism (DETS) is designed as follows:

[0153]

[0154] where Φ>0, σ>0, c1>0, and σ 2,q,tis a time-varying positive scalar given by:

[0155]

[0156] Here, χ>0 satisfies ||P||≤χ, and

[0157] The derivative of the time-varying variable η1(t) is described by the following differential equation:

[0158]

[0159] Where c2>0. From formula (21), we can get:

[0160]

[0161] Therefore, this leads to

[0162]

[0163] Therefore, if η1(t0)≥0, then η1(t)≥0 for all t≥t0.

[0164] It should be noted that in order to ensure long-term stability and exclude Zeno behavior, the dynamic event triggering mechanism (DETS) constructed in formula (26) is systematically implemented. Through rigorous analysis, it is established that the convergence rate of the dynamic variables that meets the dual key criteria converges to zero asymptotically:

[0165] (i) fast enough to ensure asymptotic tracking error stability;

[0166] (ii) Sufficient to maintain the guaranteed minimum execution interval, thereby completely eliminating the occurrence of Zeno behavior.

[0167] In addition, the adaptive parameter σ of DETS in formula (25) 2,q,t Dynamically updated at each triggering moment, controlled by the estimator K d and K p The strategic design of introducing η1(t) as a dynamic variable effectively extends the interval between events, thereby ensuring that the feedback control system triggers a limited number of events within any bounded time window.

[0168] It can be seen that for the modern anti-integral windup AW compensator, the dynamic event-triggered model reference adaptive PID control law and triggering criterion are combined with the event triggering strategy of exponential and static threshold components and the dynamic event-triggered model reference adaptive PID control law to achieve asymptotic tracking of the reference model through guaranteed state convergence.

[0169] The derivation of formula (26) in this embodiment is shown in formula (27)-formula (31):

[0170] To establish the convergence of error dynamics under the dynamic event triggering mechanism (DETS), an event triggering strategy combining exponential and static threshold components is designed. The Lyapunov function is used to verify that the tracking error converges to zero asymptotically.

[0171] Among them, the Lyapunov function is expressed as:

[0172]

[0173] Trigger interval [t q , t q+1 ], along the state trajectory described by formula (12), the time derivative of the Lyapunov function is expressed as:

[0174]

[0175] The traditional model reference adaptive control (MRAC) method essentially relies on the first term of formula (28) for adaptation. However, the event-triggered implementation introduces control discontinuity, which makes it impossible to directly perform parameter cancellation on the residual term in formula (28). Therefore, it is necessary to deliberately construct σ 2,q,t Acts as a key compensator to maintain system stability and tracking performance.

[0176] Referring to formula (23) and formula (24), we get:

[0177]

[0178] From this, we can see that based on the dynamic event triggering mechanism (DETS) and the adaptive rules of event triggering, we can deduce:

[0179]

[0180] To ensure the negativity of the right side of formula (30), the parameter σ 2,q,t must be designed to satisfy the following inequalities:

[0181]

[0182] When ‖e(t)‖=0, formula (31) is naturally established due to the inherent equilibrium state of the system. q , t q+1 ) during the non-zero tracking error, the adaptive parameter σ 2,q,t It is systematically configured through formula (26) to strictly satisfy formula (31).

[0183] σ 2,q,tThe parameter selection mechanism depends on the signal x(t q )、r(t)、x aw (t) and All these signals are measurable and accessible. This practical dependency structure ensures that the dynamic event triggering mechanism (DETS), whose adaptive parameter update is controlled by equation (26), can be efficiently implemented on a digital platform.

[0184] The parameter configuration of the parameter σ2,q,t plays a key role in ensuring asymptotic convergence. As rigorously proved by formula (31), this parameter allows real-time adjustment, and the adjustment amount is proportional to K p , K i and K d This system adjustment ensures that the Lyapunov negative definiteness condition is strictly enforced for all non-zero error states e(t)≠0. This achieves closed-loop stability.

[0185] The Lyapunov function is guaranteed to be asymptotically stable by the negative definite condition, which is expressed as:

[0186]

[0187] in,

[0188] Based on formula (32), the block matrix is ​​expressed as:

[0189]

[0190] The negative definiteness (i.e., Δ < 0) of the block matrix, Equation (33), can be ensured by systematically selecting three design parameters:

[0191] 1) scalar constant σ>0;

[0192] 2) Control coefficient c2>0 (determine X2=-Ic2, where I is the identity matrix);

[0193] 3) Positive definite matrices P and Φ.

[0194] This condition has three key properties: first, when the conditional formula (32) is satisfied, its validity is independent of the positive definite matrix P and the controlled object parameters specified in Φ; second, the inequality condition depends only on the designed parameters (P, Φ, σ, c2); finally, this independence makes formula (32) a self-contained design criterion for parameter selection.

[0195] Simulation test results:

[0196] The adaptive controller integrating the anti-saturation attitude control method of underwater vehicle based on dynamic event triggering provided by the present invention is used for simulation test. The model parameters are derived from the verified REMUS autonomous underwater vehicle (AUV) model, and the parameters of the reference model and the controller are selected as ξ = 0.7, ω n = 3. The tuning parameters of the AW compensator are also set to W = 1, ∈ = 0.1, ρ = 0.01.

[0197] The initial condition is set to x(t0) = [-1.550.5] T , x m (t0) = [-2.51] T , k N =0.5, k d,2 = k d,2 =-2, K p (0) = -1.2, k d,1 (0) = -1.5, k d,2 (0)=-1.2.

[0198] The simulation results verify the effectiveness of the event-triggered model reference adaptive PID control with AW compensator. Figure 3 The diagram shows the test results of event trigger interval in the simulation test of the present invention. Figure 4 The figure shows the tracking error test result based on event triggering in the simulation test of the present invention. Figure 4 It is shown that under the action of the AW compensator, the tracking error converges to zero asymptotically. Figure 3 The communication efficiency analysis shows that when the total simulation experiment length is 15,000 steps, a total of 622 triggers are performed, which means that only about 4.146% of the sampling signals need to be transmitted to the controller. Figure 5 The adaptive parameter estimation K in the simulation test of the present invention is shown. d Convergence test results, Figure 6 The adaptive parameter estimation K in the simulation test of the present invention is shown. p Convergence test results, Figure 7 The adaptive parameter estimation K in the simulation test of the present invention is shown. i Convergence test results, Figure 5-7 The parameter convergence was verified, and it was confirmed that all control parameters were stably and adaptively adjusted.

[0199] In this embodiment, Figure 8 shows the corrected control signal (δ e_ac ) and the uncorrected control signal (δ e), it can be seen that integrating the modern anti-integral windup AW compensator into the model reference adaptive PID control law based on dynamic event triggering successfully solves the actuator saturation constraint problem while maintaining accurate pitch angle tracking performance. The elevator deflection range is limited to |δ e |≤20, these results collectively demonstrate that the anti-saturation attitude control method for underwater vehicles based on dynamic event triggering can effectively maintain closed-loop stability and tracking performance while saving network resources.

[0200] In summary, the present invention provides an anti-saturation attitude control method for underwater vehicles based on dynamic event triggering. In an embodiment of the present invention, PID control, a modern anti-integral windup AW compensator and an event-triggered adaptive mechanism are integrated into the MRAC structure, which can simultaneously solve the problems of parameter uncertainty and actuator saturation, and only updates the adaptive parameters at the triggering moment. Compared with the traditional continuous adaptive method, the computational burden is significantly reduced. At the same time, by updating the control parameters only at discrete triggering moments, the communication efficiency is effectively maintained.

[0201] At the same time, this application combines the model reference adaptive control (MRAC) framework with PID control, modern anti-integral windup AW compensator and dynamic event triggering mechanism, so that the system updates the time-varying control parameters only at the trigger moment, while solving the parameter uncertainty and actuator constraint problems. An innovative control scheme is proposed, which is characterized by an anti-saturation compensator with adaptive control gain and time-varying adaptive parameters. Theoretical analysis shows that this method not only guarantees asymptotic stability and solves the input saturation problem, but also effectively avoids the Zeno phenomenon (Zeno behavior). Comprehensive simulation studies have verified the effectiveness of the scheme, and the results show that it has good applicability and performance advantages in engineering practice.

[0202] It should be noted that for the aforementioned embodiments, for simplicity of description, they are all expressed as a series of action combinations. However, those skilled in the art should be aware that the present invention is not limited by the order of the actions described, because according to the present invention, certain steps may be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present invention.

[0203] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the scope of protection of the invention. Obviously, the embodiments described are only some embodiments of the present invention, rather than all embodiments. Based on these embodiments, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in this field can still combine, add, delete or make other adjustments to the features in the various embodiments of the present invention according to the circumstances without conflict, without making creative work, so as to obtain different other technical solutions that do not deviate from the concept of the present invention in essence, and these technical solutions also fall within the scope of protection of the present invention.

Claims

1. An anti-saturation attitude control method for underwater vehicles based on dynamic event triggering, characterized in that: The method comprises: S10, constructing a six-degree-of-freedom nonlinear dynamic model of the underwater vehicle, and establishing a linearized state space model of the pitch channel of the autonomous underwater vehicle based on the six-degree-of-freedom nonlinear dynamic model; S20, designing a model reference adaptive PID control law based on dynamic event triggering based on the linearized state space model of the pitch channel of the autonomous underwater vehicle; S30, integrating a modern anti-windup AW compensator into a model-referenced adaptive PID control law based on dynamic event triggering; S40, design an event triggering strategy that combines exponential and static threshold components, coordinate the event triggering strategy that combines exponential and static threshold components with the model reference adaptive PID control law based on dynamic event triggering, update the adaptive parameters at the triggering moment, and realize the control of the pitch attitude of the autonomous underwater vehicle.

2. The anti-saturation attitude control method for underwater vehicles based on dynamic event triggering according to claim 1, characterized in that: The linearized state space model of the pitch channel of the autonomous underwater vehicle is expressed as:

3. The anti-saturation attitude control method for underwater vehicles based on dynamic event triggering according to claim 2, characterized in that: The model reference adaptive PID control law based on dynamic event triggering is as follows: The closed-loop equation of the model reference adaptive PID control law based on dynamic event triggering is expressed as: Among them, u = δ e .

4. The anti-saturation attitude control method for underwater vehicles based on dynamic event triggering according to claim 3, characterized in that: The reference model of the model reference adaptive PID control law based on dynamic event triggering is expressed as: The reference model is constructed based on the selected second-order transfer function, which is defined as: After substituting formula (2) into the system dynamic equation formula (3), the closed-loop system expression of the model reference adaptive PID control law based on dynamic event triggering is obtained: in, represents the parameter estimation error, the ideal gain K p , K i and K d Matching conditions: The tracking error dynamics is given by formula (7): Among them, e x (t) = x(t) - x m (t) and e(t) = x q (t)-x(t) represent the tracking error and trigger error respectively.

5. The anti-saturation attitude control method for underwater vehicles based on dynamic event triggering according to claim 4, characterized in that: The modern anti-integral windup AW compensator is integrated into the dynamic event-triggered model reference adaptive PID control law to ensure signal boundedness while achieving a bounded state tracking error. When integrating the modern anti-integral windup AW compensator, the dynamic event-triggered model reference adaptive PID control law is combined with the following saturation function: d e_ac =sat(δ e (t),δ max ) (8) In formula (8), δ e_ac represents the saturated output signal of the actuator, where δ max The saturation amplitude threshold is defined. Based on the saturation amplitude threshold, the mathematical abstraction of the actuator saturation nonlinearity is: The implementation of the AW compensator produces a corrected control input expressed as:

6. The anti-saturation attitude control method for underwater vehicles based on dynamic event triggering according to claim 5, characterized in that: The modern anti-integral windup AW compensator is integrated into the model reference adaptive PID control law based on dynamic event triggering. The model reference adaptive PID control law based on dynamic event triggering for the modern anti-integral windup AW compensator is formulated as follows: According to formula (16), the tracking error at this time is expressed as follows: Its expanded form is:

7. The anti-saturation attitude control method for underwater vehicles based on dynamic event triggering according to claim 2, characterized in that: At the triggering moment, the adaptive parameters are updated and the adaptive control law is established as: where Γ d ∈R n*n And Γ p ∈R + are all positive definite matrices, and P is the positive definite matrix used to construct the Lyapunov function; Define the following formula: Then, for each j=1,2,3,…,n, the projection term Q d =[q d,1 ,…,q d,n ] T and q p It is clearly defined as: When designing an event triggering strategy that combines exponential and static threshold components, for the time interval t∈[t q , t q+1 )’s adaptive trigger mechanism is designed as follows: where Φ>0, σ>0, c1>0, and σ 2,q,t is a time-varying positive scalar given by: Here, χ>0 satisfies ||P||≤χ, and 8. The anti-saturation attitude control method for underwater vehicles based on dynamic event triggering according to claim 7, characterized in that: When designing an event-triggered strategy that combines exponential and static threshold components, the tracking error is verified to converge asymptotically to zero using the Lyapunov function; Among them, the Lyapunov function is expressed as: Trigger interval [t q , t q+1 ], the time derivative of the Lyapunov function is expressed as: The Lyapunov function is guaranteed to be asymptotically stable by the negative definite condition, which is expressed as: in,

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