ROV adaptive sliding mode robust control method based on residual disturbance observer

Abstract

The ROV adaptive sliding mode robust control method based on residual disturbance observer described in the application belongs to the field of tethered underwater robot control. The application proposes a ROV control strategy which is based on residual disturbance observer, adaptive algorithm and sliding mode control algorithm. The algorithm highlights the unity of robustness, adaptability and engineering realizability on the basis of fully considering the nonlinear dynamics of ROV, complex external disturbance and thruster engineering constraints. It includes the following steps: step (1), establishing the dynamics, kinematics and disturbance mathematical model of ROV; step (2), ROV control; step (2.1), calculating the ideal equivalent control law; step (2.2), introducing a robust term; step (2.3), introducing a disturbance observer; step (2.4), introducing an adaptive mechanism.

Description

Technical Field

[0001] This application relates to the field of tethered underwater robot control, specifically proposing a novel adaptive sliding mode robust control method for ROVs based on a residual disturbance observer. Background Technology

[0002] With the continuous growth of deep-sea resource development, subsea pipeline inspection, and marine engineering maintenance tasks in my country, remotely operated vehicles (ROVs) have become indispensable key equipment in underwater operations. Compared with autonomous underwater vehicles (AUVs), ROVs are connected to the mother ship by cables and can perform high-power, high-precision, and long-duration operations in complex environments. However, this engineering characteristic also presents ROVs with more severe challenges in motion control. On the one hand, ROVs are affected by strong ocean currents, cable-induced damping, and random disturbance torques in actual operation; on the other hand, factors such as the open frame structure, asymmetric thruster layout due to installation errors, thruster saturation, and speed limitations cause the ROV system dynamics to exhibit obvious nonlinearity, uncertainty, and strong coupling characteristics. Therefore, how to achieve high-precision robust control of ROVs under external disturbances and model uncertainties has always been an important research direction in the field of ROV control.

[0003] Currently, ROV control technology is mainly divided into model-based control methods and data-driven control methods. Among them, data-driven control methods have disadvantages such as high dependence on data quality and completeness, risk of "premature generalization" and distribution deviation, insufficient handling of random disturbances, and poor interpretability.

[0004] Model-based control methods can be further divided into two technical paths: linear control and nonlinear control. Specifically, 1) Existing linear control methods include: Proportional-Integral-Derivative (PID), Linear Quadratic Regulator (LQR), Robust Control, Linear Active Disturbance Rejection Controller (LADRC), and Linear Model Predictive Control (LMPC). However, ROV systems have inherent nonlinear dynamic model characteristics, parameter perturbations, and input constraints, and are subject to unstructured environmental disturbances, making it difficult for linear control methods to fully utilize the performance of the ROV in actual underwater operations. Although linear control still has certain application value under specific working conditions and small-range motion conditions, it suffers from problems such as a small stability region and a limited effective envelope, making it unsuitable for complex environments and large-scale maneuvering tasks. This has prompted research to gradually shift towards the research and application of nonlinear and robust control methods. 2) Existing nonlinear control methods mainly include: Nonlinear Model Predictive Control (NMPC), Sliding Mode Control (SMC), Backstepping Control, Nonlinear Active Disturbance Rejection Control (NADRC), Fuzzy Control, S-Surface Sliding Mode Control, and Adaptive Control. The table below summarizes the characteristics, advantages, and disadvantages of several ROV nonlinear control methods.

[0005] Control Algorithm Core idea Main advantages Main disadvantages NMPC Based on the current state and model, the optimal control sequence in the future finite time domain is solved in a rolling manner, and only the first term is executed. It can explicitly handle multiple variables, state and control input constraints; it has strong feedforward optimization capabilities. It involves a heavy computational burden, requiring high real-time computing power from the processor. Control performance is heavily dependent on model accuracy. SMC Design a special sliding mode (manifold) that forces the system state trajectory to reach and remain on the manifold within a finite time using a control law. Once in sliding mode, it exhibits extremely strong robustness to parameter changes and external disturbances. There is a chattering problem, that is, the state trajectory crosses the sliding surface at high frequency. Backstep control The complex nonlinear system is recursively decomposed into multiple subsystems, and virtual control variables and Lyapunov functions are designed for each subsystem. This provides a structured controller design method for a class of nonlinear systems. The design process is complex, and high-order systems are prone to the "differential explosion" phenomenon, which means that the derivatives of high-order backstep terms are too long and contain too many computational terms. NADRC The extended state observer collectively refers to system model uncertainties, unmodeled dynamics, and external disturbances as "lumped disturbances" and performs real-time estimation and compensation. With low model dependency, it linearizes the dynamics of complex systems into a standard cascade integrator form, simplifying controller design. The observer is prone to noise; parameter adjustment is complex. Fuzzy control It mimics human experience and uses fuzzy logic based on the "if-then" rule to handle the imprecision of the system. Rules are formulated based on expert experience or knowledge, without relying on precise mathematical models, and are effective for uncertain systems. The design of the rule base and membership function relies on prior knowledge; rule explosion may occur. S-surface sliding mode control A typical model-free intelligent control method, whose control law is expressed as a nonlinear function mapping. It has an extremely simple structure, clear physical meaning, high computational efficiency, and is easy to implement on a microprocessor. The performance may not be optimal; parameter tuning relies heavily on trial and error, and lacks theoretical proof of system stability. Adaptive control The controller parameters can be automatically adjusted online according to the system operating status or performance indicators to adapt to the dynamic changes or uncertainties of the controlled object. It can cope with slow time-varying or uncertain system parameters and maintain or optimize control performance. The convergence of the estimated parameters depends on sufficient excitation conditions, and the design must ensure stability and convergence; it is more effective for parameters with slow dynamic changes and uncertainties.

[0006] In recent years, a large amount of research has focused on high-order sliding mode, terminal sliding mode, and fixed-time sliding mode control, aiming to improve the robustness and control accuracy of ROVs. Sliding mode control (SMC) has been widely used in the field of underwater robot control due to its inherent robustness to parameter uncertainties and external disturbances. However, in ROV control systems, relying solely on highly robust sliding mode feedback is insufficient to simultaneously achieve control accuracy and energy efficiency under thruster-constrained conditions. Theoretically, increasing the sliding mode gain can cover the upper bound of unknown disturbances, but it may also cause thruster saturation. Once the sliding mode term frequently enters the saturation region, its control effect will decrease, potentially introducing residual errors in the steady-state phase and causing continuous oscillations.

[0007] In view of the above, this application is hereby submitted. Summary of the Invention

[0008] The ROV adaptive sliding mode robust control method based on residual disturbance observer described in this application aims to solve the problems existing in the prior art by proposing an ROV control strategy that integrates residual disturbance observer, adaptive algorithm and sliding mode control algorithm. The algorithm adopted fully considers the nonlinear dynamic characteristics of ROV, complex external disturbances and propeller engineering constraints, highlighting the unity of robustness, adaptability and engineering feasibility.

[0009] To achieve the above-mentioned objective, the ROV adaptive sliding mode robust control method based on a residual disturbance observer includes the following steps:

[0010] Step (1): Establish mathematical models of ROV dynamics, kinematics, and disturbances;

[0011] Step (1.1): Introduce the geodetic coordinate system o n -XYZ and ROV volume coordinate system o b -xyz;

[0012] Step (1.2): Establish a dynamic model;

[0013] ROV in volume coordinate system o b The standard 6-DOF dynamics under -xyz can be expressed as:

[0014]

[0015] Where M is the generalized mass matrix, C(ν) is the Coriolis and centripetal force matrix, D(ν) is the hydrodynamic damping matrix, g(η) is the restoring force / torque vector, τ is the control force / torque vector, and τ d External disturbances and unmodeled terms;

[0016] Step (1.3), disturbance modeling;

[0017] External disturbances are uniformly modeled as follows:

[0018]

[0019] In the formula, τ b (t) is the slowly varying bias term, τ p (t) is a periodic term, τ n (t) represents random high-frequency disturbances or unmodeled residuals;

[0020] Step (2), ROV control;

[0021] Step (2.1): Calculate the ideal equivalent control law;

[0022] The ideal equivalent control law is expressed as:

[0023]

[0024] Step (2.2): Introduce robust terms;

[0025] The sliding mode control law is constructed as follows:

[0026]

[0027] The formula for closed-loop sliding mode dynamics is as follows:

[0028]

[0029] Among them, if the disturbance estimation error If it is bounded, then it can be proven that the sliding mode variable s is uniformly bounded eventually;

[0030] Step (2.3): Introduce a disturbance observer;

[0031] Step (2.3.1): Perturbation reconstruction based on dynamic residuals;

[0032] From the above formula The equivalent expression for the following perturbation is derived:

[0033]

[0034] If it is available A reliable estimate can be obtained, and the perturbation estimate based on the model residuals can be constructed as follows:

[0035]

[0036] Step (2.3.2): Introduce a first-order low-pass perturbation observer;

[0037] Apply a first-order low-pass filter to the residual perturbation estimate using the following formula:

[0038]

[0039] Step (2.4): Introduce an adaptive mechanism;

[0040] The above formula The robust terms in the code are rewritten in adaptive form:

[0041]

[0042] In the formula, ☉ represents element-wise multiplication. For adaptive robust gain vector;

[0043] The adaptive law is chosen as follows:

[0044]

[0045] Where |s| represents the absolute value of the elements; ρ is the leakage factor, ρ>0, used to prevent leakage. It grows unbounded and then automatically falls back under steady-state conditions.

[0046] In step (1.1), the origin of the geodetic coordinate system is the starting point of the ROV; the origin of the ROV's volume coordinate system is the center of gravity of the ROV; the ROV's pose vector and velocity vector are defined as: η=[x, y, z, , θ, ψ] T ,

[0047] ν=[u, v, w, p, q, r] T ;

[0048] Where (x, y, z) represents the position, ( (u, v, w) represent the roll, pitch, and yaw angles, respectively; (p, q, r) represent the volumetric linear velocity; (p, q, r) represent the angular velocity; and T represents the matrix transpose. The kinematic relationships are as follows:

[0049]

[0050] in, It is the derivative of η, representing velocity;

[0051] In the above formula (1),

[0052]

[0053] in, R( represents the transformation matrix from the ROV volumetric velocity matrix to the geodetic velocity matrix; ,θ,ψ) is from o n -XYZ to o b -xyz direction cosine matrix; T( ,θ) is the Euler angular rate transformation matrix;

[0054] in:

[0055]

[0056]

[0057] Where E is the Euler angular rate transformation matrix.

[0058] The step (1.2) includes step (1.2.1), calculating the generalized mass matrix;

[0059] The generalized mass matrix is ​​decomposed into a rigid body mass matrix M. RB and the additional mass matrix M A As shown in the following formula:

[0060]

[0061] In the formula:

[0062]

[0063]

[0064] Where m is mass, I 3×3 It is a 3×3 identity matrix, S(·) is the antisymmetric matrix operator, r g I is the vector of the center of mass relative to the origin of the volume coordinate system. g Let be the moment of inertia matrix about the origin of the volume coordinate system. , , For added mass , , To add rotational inertia;

[0065] Step (1.2.2): Calculate the Coriolis and centripetal force matrices;

[0066] Coriolis and centripetal force matrices are divided into rigid body terms C. RB (v) and the additional mass term C A The expression for (ν) is as follows:

[0067]

[0068] Step (1.2.3): Calculate the hydrodynamic damping matrix;

[0069] The damping model is a superposition of linear and nonlinear damping, expressed as follows:

[0070]

[0071] Wherein, D in the above formula L (v) is the linear damping term, D NL (v) represents the nonlinear damping term;

[0072]

[0073]

[0074] in, These represent the linear damping coefficients in the directions of sway, roll, heave, pitch, and yaw, respectively. These represent the nonlinear damping coefficients in the directions of sway, roll, heave, pitch, and yaw, respectively.

[0075] Step (1.2.4): Calculate the restoring torque;

[0076] The gravity / buoyancy recovery term is expressed as follows:

[0077]

[0078] Among them, f g =[0, 0, W] T , f b =[0, 0, -B] T W=mg is gravity, B is buoyancy, and r g =[x g ,y g ,z g ] T r b =[x g ,y g ,z b ] T These are the position vectors of the center of mass and the center of buoyancy relative to the origin of the body coordinate system, respectively.

[0079] The aforementioned step (1.3) includes step (1.3.1), calculating the slowly varying bias disturbance;

[0080] The slowly varying bias disturbance is described using the following first-order dynamic model:

[0081]

[0082] In the formula, This represents the slowly varying bias perturbation vector. It is a diagonal matrix, and its diagonal elements Describes the rate of change of the bias disturbance; w bFor small-amplitude random inputs, used to describe unmodeled slow drift or low-frequency disturbance terms;

[0083] when When, formula It transforms into a perturbation model that describes approximately constant values;

[0084] when The value range is 10 -2 Up to 10 -4 When the time interval is between, formula (18) describes the characteristics of slowly changing but not strictly constant bias perturbations;

[0085] Step (1.3.2): Calculate the periodic disturbance;

[0086] The periodic disturbance can be modeled as a superposition of a finite number of harmonic components using the following formula:

[0087]

[0088] Where, ω k Indicates the first One main frequency component; a k and These correspond to the magnitude and initial phase, respectively; N h The number of harmonic components;

[0089] Step (1.3.3): Calculate random disturbances and unmodeled terms;

[0090] The above disturbances can be uniformly expressed as a random disturbance term τ using the following formula. n (t);

[0091]

[0092] In the formula, For a zero-mean Gaussian white noise process, its covariance matrix is: ;

[0093] H(s) is a linear filter used to describe the distribution characteristics of random disturbances in the frequency domain.

[0094] Step (2.1) includes defining the speed error using the following formula:

[0095]

[0096] Among them, v d To achieve the desired speed, apply the above formula. Rewritten as:

[0097]

[0098] Take the derivative with respect to e and combine it with the above formula The following dynamic error is derived:

[0099]

[0100] To facilitate control law calculation, the following nominal model compensation term is introduced:

[0101]

[0102] The above formula Substitute into the formula The following dynamic error expression is derived:

[0103]

[0104] If external disturbance If fully obtained, the specified error dynamics satisfy the following first-order stable system: .

[0105] Step (2.2) includes defining the sliding surface as follows:

[0106]

[0107] Where Λ=diag{λ1,λ 2， …,λ6} is a diagonal matrix, and the integral term is used to suppress the steady-state error caused by the slowly varying bias;

[0108] Using a saturation function with a boundary layer and introducing a linear decay term, the reaching law is calculated as follows:

[0109]

[0110] Among them, K ss K sw For diagonal gain, >0 represents the boundary layer thickness; therefore, the saturation function is defined as:

[0111]

[0112] From the formula Differentiating both sides, we get: Combined with formula get:

[0113]

[0114] According to the formula The sliding mode control law is constructed as follows:

[0115]

[0116] The above formula Substitute into the formula The closed-loop sliding mode dynamics formula is obtained as follows:

[0117]

[0118] Step (2.3.2) includes velocity derivative estimation. The following first-order filter differential form is adopted:

[0119]

[0120] Among them, T f T is the filtering time constant. f >0;

[0121] In the discrete implementation, the following Tustin transform or exponential smoothing approximation is used:

[0122]

[0123] Among them, T s The sampling period is ∈(0,1) is the smoothing coefficient;

[0124] The residual perturbation estimate is processed by a first-order filter, and the following low-pass residual perturbation observer is constructed:

[0125]

[0126] Where Γ=diag{γ1, γ2,…, γ6} is the observer bandwidth matrix, and γ1, γ2,…, γ6 are the channel gains for sway, sway, roll, pitch and yaw, respectively.

[0127] The low-pass residual perturbation observer represented by formula (37) is equivalent in the frequency domain to applying a first-order low-pass filter to the residual perturbation estimate as follows:

[0128]

[0129] The disturbance observation error is defined as:

[0130]

[0131] According to the formula get:

[0132]

[0133] Step (2.4) includes the following: pure integral compensation is prone to integral accumulation problems under cyclic operating conditions, so the following integral dynamics with leakage are introduced:

[0134]

[0135] in, K is the leakage factor. i This is the integral gain;

[0136] Will When superimposed on the control law, it is equivalent to enhancing the disturbance suppression capability in the low-frequency band, while avoiding the long-term accumulation of periodic disturbances through leakage terms;

[0137] The zero-crossing detection time t is defined by the following formula. k Accumulated sliding mode variables in each cycle:

[0138]

[0139] Among them, s r Represents sliding mode variables;

[0140] The discrete form of the periodic bias compensation update law is constructed as follows:

[0141]

[0142] in, As a leakage factor, The learning rate;

[0143] Will Superimposed on the control channel to reduce bias and phase inconsistency issues in the periodic response.

[0144] This application proposes a novel electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the aforementioned ROV adaptive sliding mode robust control method based on a residual disturbance observer.

[0145] This application proposes a computer-readable storage medium storing a computer program that, when executed, implements the above-described ROV adaptive sliding mode robust control method based on a residual disturbance observer.

[0146] In summary, this application has the following advantages and beneficial effects compared with the prior art:

[0147] 1. This application demonstrates excellent overall control performance in complex underwater environments and various operating conditions, providing an efficient solution for high-precision and high-reliability control of ROVs.

[0148] 2. By applying this application, high-precision trajectory tracking can be achieved under the premise of significant disturbances such as superimposed enhanced ocean currents, additional cable damping, and random disturbance torque. The control accuracy and operation efficiency are significantly improved compared with the existing technology. Attached Figure Description

[0149] Figure 1 A schematic diagram of the geodetic coordinate system and the ROV coordinate system;

[0150] Figure 2 This is a schematic diagram of the logic of the ROV adaptive sliding mode robust control method based on residual disturbance observer described in this application;

[0151] Figure 3 This is a schematic diagram of ROV rectangular trajectory tracking.

[0152] Figure 4 This is a simulation result of circular trajectory tracking. Detailed Implementation

[0153] To better understand the above-mentioned objectives, features, and advantages of this application, the application will be further described below in conjunction with the accompanying drawings and embodiments. Many specific details are set forth in the following description to provide a thorough understanding of this application; however, this application may be implemented in other ways than those described herein, and therefore, this application is not limited to the specific embodiments disclosed below.

[0154] Example 1: This application proposes a novel ROV adaptive sliding mode robust control method based on a residual disturbance observer, comprising the following steps:

[0155] Step (1): Establish mathematical models of ROV dynamics, kinematics, and disturbances;

[0156] Step (1.1), as follows Figure 1 As shown, a geodetic coordinate system o is introduced. n -XYZ and ROV volume coordinate system o b -xyz;

[0157] Specifically, the origin of the geodetic coordinate system is generally chosen as the starting point of the ROV; the X-axis points due north; the Y-axis points due east; and the Z-axis is perpendicular to the XY plane and points towards the Earth's center.

[0158] The origin of the body coordinate system of an ROV is generally chosen to be the center of gravity of the ROV; the x-axis points to the bow; the y-axis is perpendicular to the x-axis and points to the starboard side; the z-axis points to the bottom of the ROV.

[0159] The ROV pose vector and velocity vector are defined as: η=[x, y, z, , θ, ψ] T ,

[0160] ν=[u, v, w, p, q, r] T ;

[0161] Where (x, y, z) represents the position, ( , θ, ψ) are roll, pitch and yaw angles respectively, (u, v, w) are volume coordinate linear velocities, (p, q, r) are angular velocities, and T is matrix transpose;

[0162] The kinematic relationship can be written as:

[0163]

[0164] in, It is the derivative of η, representing velocity;

[0165] In the above formula (1),

[0166]

[0167] in, R( represents the transformation matrix from the ROV volumetric velocity matrix to the geodetic velocity matrix; ,θ,ψ) is from o n -XYZ to o b -xyz direction cosine matrix; T( ,θ) is the Euler angular rate transformation matrix;

[0168] in:

[0169]

[0170]

[0171] Where E is the Euler angular rate transformation matrix;

[0172] Step (1.2): Establish a dynamic model;

[0173] ROV in volume coordinate system o b The standard 6-DOF dynamics under -xyz can be expressed as:

[0174]

[0175] Where M is the generalized mass matrix (containing rigid body terms and additional mass terms), C(ν) is the Coriolis and centripetal force matrix (containing rigid body terms and additional mass terms), D(ν) is the hydrodynamic damping matrix (containing linear and nonlinear terms), g(η) is the restoring force / torque vector, τ is the control force / torque vector, and τ d External disturbances and unmodeled terms;

[0176] Step (1.2.1): Calculate the generalized mass matrix;

[0177] The generalized mass matrix can be decomposed into a rigid body mass matrix M. RB and the additional mass matrix M A As shown in the following formula:

[0178]

[0179] In the formula:

[0180]

[0181]

[0182] Where m is mass, I 3×3 It is a 3×3 identity matrix, S(·) is the antisymmetric matrix operator, r g I is the vector of the center of mass relative to the origin of the volume coordinate system. g Let be the moment of inertia matrix about the origin of the volume coordinate system. , , For added mass , , To add rotational inertia.

[0183] Step (1.2.2): Calculate the Coriolis and centripetal force matrices;

[0184] Coriolis and centripetal force matrices are divided into rigid body terms C. RB (v) and the additional mass term C A The expression for (ν) is as follows:

[0185]

[0186] Generally, the centroid of the ROV is chosen as the origin of the volume coordinate system. In this case, r g When ≈0, C RB (ν) can be expressed as:

[0187]

[0188] Where ω = [p, q, r] T ;

[0189] In addition, the additional mass item C A (ν) can be derived from M A The derivation yields a skew-symmetric structure that satisfies energy conservation; as shown in the following equation, C can be expressed in Fossen's standard form. A (ν):

[0190]

[0191] Where, v1 = [u, v, w] T v2=[p, q, r] T ; , M respectively A The linear velocity and angular velocity of the 3×3 sub-block; ℝ represents the set of real numbers;

[0192] Step (1.2.3): Calculate the hydrodynamic damping matrix;

[0193] ROVs exhibit significant damping during both low-speed precision operations and medium-speed navigation. A commonly used damping model is a superposition of linear and nonlinear damping, expressed as follows:

[0194]

[0195] Wherein, D in the above formula L (v) is the linear damping term, D NL (v) represents the nonlinear damping term;

[0196]

[0197]

[0198] in, These represent the linear damping coefficients in the directions of sway, roll, heave, pitch, and yaw, respectively. These represent the nonlinear damping coefficients in the directions of sway, roll, heave, pitch, and yaw, respectively.

[0199] Step (1.2.4): Calculate the restoring torque;

[0200] The gravity / buoyancy recovery term is expressed as follows:

[0201]

[0202] Among them, f g =[0, 0, W] T , f b =[0, 0, -B] T W=mg is gravity, B is buoyancy, and r g =[x g ,y g ,z g ] T r b =[x g ,y g ,z b ] T These are the position vectors of the center of mass and the center of buoyancy relative to the origin of the volume coordinate system, respectively.

[0203] Pair Perform linearization:

[0204]

[0205] In the above formula (16), the first three terms of the matrix on the right are restoring forces, and the last three terms are restoring torques;

[0206] Therefore, the restoring torque is mainly determined by the positions of the center of mass and the center of buoyancy.

[0207] Step (1.3), disturbance modeling;

[0208] To describe in detail the slowly varying offsets caused by mean ocean currents, long-term cable towing, ROV trim errors, and periodic disturbances caused by wave excitation and cable oscillations, the external disturbances are uniformly modeled as follows:

[0209]

[0210] In the formula, τ b (t) is the slowly varying bias term, τ p (t) is a periodic term, τ n (t) represents random high-frequency disturbances or unmodeled residuals;

[0211] Step (1.3.1): Calculate the slowly varying bias disturbance;

[0212] To describe the slowly varying disturbance bias caused by mean ocean currents, long-term cable towing, and ROV trim errors, this application uses the following first-order dynamic model to describe the slowly varying bias disturbance:

[0213]

[0214] In the formula, This represents the slowly varying bias perturbation vector. It is a diagonal matrix, and its diagonal elements Describes the rate of change of the bias disturbance; w b For small-amplitude random inputs, used to describe unmodeled slow drift or low-frequency disturbance terms;

[0215] when When, style It transforms into a perturbation model that describes approximately constant values;

[0216] when The value range is 10 -2 Up to 10 -4 Between tens of seconds and thousands of seconds (i.e., corresponding to slow drifts on the scale of tens of seconds to thousands of seconds), the model can describe the characteristics of slowly changing but not strictly constant bias perturbations.

[0217] Step (1.3.2): Calculate the periodic disturbance;

[0218] Under the influence of wave excitation and cable oscillation, ROVs often exhibit periodic disturbances in some degrees of freedom channels (especially heading and heave);

[0219] To describe the main characteristics of this type of disturbance, the periodic disturbance is modeled as a superposition of a finite number of harmonic components using the following formula:

[0220]

[0221] Where, ω k Indicates the first One main frequency component; a k and These correspond to the magnitude and initial phase, respectively; N h The number of harmonic components;

[0222] Step (1.3.3): Calculate random disturbances and unmodeled terms;

[0223] In addition to slow-varying bias and periodic disturbances, ROVs are also affected by high-frequency random disturbances and unmodeled effects during underwater operations, such as vortex-induced forces, thruster thrust fluctuations, sensor noise, and high-frequency hydrodynamics.

[0224] The above disturbances can be uniformly expressed as a random disturbance term τ using the following formula. n (t);

[0225]

[0226] In the formula, For a zero-mean Gaussian white noise process, its covariance matrix is: ;

[0227] H(s) is a linear filter used to describe the distribution characteristics of random disturbances in the frequency domain;

[0228] Step (2), ROV control;

[0229] Step (2.1): Calculate the ideal equivalent control law;

[0230] Speed ​​error is defined by the following formula:

[0231]

[0232] Among them, v d To achieve the desired speed, apply the above formula. Rewritten as:

[0233]

[0234] Take the derivative with respect to e and combine it with the above formula The following dynamic error is derived:

[0235]

[0236] To facilitate control law calculation, the following nominal model compensation term is introduced:

[0237]

[0238] The above formula Substitute into the formula The following dynamic error expression is derived:

[0239]

[0240] The possible scenario is that if external disturbances occur... If fully obtained, the specified error dynamics satisfy the following first-order stable system: ;

[0241] Therefore, the ideal equivalent control law can be expressed as:

[0242]

[0243] Thus, exponential convergence of the error is achieved;

[0244] However, in actual ROV control systems, external disturbances... Since the ROV control system model cannot be directly measured and unavoidable uncertainties exist, robust terms, disturbance observers, and adaptive mechanisms need to be further introduced into the aforementioned ideal equivalent control law; specifically,

[0245] Step (2.2): Introduce robust terms;

[0246] The sliding surface is defined as follows:

[0247]

[0248] Where Λ=diag{λ1,λ 2， …,λ6} is a diagonal matrix, and the integral term is used to suppress the steady-state error caused by the slowly varying bias;

[0249] To address the problem that existing sliding mode reaching laws, which use the sign function sgn(⋅), easily introduce chattering into practical systems, this application employs a saturation function with a boundary layer and introduces a linear decay term, calculating the reaching law using the following formula:

[0250]

[0251] Among them, K ss K sw For diagonal gain, >0 represents the boundary layer thickness; therefore, the saturation function is defined as:

[0252]

[0253] This structure effectively suppresses chattering while maintaining robustness;

[0254] From the formula Differentiating both sides, we get: Combined with formula get:

[0255]

[0256] According to the formula The sliding mode control law is constructed as follows:

[0257]

[0258] The above formula Substitute into the formula The closed-loop sliding mode dynamics formula is obtained as follows:

[0259]

[0260] Among them, if the disturbance estimation error If it is bounded, then it can be proven that the sliding mode variable s is uniformly bounded eventually;

[0261] Step (2.3): Introduce a disturbance observer;

[0262] Considering the parameter errors in actual ROV engineering models, directly using a high-gain interference observer may amplify noise and cause miscompensation when the thruster is saturated;

[0263] To address disturbances in the actual operating environment of ROVs, this application employs the following two complementary disturbance control methods:

[0264] One approach is perturbation reconstruction based on dynamic residuals, used to simultaneously capture slow-varying biases and periodic perturbations;

[0265] Another option is a first-order low-pass perturbation observer, used to suppress high-frequency noise and obtain smooth perturbation estimates;

[0266] Specifically, step (2.3.1) involves perturbation reconstruction based on dynamic residuals;

[0267] From the above formula The equivalent expression for the following perturbation is derived:

[0268]

[0269] If it is available A reliable estimate can be obtained, and the perturbation estimate based on the model residuals can be constructed as follows:

[0270]

[0271] It can be seen that the above formula It includes both slowly varying bias and periodic perturbations;

[0272] Step (2.3.2): Introduce a first-order low-pass perturbation observer;

[0273] To reduce the noise amplification problem caused by numerical differentiation, velocity derivative estimation... The following first-order filter differential form is adopted:

[0274]

[0275] Among them, T f T is the filtering time constant. f >0;

[0276] In the discrete implementation, the following Tustin transform or exponential smoothing approximation is used:

[0277]

[0278] Among them, T s The sampling period is ∈(0,1) is the smoothing coefficient;

[0279] To introduce a smoother, noise-insensitive disturbance estimate into the control law, a first-order filter is applied to the residual disturbance estimate, and the following low-pass residual disturbance observer is constructed:

[0280]

[0281] Where Γ=diag{γ1, γ2,…, γ6} is the observer bandwidth matrix, and γ1, γ2,…, γ6 are the channel gains for sway, sway, roll, pitch and yaw, respectively.

[0282] The low-pass residual perturbation observer represented by formula (37) is equivalent in the frequency domain to applying a first-order low-pass filter to the residual perturbation estimate as follows:

[0283]

[0284] By dynamically adjusting γ in formula (38) i The value of can achieve an effective balance between rapid tracking of slow-changing bias and periodic disturbances, and disturbance control that suppresses high-frequency noise;

[0285] Specifically, γ i The larger the value of γ, the faster the estimator updates and the more sensitive it is to tracking disturbances; i The smaller the value of γ, the slower the estimator updates and the stronger its noise resistance; i It is a typical bandwidth parameter. Given the differences in noise levels across different channels, γ i It should not be a fixed value;

[0286] Furthermore, the disturbance observation error is defined as:

[0287]

[0288] According to the formula get:

[0289]

[0290] Therefore, it can be seen that when external disturbances occur... When including slowly varying bias terms and a finite number of dominant harmonics, if the observer bandwidth... Covering the main disturbance frequency bands can significantly reduce disturbance estimation errors. The amplitude;

[0291] Step (2.4): Introduce an adaptive mechanism;

[0292] Existing sliding mode control techniques typically require a known upper bound on the disturbance before selecting the robust gain K. sw However, under conditions such as cable towing and ocean current variations, the disturbance amplitude varies significantly; excessive robust gain may cause thruster saturation and miscompensation problems.

[0293] To this end, this application introduces an adaptive robust gain vector. This is used to adjust the magnitude of the sliding mode robustness term online, thereby reducing the reliance on prior information about the upper bound of the perturbation;

[0294] Robust gain K sw and It is equivalent, and is named K in the sliding membrane control algorithm. sw However, it was renamed in the adaptive algorithm. ;

[0295] The above formula The robust terms in the code are rewritten in adaptive form:

[0296]

[0297] In the formula, ☉ represents element-wise multiplication. For adaptive robust gain vector;

[0298] The adaptive law is chosen as follows:

[0299]

[0300] Where |s| represents the absolute value of the elements; ρ is the leakage factor, ρ>0, used to prevent leakage. Unbounded growth and its automatic decline under steady-state conditions;

[0301] Although the adaptive sliding mode term can effectively alleviate the problems caused by the unknown upper bound of the disturbance, the system may still exhibit the following two types of residual errors under long-term steady-state operation and periodic excitation conditions:

[0302] 1) Small steady-state residuals caused by slowly varying bias disturbances;

[0303] 2) Periodic residual errors with dominant frequency characteristics caused by periodic disturbances;

[0304] For the aforementioned slowly varying bias disturbance, directly using pure integral compensation is prone to integral accumulation problems under cyclic operating conditions.

[0305] Therefore, the following integral dynamics with leakage are introduced:

[0306]

[0307] in, K is the leakage factor. i This is the integral gain;

[0308] Will When superimposed on the control law, it is equivalent to enhancing the disturbance suppression capability in the low-frequency band, while avoiding the long-term accumulation of periodic disturbances through leakage terms;

[0309] For control references or disturbances dominated by a single dominant frequency, an asymmetry between positive and negative half-cycle errors often occurs in the system response. To address this, the zero-crossing detection time t is defined by the following formula. k Accumulated sliding mode variables in each cycle:

[0310]

[0311] Among them, s r Represents sliding mode variables;

[0312] The discrete form of the periodic bias compensation update law is constructed as follows:

[0313]

[0314] in, As a leakage factor, The learning rate;

[0315] Therefore, it can be concluded that... Superimposed onto the control channel can effectively reduce the bias and phase inconsistency problem in the periodic response; that is, this application is essentially a periodic average zero bias correction mechanism.

[0316] In the aforementioned ROV adaptive sliding mode robust control process, under the condition of thruster saturation, the disturbance observer may misjudge the lack of control torque caused by thruster limitation as an external disturbance, leading to miscompensation and control oscillation. To address this, this application may adopt the following engineering constraint strategy:

[0317] 1) Before thruster distribution, control torque command is issued. Amplitude and speed limits are applied, and the actual torque is... Feedback to residual disturbance calculation formula middle;

[0318] 2) When persistent thruster saturation is detected, reduce the perturbation observer bandwidth. and adaptive update rate to prevent and Drift occurs due to saturation error.

[0319] This application also proposes a novel electronic device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described ROV adaptive sliding mode robust control method based on a residual disturbance observer.

[0320] This application also proposes a novel computer-readable storage medium storing a computer program that, when executed, enables the implementation of the aforementioned ROV adaptive sliding mode robust control method based on a residual disturbance observer.

[0321] As described above, similar technical solutions can be derived from the solutions presented in the accompanying drawings and description, and all of them still fall within the scope of the claims of this application.

Claims

1. A robust adaptive sliding mode control method for ROVs based on residual disturbance observers, characterized in that: Includes the following steps, Step (1): Establish mathematical models of ROV dynamics, kinematics, and disturbances; Step (1.1): Introduce the geodetic coordinate system o n -XYZ and ROV volume coordinate system o b -xyz; Step (1.2): Establish a dynamic model; ROV in volume coordinate system o b The standard 6-DOF dynamics under -xyz can be expressed as: Where M is the generalized mass matrix, C(ν) is the Coriolis and centripetal force matrix, D(ν) is the hydrodynamic damping matrix, g(η) is the restoring force / torque vector, τ is the control force / torque vector, and τ d External disturbances and unmodeled terms; Step (1.3), disturbance modeling; External disturbances are uniformly modeled as follows: In the formula, τ b (t) is the slowly varying bias term, τ p (t) is a periodic term, τ n (t) represents random high-frequency disturbances or unmodeled residuals; Step (2), ROV control; Step (2.1): Calculate the ideal equivalent control law; The ideal equivalent control law is expressed as: Step (2.2): Introduce robust terms; The sliding mode control law is constructed as follows: The formula for closed-loop sliding mode dynamics is as follows: Among them, if the disturbance estimation error If it is bounded, then it can be proven that the sliding mode variable s is uniformly bounded eventually; Step (2.3): Introduce a disturbance observer; Step (2.3.1): Perturbation reconstruction based on dynamic residuals; From the above formula The equivalent expression for the following perturbation is derived: If it is available A reliable estimate can be obtained, and the perturbation estimate based on the model residuals can be constructed as follows: Step (2.3.2): Introduce a first-order low-pass perturbation observer; Apply a first-order low-pass filter to the residual perturbation estimate using the following formula: Step (2.4): Introduce an adaptive mechanism; The above formula The robust terms in the code are rewritten in adaptive form: In the formula, ☉ represents element-wise multiplication. ∈ℝ 6 >0 represents the adaptive robust gain vector; The adaptive law is chosen as follows: Where |s| represents the absolute value of the elements; ρ is the leakage factor, ρ>0, used to prevent leakage. It grows unbounded and then automatically falls back under steady-state conditions.

2. The ROV adaptive sliding mode robust control method based on residual disturbance observer according to claim 1, characterized in that: In step (1.1), the origin of the geodetic coordinate system is the starting point of the ROV; the origin of the volume coordinate system of the ROV is the center of gravity of the ROV. The ROV pose vector and velocity vector are defined as: η=[x, y, z, , θ, ψ] T , ν=[u, v, w, p, q, r] T ; Where (x, y, z) represents the position, ( (u, v, w) represent the roll, pitch, and yaw angles, respectively; (p, q, r) represent the volumetric linear velocity; (p, q, r) represent the angular velocity; and T represents the matrix transpose. The kinematic relationships are as follows: in, It is the derivative of η, representing velocity; In the above formula (1), in, R( represents the transformation matrix from the ROV volumetric velocity matrix to the geodetic velocity matrix; ,θ,ψ) is from o n -XYZ to o b -xyz direction cosine matrix; T( ,θ) is the Euler angular rate transformation matrix; in: Where E is the Euler angular rate transformation matrix.

3. The ROV adaptive sliding mode robust control method based on a residual disturbance observer according to claim 2, characterized in that: Step (1.2) includes, Step (1.2.1): Calculate the generalized mass matrix; The generalized mass matrix is ​​decomposed into a rigid body mass matrix M. RB and the additional mass matrix M A As shown in the following formula: In the formula: Where m is mass, I 3×3 It is a 3×3 identity matrix, S(·) is the antisymmetric matrix operator, r g I is the vector of the center of mass relative to the origin of the volume coordinate system. g Let be the moment of inertia matrix about the origin of the volume coordinate system; , , For added mass , , To add rotational inertia; Step (1.2.2): Calculate the Coriolis and centripetal force matrices; Coriolis and centripetal force matrices are divided into rigid body terms C. RB (v) and the additional mass term C A The expression for (ν) is as follows: Step (1.2.3): Calculate the hydrodynamic damping matrix; The damping model is a superposition of linear and nonlinear damping, expressed as follows: Wherein, D in the above formula L (v) is the linear damping term, D NL (v) represents the nonlinear damping term; in, These represent the linear damping coefficients in the directions of sway, roll, heave, pitch, and yaw, respectively. These represent the nonlinear damping coefficients in the directions of sway, roll, heave, pitch, and yaw, respectively. Step (1.2.4): Calculate the restoring torque; The gravity / buoyancy recovery term is expressed as follows: Among them, f g =[0, 0, W] T , f b =[0, 0, -B] T W=mg is gravity, B is buoyancy, and r g =[x g ,y g ,z g ] T r b =[x g ,y g ,z b ] T These are the position vectors of the center of mass and the center of buoyancy relative to the origin of the body coordinate system, respectively.

4. The ROV adaptive sliding mode robust control method based on residual disturbance observer according to claim 3, characterized in that: Step (1.3) includes, Step (1.3.1): Calculate the slowly varying bias disturbance; The slowly varying bias disturbance is described using the following first-order dynamic model: In the formula, This represents the slowly varying bias perturbation vector. It is a diagonal matrix, and its diagonal elements Describes the rate of change of the bias disturbance; w b For small-amplitude random inputs, used to describe unmodeled slow drift or low-frequency disturbance terms; when When, formula It transforms into a perturbation model that describes approximately constant values; when The value range is 10 -2 Up to 10 -4 When the time interval is between, formula (18) describes the characteristics of slowly changing but not strictly constant bias perturbations; Step (1.3.2): Calculate the periodic disturbance; The periodic disturbance can be modeled as a superposition of a finite number of harmonic components using the following formula: Where, ω k Indicates the first One main frequency component; a k and These correspond to the magnitude and initial phase, respectively; N h The number of harmonic components; Step (1.3.3): Calculate random disturbances and unmodeled terms; The above disturbances can be uniformly expressed as a random disturbance term τ using the following formula. n (t); In the formula, For a zero-mean Gaussian white noise process, its covariance matrix is: ; H(s) is a linear filter used to describe the distribution characteristics of random disturbances in the frequency domain.

5. The ROV adaptive sliding mode robust control method based on residual disturbance observer according to claim 4, characterized in that: Step (2.1) includes, Speed ​​error is defined by the following formula: Among them, v d To achieve the desired speed, apply the above formula. Rewritten as: Take the derivative with respect to e and combine it with the above formula The following dynamic error is derived: To facilitate control law calculation, the following nominal model compensation term is introduced: The above formula Substitute into the formula The following dynamic error expression is derived: If external disturbance If fully obtained, the specified error dynamics satisfy the following first-order stable system: .

6. The ROV adaptive sliding mode robust control method based on residual disturbance observer according to claim 5, characterized in that: Step (2.2) includes, The sliding surface is defined as follows: Where Λ=diag{λ1,λ 2， …,λ6} is a diagonal matrix, and the integral term is used to suppress the steady-state error caused by the slowly varying bias; Using a saturation function with a boundary layer and introducing a linear decay term, the reaching law is calculated as follows: Among them, K ss K sw For diagonal gain, >0 represents the boundary layer thickness; therefore, the saturation function is defined as: From the formula Differentiating both sides, we get: Combined with formula get: According to the formula The sliding mode control law is constructed as follows: The above formula Substitute into the formula The closed-loop sliding mode dynamics formula is obtained as follows: .

7. The ROV adaptive sliding mode robust control method based on residual disturbance observer according to claim 6, characterized in that: Step (2.3.2) includes, Velocity derivative estimation The following first-order filter differential form is adopted: Among them, T f T is the filtering time constant. f >0; In the discrete implementation, the following Tustin transform or exponential smoothing approximation is used: Among them, T s The sampling period is ∈(0,1) is the smoothing coefficient; The residual perturbation estimate is processed by a first-order filter, and the following low-pass residual perturbation observer is constructed: Where Γ=diag{γ1, γ2,…, γ6} is the observer bandwidth matrix, and γ1, γ2,…, γ6 are the channel gains for sway, sway, roll, pitch and yaw, respectively. The low-pass residual perturbation observer represented by formula (37) is equivalent in the frequency domain to applying a first-order low-pass filter to the residual perturbation estimate as follows: The disturbance observation error is defined as: According to the formula get: 。 8. The ROV adaptive sliding mode robust control method based on residual disturbance observer according to claim 7, characterized in that: Step (2.4) includes, Pure integral compensation is prone to integral accumulation problems under cyclic operating conditions. The following integral dynamics with leakage are introduced: in, K is the leakage factor. i This is the integral gain; Will When superimposed on the control law, it is equivalent to enhancing the disturbance suppression capability in the low-frequency band, while avoiding the long-term accumulation of periodic disturbances through leakage terms; The zero-crossing detection time t is defined by the following formula. k Accumulated sliding mode variables in each cycle: Among them, s r Represents sliding mode variables; The discrete form of the periodic bias compensation update law is constructed as follows: in, As a leakage factor, The learning rate; Will Superimposed on the control channel to reduce bias and phase inconsistency issues in the periodic response.

9. An electronic device, characterized in that: It includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the ROV adaptive sliding mode robust control method based on a residual disturbance observer as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that: It stores a computer program that, when executed, implements the ROV adaptive sliding mode robust control method based on a residual disturbance observer as described in any one of claims 1 to 8.

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