Unmanned underwater vehicle fixed time fault-tolerant tracking model and control method thereof

Abstract

The invention discloses an unmanned underwater vehicle fixed time fault-tolerant tracking model and a control method thereof. The model is composed of a kinematics model shown in a formula (1) and a dynamics model shown in a formula (2). The construction method of the control model comprises the steps of determining known parameters and uncertain parameters, inputting constraints, and constructing a kinetic model and a kinematic model. The control method of the model for the unmanned underwater vehicle comprises the steps of constructing a smooth disturbance observer, constructing a tracking error dynamic model, constructing a preset performance control method, constructing a preset sliding mode control surface and constructing a fixed time fault-tolerant controller. According to the invention, a fixed time fault-tolerant controller is constructed, and an adaptive law is introduced to estimate unknown input gain and observation errors, so that tracking errors are ensured to be irrelevant to initial conditions, and the convergence speed is higher. Compared with the prior art, the method has the advantages of fast convergence, good fault tolerance, strong robustness and the like, and can be used as a tracking controller of the unmanned underwater vehicle.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater unmanned system control, and in particular relates to fixed-time fault-tolerant tracking control of an unmanned underwater vehicle considering input and output constraints. Background Art

[0002] Unmanned underwater vehicles (UUVs) are powerful tools for entering the ocean for various marine engineering applications, including monitoring, exploration, development, and military operations. Accurate trajectory tracking is crucial for accomplishing these tasks. As a typical nonlinear system, UUVs possess inherent characteristics such as strong coupling and nonlinearity. Parameter perturbations and unmodeled dynamics are unavoidable, making it difficult to establish accurate models for controller feedback design. Furthermore, complex disturbances such as waves, surges, and currents acting on UUVs generate nonlinear and time-varying impact forces and torques, making UUV motion complex and unpredictable, leading to degraded tracking performance and even instability. Therefore, there is an urgent need to design high-precision control schemes to meet application requirements.

[0003] To address the aforementioned model uncertainty and external disturbance issues, sliding mode control has attracted increasing attention due to its ease of implementation, low sensitivity, and strong robustness. However, its negative chattering effects can cause actuator wear and degrade control performance. Various disturbance-based observer-based control methods, such as extended state observers, high-gain observers, and nonlinear disturbance observers, have been combined with sliding mode control to suppress chattering. These are inherently discontinuous controllers and are still subject to bandwidth and chattering limitations. To design continuous controllers, neural networks and fuzzy logic systems have been incorporated into these designs, eliminating the reliance on prior knowledge of the UUV dynamics and external disturbances. These approaches rarely consider input constraints, such as actuator failures and input saturation. Actuator failures are common phenomena caused by mechanical and actuator faults, with multiplicative and additive faults being a primary concern in UUV control research, impacting the vehicle's reliability and safety. To mitigate these negative effects, numerous fault-tolerant control schemes have been proposed to estimate, compensate, and suppress fault effects. Input saturation, on the other hand, is a phenomenon in which control commands exceed their maximum limits due to the physical limitations of the UUV.

[0004] Unlike asymptotic or exponential stability, in which the system state converges to a region near the origin as time approaches infinity, finite-time stability can converge quickly to zero, a benefit particularly beneficial for time-sensitive applications. The convergence characteristics of finite-time control are heavily dependent on the initial state. To overcome this limitation, fixed-time control has been developed with an upper bound independent of the initial state, ensuring faster response and greater accuracy. This has led to the development of terminal sliding mode control, integral sliding mode control, and fast fixed-time control systems, which ignore both the transient and steady-state performance of the output state.

[0005] Due to system safety requirements, output constraints must be maintained within specified limits. Preset performance control, consisting of a preset performance function and a transformation error function, ensures both transient and steady-state performance. It is widely used in the field of unmanned underwater vehicle tracking control, but suffers from drawbacks such as long convergence time and dependence on initial values. Existing research has employed a finite domain for the transformation error function. This can lead to system instability when disturbances cause the output error to exceed the predetermined definition set. Summary of the Invention

[0006] A technical problem to be solved by the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a fixed-time fault-tolerant tracking model for an unmanned underwater vehicle.

[0007] Another technical problem to be solved by the present invention is to provide a method for constructing a fixed-time fault-tolerant tracking model for an unmanned underwater vehicle.

[0008] Another technical problem to be solved by the present invention is to provide a control method for an underwater unmanned underwater vehicle with high tracking control convergence, fault tolerance, good stability, and input and output constraints.

[0009] The fixed-time fault-tolerant tracking model of the unmanned underwater vehicle is composed of the kinematic model and dynamic models constitute.

[0010] The kinematic model As shown in formula (1):

[0011]

[0012] Where η represents the position (x, y) and heading ψ∈[0, 2π) vectors, and v represents the velocity vector composed of swell u, sway υ, and pitch r. 3×3 Represents a rotation matrix.

[0013] The kinetic model As shown in formula (2):

[0014]

[0015] Among them, d n represents external interference, τ n represents the longitudinal surge force τ nu , lateral force τ nυ , yaw moment τ nr The control input vector composed of n ∈R 3×3 、C n ∈R 3×3 、D n ∈R 3×3denote the inertia matrix, Coriolis matrix and damping matrix respectively, m is the total mass of the unmanned underwater vehicle, I z is the torque, x g is the distance from the center of gravity to the origin of the coordinate system, is the additional mass, X u 、Y υ 、N υ They represent the linear damping coefficients in surge, sway and pitch directions, respectively, and Y r 、N υ represents the sway-yaw coupling damping coefficient, ΔM, ΔC and ΔD are uncertain parameters; X |u|u 、Y |υ|υ 、N |r|r They represent the secondary damping coefficients in surge, sway and pitch directions, respectively, and Y |r|υ 、Y |υ|r 、N |r|υ 、N |υ|r represents the secondary damping coefficient of sway-yaw coupling.

[0016] In the kinematic model of formula (1) of the present invention The longitudinal surge force τ nu The maximum value of τ u，max 45N, minimum value -τ u，min is 45N; the lateral force τ nυ The maximum value of τ υ，max 45N, minimum value -τ υ，min is 45N; yaw moment τ nr The maximum value of τ r，max 10Nm, minimum value -τ r，min is 10Nm.

[0017] In the kinetic model of formula (2) of the present invention, The optimal value of m is 23.8, x g The best value is 0.046, I z The best value is 1.76. The best value is -2. The best value is -10. The best value is 0. The best value is -1, X u The best value is -0.7225, X |u|u The best value is -1.3274, Y υ The best value is -0.8896, Y |υ|υ The best value is -36.4728, Y r The best value is -7.25, Y |υ|r The best value is -0.845, Y |r|rThe best value is -3.45, N υ The best value is -0.0313, N |υ|υ The best value is 3.9564, N |r|υ The best value is 0.13, N r The best value is -1.9, N |υ|r The best value is 0.8, Y |r|υ The best value is -0.805, N |r|r The optimal value is -0.750, the optimal value of ΔM is 0.2sin(t)M, the optimal value of ΔC is 0.2sin(t)C, and the optimal value of ΔD is 0.2sin(t)D.

[0018] The method for constructing a fixed-time fault-tolerant tracking model for an unmanned underwater vehicle of the present invention comprises the following steps:

[0019] (1) Determine known parameters and uncertain parameters

[0020] Press the formula to change M n 、C n 、D n Divided into two categories: known parameters and uncertain parameters:

[0021] M n =M+ΔM

[0022] C n =C+ΔC

[0023] C n =C+ΔC

[0024] Among them, M, C, and D are known parameters, and ΔM, ΔC, and ΔD are uncertain parameters. The kinetic model can be expressed as:

[0025]

[0026] (2) Input constraints

[0027] Input constraint τ according to formula (4) n :

[0028]

[0029] Where τ represents the ideal input signal generated by the subsequent controller, φ represents the diagonal matrix of multiplicative faults, and its components satisfy 0<φ i - ≤φ i ≤φ i + ≤1,φ i - and φ i + Two positive constants, represents the additive fault vector, s τ (τ i ) represents τ i Saturation function subject to nonlinearity:

[0030]

[0031] Among them, τ i，max >0,τ i，min <0 represents the maximum and minimum limits of the control force and torque respectively; the smooth function g is used i (τ i ) instead of nonlinear sat(τ i )for:

[0032]

[0033] in, Indicated by τ i is the Gaussian error function of the variable, sat(τ i ) is approximated as:

[0034] sat(τ i )=g i (τ i )+h i (τ i ) (7)

[0035] Among them, h(τ i ) represents the approximation error, satisfying |h i (τ i )|=|τ ni -g i (τ i )|≤Δ τ , Δ τ represents a positive upper bound on the error.

[0036] Determine the smooth function g according to formula (8) i (τ i ):

[0037]

[0038] Among them, χ i and Represents the intermediate variable, and the adjustment parameter l satisfies 0<l<1.

[0039]

[0040] Among them, χ i Satisfying 0<χ i <1.

[0041] Determine the vector g(τ), vector h(τ), and diagonal matrix χ as follows:

[0042] g(τ)=[g u (τ u ), g υ (τ υ ), g r (τ r )] T ,

[0043] h(τ)=[h u (τ u ), h υ (τ υ ), h r (τ r )] T

[0044] χ=diag{χ u , χ υ , χ r},

[0045] From formulas (5)-(9), we get formula (10):

[0046]

[0047] in, represents a positive definite diagonal matrix.

[0048] (3) Constructing dynamic and kinematic models

[0049]

[0050] Construct coordinates x1 and x2 as follows:

[0051]

[0052] The dynamic and kinematic models are transformed into:

[0053]

[0054] Where f represents the known kinetic model, d sum represents the integrated disturbance.

[0055] The dynamic model is constructed as shown in formula (1) and the kinematic model is constructed as shown in formula (2).

[0056] The control method of the model of the present invention for the unmanned underwater vehicle consists of the following steps:

[0057] (1) Constructing a smooth disturbance observer

[0058] 1) Determine the smooth disturbance observer according to formula (14):

[0059]

[0060] in, is the observation value of the disturbance observer, 0<m1<1, n1 is a finite positive number greater than 1, A∈R 3×3 and B∈R 3×3 is a positive definite diagonal matrix, Θ(x2) represents the fuzzy basis function with x2 as the input variable.

[0061] Determine the update rate according to formula (15)

[0062]

[0063] in, Represents the estimated value of the fuzzy inference system weight, Γ represents the adaptive gain and is a finite positive number greater than 0, and σ represents the correction parameter and is a finite positive number greater than 0.

[0064] 2) Construct Lyapunov function V1:

[0065]

[0066] in, is the observation error of the smooth disturbance observer, is the estimation error, W * is the ideal weight of the fuzzy inference system.

[0067] 3) Determine the convergence region Φ1

[0068]

[0069] According to formula (17), There is an upper bound And from formula (16) we know further

[0070] (2) Constructing a tracking error dynamics model

[0071] 1) Construct an ideal smooth path η d

[0072] η d =[x d ,y d , ψ d ] T (18)

[0073] Its first-order differential and the second-order differential is known and bounded, satisfying:

[0074]

[0075] Among them, B0 is a positive number.

[0076] 2) Construct tracking error

[0077] According to formula (20), the tracking error e is constructed

[0078]

[0079] Among them, ψ a As the unmanned underwater vehicle approaches η d The approach angle, represents the Gaussian error function, a0 represents ψ d and arctan(H1) is the control parameter for the conversion rate.

[0080] 3) Build error state

[0081]

[0082] Combining formula (21) and formula (13), we can get:

[0083]

[0084] (3) Constructing a preset performance control method

[0085] 1) According to formula (23), the tracking error e is limited to:

[0086]

[0087] Among them, ρ i ∈ρ=[ρ1,ρ2,ρ3] T Indicates the preset performance function of the agreed time

[0088]

[0089] Where m2, n2, p2 and q2 are all finite positive odd numbers, satisfying m2<n2 and p2<q2. 01 and σ 02 are control parameters and are both finite positive numbers, ρ0 and ρ N represents the initial value and steady-state value of the preset performance function, N is a finite positive integer, satisfying ρ0>ρ N , and ρ0 and ρ N are all finite positive numbers, T b Indicates an agreed time that does not depend on the initial state, satisfying And ρ(t) remains unchanged when t≥T b , sign represents the sign function.

[0090] 2) The conversion error function Λ(z i ) to convert:

[0091]

[0092] Among them, z i represents an intermediate scalar, and are control parameters and are all finite positive numbers;

[0093] The error vector γ is converted as follows:

[0094]

[0095] Formula (28) can be written into a compact matrix form as follows:

[0096]

[0097] (4) Constructing a preset sliding mode control surface

[0098] 1) Construct the sliding surface ζ according to formula (29):

[0099]

[0100]

[0101] Among them, μ 1i , μ 2i are all finite positive numbers, 0<m3<1, n3 is a finite positive number greater than 1, ε e represents the control parameter and is a finite positive number;

[0102] 2) Determine the sliding surface error dynamic model

[0103]

[0104] Among them, π(γ) and Λ are intermediate variables.

[0105] (5) Constructing a fixed-time fault-tolerant controller

[0106] 1) Construct a fixed-time fault-tolerant controller τ according to formula (31):

[0107]

[0108] Where, 0<m4<1, n4 is a finite positive number greater than 1, μ3 and μ4 are both finite positive numbers, 0<α0<1, μ5 is a finite positive number and satisfies μ5≥Δd sum , μ θ1 and μ θ2 are control parameters and are all finite positive numbers.

[0109] 2) Construct the fixed time arrival rate according to formula (32)

[0110]

[0111] The present invention has the following beneficial effects:

[0112] When constructing the control model of the unmanned underwater vehicle, the technical issues of model uncertainty, external disturbances, actuator failures and input saturation were taken into consideration. A lumped construction model was adopted to construct the four constraints into a lumped disturbance term, which solved the defects of the traditional separate model. The continuous finite-time disturbance observer based on fuzzy logic estimates the lumped disturbance term, which solves the jitter phenomenon existing in traditional discontinuous asymptotically stable or exponentially stable observers. A preset performance function with a preset time and a conversion error function with an unrestricted domain were used to transform the original constrained system into an unconstrained system. Since the present invention constructs a fixed-time fault-tolerant controller and introduces an adaptive law to estimate the unknown input gain and observation error, it ensures that the tracking error is independent of the initial conditions and the convergence speed is faster. Compared with the existing technology, the present invention has the advantages of fast convergence, good fault tolerance and strong robustness, and can be used as a tracking controller for unmanned underwater vehicles. BRIEF DESCRIPTION OF THE DRAWINGS

[0113] Figure 1 4 is a flow chart of the control method of embodiment 1 of the present invention.

[0114] Figure 2 It is the ideal path trajectory and actual position trajectory diagram.

[0115] Figure 3 is the comparison curve of the lumped disturbance and its estimated value.

[0116] Figure 4 is the convergence curve of the disturbance observer's observation error.

[0117] Figure 5 is the normalized weight norm curve of the fuzzy inference system.

[0118] Figure 6 It is the actual response curve of the control signal in the longitudinal and swaying direction.

[0119] Figure 7 It is the actual response curve of the control signal in the sway direction.

[0120] Figure 8 It is the actual response curve of the control signal in the heading direction.

[0121] Figure 9 is the response curve of the tracking error. DETAILED DESCRIPTION

[0122] The present invention will be further described in detail below with reference to the accompanying drawings and examples, but the present invention is not limited to the following examples.

[0123] Example 1

[0124] The fixed-time fault-tolerant tracking model of the unmanned underwater vehicle in this embodiment is composed of the kinematic model and dynamic models constitute.

[0125] Kinematic model of this embodiment As shown in formula (1):

[0126]

[0127] Where η represents the position (x, y) and heading ψ∈[0, 2π) vectors, and v represents the velocity vector composed of swell u, sway υ, and pitch r. 3×3 Represents a rotation matrix.

[0128] The kinetic model of this embodiment As shown in formula (2):

[0129]

[0130] Among them, d n represents external interference, τ n represents the longitudinal surge force τ nu , lateral force τ nυ , yaw moment τ nr The control input vector composed of n ∈R 3×3 、C n ∈R 3×3 、D n ∈R 3×3 denote the inertia matrix, Coriolis matrix and damping matrix respectively, m is the total mass of the unmanned underwater vehicle, I z is the torque, x g is the distance from the center of gravity to the origin of the coordinate system, is the additional mass, X u 、Y υ 、N υ They represent the linear damping coefficients in surge, sway and pitch directions, respectively, and Y r 、N υ represents the sway-yaw coupling damping coefficient, ΔM, ΔC and ΔD are uncertain parameters; X |u|u 、Y |υ|υ 、N |r|r They represent the secondary damping coefficients in surge, sway and pitch directions, respectively, and Y |r|υ 、Y |υ|r 、N |r|υ 、N|υ|r represents the secondary damping coefficient of sway-yaw coupling.

[0131] In the kinematic model of formula (1) In this embodiment, the longitudinal surge force τ nu The maximum value of τ u，max 45N, minimum value -τ u，min is 45N; the lateral force τ nυ The maximum value of τ υ，max 45N, minimum value -τ υ，min is 45N; yaw moment τ nr The maximum value of τ r，max 10Nm, minimum value -τ r，min is 10Nm.

[0132] In the kinetic model of formula (2) In this embodiment, the value of m is 23.8, and x g The value is 0.046, I z The value is 1.76, The value is -2. The value is -10. The value is 0. The value is -1, X u The value is -0.7225, X |u|u The value is -1.3274, Y υ The value is -0.8896, Y |υ|υ The value is -36.4728, Y r The value is -7.25, Y |υ|r The value is -0.845, Y |r|r The value is -3.45, N υ The value is -0.0313, N |υ|υ The value is 3.9564, N |r|υ The value is 0.13, N r The value is -1.9, N |υ|r The value is 0.8, Y |r|υ The value is -0.805, N |r|r The value is -0.750, ΔM is 0.2sin(t)M, ΔC is 0.2sin(t)C, and ΔD is 0.2sin(t)D.

[0133] The method for constructing a fixed-time fault-tolerant tracking model for an unmanned underwater vehicle in this embodiment comprises the following steps:

[0134] (1) Determine known parameters and uncertain parameters

[0135] Press the formula to change M n 、Cn 、D n Divided into two categories: known parameters and uncertain parameters:

[0136] M n =M+ΔM

[0137] C n =C+ΔC

[0138] C n =C+ΔC

[0139] Among them, M, C, and D are known parameters, and ΔM, ΔC, and ΔD are uncertain parameters. The kinetic model can be expressed as:

[0140]

[0141] (2) Input constraints

[0142] Input constraint τ according to formula (4) n :

[0143]

[0144] Where τ represents the ideal input signal generated by the subsequent controller, φ represents the diagonal matrix of multiplicative faults, and its components satisfy 0<φ i - ≤φ i ≤φ i + ≤1,φ i - and φ i + Two positive constants, φ in this embodiment i - ≤φ i ≤φ i + φ i - The value is 0.4, φ i The value is 0.5, The value is 0.6, represents the additive fault vector, s τ (τ i ) represents τ i Saturation function subject to nonlinearity:

[0145]

[0146] Among them, τ i，max >0,τ i，min <0 represents the maximum and minimum limits of the control force and torque respectively; the smooth function g is used i (τ i ) instead of nonlinear sat(τi )for:

[0147]

[0148] in, Indicated by τ i is the Gaussian error function of the variable, sat(τ i ) is approximated as:

[0149] sat(τ i )=g i (τ i )+h i (τ i ) (7)

[0150] Among them, h(τ i ) represents the approximation error, satisfying |h i (τ i )|=|τ ni -g i (τ i )|≤Δ τ , Δ τ represents a positive upper bound on the error.

[0151] Determine the smooth function g according to formula (8) i (τ i ):

[0152]

[0153] Among them, χ i and It represents an intermediate variable, and the adjustment parameter l satisfies 0<l<1. In this embodiment, the value of l is 0.5.

[0154]

[0155] Among them, χ i Satisfying 0<χ i <1.

[0156] Determine the vector g(τ), vector h(τ), and diagonal matrix χ as follows:

[0157] g(τ)=[g u (τ u ), g υ (τ υ ), g r (τ r )] T ,

[0158] h(τ)=[h u (τ u ), h υ (τυ ), h r (τ r )] T

[0159] χ=diag{χ u , χ υ , χ r},

[0160] From formulas (5)-(9), we get formula (10):

[0161]

[0162] in, represents a positive definite diagonal matrix.

[0163] (3) Constructing dynamic and kinematic models

[0164]

[0165] Construct coordinates x1 and x2 as follows:

[0166]

[0167] The dynamic and kinematic models are transformed into:

[0168]

[0169] Where f represents the known kinetic model, d sum represents the integrated disturbance.

[0170] The dynamic model is constructed as shown in formula (1) and the kinematic model is constructed as shown in formula (2).

[0171] Figure 1 A flow chart of the method for controlling an unmanned underwater vehicle using a fixed time fault-tolerant tracking model is given. Figure 1 In this embodiment, the fixed-time fault-tolerant tracking model for controlling an unmanned underwater vehicle comprises the following steps:

[0172] (1) Constructing a smooth disturbance observer

[0173] 1) Determine the smooth disturbance observer according to formula (14):

[0174]

[0175] in, is the disturbance observer observation value, 0<m1<1, and m1 in this embodiment is 0.5. n1 is a finite positive number greater than 1, A∈R 3×3 and B∈R 3×3is a positive definite diagonal matrix, Θ(x2) represents the fuzzy basis function with x2 as the input variable.

[0176] Determine the update rate according to formula (15)

[0177]

[0178] in, Represents the estimated value of the fuzzy inference system weight, Γ represents the adaptive gain and is a finite positive number greater than 0, and σ represents the correction parameter and is a finite positive number greater than 0.

[0179] 2) Construct Lyapunov function V1:

[0180]

[0181] in, is the observation error of the smooth disturbance observer, is the estimation error, W * is the ideal weight of the fuzzy inference system.

[0182] 3) Determine the convergence region Φ1

[0183]

[0184] According to formula (17), There is an upper bound And from formula (16) we know further

[0185] (2) Constructing a tracking error dynamics model

[0186] 1) Construct an ideal smooth path η d

[0187] η d =[x d ,y d , ψ d ] T (18)

[0188] Its first-order differential and the second-order differential is known and bounded, satisfying:

[0189]

[0190] Among them, B0 is a positive number.

[0191] 2) Construct tracking error

[0192] According to formula (20), the tracking error e is constructed

[0193]

[0194] Among them, ψ a As the unmanned underwater vehicle approaches η d The approach angle, represents the Gaussian error function, a0 represents ψ d and arctan(H1) is the control parameter for the conversion rate.

[0195] 3) Build error state

[0196]

[0197] Combining formula (21) and formula (13), we can get:

[0198]

[0199] (3) Constructing a preset performance control method

[0200] 1) According to formula (23), the tracking error e is limited to:

[0201]

[0202] Among them, ρ i ∈ρ=[ρ1,ρ2,ρ3] T Indicates the preset performance function of the agreed time

[0203]

[0204] Where m2, n2, p2 and q2 are all finite positive odd numbers, satisfying m2<n2 and ρ2<q2. σ0, σ 01 and σ 02 are control parameters and are both finite positive numbers, ρ0 and ρ N represents the initial value and steady-state value of the preset performance function, N is a finite positive integer, satisfying ρ0>ρ N , and ρ0 and ρ N are all finite positive numbers, T b Indicates an agreed time that does not depend on the initial state, satisfying And ρ(t) remains unchanged, when t≥T b , sign represents the sign function.

[0205] 2) The conversion error function Λ(z i ) to convert:

[0206]

[0207] Among them, z i represents an intermediate scalar, and are control parameters and are all finite positive numbers;

[0208] The error vector γ is converted as follows:

[0209]

[0210] 3) Equation (28) can be written as a compact matrix as follows:

[0211]

[0212] (4) Constructing a preset sliding mode control surface

[0213] 1) Construct the sliding surface ζ according to formula (29):

[0214]

[0215]

[0216] Among them, μ 1i , μ 2i are all finite positive numbers, 0<m3<1, m3 in this embodiment is 0.5, n3 is a finite positive number greater than 1, ε e represents the control parameter and is a finite positive number;

[0217] 2) Determine the sliding surface error dynamic model

[0218]

[0219] Among them, π and Λ are intermediate variables.

[0220] (5) Constructing a fixed-time fault-tolerant controller

[0221] 1) Construct a fixed-time fault-tolerant controller τ according to formula (31):

[0222]

[0223] Wherein, 0<m4<1, n4 is a finite positive number greater than 1, μ3 and μ4 are both finite positive numbers, 0<α0<1, α0 in this embodiment is 0.5, μ5 is a finite positive number and satisfies μ5≥Δd sum , μ θ1 and μ θ2 are control parameters and are all finite positive numbers.

[0224] 2) Construct the fixed time arrival rate according to formula (32)

[0225]

[0226] Complete the control method of the unmanned underwater vehicle using the fixed-time fault-tolerant tracking model of the unmanned underwater vehicle.

[0227] Example 2

[0228] The fixed-time fault-tolerant tracking model of the unmanned underwater vehicle in this embodiment is composed of the kinematic model and dynamic models constitute.

[0229] The fixed-time fault-tolerant tracking model of the unmanned underwater vehicle in this embodiment is the same as that in embodiment 1. Kinematic model As shown in formula (1), the dynamic model As shown in formula (2), the expressions of formula (1) and formula (2) are the same as those in Example 1.

[0230] In formula (1) and formula (2), the meanings of variables and functions are the same as those in embodiment 1, and the meanings and value ranges of coefficients and constants are the same as those in embodiment 1.

[0231] The method for constructing a fixed-time fault-tolerant tracking model for an unmanned underwater vehicle in this embodiment comprises the following steps:

[0232] (1) Determine known parameters and uncertain parameters

[0233] This step is the same as in Example 1.

[0234] (2) Input constraints

[0235] Input constraint τ according to formula (4) n :

[0236] The expression of formula (4) is the same as that of Example 1.

[0237] In equation (4), φ represents the diagonal matrix of multiplicative faults, whose components satisfy 0<φ i - ≤φ i ≤φ i + ≤1, φ in this embodiment i - ≤φ i ≤φ i + φ i - The value is 0.1, φ i The value is 0.2, φ i + The value is 0.3.

[0238] Determine the smooth function g according to formula (8) i (τ i ):

[0239] The expression of formula (8) is the same as that of Example 1.

[0240] In formula (8), the adjustment parameter l satisfies 0<l<1, and the value of l in this embodiment is 0.1. The meanings and values ​​of other parameters and variables are the same as those in embodiment 1.

[0241] The other steps of this step are the same as those in Example 1.

[0242] The other steps are the same as those in Example 1. A fixed-time fault-tolerant tracking model for the unmanned underwater vehicle is constructed.

[0243] The control method of the fixed time fault-tolerant tracking model for an unmanned underwater vehicle in this embodiment comprises the following steps:

[0244] (1) Constructing a smooth disturbance observer

[0245] 1) Determine the smooth disturbance observer according to formula (14):

[0246] The expression of formula (14) is the same as that of Example 1.

[0247] In formula (14), 0<m1<1, and the value of m1 in this embodiment is 0.1. The meanings and values ​​of other parameters and variables are the same as those in embodiment 1.

[0248] The other steps of this step are the same as those in Example 1.

[0249] (2) Constructing a tracking error dynamics model

[0250] This step is the same as in Example 1.

[0251] (3) Constructing a preset performance control method

[0252] This step is the same as in Example 1.

[0253] (4) Constructing a preset sliding mode control surface

[0254] 1) Construct the sliding surface ζ according to formula (29):

[0255] The expression of formula (29) is the same as that of Example 1.

[0256] In formula (29), 0<m3<1, the value of m3 in this embodiment is 0.1, and the meanings and values ​​of other parameters and variables are the same as those in embodiment 1.

[0257] The other steps of this step are the same as those in Example 1.

[0258] (5) Constructing a fixed-time fault-tolerant controller

[0259] 1) Construct a fixed-time fault-tolerant controller τ according to formula (31):

[0260] The expression of formula (31) is the same as that of Example 1.

[0261] In formula (31), 0<α0<1, the value of α0 in this embodiment is 0.1, and the meanings and values ​​of other parameters and variables are the same as those in embodiment 1.

[0262] The other steps of this step are the same as those in Example 1.

[0263] The other steps are the same as those in Example 1. The method for controlling the unmanned underwater vehicle using the fixed-time fault-tolerant tracking model is completed.

[0264] Example 3

[0265] The fixed-time fault-tolerant tracking model of the unmanned underwater vehicle in this embodiment is composed of the kinematic model and dynamic models constitute.

[0266] The fixed-time fault-tolerant tracking model of the unmanned underwater vehicle in this embodiment is the same as that in embodiment 1. Kinematic model As shown in formula (1), the dynamic model As shown in formula (2), the expressions of formula (1) and formula (2) are the same as those in Example 1.

[0267] In formula (1) and formula (2), the meanings of variables and functions are the same as those in embodiment 1, and the meanings and value ranges of coefficients and constants are the same as those in embodiment 1.

[0268] The method for constructing a fixed-time fault-tolerant tracking model for an unmanned underwater vehicle in this embodiment comprises the following steps:

[0269] (1) Determine known parameters and uncertain parameters

[0270] This step is the same as in Example 1.

[0271] (2) Input constraints

[0272] Input constraint τ according to formula (4) n :

[0273] The expression of formula (4) is the same as that of Example 1.

[0274] In equation (4), φ represents the diagonal matrix of multiplicative faults, whose components satisfy 0<φ i - ≤φ i ≤φ i + ≤1, φ in this embodiment i -≤φ i ≤φ i + φ i - The value is 0.7, φ i The value is 0.8, φ i + The value is 0.9.

[0275] Determine the smooth function g according to formula (8) i (τ i ):

[0276] The expression of formula (8) is the same as that of Example 1.

[0277] In formula (8), the adjustment parameter l satisfies 0<l<1, and the value of l in this embodiment is 0.9. The meanings and values ​​of other parameters and variables are the same as those in embodiment 1.

[0278] The other steps of this step are the same as those in Example 1.

[0279] The other steps are the same as those in Example 1. A control model is constructed.

[0280] The method for controlling an unmanned underwater vehicle using a fixed-time fault-tolerant tracking model of the unmanned underwater vehicle of this embodiment comprises the following steps:

[0281] (1) Constructing a smooth disturbance observer

[0282] 1) Determine the smooth disturbance observer according to formula (14):

[0283] The expression of formula (14) is the same as that of Example 1.

[0284] In formula (14), 0<m1<1, and the value of m1 in this embodiment is 0.9. The meanings and values ​​of other parameters and variables are the same as those in embodiment 1.

[0285] The other steps of this step are the same as those in Example 1.

[0286] (2) Constructing a tracking error dynamics model

[0287] This step is the same as in Example 1.

[0288] (3) Constructing a preset performance control method

[0289] This step is the same as in Example 1.

[0290] (4) Constructing a preset sliding mode control surface

[0291] 1) Construct the sliding surface ζ according to formula (29):

[0292] The expression of formula (29) is the same as that of Example 1.

[0293] In formula (29), 0<m3<1, the value of m3 in this embodiment is 0.9, and the meanings and values ​​of other parameters and variables are the same as those in embodiment 1.

[0294] The other steps of this step are the same as those in Example 1.

[0295] (5) Constructing a fixed-time fault-tolerant controller

[0296] 1) Construct a fixed-time fault-tolerant controller τ according to formula (31):

[0297] The expression of formula (31) is the same as that of Example 1.

[0298] In formula (31), 0<α0<1, the value of α0 in this embodiment is 0.9, and the meanings and values ​​of other parameters and variables are the same as those in embodiment 1.

[0299] The other steps of this step are the same as those in Example 1.

[0300] The other steps are the same as those in Example 1. The control method of the control model for the unmanned underwater vehicle is completed.

[0301] In order to verify the beneficial effects of the present invention, a comparative simulation experiment was conducted using the control model of Example 1 of the present invention and two commonly used control methods, namely, a disturbance observer-based preset hypertorsional sliding mode controller (hereinafter referred to as DOPSSMC) and a fixed-time fault-tolerant preset performance control (hereinafter referred to as FTFTPPC). The experimental results are as follows:

[0302] 1. Set the comparative simulation experiment parameters

[0303] The fixed-time fault-tolerant tracking model of the unmanned underwater vehicle in Example 1 is adopted, and the parameter values ​​of the model are as follows:

[0304] In the kinematic model of formula (1) The kinetic model of formula (2) In the embodiment, the values ​​of variables and parameters are the same as those in embodiment 1.

[0305] The external disturbance d(t) is selected as follows:

[0306]

[0307] Ideal path η d The choices are as follows:

[0308]

[0309] The initial state η(0) is:

[0310] η(0)=[0m,3m,-π / 20rad] T and v = [0.1 m / s, 0.1 m / s, 0.1 rad / s] T

[0311] Multiplicative fault φ and additive fault The vector is:

[0312]

[0313] The disturbance observer parameters are:

[0314] N=20,

[0315] A=diag{0.45, 0.45, 0.45},

[0316] B=diag{0.5, 0.5, 0.5}, m1=0.75,

[0317] n1=1.15, σ=0.2, Γ=15I 3×3 ,

[0318] The preset performance control measurement parameters for the agreed time are:

[0319] m2=3, n2=5, p2=5, q2=7, σ 01 =0.16,σ 02 =0.21,ρ0=[ρ 0，1 ,ρ 0，2 ,ρ 0，3 ] T =[2, 2, 2] T ,ρ ∞ =[ρ ∞，1 ,ρ ∞，2 ,ρ ∞，3 ] T =[0.1, 0.1, 0.1] T ,

[0320] The fixed-time fault-tolerant controller parameters are:

[0321] μ1=diag{3.5, 3.5, 3.5}, μ2=diag{0.15, 0.15, 0.15}, μ3=10, μ4=10, μ5=2, μ θ1 =50,μ θ2 =50, α0=0.3, n3=7 / 5, n4>13 / 9, m3=5 / 7, m4=9 / 13, ε e =5 / 7.

[0322] 2. Determine the evaluation indicators of experimental effects

[0323] The convergence time (hereafter referred to as CT), integrated absolute error (hereafter referred to as IAE), integrated time weighted absolute error (hereafter referred to as ITAE), and average squared control input (hereafter referred to as ASC) are used as quantitative evaluation indicators.

[0324] 3. Experimental results

[0325] The simulation and comparison experimental results are shown in Figure 2-9 and Table 1.

[0326] Figure 2 Given the ideal path trajectory and actual position trajectory diagram, Figure 2 It can be seen that the proposed controller has good tracking performance.

[0327] Figure 3 The comparison curve of the lumped disturbance and its estimated value is given.

[0328] Figure 4 The convergence curve of the disturbance observer's observation error is given.

[0329] Figure 5 The weight norm curve of the fuzzy inference observer is given.

[0330] Figure 3 、 4 、 Figure 5 The results show that the disturbance observer can accurately estimate the lumped disturbance.

[0331] Figure 6 The actual response curve of the control signal in the longitudinal surge direction is given.

[0332] Figure 7 The actual response curve of the control signal in the sway direction is given.

[0333] Figure 8 The actual response curve of the control signal in the heading direction is given.

[0334] As can be seen from Figures 6, 7, and 8, the present invention controls the input to not exceed the saturation level of the preset amplitude, thereby avoiding system chattering in the event of actuator failure and input saturation.

[0335] Figure 9 The response curve of the tracking error is given by Figure 9 It can be seen that within the specified time, the tracking errors converge to a neighborhood near zero and evolve strictly within the specified performance range.

[0336] Table 1 Comparative experimental results of Example 1 and comparative experimental method

[0337] plan CT IAE ITAE ASC DOPSSMC 4.75 7.54 20.36 7.05 FTFTPPC 4.54 7.18 19.58 6.87 The present invention 3.43 6.34 16.63 6.71

[0338] In Table 1, the tracking errors of all three methods converged to near-zero before the preset convergence time limit. Compared with the other methods, the method in Example 1 demonstrates a faster convergence response and effectively controls the system to offset lumped interference. The lower IAE and ITAE values ​​demonstrate that the present invention exhibits superior transient and steady-state performance. Furthermore, the present invention exhibits the lowest ASC value, demonstrating higher efficiency.

Claims

1. A fixed-time fault-tolerant tracking model for unmanned underwater vehicles, characterized by The model consists of a kinematic model and dynamic models constitute; The kinematic model As shown in formula (1): Where η represents the vector of position (x, y) and heading ψ∈[0, 2π), v represents the velocity vector composed of sway u, sway v and pitch r, and J(ψ)∈R 3×3 represents the rotation matrix; The kinetic model As shown in formula (2): Among them, d n represents external interference, τ n represents the longitudinal surge force τ nu , lateral force τ nv , yaw moment τ nr The control input vector composed of n ∈R 3×3 、C n ∈R 3×3 、D n ∈R 3×3 denote the inertia matrix, Coriolis matrix and damping matrix respectively, m is the total mass of the unmanned underwater vehicle, I z is the torque, x g is the distance from the center of gravity to the origin of the coordinate system, is the additional mass, X u 、Y v 、N v They represent the linear damping coefficients in surge, sway and pitch directions, respectively, and Y r 、N v represents the sway-yaw coupling damping coefficient, ΔM, ΔC and ΔD are uncertain parameters; X |u|u 、Y |v|v 、N |r|r They represent the secondary damping coefficients in surge, sway and pitch directions, respectively, and Y |r|v 、Y |v|r 、N |r|v 、N |v|r represents the secondary damping coefficient of sway-yaw coupling.

2. The fixed-time fault-tolerant tracking model for unmanned underwater vehicles according to claim 1, characterized in that: In the kinematic model of formula (1) The longitudinal surge force τ nu The maximum value of τ u，maX 45N, minimum value -τ u，min is 45N; the lateral force τ nv The maximum value of τ v，max 45N, minimum value -τ v，min is 45N; yaw moment τ nr The maximum value of τ r，max 10Nm, minimum value -τ r，min is 10Nm.

3. The fixed-time fault-tolerant tracking model for unmanned underwater vehicles according to claim 1, characterized in that: In the kinetic model of formula (2) In the example, m is 23.8, x g The value is 0.046, I z The value is 1.76, The value is -2. The value is -10. The value is 0. The value is -1, X u The value is -0.7225, X |u|u The value is -1.3274, Y v The value is -0.8896, Y |v|v The value is -36.4728, Y r The value is -7.25, Y |v|r The value is -0.845, Y |r|r The value is -3.45, N v The value is -0.0313, N |v|v The value is 3.9564, N |r|v The value is 0.13, N r The value is -1.9, N |v|r The value is 0.8, Y |r|v The value is -0.805, N |r|r The value is -0.750, ΔM is 0.2sin(t)M, ΔC is 0.2sin(t)C, and ΔD is 0.2sin(t)D.

4. A method for constructing a fixed-time fault-tolerant tracking model for an unmanned underwater vehicle according to claim 1, characterized in that It consists of the following steps: (1) Determine known parameters and uncertain parameters Press the formula to change M n 、C n 、D n Divided into known parameters and uncertain parameters: M n =M+ΔM C n =C+ΔC C n =C+ΔC Among them, M, C, and D are known parameters, and ΔM, ΔC, and ΔD are uncertain parameters. The kinetic model can be expressed as: (2) Input constraints Input constraint τ according to formula (4) n : τ=[τ u ,t v ,t r ] T φ=diag{φ u ,f v ,f r } s τ (τ)=[s τ (t u ),s τ (t v ),s τ (t r )] T sat(τ)=[sat(τ u ),sat(τ v ),sat(τ r )] T Where τ represents the ideal input signal generated by the subsequent controller, φ represents the diagonal matrix of multiplicative faults, and its components satisfy 0<φ i - ≤φ i ≤φ i + ≤1,φ i - and φ i + Two positive constants, represents the additive fault vector, s τ (τ i ) represents τ i Saturation function subject to nonlinearity: Among them, τ i，max >0,τ i，min <0 represents the maximum and minimum limits of the control force and torque respectively; the smooth function g is used i (τ i ) instead of nonlinear sat(τ i )for: in, Indicated by τ i is the Gaussian error function of the variable, sat(τ i ) is approximated as: sat(t i )=g i (t i )+h i (t i ) (7) Among them, h(τ i ) represents the approximation error, satisfying |h i (τ i )|=|τ ni -g i (τ i )|≤Δ τ , Δ τ represents a positive upper bound on the error; Determine the smooth function g according to formula (8) i (τ i ): Among them, χ i and Represents the intermediate variable, and the adjustment parameter l satisfies 0<l<1; Among them, χ i Satisfying 0<χ i <1; Determine the vector g(τ), vector h(τ), and diagonal matrix χ as follows: g(τ)=[g u (t u ),g v (t v ),g r (t r )] T , h(τ)=[h u (t u ),h v (t v ),h r (t r )] T x=diag{x u ,x v ,x r }, From formulas (5)-(9), we get formula (10): in, represents a positive definite diagonal matrix; (3) Constructing dynamic and kinematic models Construct coordinates x1 and x2 according to formula (12): According to formula (13), the dynamic and kinematic models are transformed into: Where f represents the known kinetic model, d sum represents the integrated disturbance; The dynamic model is constructed as shown in formula (1) and the kinematic model is constructed as shown in formula (2).

5. A method for controlling an unmanned underwater vehicle using a fixed time fault-tolerant tracking model according to claim 1, characterized in that It consists of the following steps: (1) Constructing a smooth disturbance observer 1) Determine the smooth disturbance observer according to formula (14): in, is the observation value of the disturbance observer, 0<m1<1, n1 is a finite positive number greater than 1, A∈R 3×3 and B∈R 3×3 is a positive definite diagonal matrix, Θ(x2) represents the fuzzy basis function with x2 as the input variable; Determine the update rate according to formula (15) in, represents the estimated value of the fuzzy inference system weight, Γ represents the adaptive gain and is a finite positive number greater than 0, σ represents the correction parameter and is a finite positive number greater than 0; 2) Construct Lyapunov function V1: in, is the observation error of the smooth disturbance observer, is the estimation error, W * is the ideal weight of the fuzzy inference system; 3) Determine the convergence region Φ1 According to formula (17), There is an upper bound And from formula (16) we know further (2) Constructing a tracking error dynamics model 1) Construct an ideal smooth path η d or d =[x d ,y d ,ψ d ] T (18) Its first-order differential and the second-order differential is known and bounded, satisfying: Among them, B0 is a positive number; 2) Construct tracking error According to formula (20), the tracking error e is constructed Among them, ψ a As the unmanned underwater vehicle approaches η d The approach angle, represents the Gaussian error function, a0 represents ψ d and arctan(H1) are the control parameters for the conversion rate; 3) Build error state Combining formula (21) and formula (13), we can get (3) Constructing a preset performance control method 1) According to formula (23), the tracking error e is limited to: Among them, ρ i ∈ρ=[ρ1,ρ2,ρ3] T Indicates the preset performance function of the agreed time Where m2, n2, p2 and q2 are all finite positive odd numbers, satisfying m2<n2 and p2<q2. 01 and σ 02 are control parameters and are both finite positive numbers, ρ0 and ρ N represents the initial value and steady-state value of the preset performance function, N is a finite positive integer, satisfying ρ0>ρ N , and ρ0 and ρ N are all finite positive numbers, T b Indicates an agreed time that does not depend on the initial state, satisfying And ρ(t) remains unchanged when t≥T b .sign represents the sign function; 2) The conversion error function Λ(z i ) to convert: z i =e i / ρ i Among them, z i represents an intermediate scalar, and are control parameters and are all finite positive numbers; The error vector γ is converted as follows: γ=[γ1,γ2,γ3] T (26) Ξ=diag[Ξ1,Ξ2,Ξ3] H=diag[H1,H2,H3] H i =ρ i Formula (28) can be written into a compact matrix form as follows: (4) Constructing a preset sliding mode control surface 1) Construct the sliding surface ζ according to formula (29): μ1=diag{μ 11 ,m 12 ,m 13 } μ2=diag{μ 21 ,m 22 ,m 23 } p1=[p 11 ,p 12 ,p 13 ] T p2=[p 21 ,p 22 ,p 23 ] T Among them, μ 1i , μ 2i are all finite positive numbers, 0<m3<1, n3 is a finite positive number greater than 1, ε e represents the control parameter and is a finite positive number; 2) Determine the sliding surface error dynamic model Among them, π(γ) and Λ are intermediate variables; (5) Constructing a fixed-time fault-tolerant controller 1) Construct a fixed-time fault-tolerant controller τ according to formula (31): Where, 0<m4<1, n4 is a finite positive number greater than 1, μ3 and μ4 are both finite positive numbers, 0<α0<1, μ5 is a finite positive number and satisfies μ5≥Δd sum , μ θ1 and μ θ2 are control parameters and are all finite positive numbers. 2) Construct the fixed time arrival rate according to formula (32)

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