Unmanned underwater vehicle trajectory tracking control system based on preset time and performance

Abstract

The invention provides an unmanned underwater vehicle trajectory tracking control system based on preset time and performance, and aims to improve trajectory tracking precision and stability in underwater operation tasks. The method comprises the following steps: establishing an unmanned underwater vehicle mathematical model; designing a preset time preset performance function, and introducing an adjustable function changing along with time to enable the boundary function to have a smooth characteristic in a convergence process; a time-varying gain auxiliary system is adopted to process an input saturation problem; designing a disturbance observer to realize rapid attenuation of disturbance, and enhancing the robustness of the system by introducing a residual adjustment function based on a smooth nonlinear model; and finally, integrating the interference observer and an auxiliary system to deduce a trajectory tracking scheme. The result shows that the longitudinal speed fluctuation is reduced by 69.2%, and the swaying speed fluctuation is reduced by 32.7%; the north position tracking performance is improved by 30.8%, the east position tracking performance is improved by 16.7%, the speed fluctuation is effectively reduced, and the tracking performance, the system stability and the anti-interference capability are improved.

Description

Technical Field

[0001] The present invention relates to the field of marine engineering detection and control equipment, in particular to unmanned systems and robot control, and specifically to an unmanned underwater vehicle trajectory tracking control system based on preset time and performance. Background Art

[0002] Unmanned underwater vehicles play a vital role in the fields of ocean exploration, environmental monitoring, marine water quality and ecological element assessment, scientific research and military missions. With the increasing attention paid to marine resources and the increasing demand for underwater salvage equipment, the application demand for unmanned underwater vehicles continues to expand, which puts higher requirements on their motion control technology. In the trajectory tracking control of unmanned underwater vehicles, achieving high-precision and stable control is the key to ensuring the success of their missions. In recent years, in order to improve the trajectory tracking performance of unmanned underwater vehicles, researchers have continuously explored and innovated in controller design, intelligent perception and control equipment manufacturing, and control system innovation. Among them, preset time preset performance control technology has become an important research direction. The preset time preset performance trajectory tracking control system can complete the tracking of the target trajectory within the preset time, which is of great significance to improving the performance of unmanned underwater vehicles in dynamic environments.

[0003] (1) In the paper "Ship Trajectory Tracking with Adaptive Neural Network Based on Preset Performance", a ship trajectory tracking control strategy with preset performance requirements is proposed to solve the ship trajectory tracking problem under the interference of model parameter perturbations and external unknown ocean environment. However, the error conversion function is complex to calculate, and the inverse transformation calculation of the error conversion function takes a long time. The convergence speed is slow when processing errors, especially when the error is large, the dynamic response of the system is not fast, which will become a significant disadvantage in application scenarios with high real-time requirements.

[0004] (2) In the paper "Ship trajectory tracking dynamic surface control with preset performance", a ship trajectory tracking system controller with preset performance is designed to achieve accurate trajectory tracking of underactuated ships. Patent CN107015562A "A control method for underactuated surface ships meeting preset tracking performance" effectively solves the control difficulties of underactuated ships and achieves accurate tracking of any smooth trajectory. Patent CN112363393A "Model-free adaptive preset performance control method for unmanned boat dynamic positioning" provides a model-free adaptive preset performance control method for unmanned boat dynamic positioning, which can achieve preset performance control under external disturbances and input saturation. In the paper "Spacecraft attitude tracking control method based on preset performance", the rapid attitude maneuvering and tracking problem of flexible spacecraft is studied, and a trajectory planning strategy combining time optimization and flexible component vibration suppression, as well as a control law for preset tracking error response are proposed. However, the above control methods do not clearly specify the time required for the system to achieve the target accuracy, and lack preset time control. Therefore, the system response time is not accurate enough to ensure that the expected performance requirements are achieved within a specific time, affecting the overall performance of the system.

[0005] (3) Patent CN115617044A "Non-singular finite-time preset performance dynamic positioning control method and system for unmanned boats": ensure non-singular finite-time preset performance dynamic positioning control of unmanned boats in the presence of model uncertainty and input saturation constraints. Patent CN113238572A "Preset time quadcopter attitude tracking method based on preset performance control" proposes a quadcopter attitude tracking method based on preset performance control, which achieves high-precision trajectory tracking of the quadcopter within a preset time by establishing an attitude error dynamics model. However, the finite-time operator it uses is a function similar to a power function, with a high initial rate, which will lead to a significant increase in the amount of control in the initial stage. A larger amount of control usually means that the system needs to consume more energy. This may increase operating costs, especially in application scenarios where energy is limited or high efficiency is required.

[0006] (4) In the paper "Preset Control of Dynamic Performance of Trajectory Tracking for Autonomous Underwater Vehicles under Underactuated Conditions", a three-dimensional trajectory tracking control method with preset dynamic performance and convergence time is proposed to solve the high-performance trajectory tracking requirements of underactuated underwater vehicles under complex disturbances and parameter uncertainties. However, when a process function in the form of a sine function is used in the preset performance part, the error will fluctuate due to the periodicity and volatility of the sine function. This fluctuation may cause the system to deviate further from the target state at certain moments. In addition, the oscillatory characteristics of the sine function itself may introduce additional system oscillations.

[0007] (5) In the paper "Prescribed time observer-based trajectory tracking control of autonomous underwater vehicle with tracking error constraints", a disturbance observer and an auxiliary dynamic system with time-varying gain are proposed to solve the trajectory tracking problem of underwater vehicles under input saturation and unknown disturbances, and to achieve disturbance attenuation and tracking control within a preset time. However, the performance function used is a traditional performance function, which cannot define its convergence time, has low adaptability and practicality, and cannot flexibly change the shape of the function, which makes it impossible to flexibly design a high-performance controller. Summary of the invention

[0008] Based on the above problems, the present invention combines the preset time disturbance observer with the time-varying gain auxiliary dynamic system and embeds it into the preset performance control framework. By introducing the time-varying gain, the convergence time of the preset performance function can be flexibly set by the user, thereby designing an unmanned submersible trajectory tracking control system based on preset time and performance. The problem of excessive control quantity in the initial control stage is solved, the speed fluctuation of the unmanned submersible in the process of tracking the preset trajectory is reduced, and the tracking accuracy of the unmanned submersible is improved.

[0009] To achieve the above objectives, the present invention proposes an unmanned underwater vehicle trajectory tracking control system based on preset time and performance, the system comprising: an auxiliary dynamic system, a preset time interference observer, a preset time controller and an error conversion part.

[0010] S1: Establish an unmanned underwater vehicle model;

[0011] S1.1: The motion of an unmanned underwater vehicle can be expressed by a three-degree-of-freedom nonlinear equation:

[0012]

[0013] Where: η=[x,y,ψ] T is the position vector in the earth-fixed coordinate system, x, y and ψ represent the position and heading angle of the unmanned underwater vehicle respectively; v = [u, v, r] T represents the velocity in the fixed coordinate system, u, v and r represent the longitudinal, sway and yaw angular velocities respectively, and R(ψ) represents the rotation matrix;

[0014]

[0015] In the presence of external disturbances and input saturation, the dynamic equation of the unmanned underwater vehicle can be expressed as:

[0016]

[0017] Where: M is the inertia matrix, C(v) is the Coriolis matrix, D(v) is the damping matrix, g(η) is the restoring force and torque generated by gravity / buoyancy, d(t) = [d1, d2, d3] T Represents unknown external interference. τ=[τ1,τ2,τ3] T represents the actual control input of the unmanned underwater vehicle, τ c =[τ c1 ,τ c2 ,τ c3 ] T Represents the input calculated by the control system. Δτ=τ-τ c Represents τ and τ c The difference between τ and τ c The relationship between can be described as:

[0018]

[0019] Where: τ max i is the maximum allowable control input of the UUV.

[0020] S1.2: Introduce a time-varying function used in the performance function, the mathematical form is as follows:

[0021]

[0022] In the formula: m∈(0,ln(2) / T f ], T f represents the maximum allowable setting time, in t∈[0,T f ) ρ (t) from the initial value exp[mT f ]-1 decays to a small positive number close to zero, and then at t∈[T f ,∞) increases monotonically, which means μ ρ (t) is always a positive number.

[0023] S2: Design a preset time and preset performance function. The present invention applies the following performance specifications to the error state:

[0024] -δ 1k ρ k (t)<e i (t)<δ 2k ρ k (t),t>0 (6)

[0025] Where: 1k ρ k(t),δ 2k ρ k (t) represent the upper and lower boundaries of the tracking error respectively; δ 1k , δ 2k is the design parameter, e i (t) represents the tracking error, ρ k (t)=[ρ1(t),ρ2(t),ρ3(t)] T is a bounded strictly positive decreasing smooth function.

[0026] The preset time preset performance function is designed as:

[0027]

[0028] Where: k ρ 、c ρ is a positive definite design matrix, ρ kTf For the defined parameters, As shown below;

[0029]

[0030] Where: T m For transition time, where ρ k (0) is a design parameter, f ρk As shown below:

[0031]

[0032]

[0033]

[0034] Where:

[0035] S3: Design the controller. The design goal here is to ensure that the tracking error and the estimation error converge within the preset time through the design of the control law. And ensure that the preset constraints are not violated during the tracking process. The design process is as follows:

[0036] S3.1: Define s1 = [s 11 ,s 12 ,s 13 ] T , Ψ = diag (Ψ1, Ψ2, Ψ3), Φ = diag (Φ1, Φ2, Φ3), where

[0037] where Ψ is a diagonal matrix, Ψ i Non-zero means that the matrix has full rank, so Ψ is an invertible matrix.

[0038] Tracking error is defined as e = [e1, e2, e3] T =η-η d , η d For the desired trajectory, the present invention aims to design an appropriate controller so that the tracking error always meets the requirements, and the error conversion is defined as follows:

[0039]

[0040]

[0041] Ψ i =(1 / 2(e i +δ 1k ρ k )-1 / 2(e i +δ 2k ρ k )) (14)

[0042]

[0043] Assuming α is used as a virtual intermediate signal, the present invention selects the following virtual control law:

[0044]

[0045]

[0046] Where: K1 and C1 are positive definite design matrices, and C1 satisfies T E is a positive design parameter m∈(0,ln(2) / T], where T represents the maximum allowable setting time.

[0047] In order to deal with input saturation, the following auxiliary dynamic system is constructed:

[0048]

[0049] Where: K ε , K2, C2 and is a positive parameter of the design, C2 satisfies ε is the state vector of the system, s2=v-α.

[0050] S3.2: Then, the interference observer is designed to construct the preset time interference observer as shown in the following equations (19)-(20) to achieve rapid estimation and compensation of interference, thereby reducing the impact of interference on the system.

[0051]

[0052] Where: represents an estimate of interference;

[0053]

[0054] Where: γ, υ, k a , C a and ω=diag(ω1,ω2,ω3) are positive design parameters, I 3×1 represents a unit vector, is the estimated state variable of s2, is the state estimation error vector;

[0055] In order to track the reference trajectory within the predetermined time, the trajectory tracking control law is designed as:

[0056]

[0057] Where: K3 and C3 are positive definite design matrices, and C3 satisfies The present invention has the following beneficial effects:

[0058] (1) Compared with the traditional preset performance function, the preset time preset performance function adopted by the present invention has significant advantages. The preset performance function allows the user to independently set the convergence time, making the convergence characteristics of the system more flexible and easy to control. In addition, a time-related adjustable function is introduced into the preset time function to accurately optimize its time response characteristics. By adjusting T m , users can flexibly adjust the form of the function to better adapt to specific application requirements and thus improve the overall performance of the controller.

[0059] (2) The improved system exhibits excellent asymptotic characteristics when approaching the target value. Compared with the previous design, the new design can approach the final value more smoothly, avoiding the rapid changes or instability that may occur in the original system when approaching the target. This can effectively reduce system jitter and improve the stability and accuracy of the control process. In the present invention, the speed fluctuation during the tracking process is significantly reduced, the fluctuation amplitude of the longitudinal speed u is reduced by 69.2%, and the fluctuation amplitude of the lateral speed v is reduced by 32.7%. The reduction in fluctuation amplitude indicates that the speed control of the system is smoother, avoiding frequent acceleration and deceleration, thereby effectively reducing overall energy consumption, reducing operating costs, and improving the economy and efficiency of the system.

[0060] (3) In the context of the present invention, in order to further enhance the robustness of the system, a residual adjustment mechanism is introduced into the interference observer. The residual adjustment function adopted by the present invention is based on a smooth nonlinear model. The action mechanism of the model is based on the conversion from discontinuous to continuous. A smooth transition zone is introduced to replace the hard switching of the function in the traditional residual adjustment mechanism. The model shows excellent robustness in dealing with external disturbances and noise. By slowing down the fluctuations of the control signal caused by noise and disturbance, the tracking stability of the system in complex environments is significantly improved. In the simulation, the tracking performance of the system at the north position x is improved by 30.8%, and the tracking performance at the east position y is improved by 16.7%. This shows that the designed system has a significant improvement in tracking accuracy and can quickly correct the deviation from the reference trajectory, thereby more accurately tracking the desired trajectory. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a block diagram of the trajectory tracking control system of an unmanned underwater vehicle based on preset time and performance;

[0062] Figure 2 It is a comparison chart of different preset performance functions;

[0063] Figure 3 It is the trajectory tracking result diagram;

[0064] Figure 4 It is the tracking result diagram of each component;

[0065] Figure 5 is the tracking error and constraint graph;

[0066] Figure 6 is an interference estimation result diagram of the present invention;

[0067] Figure 7 It is a graph of interference estimation results of comparative papers;

[0068] Figure 8 is the control input diagram of the present invention;

[0069] Fig. 9 It is a control input graph of the comparative paper;

[0070] Fig.10 It is a trajectory tracking comparison chart;

[0071] Fig.11 It is a speed comparison chart. DETAILED DESCRIPTION

[0072] The technical solutions in the embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. It should be noted that the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0073] Embodiment: The present invention is further described below in conjunction with the accompanying drawings;

[0074] The specific steps are as follows:

[0075] S1: Figure 1 As shown, Figure 1 This is a block diagram of an unmanned underwater vehicle trajectory tracking control system based on preset time and performance, including: unmanned underwater vehicle mathematical model, preset time preset performance function, error conversion function, disturbance observer, auxiliary system. First, the unmanned underwater vehicle model is established to lay a theoretical foundation for the subsequent preset time preset performance control design, and the assumptions, definitions, theorems and functions used in the subsequent stability proof process are pointed out. The process is as follows:

[0076] S1.1: The motion of an unmanned underwater vehicle can be expressed by a three-degree-of-freedom nonlinear equation:

[0077]

[0078] Where: η=[x,y,ψ] T is the position vector in the earth-fixed coordinate system, x, y and ψ represent the position and heading angle of the unmanned underwater vehicle respectively; v = [u, v, r] T represents the velocity in the fixed coordinate system, u, v and r represent the longitudinal, sway and yaw angular velocities respectively, and R(ψ) represents the rotation matrix, which is expressed by the following formula:

[0079]

[0080] In the presence of external disturbances and input saturation, the dynamic equation of the unmanned underwater vehicle can be expressed as:

[0081]

[0082] Where: M is the inertia matrix, C(v) is the Coriolis matrix, D(v) is the damping matrix, g(η) is the restoring force and torque generated by gravity / buoyancy, d(t) = [d1, d2, d3] T represents unknown external disturbance, τ=[τ1,τ2,τ3] T represents the actual control input of the unmanned underwater vehicle, τ c =[τ c1 ,τ c2,τ c3 ] T represents the input calculated by the control system, Δτ=τ-τ c Represents τ and τ c The difference between τ and τ c The relationship between can be described as:

[0083]

[0084] Where: τ max i is the maximum allowable control input of the UUV.

[0085] S1.2: Establish the necessary definitions and lemmas for subsequent proofs;

[0086] A time-varying function is introduced to be used in the performance function. The mathematical form is as follows:

[0087]

[0088] In the formula: m∈(0,ln(2) / T f ], T f represents the maximum allowable setting time. f ) ρ (t) from the initial value exp[mT f ]-1 decays to a small positive number close to zero, and then at t∈[T f ,∞) increases monotonically, which means μ ρ (t) is always a positive number.

[0089] Definition 1: For the following system

[0090]

[0091] Where: represents the state vector, and f(·) represents a locally uniformly bounded function. Assuming that (27) is globally uniformly asymptotically stable, it is also globally uniformly finite-time stable. In addition, there exists a locally bounded function T h (·), so that for all t>T h (σ0), σ(t,σ0) = 0 holds, where σ(t,σ0) is any solution of the Cauchy problem of equation (27), and T h (·) is called a steady-state time function.

[0092] Definition 2: Assume that equation (27) has a preset time T h A globally finite-time stable system, namely T h Can be predefined as T p ≤T h ≤Tmax <∞, where T p represents the physically possible time range. Formula (27) can ensure convergence within the preset time.

[0093] Lemma 1: Assume a continuously differentiable function V(σ(t), t) satisfies

[0094] V(0,t)=0 V(σ(t),t)>0 (28)

[0095]

[0096] Where: l is a design parameter, then Equation (27) can ensure the convergence of the preset time, and the convergence time is T h .

[0097] The following assumptions need to be made to facilitate controller design:

[0098] Assumption 1: The external environmental disturbance to the unmanned underwater vehicle is bounded and changes slowly over time.

[0099] Assumption 2: The saturation difference Δτ is limited to the range ||Δτ||≤τ, where τ is a known constant.

[0100] Assumption 3: The initial error satisfies the proposed error constraint -δ 1k ρ k (t)<e i (t)<δ 2k ρ k (t), t>0.

[0101] S2: Design a preset time and preset performance function. To ensure high performance, the present invention applies the following performance specifications to the error state:

[0102] -δ 1k ρ k (t)<e i (t)<δ 2k ρ k (t), t>0 (30)

[0103] Where: 1k ρ k (t),δ 2k ρ k (t) represent the upper and lower boundaries of the tracking error respectively; δ 1k , δ 2k is the design parameter, e i (t) represents the tracking error, ρ k (t)=[ρ1(t),ρ2(t),ρ3(t)]T is a bounded strictly positive decreasing smooth function.

[0104] The preset time preset performance function is designed as:

[0105]

[0106] Where: k ρ 、c ρ is a positive definite design matrix, For the defined parameters, As shown below:

[0107]

[0108] Where: T m For transition time, where ρ k (0) is a design parameter, f ρk As shown below:

[0109]

[0110]

[0111]

[0112] Where:

[0113] Theorem 1: Considering the preset time preset performance function given by equations (31) to (33), the state ρ k You can set the time T f Converges to ρ kTf , for t∈[T f ,∞), Established.

[0114] Proof: Define the error as Taking the derivative, we get the following expression:

[0115]

[0116] Decompose formula (36):

[0117]

[0118]

[0119] From Lemma 1, we can see that You can set the time T f converges to zero, and in addition satisfy and When T>T f Therefore, the proposed preset time preset performance function can be used at the preset time T f Converges to ρ kTf , Theorem 1 is proved. In the following content, in order to verify the superiority of the designed preset time preset performance function, several other representative preset performance functions are introduced as follows:

[0120] First, a traditional preset performance function is introduced as follows:

[0121] ρ(t)=(ρ0-ρ Tf )exp(-κt)+ρ Tf (39)

[0122] Where: ρ0,κ>0 is a design parameter;

[0123] In addition, a fixed-time preset performance function is defined as follows:

[0124]

[0125] Figure 2 The comparison of several different preset performance functions is shown. The introduction of a time-dependent adjustable function makes the boundary function have a smooth transition characteristic during the convergence process, which has a positive impact on the system performance. This shows that the preset time preset performance function not only makes the convergence time flexible and controllable, but also has flexibility in shape, making it easier to design a high-performance controller.

[0126] S3: Design the controller. The design goal here is to ensure that the tracking error and the estimation error converge within the preset time through the design of the control law. And ensure that the preset constraints are not violated during the tracking process. The design process is as follows:

[0127] S3.1: Define s1 = [s 11 ,s 12 ,s 13 ] T , Ψ = diag (Ψ1, Ψ2, Ψ3), Φ = diag (Φ1, Φ2, Φ3), where

[0128] Ψ is a diagonal matrix, Ψ i Non-zero means that the matrix has full rank, so Ψ is an invertible matrix.

[0129] Tracking error is defined as e = [e1, e2, e3] T =η-η d , η d For the desired trajectory, the present invention aims to design an appropriate controller so that the tracking error always meets the requirements, and the error conversion is defined as follows:

[0130]

[0131]

[0132] Ψ i =(1 / 2(e i +δ 1k ρ k )-1 / 2(e i +δ 2k ρ k )) (43)

[0133]

[0134] Then consider the Lyapunov candidate function Its derivative is:

[0135]

[0136] Assuming α is used as a virtual intermediate signal, the present invention selects the following virtual control law:

[0137]

[0138]

[0139] Where: K1 and C1 are positive definite design matrices, and C1 satisfies T E is a positive design parameter, m∈(0,ln(2) / T], where T represents the maximum allowable setting time;

[0140] Next, define the speed error vector as s2=v-α, and then substitute v=s2+α and the virtual control law (46) into (45) to obtain:

[0141]

[0142] In order to deal with input saturation, the following auxiliary dynamic system is constructed:

[0143]

[0144] Where: K ε , K2, C2 and is a positive parameter of the design, C2 satisfies ε is the state vector of the system, s2 = v-α;

[0145] In formula (49), to avoid singularity, is a small positive constant close to zero. To ensure the normal operation of the auxiliary dynamic system at the beginning of automatic control, the initial state of ε should satisfy

[0146] S3.2: Construct a preset time interference observer as shown in equations (29)-(30) below to achieve rapid estimation and compensation of interference, thereby reducing the impact of interference on the system.

[0147]

[0148] Where: represents an estimate of interference;

[0149]

[0150] Where: γ, υ, k a , C a and ω=diag(ω1,ω2,ω3) are positive design parameters, I 3×1 represents a unit vector, is the estimated state variable of s2, is the state estimation error vector;

[0151] Next, consider the Lyapunov candidate function

[0152]

[0153] In order to track the reference trajectory within the predetermined time, the trajectory tracking control law is designed as:

[0154]

[0155] Where: K3 and C3 are positive definite design matrices, and C3 satisfies Substituting formula (53) into formula (52) yields:

[0156]

[0157] S4: Stability analysis:

[0158] Theorem 2: Considering the unmanned underwater vehicle (22) and (24) under assumption 1, the constructed disturbance observer (50) and (51) ensure that the state estimation error Converges to a compact set Ω within a preset time T, where So the disturbance estimation error Stability with preset time.

[0159] Proof: Choose the following Lyapunov candidate function

[0160] According to equation (24), equation (50) and equation (51), we can get the following equation:

[0161]

[0162] Where: β1=min{2λ min (C a )}, so the above inequality can be transformed into Then, when t∈[0,T), calculate V b =V a / μ:

[0163]

[0164] So we get:

[0165]

[0166] Solving the above inequality yields:

[0167]

[0168] Multiplying both sides of the above inequality by μ, we get:

[0169]

[0170] According to the properties of μ function, we can get This means that V a (t) converges to a compact set When t∈[0,T).

[0171] In the case of t∈[T,∞), from equation (47) we can get μ≥1. According to Scaling the inequality gives:

[0172]

[0173] Then by solving the above inequality we can get:

[0174]

[0175] By properly choosing the control parameter K a , which ensures that β0 is greater than m. In this case, equation (61) can be restated as:

[0176]

[0177] Obviously, the estimation error will remain in the predefined compact set under t∈[T,∞). Based on the above analysis, it can be inferred that the observation error will arrive and remain in a compact set within the preset time T, which completes the proof of Theorem 2.

[0178] Theorem 3: Consider a closed-loop system consisting of the kinematic equations (22) with unknown external disturbances and input saturation, the dynamic equations (24), the disturbance observers (50) and (51), the virtual control law (46), the control law (53), and the auxiliary dynamic system (49). If assumptions 1-3 hold, the closed-loop system is stable within a preset time by properly selecting the control parameters. In addition, the trajectory tracking error is limited to the preset constraints, which helps to ensure transient and steady-state performance.

[0179] Proof: The proof of the above theorem consists of two parts:

[0180] Design the following Lyapunov candidate function:

[0181]

[0182] when

[0183]

[0184] Deriving equation (63) and substituting equations (48), (54), (55) and (64) into the derivative of equation (63), we can obtain the following equation according to Young's inequality:

[0185]

[0186] That is:

[0187]

[0188] Where:

[0189]

[0190] β3={2λ min C1),2λ min C2),2λ min (C3),2λ min (C a )} (68)

[0191] when

[0192]

[0193] By taking the derivative of formula (63) and substituting formula (48), formula (54), formula (55) and formula (69) into the derivative of formula (63), we can obtain:

[0194]

[0195] That is:

[0196]

[0197] Where:

[0198]

[0199] According to equation (66) and equation (71), we can get In addition, through a proof similar to Theorem 2, we can get:

[0200]

[0201] It can be clearly seen from the above formula that ||s1||, ||s2||, ||ε|| and It is stable within the preset time, so the closed-loop system is also stable within the preset time. At the same time, according to 0≤||s1||≤(2V) 1 / 2 ≤(2γ / m) 1 / 2 ≤∞ and the control characteristics of the preset performance. It can be concluded that the preset performance constraints are not violated, that is, -δ 1k ρ k (t)<e i (t)<δ 2k ρ k (t) holds true. This is the proof of Theorem 3.

[0202] The following is an offline simulation verification of the unmanned underwater vehicle trajectory tracking control system based on preset time and performance according to the present invention. The simulation parameters are set as follows: M = diag (215, 265, 80), m = 0.03, T E =6, T m =15, c ρ =2, T = 20, D = diag(70+100|u|, 100+200|v|, 50+100|r), K3 = diag(100, 100, 25), the expected trajectory is: η d =[4sin(0.05t),4(1-cos(0.05t)),0.01t] T , ,K a=diag(350,420,100), C1=C2=C3=diag(1.2,1.2,1.2), ω=diag(0.01,0.01,0.01), A=diag(100,50,100), C a =diag(100,100,200),K1=K2=K ε =diag(10,10,10), external disturbance is: d(t) = R T (ψ)b; B=diag(100,100,100), η(0)=[-4m,-4m,-π / 20rad] T , where the first-order Markov process is

[0203] Figure 3 The trajectory tracking results under the proposed scheme are shown. Figure 4 It is demonstrated that the control law can adjust the position and heading of the unmanned underwater vehicle to the desired value. Figure 5 The tracking error and its bounds are shown.

[0204] The observation results of the control system are as follows Figure 6 and Figure 7 As shown in the figure, it is shown that the proposed disturbance observer can quickly estimate unknown disturbances with small errors even in the presence of random noise. This provides a reliable guarantee for the system to perform tasks in complex underwater environments, such as monitoring of marine water quality and ecological elements, underwater salvage, etc., and ensures the accuracy and stability of control.

[0205] Figure 8 and Fig. 9 The control inputs performed in the UUV system are described. At 20 seconds, the observed value changes momentarily, which is caused by the preset performance function itself. This change causes the control gain to fluctuate, which in turn affects the change of the control input.

[0206] pass Fig.10It can be seen that the design scheme proposed in the present invention can effectively guide the unmanned underwater vehicle to track the reference trajectory. With the real-time feedback of intelligent perception and control equipment, the system's anti-interference ability in complex underwater environments is significantly enhanced, which can eliminate the initial trajectory deviation phenomenon and avoid deviation and regression adjustment during the tracking process. Compared with the method in the paper "Prescribed time observer based trajectory tracking control of autonomous underwater vehicle with tracking error constraints", the control system designed by the present invention shortens the tracking time of the north position x from 13s to 9s, and the response speed is increased by 30.8%; the tracking time of the east position y is shortened from 12s to 10s, and the response speed is increased by 16.7%. These improvements show that the system has higher tracking accuracy and can quickly correct deviations from the reference trajectory. It is particularly suitable for precise control tasks such as ocean exploration and underwater salvage equipment.

[0207] The speed curve is as follows Fig.11 As shown. Since the unmanned underwater vehicle is tracking a circular trajectory, the longitudinal velocity u, the sway velocity v, and the yaw rate r will eventually be non-zero values. About 40 seconds later, the expected x-coordinate change trend is almost opposite to the heading, so the longitudinal velocity u becomes a negative value. It can be seen from the speed curve that the initial speed fluctuation of the present invention is smaller than that of the comparison system. The longitudinal speed fluctuation amplitude decreases from 1.3 to 0.4, a reduction of 69.2%; the sway velocity fluctuation amplitude decreases from 0.49 to 0.33, a reduction of 32.7%, which significantly improves the tracking stability and control accuracy of the unmanned underwater vehicle.

[0208] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to be limiting. Although the technical solutions of the present invention have been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the present invention, and all of them should be included in the protection scope of the present invention.

Claims

1. An unmanned underwater vehicle trajectory tracking control system based on preset time and performance, characterized in that: The following steps are involved: S1: Establish an unmanned underwater vehicle model; S1.1: The motion of an unmanned underwater vehicle can be expressed by a three-degree-of-freedom nonlinear equation: Where: η=[x,y,ψ] T is the position vector in the earth-fixed coordinate system, x, y and ψ represent the position and heading angle of the unmanned underwater vehicle respectively; v = [u, v, r] T represents the velocity in the fixed coordinate system, u, v and r represent the longitudinal, sway and yaw angular velocities respectively, and R(ψ) represents the rotation matrix: In the presence of external disturbances and input saturation, the dynamic equation of the unmanned underwater vehicle can be expressed as: Where: M is the inertia matrix, C(v) is the Coriolis matrix, D(v) is the damping matrix, g(η) is the restoring force and torque generated by gravity / buoyancy, d(t) = [d1, d2, d3] T represents unknown external disturbance, τ=[τ1,τ2,τ3] T represents the actual control input of the unmanned underwater vehicle, τ c =[τ c1 ,τ c2 ,τ c3 ] T represents the input calculated by the control system, Δτ=τ-τ c Represents τ and τ c The difference between τ and τ c The relationship between can be described as: Where: τ maxi is the maximum allowable control input for the UUV; S1.2: Introduce a time-varying function used in the performance function, the mathematical form is as follows: In the formula: m∈(0,ln(2) / T f ], T f represents the maximum allowable setting time, in t∈[0,T f ) ρ (t) from the initial value exp[mT f ]-1 decays to a small positive number close to zero, and then at t∈[T f ,∞) increases monotonically, which means μ ρ (t) is always a positive number; S2: Design a preset time and preset performance function, and impose the following performance specifications on the error state: -δ 1k ρ k (t)<e i (t)<δ 2k ρ k (t), t>0 (6)Where:δ 1k ρ k (t),δ 2k ρ k (t) represent the upper and lower boundaries of the tracking error respectively; δ 1k , δ 2k is the design parameter, e i (t) represents the tracking error, ρ k (t)=[ρ1(t),ρ2(t),ρ3(t)] T is a bounded strictly positive decreasing smooth function; The preset time preset performance function is designed as: Where: k ρ 、c ρ is a positive definite design matrix, For the defined parameters, As shown below; Where: T m For transition time, where ρ k (0) is a design parameter, f ρk As shown below: Where: S3: Design the controller. By designing the control law, ensure that the tracking error and the estimation error converge within the preset time; and ensure that the preset constraints are not violated during the tracking process. The design process is as follows: S3.1:Definitions1=[s 11 ,s 12 ,s 13 ] T 、Ψ=diag(Ψ1,Ψ2,Ψ3)、Φ=diag(Φ1,Φ2,Φ3); Tracking error is defined as e = [e1, e2, e3] T =η-η d , η d For the desired trajectory, the error transformation is defined as follows: P i =(1 / 2(e i +d 1k r k )-1 / 2(e i +d 2k r k )) (14) The present invention selects the following virtual control law: Where: K1 and C1 are positive definite design matrices, and C1 satisfies T E is a positive design parameter m∈(0,ln(2) / T], where T represents the maximum allowable setting time; In order to deal with input saturation, the following auxiliary dynamic system is constructed: Where: K ε , K2, C2 and is a positive parameter of the design, C2 satisfies ε is the state vector of the system, s2 = v-α; S3.2: Construct the preset time interference observer as shown in equations (19)-(20) to achieve fast estimation and compensation of interference: Where: represents an estimate of interference; Where: γ, υ, k a , C a and ω=diag(ω1,ω2,ω3) are positive design parameters, I 3×1 represents a unit vector, is the estimated state variable of s2, is the state estimation error vector; The trajectory tracking control law is designed as: Where: K3 and C3 are positive definite design matrices, and C3 satisfies

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