An underwater glider passive fault-tolerant control method considering control allocation

Abstract

The application relates to a passive fault-tolerant control method of an underwater glider considering control allocation, aiming at the longitudinal motion attitude control of the underwater glider. First, a control allocation method is designed to combine the forces of redundant actuators with similar control effects, then a control allocation scheme is given to minimize the cost function, and finally a sliding mode component is added to realize stable control of the actuators in the case of failure, bias failure and stuck failure. Compared with the existing controller, the controller designed by the application can converge to a stable state within a pre-designed time under the premise of realizing fault-tolerant control, and the pre-designed time is irrelevant to the initial state of the system.

Description

Technical Field

[0001] This invention belongs to the field of underwater glider technology and relates to a passive fault-tolerant control method for underwater gliders, specifically a passive fault-tolerant control method for underwater gliders that considers control allocation. Background Technology

[0002] The concept of underwater gliders was first proposed by Stommel (1989) and has attracted widespread attention. Generally, these gliders are designed as winged underwater vehicles without external propulsion. The glider changes its attitude by adjusting the position of a movable internal slider, and achieves vertical movement by adjusting net buoyancy. Furthermore, hydrodynamic forces applied to the wings propel the glider forward. Due to their low energy consumption and ability to perform long-distance and long-duration missions, underwater gliders are used in marine science, oil field exploration, long-term monitoring of underwater oil and gas pipelines, and other marine industrial fields, and are also known as "ocean-going underwater gliders." In terms of design, these vehicles face challenges such as nonlinear modeling, path planning and obstacle avoidance, reliable controller design, and risk assessment.

[0003] As a crucial subsystem in underwater vehicle systems engineering, the control system of an underwater glider plays a vital role in missions such as marine resource exploration, marine life tracking, ocean profile data collection, and submarine detection. The prerequisite for ensuring the high performance of these underwater missions is the reliable and normal operation of the vehicle's control system. However, the harsh underwater environment and component aging inevitably lead to various failures in the vehicle's actuators. If the underwater glider cannot implement effective fault-tolerant measures to ensure attitude control stability when actuators experience failures such as malfunctions, paralysis, or jamming, the glider's survivability will be severely challenged. Therefore, it is essential to design corresponding fault-tolerant control methods in advance to address potential actuator failures. Summary of the Invention

[0004] Technical problems to be solved

[0005] To avoid the shortcomings of the prior art, the present invention provides a passive fault-tolerant control method for underwater gliders that considers control allocation. This method can achieve stable control when the actuators of the underwater glider experience failure, bias fault, or jamming fault during longitudinal motion.

[0006] Technical solution

[0007] A passive fault-tolerant control method for underwater gliders considering control allocation, characterized by the following steps:

[0008] Step 1: Give the longitudinal state-space equations for the underwater glider;

[0009] Step 2: Rearrange the state-space equations into the following form:

[0010]

[0011] in, For state variables, The coefficient matrix of the state variables. For matrix transformation terms, It is a nonlinear term. To control the input, The coefficient matrix for controlling the input;

[0012] Step 3: Design an invertible matrix This allows actuators with similar control functions to be merged into a single unit, resulting in a virtual controller V = NU = [x p_v δ v ] T and its coefficient matrix B′=BN -1 = [b′1 b′2], thus rewriting the state equation as:

[0013] Step 4: Design the control allocation matrix Φ such that the cost function Minimize to achieve optimal control, where ω1 and ω2 are weighting coefficients, v 1_1 v 1_2 These are the forces acting on the slider and the horizontal rudder, respectively.

[0014] Step 5: Present the final model after the control allocation transformation: Where B″=b′1,V′=x p_v ;

[0015] Step 6: Provide fault models for the actuator under the conditions of bias fault, failure fault and jamming fault;

[0016] Step 7: Design the controller based on sliding mode control and specified-time stability theory, where the stability time theory is expressed as follows:

[0017] For an autonomous system And given that it is a state vector, assume there exists a Lyapunov candidate function. Satisfying V(0)=0, when When the following condition is satisfied, it can be concluded that the autonomous system can achieve T when x(t0)≠0. c Globally stable at a specified time within a given time period:

[0018]

[0019] Further technical solution: The longitudinal state-space equation of the underwater glider described in step 1 is:

[0020]

[0021] in:

[0022]

[0023] In the model, the center of buoyancy is chosen as the origin of the carrier coordinate system; where m is the total weight of the glider; λ 11 , λ 22 , λ 26 , λ 66 For added mass; x c y c These are the coordinates of the center of gravity in the carrier coordinate system; C x This is the longitudinal force coefficient; and This is the position force coefficient, and the corresponding position force is generated when an underwater glider moves at a constant speed in a straight line under a fixed angle of attack. and The rotation coefficient is the dimensionless angular velocity, and the corresponding rotational force is generated when the underwater glider performs stable rotational motion. and ΔG = GB, where G = mg is the weight of the glider, B = ρgV is the buoyancy force on the glider, V is the total volume of the glider, ρ is the density of water, and S is the maximum cross-sectional area. Here are dimensionless coefficients, where L is the length of the underwater glider; J zz v is the moment of inertia. x v is the horizontal velocity in the longitudinal plane. y ω is the vertical velocity in the longitudinal plane; z It is the pitch angular velocity; Where, m p For the mass of the slider, x p δ and δ represent the slider displacement and the horizontal rudder size, respectively, serving as the two control inputs to the system.

[0024] Further technical solution: Fault model of the bias fault mentioned in step 6:

[0025]

[0026] Where, ΔV′=(B″Φ) -1 B′NΔU=[Δu], assuming the bias fault effect ΔU is bounded, then Δu is also bounded, and ||Δu||≤Δu max ;

[0027] The failure model of the aforementioned failure:

[0028]

[0029] The fault model of the stuck fault:

[0030]

[0031] Where, ΔV′ F =Δv=(B″Φ) -1 B′ΔV F .

[0032] Further technical solutions: Step 7 is as follows:

[0033] Based on sliding mode control and specified-time stability theory, it is assumed that the effects of disturbance d and bias fault Δv are bounded, satisfying... ||Δv||≤Δv max , Define ω as the upper bound of the perturbation d. d For the desired pitch angular velocity, θ d For the desired pitch angle, the pitch angular velocity error ω e and pitch angle error θ e It can be represented as:

[0034] ω e =ω z -ω d θ e =θ-θ d The sliding surface is designed as follows: S = ω e +β;Take

[0035] The controller is designed as follows:

[0036]

[0037] in:

[0038]

[0039] And satisfy:

[0040] K≥max{K x ,K y ,K z ,K s}

[0041] Where: K,K x ,K y ,K z ,K s All are sliding mode gain coefficients;

[0042]

[0043]

[0044]

[0045]

[0046] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0047] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0048] Beneficial effects

[0049] This invention provides a passive fault-tolerant control method for underwater gliders that considers control allocation. For the longitudinal motion attitude control of underwater gliders, firstly, a control allocation method is designed to merge the forces of redundant actuators with similar control functions. Then, a control allocation scheme that minimizes the cost function is given. Finally, a sliding mode component is added to achieve stable control of the actuators in the event of failure, bias fault, or jamming fault.

[0050] Compared with the prior art, the beneficial effects of the technical solution of the present invention are as follows:

[0051] 1. This invention addresses the characteristic of underwater gliders having redundant actuators in pitch control by designing a control merging matrix and an allocation matrix. The forces of the two actuators are merged into a total virtual force for control calculation. After the calculation is completed, the control allocation is optimized by minimizing the cost function.

[0052] 2. Compared with existing controllers, the controller designed in this invention can ensure convergence to a stable state within a pre-designed time while achieving fault-tolerant control, and this pre-designed time is independent of the initial state of the system. Attached Figure Description

[0053] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0054] Figure 1 Flowchart of control allocation and fault modeling;

[0055] Figure 2 Pitch angle control under fault-free conditions;

[0056] Figure 3 : Controller input under fault-free conditions;

[0057] Figure 4 Pitch angle control under bias fault conditions at T=30s;

[0058] Figure 5 : Controller input under bias fault condition T=30s;

[0059] Figure 6 Pitch angle control under failure conditions at T=20s;

[0060] Figure 7 : Controller input under failure condition where T=20s. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0062] This invention provides a passive fault-tolerant control method for underwater gliders that considers control allocation, comprising a control allocation stage and a fault-tolerant design stage:

[0063] (1) In the control allocation stage, the longitudinal plane model of the underwater glider is first organized and rewritten into the form required by the design. Then, the control merging matrix is ​​designed through the similarity relationship between the forces of redundant actuators. Finally, the control allocation matrix is ​​given through the condition of minimizing the cost function, and the transformation of the model is completed.

[0064] (2) In the fault-tolerant design stage, the controller is designed using sliding mode control and specified time stability theory for the transformed model.

[0065] The process of this method is as follows: Figure 1 As shown, the specific embodiments of the present invention are described in detail below, and the steps are as follows:

[0066] Step 1: Give the longitudinal state-space equations for the underwater glider. Detailed implementation method:

[0068] The details of step 1 are described below:

[0069] The longitudinal state-space equation of the underwater glider is:

[0070]

[0071] in:

[0072]

[0073] In the model, the center of buoyancy is chosen as the origin of the carrier coordinate system. Here, m represents the total weight of the glider; λ... 11 , λ 22 , λ 26 , λ 66 For added mass; x c y c These are the coordinates of the center of gravity in the carrier coordinate system; C x This is the longitudinal force coefficient; and This is the position force coefficient, and the corresponding position force is generated when an underwater glider moves at a constant speed in a straight line under a fixed angle of attack. and The rotation coefficient is the dimensionless angular velocity, and the corresponding rotational force is generated when the underwater glider performs stable rotational motion. and ΔG = GB, where G = mg is the weight of the glider, B = ρgV is the buoyancy force on the glider, V is the total volume of the glider, ρ is the density of water, and S is the maximum cross-sectional area. Here are dimensionless coefficients, where L is the length of the underwater glider; J zz v is the moment of inertia. x v is the horizontal velocity in the longitudinal plane. y ω is the vertical velocity in the longitudinal plane; z It is the pitch angular velocity; Where, m p For the mass of the slider, x p δ and δ represent the slider displacement and the horizontal rudder size, respectively, serving as the two control inputs to the system.

[0074] Step 2: Rearrange the state-space equations into In the form of. Detailed implementation method:

[0076] The details of step 2 are described below:

[0077] Step 2-1: This invention mainly studies pitch angle attitude control. Considering the unknown bounded disturbance d, equation (0.2) can be written in the following form:

[0078]

[0079] Step 2-2: For A and B respectively F (x) B and U take the following matrices:

[0080]

[0081]

[0082] F (x) =[f z +d]

[0083] B = [-cb]

[0084]

[0085] Equation (0.3) can be rearranged as follows:

[0086]

[0087] Step 3: Design an invertible matrix This allows actuators with similar control functions to be merged into a single unit, resulting in a virtual controller V and its coefficient matrix B′. Detailed implementation method:

[0089] Regarding step 3, this step will be described in detail below:

[0090] Step 3-1: Select the merge matrix N as:

[0091]

[0092] Wherein, γ is the proportionality coefficient when the forces between the designed control inputs can be converted into each other. In the underwater glider model, it can be designed as the ratio of the torques generated by the two actuators performing a unit distance movement.

[0093] Step 3-2: Based on the merging matrix N, the virtual controller V and its coefficient matrix B′ can be further obtained:

[0094]

[0095]

[0096] Where, x p_v and δ v Defined as the transformed virtual control input.

[0097] Step 4: Design the control allocation matrix Φ such that the cost function Minimize to achieve optimal control. Detailed implementation method:

[0099] Regarding step 4, this step will be described in detail below:

[0100] Step 4-1: Select the cost function J and constraint C as follows:

[0101]

[0102] C = cx p_v +cγδ v (0.9)

[0103] Where ω1 and ω2 are weighting coefficients, V = [v1] = [v 1_1 v 1_2 ] T =[x p_v δ v ] T .

[0104] Step 4-2: According to the Lagrange multiplier method, to minimize the cost function, matrices Φ, B″, and V′ need to satisfy:

[0105]

[0106] B″=b′1 (0.11)

[0107] V′=v 1_1 (0.12)

[0108] in,

[0109] Step 5: Give the final model after the control allocation transformation. Detailed implementation method:

[0111] The details of step 5 are described below:

[0112] Step 5-1: Select the weight coefficients ω1=ω2=1 for the cost function. From equation (0.10), we can obtain:

[0113]

[0114] Then we have:

[0115]

[0116] V′=v 1_1 =x p_v (0.15)

[0117] Step 5-2: The final model can be organized from Step 5-1 as follows:

[0118]

[0119] Step 6: Fault modeling of the actuator. Detailed implementation method:

[0121] The details of step 6 are described below:

[0122] Step 6-1: Bias Fault Modeling:

[0123] If the actuator experiences a bias fault, the original system (0.4) can be rewritten as follows:

[0124]

[0125] Where ΔU represents the effect of bias fault.

[0126] Define ΔV = NΔU, the above fault system can be written as:

[0127]

[0128] Where, ΔV′=(B″Φ) -1 B′NΔU=[Δu], assuming the bias fault effect ΔU is bounded, then Δu is also bounded, and ||Δu||≤Δu max .

[0129] Step 6-2: Failure Modeling

[0130] When a system failure occurs, the original system (0.4) can be rewritten as:

[0131]

[0132] in, When no fault occurs When a failure occurs, the failure factor Failures in the actual actuator can be reflected in the virtual control quantity through conversion.

[0133] Define NΓN -1 for:

[0134] Γ′=NΓN -1 =[Γ′1 Γ′2] (0.20)

[0135] Among them, Γ′ i =[Γ′ i_1 Γ′ i_2 ].

[0136] After that, we can obtain:

[0137] NΓN -1 V=[Γ′1 Γ′2] T[v1] (0.21)

[0138] make We can obtain:

[0139]

[0140] make Combining equations (0.20), (0.21), and (0.22), we can obtain:

[0141] B′NΓN -1 V = B′PV′ (0.23)

[0142] Define Ξ as:

[0143] Ξ=(B″Φ) -1 B′P (0.24)

[0144] Combining equations (0.23) and (0.24), the faulty system (0.19) can be rewritten as:

[0145]

[0146] Step 6-3: Modeling the stuck fault:

[0147] When a system freezes, it can be equivalent to a system failure and a bias fault occurring simultaneously. The input U can be rewritten as:

[0148] ΓU+ΔU F (0.26)

[0149] in, ΔU F =[Δu F1 Δu F2 ] T When no faults occur, Δu Fi =0; when a jamming fault occurs, Δu Fi ≠0.

[0150] Based on equation (0.26), the original system (0.4) can be rewritten as:

[0151]

[0152] Define ΔV F =NΔU F Based on the results of bias faults and failure faults, the system can be rewritten as follows:

[0153]

[0154] Where, ΔV′F =Δv=(B″Φ) -1 B′ΔV F .

[0155] Step 7: Design the controller based on sliding mode control and specified-time stability theory. The stability time theory is expressed as follows:

[0156] For an autonomous system And given that it is a state vector, assume there exists a Lyapunov candidate function. Satisfying V(0)=0, when When the following condition is satisfied, it can be concluded that the autonomous system can achieve T when x(t0)≠0. c Globally stable at a specified time within a given time period:

[0157] Detailed implementation method:

[0159] The details of step 7 are described below:

[0160] Step 7-1: Based on sliding mode control and specified time stability theory, assume that the disturbance d and the influence of the bias fault Δv are bounded, satisfying... ||Δv||≤Δv max , Define ω as the upper bound of the perturbation d. d For the desired pitch angular velocity, θ d For the desired pitch angle, the pitch angular velocity error ω e and pitch angle error θ e It can be represented as:

[0161] ω e =ω z -ω d θ e =θ-θ d The sliding surface is designed as follows: S = ω e +β;Take

[0162] The controller is designed as follows:

[0163]

[0164] in:

[0165]

[0166] And satisfy:

[0167] K≥max{K x,K y ,K z ,K s} (0.31)

[0168] Where: K,K x ,K y ,K z ,K s All are sliding mode gain coefficients.

[0169]

[0170]

[0171]

[0172]

[0173] Step 7-2: The designed passive fault-tolerant controller U can achieve stability within a specified time under four conditions: no fault, bias fault, failure fault, and jamming fault. Furthermore, the parameter design related to the stability time is independent of the initial conditions. The specified time is T. c =T c1 +T c2 .

[0174] Simulation example:

[0175] (1) Obtain controller parameter T c1 =30, T c2 =30, p1=0.1, p2=0.1, set the desired pitch angle to -30°, such as Figure 2 , 3 As shown, the controller can reach stability within a preset time.

[0176] (2) The controller parameters are the same as (1), and the bias fault is set to occur when T = 30s, such as Figure 4 , 5 As shown, if a fault occurs after the controller has stabilized, it can still regain stability within a preset time.

[0177] (3) The controller parameters are the same as (2), and the failure occurs when T = 30s. Figure 6 , 7 As shown, if a fault occurs after the controller has stabilized, it can still regain stability within a preset time.

[0178] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A passive fault-tolerant control method for an underwater glider considering control allocation, characterized in that... The steps are as follows: Step 1: Give the longitudinal state-space equations for the underwater glider; Step 2: Rearrange the state-space equations into the following form: in, For state variables, The coefficient matrix of the state variables. For matrix transformation terms, It is a nonlinear term. To control the input, The coefficient matrix for controlling the input; Step 3: Design an invertible matrix This allows actuators with similar control functions to be merged into a single unit, resulting in a virtual controller V = NU = [x p_v δ v ] T and its coefficient matrix B′=BN -1 = [b′1 b′2], thus rewriting the state equation as: Step 4: Design the control allocation matrix Φ such that the cost function Minimize to achieve optimal control, where ω1 and ω2 are weighting coefficients, v 1_1 v 1_2 These are the forces acting on the slider and the horizontal rudder, respectively. Step 5: Present the final model after the control allocation transformation: Where B″=b′1, V′=x p_v ; Step 6: Provide fault models for the actuator under the conditions of bias fault, failure fault and jamming fault; Step 7: Design the controller based on sliding mode control and specified-time stability theory, where the stability time theory is expressed as follows: For an autonomous system And given that it is a state vector, assume there exists a Lyapunov candidate function. Satisfying V(0)=0, when When the following condition is satisfied, it can be concluded that the autonomous system can achieve T when x(t0)≠0. c Globally stable at a specified time within a given time period:

2. The passive fault-tolerant control method for underwater gliders considering control allocation according to claim 1, characterized in that: The longitudinal state-space equation of the underwater glider described in step 1 is: in: In the model, the center of buoyancy is chosen as the origin of the carrier coordinate system; where m is the total weight of the glider; λ 11 , λ 22 , λ 26 , λ 66 For added mass; x c y c These are the coordinates of the center of gravity in the carrier coordinate system; C x This is the longitudinal force coefficient; and This is the position force coefficient, and the corresponding position force is generated when an underwater glider moves at a constant speed in a straight line under a fixed angle of attack. and The rotation coefficient is the dimensionless angular velocity, and the corresponding rotational force is generated when the underwater glider performs stable rotational motion. and ΔG = GB, where G = mg is the weight of the glider, B = ρgV is the buoyancy force on the glider, V is the total volume of the glider, ρ is the density of water, and S is the maximum cross-sectional area. Here are dimensionless coefficients, where L is the length of the underwater glider; J zz v is the moment of inertia. x v is the horizontal velocity in the longitudinal plane. y ω is the vertical velocity in the longitudinal plane; z It is the pitch angular velocity; Where, m p For the mass of the slider, x p δ and δ represent the slider displacement and the horizontal rudder size, respectively, serving as the two control inputs to the system.

3. The passive fault-tolerant control method for underwater gliders considering control allocation according to claim 1, characterized in that: The fault model for the bias fault described in step 6: Where, ΔV′=(B″Φ) -1 B′NΔU=[Δu], assuming the bias fault effect ΔU is bounded, then Δu is also bounded, and ||Δu||≤Δu max ; The failure model of the aforementioned failure: The fault model of the stuck fault: among them,ΔV′ F =Δv=(B″Φ) -1 B′ΔV F 。 4. The passive fault-tolerant control method for underwater gliders considering control allocation according to claim 3, characterized in that: Step 7 is as follows: Based on sliding mode control and specified-time stability theory, it is assumed that the effects of disturbance d and bias fault Δv are bounded, satisfying... ||Δv||≤Δv max , Define ω as the upper bound of the perturbation d. d For the desired pitch angular velocity, θ d For the desired pitch angle, the pitch angular velocity error ω e and pitch angle error θ e It can be represented as: ω e = ω z - ω d , θ e = θ - θ d ; The sliding surface is designed as: S = ω e + β; Take The controller is designed as follows: in: And satisfy: K≥max{K x ,K y ,K z ,K s } Where: K,K x ,K y ,K z ,K s All are sliding mode gain coefficients; 5. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

6. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

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