CN109343347B - Track tracking control method for submarine flight nodes - Google Patents

Abstract

The invention discloses a track tracking control method for a submarine flight node, and relates to a track tracking control method for a submarine flight node. The invention aims to solve the problems that the existing method lacks the control capability on the track tracking error convergence dynamic process, and is difficult to realize overshoot limit, presetting of error convergence time and tracking with any precision. The specific process is as follows: firstly, establishing an OBFN dynamic model based on a Fossen outline six-degree-of-freedom nonlinear model; secondly, transforming the established OBFN dynamic model to obtain a transformed OBFN dynamic model; thirdly, defining a performance function; fourthly, the method comprises the following steps: performing error transformation on the transformed OBFN dynamic model obtained by the second step according to the performance function defined by the third step; fifthly, selecting parameters of a radial basis function neural network; and sixthly, designing an adaptive trajectory tracking controller based on four and five. The invention is used for the field of track tracking control of the submarine flight nodes.

Description

Track tracking control method for submarine flight nodes

Technical Field

The invention relates to a track tracking control method of a submarine flight node.

Background

In recent years, Autonomous Underwater Vehicles (AUV) have been widely used in research fields such as marine environment observation and military information gathering. With the enhancement of ocean development, the application of AUV gradually expands from observation to mild operation. Such as the inspection of underwater infrastructure, deep sea oil and gas exploration, and the like. Among them, the Ocean Bottom Flying Node (OBFN) is a kind of expanded AUV, which carries with a geophone and can be deployed on the seabed surface in a large scale for deep sea oil and gas resource exploration, as shown in fig. 1.

The trajectory tracking is a basic function of the AUV control system, but due to the highly nonlinear and cross-coupled system dynamics and unpredictable complex underwater environment, larger model uncertainty and external disturbance are introduced to the AUV system dynamics model, and the design difficulty of the controller is further increased. And the requirement on the AUV control precision is further increased due to the complexity of the task requirement.

Common disturbances and uncertainties of AUVs include ocean current disturbances, propeller failures, and modeling uncertainties. The common processing method generally considers the influence of one or more factors on the trajectory tracking control, and the analysis result is not comprehensive enough; or algorithm constraint influence is designed for the factors respectively, and the analysis process is too complex. In recent years, a method for considering factors such as ocean current disturbance, propeller failure and modeling uncertainty as the total uncertainty of the system is developed, and the total uncertainty of the system is approximated by a neural network. However, the method lacks the capability of controlling the dynamic process of trajectory tracking error convergence, and particularly has the characteristics of large-scale deployment, high-precision trajectory tracking, submarine sinking and the like facing to the OBFN, so that the AUV of the dynamic process of error convergence needs to be strictly controlled, and overshoot limitation, presetting of error convergence time and tracking with any precision are difficult to realize. The overshoot is an index for evaluating an OBFN trajectory tracking control system, and refers to the maximum deviation (smaller is better) of the adjusted parameter from a given value.

Disclosure of Invention

The invention aims to solve the problems that the existing method lacks the control capability of a track tracking error convergence dynamic process, and is difficult to realize overshoot limit, presetting of error convergence time and tracking with any precision, and provides a track tracking control method of a submarine flight node.

The track tracking control method of the submarine flight node comprises the following specific processes:

step one, establishing an OBFN dynamic model based on a Fossen outline six-degree-of-freedom nonlinear model;

the dynamic model of the OBFN is represented by a six-degree-of-freedom nonlinear model based on the Fossen outline:

the OBFN is a submarine flight node;

in the formula, M_ηA derived variable for M, M being a mass inertia matrix for OBFN; c_RBηIs C_RBDerived variable of (2), C_RBA matrix of coriolis and centripetal forces that is a rigid body of the OBFN; c_AηIs C_ADerived variable of (2), C_AAdding a matrix of coriolis forces and centripetal forces of mass to the OBFN; d_ηD is a derived variable of D, and D is a hydrodynamic damping matrix; g_ηForce and moment vectors generated by gravity and buoyancy of the OBFN, wherein eta is a six-degree-of-freedom position and attitude vector of the OBFN under a fixed coordinate system;

is the first derivative of η;

is the second derivative of η;

is the first derivative of displacement vector of OBFN relative to ocean current under a fixed coordinate system; τ is the actual control force of the propeller of the OBFN;

step two, transforming the dynamic model of the OBFN established in the step one to obtain a transformed dynamic model of the OBFN;

step three, defining a performance function;

step four: performing error transformation on the transformed OBFN dynamic model obtained in the step two according to the performance function defined in the step three;

selecting parameters of a radial basis function neural network;

and step six, designing the self-adaptive track tracking controller based on the step four and the step five.

The invention has the beneficial effects that:

aiming at the problem of position and attitude tracking control of the OBFN, the invention comprehensively considers the influence caused by ocean current, modeling uncertainty and propeller faults, and provides a self-adaptive neural network controller based on a preset performance method to realize the trajectory tracking control of the OBFN. First, the traditional AUV six-degree-of-freedom kinetic equation is converted into an OBFN kinetic equation that takes into account ocean current disturbances, modeling uncertainty, and propeller faults. Secondly, designing a performance function and corresponding error transformation, and converting the trajectory tracking error system of the OBFN into an equivalent 'unconstrained' system. Then, a Radial Basis Function Neural Network (RBFNN) is utilized to approximate the total uncertainty of the system consisting of ocean current, modeling uncertainty and propeller faults, and an adaptive technology is introduced to estimate the upper bound of the error of the total uncertainty of the RBFNN approximation system. And finally, designing an OBFN (on-board network) track tracking controller, substituting the total uncertainty value of the system approximated by the RBFNN and an error upper bound value obtained by self-adaptive estimation to offset the influence of the total uncertainty of the system on an OBFN track tracking control system, and proving the stability of an 'unconstrained' closed loop system by means of Lyapunov theory, so that the original OBFN track tracking obtains preset performance, namely the overshoot limit of the OBFN track tracking, the preset of error convergence time and the tracking requirement of any precision are realized.

Fig. 3-8 show 6-degree-of-freedom trajectory tracking error curves for the OBFN. Wherein, the solid curve represents the tracking error curve of the position and attitude angle of the adaptive tracker (39) - (41) applying the preset performance of the invention, and the dashed curve represents the preset performance boundary. As can be seen from fig. 3 to 8, the tracking error of the position and attitude angle of six degrees of freedom of the OBFN is always within the preset performance boundary defined by the performance function, and the preset performance boundary represents the expected error convergence process, so that the method provided by the present invention realizes the expected error convergence dynamic process and the steady-state control accuracy. According to the simulation parameter setting of the invention, the track tracking steady-state error of the OBFN is lower than 0.0035, and the error convergence rate is higher than e^-0.15t。

Drawings

FIG. 1 is a schematic view of a subsea flight node;

FIG. 2 is a schematic diagram of an OBFN thruster layout, T-1, T-2, T-3, T-4, T-5 and T-6 are OBFN thrusters;

FIG. 3 shows surging tracking error e under sudden failure of propeller₁A schematic diagram;

FIG. 4 shows the following error e of the surge in case of sudden failure of the propeller₂A schematic diagram;

FIG. 5 shows the heave tracking error e under sudden failure of a propeller₃A schematic diagram;

FIG. 6 shows the roll tracking error e under sudden failure of the propeller₄A schematic diagram;

FIG. 7 shows pitch tracking error e in sudden propeller failure₅A schematic diagram;

FIG. 8 shows the tracking error e of the rocker in sudden failure of the propeller₆Schematic representation.

Detailed Description

The first embodiment is as follows: the track tracking control method of the submarine flight node of the embodiment comprises the following specific processes:

step one, establishing an OBFN dynamic model based on a Fossen outline six-degree-of-freedom nonlinear model;

inertial coordinate system (E- ξ η ζ): the origin E can be selected at a certain point of the sea surface, the E xi axis and the E eta axis are arranged in the horizontal plane and are mutually vertical, and the E xi axis points to the positive north direction. E ζ is perpendicular to the E ξ η plane, pointing forward towards the earth's center.

Motion coordinate system (G-xyz): the origin G is taken at the center of gravity of the OBFN, and the x-axis, y-axis, and z-axis are the intersection of the water plane, cross section, and mid-longitudinal section through the origin, respectively.

The dynamical model of OBFN can be expressed by a six-degree-of-freedom nonlinear model based on the Fossen outline [1] (Fossen T I.handbook of Marine Craft Hydrodynamics and Motion Control [ M ]. 2011.):

the OBFN is a submarine flight node;

in the formula, M_ηA derived variable for M, M being a mass inertia matrix for OBFN; c_RBηIs C_RBDerived variable of (2), C_RBA matrix of coriolis and centripetal forces that is a rigid body of the OBFN; c_AηIs C_ADerived variable of (2), C_AAdding a matrix of coriolis forces and centripetal forces of mass to the OBFN; d_ηD is a derived variable of D, and D is a hydrodynamic damping matrix; g_η＝g(η)，g_ηForce and moment vectors generated by gravity and buoyancy of the OBFN, wherein eta is a six-degree-of-freedom position and attitude vector of the OBFN under a fixed coordinate system;

is the first derivative of η;

is the second derivative of η;

is the first derivative of displacement vector of OBFN relative to ocean current under a fixed coordinate system; τ is the actual control force of the propeller of the OBFN;

the preset performance control method comprises the following steps: the method leads the convergence speed, the overshoot and the tracking error to obtain the preset performance by introducing the performance function and the error transformation, and relaxes the requirement on the selection of the control parameters to a certain extent.

Radial basis function neural network: the method is a forward network constructed on the basis of a function approximation theory, and the learning of the network is equivalent to finding a best fit plane of training data in a multidimensional space. The neural network has the advantages of simple structure, concise training, high learning convergence speed and capability of approximating any nonlinear function.

Step two, transforming the dynamic model of the OBFN established in the step one to obtain a transformed dynamic model of the OBFN considering ocean current disturbance, modeling uncertainty and propeller fault influence;

step three, defining a performance function;

step four: performing error transformation on the transformed OBFN dynamic model (3) obtained in the step two according to the performance function defined in the step three;

selecting parameters of a radial basis function neural network;

and step six, designing the self-adaptive track tracking controller based on the step four and the step five.

The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: in the step one

Derived variable M of M_η＝MJ^-1J is a conversion matrix between the fixed coordinate system and the moving coordinate system;

C_RBderived variable of

Is the first derivative of J, v is the velocity and angular velocity of OBFN in motion coordinate system, v ═ u', a, w, p, q, r]^T，

In the formula, u' is the surging speed of the OBFN in a moving coordinate system, a is the swaying speed of the OBFN in the moving coordinate system, w is the heaving speed of the OBFN in the moving coordinate system, p is the transverse inclination angle speed of the OBFN in the moving coordinate system, q is the surging angle speed of the OBFN in the moving coordinate system, r is the shaking head angular speed of the OBFN in the moving coordinate system, and an upper corner mark T is a matrix transposition symbol;

C_Aderived variable C of_Aη＝C_A(v_r)J^-1，v_rVelocity of OBFN relative to ocean current;

derived variable D of D_η＝D(v_r)J^-1；

The six-freedom-degree position and attitude vector eta of the OBFN in a fixed coordinate system is [ x, y, z, phi, theta, psi [ ]]^T，

Wherein x is the displacement of the OBFN in the x-axis direction under the fixed coordinate system, y is the displacement of the OBFN in the y-axis direction under the fixed coordinate system, z is the displacement of the OBFN in the z-axis direction under the fixed coordinate system, phi is the transverse inclination angle of the OBFN under the fixed coordinate system, theta is the longitudinal inclination angle of the OBFN under the fixed coordinate system, and psi is the rock head angle of the OBFN under the fixed coordinate system;

first derivative of displacement vector of OBFN relative to ocean current under fixed coordinate system

v_r＝v-v_c，v_cThe velocity of the ocean current in the motion coordinate system.

Other steps and parameters are the same as those in the first embodiment.

The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: in the second step, the dynamic model of the OBFN established in the first step is transformed to obtain a transformed dynamic model of the OBFN, wherein the transformed dynamic model of the OBFN considers ocean current disturbance, modeling uncertainty and propeller fault influence;

aiming at model uncertainty, ocean current disturbance and propeller faults considered by the invention patent, feasible mathematical expression forms are considered.

The fault impact of the OBFN propellers may be represented in the form of a thrust distribution matrix, defined as Δ B [3] (Wang Y, Zhang M, Wilson PA, et al, adaptive neural network-based backstepping fault complete control for underserver vehicles with a fault [ J ]. Ocean Engineering,2015,110: 15-24.);

the actual control force and torque of the propeller of the OBFN may be rewritten as τ + Δ τ:

τ+Δτ＝(B₀-KB)u＝(B₀+ΔB)u (2)

in the formula, B₀Is the nominal value of the thrust distribution matrix B (nominal value obtained for the actual measurement), u is the control input of the propeller of the OBFN, B is the thrust distribution matrix, K is a diagonal matrix whose elements K_ii∈[0,1]Indicating a corresponding propeller failure level, and 1 indicating a high failure level.

Equation (1) can be transformed into an OBFN dynamics model:

in the formula, M_η0Deriving a variable M for M_ηNominal value of (C)_RBη0Is C_RBDerived variable C_RBηNominal value of (C)_Aη0Is C_ADerived variable C_AηNominal value of (D)_η0Deriving a variable D for D_ηNominal value of (g)_η0Is g_ηSubscript 0 represents the nominal value; f denotes the total uncertainty of the trajectory tracking control system of the OBFN.

Other steps and parameters are the same as those in the first or second embodiment.

The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: the total uncertainty F expression of the trajectory tracking control system of the OBFN is as follows:

in the formula (I), the compound is shown in the specification,

representing the effect of the ocean current disturbance; Δ denotes an uncertainty value, Δ M_ηIs M_ηOf an indeterminate value of, Δ C_RBηIs C_RBηOf an indeterminate value of, Δ C_AηIs C_AηOf indeterminate value, Δ D_ηIs D_ηUncertain value of,. DELTA.g_ηUncertainty values, η, of force and moment vectors generated for gravity and buoyancy_rIs the displacement vector of OBFN relative to ocean current under a fixed coordinate system.

The uncertainty value can be artificially set to a value in the simulation to prove that the proposed method can effectively overcome this uncertainty.

Other steps and parameters are the same as those in one of the first to third embodiments.

The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: defining a performance function in the third step; the specific process is as follows:

defining a performance function:

ρ(t)＝(ρ₀-ρ_∞)e^-kt+ρ_∞ (5)

in the formula, ρ₀Is a normal number (initial position of OBFN in a fixed coordinate system and initial position of expected track, rho) determined according to initial control precision of OBFN₀Needs to be slightly larger than the difference between the two or the system diverges at the initial time); rho_∞A normal number depending on the steady-state control accuracy of the OBFN (this value is the final accuracy value depending on what accuracy the controller wants the trajectory tracking control system of the OBFN to achieve last time); k is a normal number determined according to the convergence rate of the trajectory tracking control system of the OBFN, and the convergence speed is higher when the k value is larger; rho (t) is a performance function, and t is time;

utilizing the performance function rho (t) to calculate the position and attitude angle error e of the OBFN in a fixed coordinate system_i(t) is expressed as:

in the formula, e_i(t) is the position and attitude angle error of the OBFN in a fixed coordinate system, i is a variable, and since the position and attitude angle error of the OBFN comprises 6 degrees of freedom, i is 1,2,3,4,5 and 6; delta_iIs a variable, 0 is not more than delta_i≤1；ρ_i(t) is a performance function for the ith degree of freedom;

according to the form of the performance function formula (5) and the formula (6), if the OBFN position and attitude angle error e is known_i(t) initial value satisfies 0 | | | e ≦_i(0)||≤ρ_i(0) K limits the minimum convergence rate of the tracking error, and p_i∞Given the upper bound of allowable steady state tracking error, while the overshoot of the trajectory tracking control system response of the OBFN does not exceed δ_iρ_i(t)；

ρ_i∞Is the upper bound of the allowed steady state tracking error in the ith degree of freedom.

Other steps and parameters are the same as in one of the first to fourth embodiments.

The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is: in the fourth step, the OBFN dynamic model transformed in the second step is subjected to error transformation according to the performance function defined in the third step; the specific process is as follows:

performing error transformation on the OBFN dynamic model formula (3) in the second step according to the performance function defined in the third step; an error conversion mode is adopted to convert the tracking control problem under constraint into the stable control problem without constraint, and an auxiliary function S is defined_i(ε_i)：

In the formula, epsilon_iE (-infinity, + ∞) is called the transformation error;

auxiliary function S_i(ε_i) Has the following properties:

(1)S_i(ε_i) Smooth and strictly monotonic increase;

(2)

(3)

according to S_i(ε_i) Is represented by the formula (6) which is equivalent to

e_i(t)＝ρ_i(t)S_i(ε_i) (8)

Because of S_i(ε_i) Is strictly monotonically increasing, so that there is an inverse function from which the transformation error epsilon is obtained_i：

At the moment, the tracking control problem of the OBFN dynamic model formula (3) is converted into epsilon_iStability control problems for closed loop systems that are variable;

consider S_i(ε_i) In the form of equation (7), then

In the formula, z_iAn auxiliary variable for the ith degree of freedom, z_i＝e_i(t)/ρ_i(t)；

Let epsilon_iThe first and second derivatives are taken over time t:

in the formula, r_iIs an auxiliary variable for the ith degree of freedom,

can be obtained by calculation according to the formula (10),

is r_iThe first derivative of (a) is,

representing the actual position and attitude angle of the OBFN,

indicating the desired position and attitude angle of the OBFN, i is 1,2,3,4,5,6；

As the first derivative of the auxiliary variable of the ith degree of freedom, e_iFor the position and attitude angle error of the OBFN in the fixed coordinate system,

is e_iThe first derivative of (a) is,

is the first derivative of the ith degree of freedom performance function;

is the second derivative of the ith degree of freedom performance function;

taking the error variable s epsilon R⁶Is in the form of

Wherein ε ═ ε₁,ε₂,ε₃,ε₄,ε₅,ε₆]^T,λ＝diag[λ₁,λ₂,λ₃,λ₄,λ₅,λ₆]More than 0 is a parameter to be designed;

is the first derivative of ε; t is transposition; r is a real number domain; epsilon_iFor transforming errors, λ_iThe parameter to be designed for the ith degree of freedom, i ═ 1,2,3,4,5, 6;

note the book

D＝-F

The OBFN kinetic model formula (3) is abbreviated as follows:

wherein A, B, D is an intermediate variable;

further comprising:

in the formula (I), the compound is shown in the specification,

is the first derivative of s and is,

is the first derivative of epsilon and,

is the second derivative of ε; l and R are intermediate variables.

Other steps and parameters are the same as those in one of the first to fifth embodiments.

The seventh embodiment: the difference between this embodiment and one of the first to sixth embodiments is: the above-mentioned

L＝[l₁,l₂,l₃,l₄,l₅,l₆]^T，

i＝1,2,3,4,5,6,

R＝diag[r₁,r₂,r₃,r₄,r₅,r₆]

In the formula I_iIs an intermediate variable of the ith degree of freedom,

auxiliary variable r for ith degree of freedom_iThe first derivative of (a).

Other steps and parameters are the same as those in one of the first to sixth embodiments.

The specific implementation mode is eight: the present embodiment differs from one of the first to seventh embodiments in that: in the fifth step, the controller selects parameters of the radial basis function neural network; the specific process is as follows:

an uncertain nonlinear term D exists in the simplified OBFN dynamic model formula (14), and the uncertain nonlinear term D is approximated by adopting an RBF neural network, wherein the process comprises the following steps:

taking the neural network input as

The estimate of the uncertain non-linear term D can be written as

In the formula (I), the compound is shown in the specification,

as an estimate of the weight matrix,

h (x) is a radial basis function, h (x) h₁(x),h₂(x),...,h_j(x),...h_m(x)^T]∈R^mM is the number of hidden nodes of the RBF neural network; h is_j(x) The j-th radial basis function can be in the form of a Gaussian basis function; j is more than or equal to 1 and less than or equal to m;

e＝[e₁,e₂,e₃,e₄,e₅,e₆]，e_ithe position and attitude angle error of the OBFN in the fixed coordinate system is represented by i 1,2,3,4,5,6,

is the first reciprocal of e and T is transposed.

Other steps and parameters are the same as those in one of the first to seventh embodiments.

The specific implementation method nine: the present embodiment differs from the first to eighth embodiments in that: the number m of hidden nodes of the RBF neural network is more than or equal to 3.

Other steps and parameters are the same as those in one to eight of the embodiments.

The detailed implementation mode is ten: the present embodiment differs from one of the first to ninth embodiments in that: in the sixth step, an adaptive trajectory tracking controller is designed based on the fourth step and the fifth step; the specific process is as follows:

considering the unknown upper bound mu of the approximation error, the invention provides the following self-adaptive trajectory tracking controller:

in the formula (I), the compound is shown in the specification,

represents the upper bound mu of the approximation error^*The estimate of (obtained by equation 19),

is composed of

The first order reciprocal of (1), wherein, | s | | | is a two-norm of an error variable s, K is more than 0, and σ is more than 0 and is a control parameter to be designed; tau is_wi＞0,β＞0,τ_μThe self-adaptive gain is more than 0, and gamma is more than 0; s ═ s₁,s₂,s₃,s₄,s₅,s₆]，s_iI is a value of the error variable s, 1,2,3,4,5, 6.

Equation (17) is the controller, and equations (18) and (19) are the adaptive laws to which the controller is attached.

Other steps and parameters are the same as those in one of the first to ninth embodiments.

Theoretical basis

Kinetic model of OBFN

The kinetic equation of OBFN can be expressed by a six-degree-of-freedom nonlinear model based on the Fossen outline [1] (Fossen T I.handbook of Marine Craft Hydrodynamics and Motion Control [ M ]. 2011.):

in the formula, M_η＝MJ^-1；

C_Aη＝C_A(v_r)J^-1；D_η＝D(v_r)J^-1；gh＝g(η)；

v_r＝v-v_c(ii) a M is a mass inertia matrix, η ═ x, y, z, φ, θ, ψ]^TRepresents the six-freedom position and the attitude of the OBFN in an inertial coordinate system, and v is [ u, v, w, p, q, r [ ]]^TExpressing the speed and the angular speed under a motion coordinate system, wherein J is a conversion matrix between an inertia coordinate system and the motion coordinate system; c_RBIs a matrix of Coriolis and centripetal forces of a rigid body, C_AIs a matrix of coriolis forces and centripetal forces for the additional mass; d is a hydrodynamic damping matrix, g_ηForce and moment vectors generated for gravity and buoyancy, τ control forces and moments generated by the propulsion system, v_rIs the velocity of the OBFN relative to the sea current, v_cIs the velocity of the ocean current in the motion coordinate system.

Thrusters are an important component of OBFN and are a major source of failure problems. The failure impact of a propeller can be represented in the form of a thrust allocation matrix, defined as Δ B. Therefore, the actual control force and torque can be rewritten as τ + Δ τ:

τ+Δτ＝(B₀-KB)u＝(B₀+ΔB)u (21)

in the formula, B₀Is the nominal value of the thrust distribution matrix, u is the control action of the thruster, and K is a pairCorner matrix of element k_ii∈[0,1]Indicating the corresponding propeller failure level. Thus, equation (20) can be transformed to:

wherein subscript 0 represents a nominal value; f represents the total uncertainty of the system, and the expression is as follows:

in the formula (I), the compound is shown in the specification,

representing the effect of the ocean current disturbance; Δ represents an indeterminate value.

The control objective of the present invention can be expressed as: the controller u is designed so that the position and attitude vectors η of the OBFN in the presence of system uncertainty and propeller faults can still track the expected values η_dAnd making the tracking error e equal to eta-eta_dHas the given dynamic performance and steady-state response condition.

In conjunction with the practical engineering background we propose 3 hypotheses:

assume 1 position and attitude vector η and its first derivative

Can be measured.

Assume 2 the desired position and attitude angle η_dKnown and bounded to both its first and second derivatives.

Assume that the total uncertainty F of the 3 system is bounded, i.e., | | F | ≦ χ, where χ is an unknown normal.

Preset performance control method

A common Performance function is shown below [2] (Bechlioulis C P, Rowthakis G A. Robust Adaptive Control of Feedback Linear MIMO Nonlinear Systems With Prescribed Performance [ J ]. IEEE Transactions on Automatic Control,2008,53(9): 2090-:

ρ(t)＝(ρ₀-ρ_∞)e^-kt+ρ_∞ (24)

in the formula, ρ₀、ρ_∞And k is a predetermined normal number. It satisfies the following conditions:

(1) ρ (t) decreases monotonically and is always positive;

(2)

let ρ (t) be a performance function.

Using a performance function, the tracking error can be expressed as

In the formula, e_i(t), i is 1,2,3,4,5,6 is OBFN position and attitude angle error, 0 ≦ δ_iLess than or equal to 1. According to the form of the performance function (24) and the formula (25), if the initial value of the tracking error meets the condition that the tracking error is less than or equal to 0 | | | e_i(0)||≤ρ_i(0) Then parameter k_iLimits the minimum convergence rate of the tracking error, p_i∞Given the upper bound of allowable steady state tracking error, overshoot of the system response does not exceed δ_iρ_i(t) of (d). Therefore, an appropriate performance function ρ is designed_i(t) and δ_iA desired system error response may be obtained.

To solve the preset performance control problem represented by equation (25), an error transformation approach is used to transform the tracking control problem under constraint into an unconstrained stable control problem. Defining a function S_i(ε_i) Having the following properties:

(1)S_i(ε_i) Smooth and strictly monotonic increase;

(2)

(3)

in the formula, epsilon_iE (- ∞, + ∞) is called the transformation error. A function S satisfying the above conditions_i(ε_i) Given by:

according to S_i(ε_i) Is represented by the formula (25) which is equivalent to

e_i(t)＝ρ_i(t)S_i(ε_i) (27)

Because of S_i(ε_i) Is strictly monotonically increasing, so that there is an inverse function

If can control ε_iBounded, then it can be guaranteed that equation (25) holds, further in the performance function ρ_i(t) to achieve the desired tracking error under the constraint of (t). The tracking control problem of the system (22) is then converted to e_iIs a problem of stable control of a closed loop system of variables.

Consider S_i(ε_i) Taking the form of equation (26), then

In the formula, z_i＝e_i(t)/ρ_i(t)

Let epsilon_iThe first and second derivatives are taken over time t, respectively:

in the formula (I), the compound is shown in the specification,

can be obtained by calculation of the formula (29)

Representing the actual and desired position and attitude angles of the OBFN, respectively. Due to the fact that

And ρ_i(t) > 0 indicates that r_iIs constantly greater than zero, and as long as the error e_iIf the trajectory of (t) is strictly limited to the range of equation (25), r is_iIs bounded as to satisfy

And

is a normal number.

Taking the error variable s epsilon R⁶Is in the form of

Wherein ε ═ ε₁,ε₂,ε₃,ε₄,ε₅,ε₆]^T,λ＝diag[λ₁,λ₂,λ₃,λ₄,λ₅,λ₆]And > 0 is a parameter to be designed.

Kinetic model according to OBFN (22):

note the book

D ═ F, model (22) can be abbreviated as follows:

further comprising:

wherein L ═ L₁,l₂,l₃,l₄,l₅,l₆]^T，

R＝diag[r₁,r₂,r₃,r₄,r₅,r₆]. If the controller u is designed to be bounded by s, then ε can be obtained according to equation (34)_iAnd

is bounded.

Adaptive attitude tracking controller design

The system (33) has uncertain nonlinear terms D, and adopts RBF neural network to carry out approximation, namely

D＝W^*Th(x)+μ (35)

In the formula (I), the compound is shown in the specification,

for neural network input vector, h (x) ═ h₁(x),h₂(x),...,h_j(x),...h_m(x)]^T∈R^mAnd m is the number of hidden nodes in the network. h is_j(x) Usually in the form of a Gaussian basis function, of

In the formula, c_jAs the central vector of the jth node in the network, c_j＝[c_j1,c_j2,...,c_jq]^TIs the base width value of node j.

Is an ideal weight matrix of the network, and is mu epsilon to R⁶Is an approximation error and satisfies the condition that | | | mu | | | is less than or equal to mu | |^*,μ^*Is an unknown normal number. For weight matrix W ∈ R^m+3W in the ideal case^*Is defined as

Taking the neural network input as

The estimate of uncertainty term D can be written as

In the formula (I), the compound is shown in the specification,

is a weight matrix W^*Is estimated.

Integrating the above analysis processes and taking into account the upper bound mu of the approximation error^*Not known, the following adaptive control laws are proposed

In the formula (I), the compound is shown in the specification,

represents the upper bound mu of the approximation error^*Estimate of (d), K > 0, [ sigma ] tau_wi＞0，β＞0,τ_μAnd the control parameters and the adaptive gain to be designed are more than 0 and gamma is more than 0. It can be seen that when the OBFN dynamics model (22) is transformed into an error system (34) by an error transformation (28), the error epsilon is transformed if the controller u is designed in the form of equation (39) and adopts an adaptive law of equations (40) and (41)_iThe agreement is finally bounded and the tracking error e_iSatisfies the predetermined performance constraint (25).

And (3) proving that: because the matrix R is positively determined symmetrically and R_iBounded, the Lyapunov function can be chosen as

In the formula (I), the compound is shown in the specification,

for corresponding estimation errors, Γ_w＝diag[τ_w1,τ_w2,τ_w3,τ_w4,τ_w5,τ_w6]. Deriving and substituting V into equations (34), a controller (39) and adaptive laws (40) and (41) are available

The application of the Young inequality has

According to the adaptive law (41)

So that there are

Further simplified to obtain formula (43)

Order to

Then it can be known as

Or

Or is

Then can obtain

Therefore variable s, the estimated error matrix

And estimation error

Consistent final bounding, and convergence to sets:

in the formula, λ_min(K) Representing momentsMinimum eigenvalues of matrix K. And then has a transformation error epsilon_iConsistent final bounding and convergence on

According to the function S_i(ε_i) Property 2 of (2), the obtainable constraint (25), i.e. the tracking error e of the OBFN dynamics model (22)_iAnd obtaining the pre-specified dynamic performance and steady-state response after the certification.

The following examples were used to demonstrate the beneficial effects of the present invention:

the first embodiment is as follows:

the track tracking control method of the submarine flight node is specifically prepared according to the following steps:

compared with the prior art

If the control requirement of the submarine flight node trajectory tracking under the influence of ocean current disturbance, model uncertainty and propeller fault is to be realized, the invention algorithm is also provided with a fault detection-based scheme, an adaptive neural network and other schemes, the two schemes are briefly introduced below and compared with the algorithm.

Scheme based on fault detection

Document [4] (Sun B, Zhu D, Yang S X.A Novel Tracking Controller for Autonomous Underwater Vehicles with thrust Fault adaptation [ J ]. Journal of Navigation,2016,69(3): 593-. After a normal propeller reaches a thrust limit, quantum behavior particle swarm optimization is introduced for using a fault propeller with a limit, and a solution for controlling redistribution problem is found in a limit range. In the document [5] (zhang jun, zhuangzai, autonomous underwater robot propeller fault detection, separation and reconstruction [ J ]. Nanjing university of aerospace, 2011(s1):142 + 146.), aiming at the problem that a residual error threshold value is not easy to select in an underwater robot fault diagnosis residual error method, an observer-based underwater robot propeller fault detection and separation method is provided, a fault detection observer is constructed to decouple a propeller fault and a residual error signal, so that only residual errors related to the propeller fault are monotonous and changed, and a larger threshold value can be selected for fault detection to improve the reliability of a diagnosis system. However, compared with the algorithm of the invention, the scheme separately designs a set of diagnosis fault-tolerant models for the propeller faults without considering factors influencing the OBFN control, such as ocean current disturbance, model uncertainty and the like.

Therefore, the algorithm of the invention is improved on the basis of the method, by regarding the ocean current disturbance, the model uncertainty and the propeller fault as the integral uncertainty of the system, using the radial basis function neural network to approximate the uncertainty, and introducing the adaptive strategy to estimate the upper bound of the approximation error, so that several factors influencing the OBFN control accuracy are included in the design of the controller and are closer to the actual engineering requirements.

Neural network based scheme

The neural network is mainly used for approaching the problem of model uncertainty or unknown external disturbance of the AUV, thruster faults are taken into consideration as a general uncertainty part together with the model uncertainty and the external disturbance, the disturbance is estimated by using the neural network, and relatively good control schemes can be obtained by applying some common control methods such as PID control, sliding mode control, backstepping control, adaptive control and the like, such as [6] - [8] ([6] Jiaming, Zhangjun, Qixue, and the like, the neural network-based underwater robot three-dimensional track tracking control [ J ] control theory and application, 2012, 29(7) 56-62.[7] Brookada, Zhu-strange, self-owned underwater robot fault-tolerant control based on adaptive region tracking [ J ]. university of Shandong: Eryu edition, 2017, 47(5) 57-63.[8] Zhang Jun, self-contained underwater robot adaptive area tracking control [ J ] mechanical engineering report 2014, 50(19):50-57 ].

However, compared with the algorithm of the present invention, the above scheme does not consider the overshoot problem of the control, and the control precision is highly dependent on the selection of the model parameters. Therefore, the algorithm of the invention is improved on the basis, and the convergence speed, the overshoot and the tracking error obtain the preset performance by introducing the preset performance method and the error transformation, thereby relaxing the requirement on the selection of the control parameters to a certain extent.

Preparation of simulation

In order to verify the effectiveness of the control method designed by the invention, the control method is applied to an OBFN model for simulation verification, and the influence caused by model uncertainty, ocean current disturbance and propeller fault is considered. The corresponding hydrodynamic coefficients, inertial coefficients, and initial values of position and attitude of the OBFN model are shown in tables 1-3, respectively.

TABLE 1 OBFN hydrodynamic coefficient

TABLE 2 OBFN inertia coefficients

TABLE 3 OBFN position and posture simulation initial value table

Model uncertainty

In order to facilitate simulation analysis, the invention quantifies model uncertainty. Consider 20% of the model nominal value as a modeling error and incorporate it into the simulation module as part of the perturbation.

Disturbance of ocean currents

A first order Gaussian-Markov process is introduced into the simulation process applied to the ocean current disturbance, and the expression is as follows:

in the formula, V_cIs under the terrestrial coordinate systemThe size of the ocean current, omega, is Gaussian white noise with mean and variance both 1; mu is 3. The invention assumes that the direction of the ocean current is constant and is the same as the positive direction of the X axis under the terrestrial coordinate system.

Propeller failure

Since the propeller arrangement of the OBFN employs a full drive mode, the arrangement is substantially the same in all directions, as shown in fig. 2. Therefore, in the simulation, only a certain fixed propeller is considered to be out of order, and the failure condition of any propeller can be represented. The invention assumes that the propeller No. 1 is a failure propeller, the failure mode of the propeller is shown as a formula (51),

controller parameters

The steady-state control precision of the system is required to reach 0.0035. The tracking control performance considering OBFN position and attitude expectation is designed as: (1) the steady-state tracking error does not exceed 0.0035; (2) minimum convergence speed limit is e^-0.15t(ii) a (3) The system response is not overshot. From which a performance function p can be determined_i(t) and δ_iThe values of (a) are shown in Table 4.

Table 4 preset performance parameter values

The controller parameters are selected to be λ ═ diag [0.125,0.125,0.125,0.125,0.125,0.125]、K＝diag[0.6,0.6,0.6,0.6,0.6,0.6]σ ═ 0.01; the adaptive gain is chosen to be tau_wi＝τ_μ0.5, 0.01 for beta and 0.01 for gamma; taking the number of nodes of the hidden layer of the RBF neural network as j-7, and expressing the center of the Gaussian function as c-c₁,...,c₇]The value is shown as formula (52), and the base width b_j＝0.09。

Simulation analysis

Considering that the trajectory that is desired to be tracked is complex, most cases can be covered and thus representative. Therefore, the invention selects a spiral descending navigation track as the expected track, and the specific expression is as follows:

x_d＝2sin(0.1t),y_d＝2cos(0.1t)+2,z_d＝-0.5144t

φ_d＝0,θ_d＝0,ψ_d＝0

η_d＝[x_d；y_d；z_d；φ_d；θ_d；ψ_d]

in the simulation analysis, the propeller failure mode is based on equation (51) and takes into account the model uncertainty and the effect of ocean current disturbances on the OBFN. Fig. 3-8 show 6-degree-of-freedom trajectory tracking error curves for the OBFN. Wherein, the solid line curve represents the tracking error curve of the position and attitude angle of the adaptive tracker (39) - (41) with the preset performance, and the dotted line curve represents the preset performance boundary.

As can be seen from fig. 3 to 8, the method provided by the present invention maintains the tracking error of both the position and attitude angles within the preset limits determined by the performance function, and obtains a good dynamic process and a desired steady-state control accuracy.

The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (7)

1. A track tracking control method of a submarine flight node is characterized by comprising the following steps: the method comprises the following specific processes:

step one, establishing an OBFN dynamic model based on a Fossen outline six-degree-of-freedom nonlinear model; the specific process is as follows:

the dynamic model of the OBFN is represented by a six-degree-of-freedom nonlinear model based on the Fossen outline:

the OBFN is a submarine flight node;

in the formula, M_ηA derived variable for M, M being a mass inertia matrix for OBFN; c_RBηIs C_RBDerived variable of (2), C_RBA matrix of coriolis and centripetal forces that is a rigid body of the OBFN; c_AηIs C_ADerived variable of (2), C_AAdding a matrix of coriolis forces and centripetal forces of mass to the OBFN; d_ηD is a derived variable of D, and D is a hydrodynamic damping matrix; g_ηForce and moment vectors generated by gravity and buoyancy of the OBFN, wherein eta is a six-degree-of-freedom position and attitude vector of the OBFN under a fixed coordinate system;

is the first derivative of η;

is the second derivative of η;

is the first derivative of displacement vector of OBFN relative to ocean current under a fixed coordinate system; τ is the actual control force of the propeller of the OBFN;

step two, transforming the dynamic model of the OBFN established in the step one to obtain a transformed dynamic model of the OBFN;

step three, defining a performance function;

step four: performing error transformation on the transformed OBFN dynamic model obtained in the step two according to the performance function defined in the step three;

selecting parameters of a radial basis function neural network;

designing a self-adaptive track tracking controller based on the fourth step and the fifth step;

in the step one

Derived variable M of M_η＝MJ^-1J is a conversion matrix between the fixed coordinate system and the moving coordinate system;

C_RBderived variable of

Is the first derivative of J, v is the velocity and angular velocity of OBFN in motion coordinate system, v ═ u', a, w, p, q, r]^T，

In the formula, u' is the surging speed of the OBFN in a moving coordinate system, a is the surging speed of the OBFN in the moving coordinate system, w is the surging speed of the OBFN in the moving coordinate system, p is the transverse inclination angle speed of the OBFN in the moving coordinate system, q is the surging angle speed of the OBFN in the moving coordinate system, r is the shaking head angular speed of the OBFN in the moving coordinate system, and T is the transposition;

C_Aderived variable C of_Aη＝C_A(v_r)J^-1，v_rVelocity of OBFN relative to ocean current;

derived variable D of D_η＝D(v_r)J^-1；

The six-freedom-degree position and attitude vector eta of the OBFN in a fixed coordinate system is [ x, y, z, phi, theta, psi [ ]]^T

Wherein x is the displacement of the OBFN in the x-axis direction under the fixed coordinate system, y is the displacement of the OBFN in the y-axis direction under the fixed coordinate system, z is the displacement of the OBFN in the z-axis direction under the fixed coordinate system, phi is the transverse inclination angle of the OBFN under the fixed coordinate system, theta is the longitudinal inclination angle of the OBFN under the fixed coordinate system, and psi is the rock head angle of the OBFN under the fixed coordinate system;

first derivative of displacement vector of OBFN relative to ocean current under fixed coordinate system

v_r＝v-v_c，v_cThe speed of the ocean current under the motion coordinate system is used as the speed of the ocean current;

in the second step, the dynamic model of the OBFN established in the first step is transformed to obtain the transformed dynamic model of the OBFN; the specific process is as follows:

the fault influence of the propeller of the OBFN is expressed in a thrust distribution matrix form and is defined as delta B;

the actual control force and torque of the propeller of the OBFN are rewritten as τ + Δ τ:

τ+Δτ＝(B₀-KB)u＝(B₀+ΔB)u (2)

in the formula, B₀Is the nominal value of the thrust distribution matrix B, u is the control input of the propeller of the OBFN, B is the thrust distribution matrix, K is a diagonal matrix whose elements K_ii∈[0,1]；

Equation (1) transforms to an OBFN dynamics model:

in the formula, M_η0Deriving a variable M for M_ηNominal value of (C)_RBη0Is C_RBDerived variable C_RBηNominal value of (C)_Aη0Is C_ADerived variable C_AηNominal value of (D)_η0Deriving a variable D for D_ηNominal value of (g)_η0Is g_ηA nominal value of (d); f represents the total uncertainty of the trajectory tracking control system of the OBFN;

the total uncertainty F expression of the trajectory tracking control system of the OBFN is as follows:

in the formula (I), the compound is shown in the specification,

representing the effect of the ocean current disturbance; Δ denotes an uncertainty value, Δ M_ηIs M_ηOf an indeterminate value of, Δ C_RBηIs C_RBηOf an indeterminate value of, Δ C_AηIs C_AηOf indeterminate value, ΔD_ηIs D_ηUncertain value of,. DELTA.g_ηUncertainty values, η, of force and moment vectors generated for gravity and buoyancy_rIs the displacement vector of OBFN relative to ocean current under a fixed coordinate system.

2. The method for controlling the trajectory tracking of the subsea flight node according to claim 1, wherein: defining a performance function in the third step; the specific process is as follows:

defining a performance function:

ρ(t)＝(ρ₀-ρ_∞)e^-kt+ρ_∞ (5)

in the formula, ρ₀、ρ_∞K is a normal number; rho (t) is a performance function, and t is time;

utilizing the performance function rho (t) to calculate the position and attitude angle error e of the OBFN in a fixed coordinate system_i(t) is expressed as:

in the formula, e_i(t) is the position and attitude angle error of the OBFN in a fixed coordinate system, i is a variable, and since the position and attitude angle error of the OBFN comprises 6 degrees of freedom, i is 1,2,3,4,5 and 6; delta_iIs a variable, 0 is not more than delta_i≤1；ρ_i(t) is the performance function for the ith degree of freedom.

3. The method for controlling the trajectory tracking of the subsea flight node according to claim 2, wherein: in the fourth step, the OBFN dynamic model transformed in the second step is subjected to error transformation according to the performance function defined in the third step; the specific process is as follows:

performing error transformation on the OBFN dynamic model formula (3) in the second step according to the performance function defined in the third step;

defining an auxiliary function S_i(ε_i)：

Wherein epsilon_iE (-infinity, + ∞) is called the transformation error;

auxiliary function S_i(ε_i) Has the following properties:

(1)S_i(ε_i) Smooth and strictly monotonic increase;

(2)

(3)

according to S_i(ε_i) Is represented by the formula (6) as an equivalent

e_i(t)＝ρ_i(t)S_i(ε_i) (8)

Because of S_i(ε_i) Presence of an inverse function, resulting in a transformation error epsilon_i：

Consider S_i(ε_i) In the form of equation (7), then

In the formula, z_iAn auxiliary variable for the ith degree of freedom, z_i＝e_i(t)/ρ_i(t)；

Let epsilon_iThe first and second derivatives are taken over time t:

in the formula, r_iIs an auxiliary variable for the ith degree of freedom,

is r_iThe first derivative of (a) is,

representing the actual position and attitude angle of the OBFN,

represents the desired position and attitude angle of the OBFN, i is 1,2,3,4,5, 6;

as the first derivative of the auxiliary variable of the ith degree of freedom, e_iFor the position and attitude angle error of the OBFN in the fixed coordinate system,

is e_iThe first derivative of (a) is,

is the first derivative of the ith degree of freedom performance function;

is the second derivative of the ith degree of freedom performance function;

taking the error variable s epsilon R⁶Is in the form of

Wherein ε ═ ε₁,ε₂,ε₃,ε₄,ε₅,ε₆]^T,λ＝diag[λ₁,λ₂,λ₃,λ₄,λ₅,λ₆]More than 0 is a parameter to be designed;

is the first derivative of ε; t is transposition; r is a real number domain; lambda [ alpha ]_iThe parameter to be designed for the ith degree of freedom, i ═ 1,2,3,4,5, 6;

note the book

D＝-F，

The OBFN kinetic model formula (3) is abbreviated as follows:

wherein A, B, D is an intermediate variable;

further comprising:

in the formula (I), the compound is shown in the specification,

is the first derivative of s and is,

is the first derivative of epsilon and,

is the second derivative of ε; l and R are intermediate variables.

4. The method for controlling the trajectory tracking of the subsea flight node according to claim 3, wherein: l ═ L₁,l₂,l₃,l₄,l₅,l₆]^T，

i＝1,2,3,4,5,6,

R＝diag[r₁,r₂,r₃,r₄,r₅,r₆]

In the formula I_iIs an intermediate variable of the ith degree of freedom,

auxiliary variable r for ith degree of freedom_iThe first derivative of (a).

5. The method for controlling the trajectory tracking of the subsea flight node according to claim 4, wherein: selecting parameters of a radial basis function neural network in the fifth step; the specific process is as follows:

d exists in the simplified OBFN dynamic model formula (14), and is approximated by an RBF neural network, wherein the process is as follows:

taking the neural network input as

The estimate of D is written as

In the formula (I), the compound is shown in the specification,

as an estimate of the weight matrix,

h (x) is a radial basis function, h (x) h₁(x),h₂(x),...,h_j(x),...h_m(x)^T]∈R^mM is the number of hidden nodes of the RBF neural network; h is_j(x) A radial basis function in the j dimension; j is more than or equal to 1 and less than or equal to m;

e＝[e₁,e₂,e₃,e₄,e₅,e₆]，e_ithe position and attitude angle error of the OBFN in the fixed coordinate system is represented by i 1,2,3,4,5,6,

is the first reciprocal of e and T is transposed.

6. The method for controlling the trajectory tracking of the subsea flight node according to claim 5, wherein: the number m of hidden nodes of the RBF neural network is more than or equal to 3.

7. The method for controlling the trajectory tracking of the subsea flight node according to claim 6, wherein: in the sixth step, an adaptive trajectory tracking controller is designed based on the fourth step and the fifth step; the specific process is as follows:

the following adaptive trajectory tracking controller is proposed:

in the formula (I), the compound is shown in the specification,

represents the upper bound mu of the approximation error^*Is estimated by the estimation of (a) a,

is composed of

The first order reciprocal of (1), wherein, | s | | | is a two-norm of an error variable s, K is more than 0, and σ is more than 0 and is a control parameter to be designed; tau is_wi＞0,β＞0,τ_μThe self-adaptive gain is more than 0, and gamma is more than 0; s ═ s₁,s₂,s₃,s₄,s₅,s₆]，s_iI is a value of the error variable s, 1,2,3,4,5, 6.

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