CN113238567B - Benthonic AUV weak buffeting integral sliding mode point stabilizing control method based on extended state observer - Google Patents
Benthonic AUV weak buffeting integral sliding mode point stabilizing control method based on extended state observer Download PDFInfo
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Abstract
A benthonic AUV weak buffeting integral sliding mode point stabilizing control method based on an extended state observer relates to the field of underwater vehicle control, aims at the problems of limited control precision and low adjusting speed of a control method in the prior art, and comprises the following steps: the method comprises the following steps: establishing a benthonic AUV motion equation, and constructing a benthonic AUV error model according to the benthonic AUV motion equation; step two: constructing a benthonic AUV point stabilized tracking error model according to the benthonic AUV error model; step three: designing a self-adaptive supercoiled extended state observer; step four: constructing a second-order buffeting-free nonsingular integral terminal sliding mode surface; step five: and designing a controller according to a benthonic AUV point stabilized tracking error model, a self-adaptive supercoiled extended state observer and a second-order buffeting-free nonsingular integral terminal sliding mode surface. The method and the device can converge to a stable state within a limited time, can keep better stability after the pose error converges to zero, and have high convergence speed.
Description
Technical Field
The invention relates to the field of underwater vehicle control, in particular to a benthonic AUV weak trembling integral sliding mode point stabilizing control method based on an extended state observer.
Background
The ocean occupies two thirds of the total area of the earth, and the abundant mineral and aquatic resources are deeply valued by all countries in the world. As an important tool for marine information detection and marine resource development, Autonomous Underwater Vehicles (AUVs) play a very large role in various fields. At present, as the development demand for deeper and wider oceans increases, the existing cruise-type AUV suitable for large-range operation and hover-type AUV suitable for small-range operation have not been able to meet the demand. The main reasons are that the fixed-point observation capability of the cruise AUV is poor, and the large-range investigation capability of the hovering AUV is poor. Under the background, the concept of the benthonic AUV is also proposed, and as a novel underwater vehicle combining all characteristics of the hovering AUV and the cruise AUV, the benthonic AUV is characterized in that the benthonic AUV can meet the requirement for identifying a tiny target while completing a submarine seat elevation precision detection task. However, due to the complex motion system, such modified AUV is also a typical nonlinear strong coupling system, which not only has the research obstacles of AUV commonalities such as poor convergence performance of control method, complex working environment, difficult accurate solution of hydrodynamic parameters, but also has the influence factors of hydrodynamic coefficient perturbation, easy collision of carriers (huge, sea peak correction. intelligent underwater robot research progress [ J ] Science and Technology introduction, 2015,33(23):66-71.pan sho, JIU haifeng. The concept diagram of the benthic AUV is shown in figure 1, figure 2 and figure 3, and the outline diagram is shown in figure 4.
The final goal of the benthonic AUV navigation motion is that the benthonic AUV can sit in a fixed circle with the preset position as the center of the circle from the bottom to the sea bottom. Accurate trajectory tracking precision and point stabilization precision are important determinants that the AUV can accurately reach a preset seabed area. In navigation and fixed-point hovering, factors such as external interference, uncertainty of parameters of the benthonic AUV model, limitation of an actuator and the like have great influence on the control precision and stability of the benthonic AUV. Therefore, high point-stabilizing control accuracy and stability are important for accurate landing of the benthonic AUV, and the fixed-point hovering motion of the benthonic AUV after reaching the offshore fixed area is an extremely important step for landing the benthonic AUV to the seabed fixed position by adjusting the vertical reverse thrust. The premise for enabling the benthonic AUV to realize fixed-point hovering motion and complete specified tasks is to design an effective control law and guarantee high-precision sitting at a fixed point on the sea bottom in a short time (Xuyu such as Xiaokun. Intelligent ocean robot technical progress [ J ]. Automation report, 2007(05):518-521.Xu yuru, Xiao Kun. technical progress of intracellular ocean robot [ J ]. Acta Automatica Sinica,2007(05): 518-521). The current common AUV point stabilization method is usually to design a robust controller for external disturbance or to approximate the total interference of the system by a neural network. However, such methods have the following disadvantages: firstly, the control precision is limited or the calculated amount is overlarge; and secondly, the adjusting speed is slower. Therefore, the existing AUV point stabilization control method cannot meet the requirement of the benthonic AUV on the bottom movement.
Disclosure of Invention
The purpose of the invention is: aiming at the problems of limited control precision and low adjustment speed of a control method in the prior art, the benthonic AUV weak buffeting integral sliding mode point stabilizing control method based on the extended state observer is provided.
The technical scheme adopted by the invention to solve the technical problems is as follows:
a benthonic AUV weak buffeting integral sliding mode point stabilizing control method based on an extended state observer comprises the following steps:
the method comprises the following steps: establishing a benthonic AUV motion equation, and constructing a benthonic AUV error model according to the benthonic AUV motion equation;
step two: constructing a benthonic AUV point stabilized tracking error model according to the benthonic AUV error model;
step three: designing a self-adaptive supercoiled extended state observer;
step four: constructing a second-order buffeting-free nonsingular integral terminal sliding mode surface;
step five: and designing a controller according to a benthonic AUV point stabilized tracking error model, a self-adaptive supercoiled extended state observer and a second-order buffeting-free nonsingular integral terminal sliding mode surface.
Further, the benthonic AUV equation of motion is expressed as:
where M is a mass inertia matrix, η [ [ ξ n ζ φ θ ψ [ ]]ΤWhen a benthonic AUV moves under a fixed coordinate system, the position and the posture of six degrees of freedom in a three-dimensional space are divided into upsilon [ uv w p q r ═ v]ΤThe speed and the angular speed in the three-dimensional space when moving under the carrier coordinate system,
when the benthonic AUV moves, a coordinate transformation matrix between a coordinate system and a carrier coordinate system is fixed,
for the nominal values of the parameters of the model,
the control force and the moment vector generated when the benthonic AUV actuator operates,
for model parameter uncertainty and ambianceThe time-varying interference is superposed with the comprehensive interference item,
perturbation values of model parameters, τd(t) is the external time-varying interference,
is the first derivative of v and,
is a comprehensive interference item formed by superposing model parameter uncertainty and external time-varying interference,
the first derivative of η.
Further, the benthonic AUV point stabilized tracking error model is expressed as:
in the formula (I), the compound is shown in the specification,
as an auxiliary variable, the number of variables,
is omegaeThe first derivative of (a) is,
is omegaeThe second derivative of (a) is,
is etaeFirst derivative of, ηeIs the position tracking error;
b＝R(η)M-1；
the above-mentioned
The following relationship is satisfied:
||F(t)||＜Dm
Dmactual value of unknown boundary, δ, of F (t)mIs composed of
Is determined by the actual value of the unknown boundary,
is deltamIs determined by the estimated value of (c),
is composed of
B is the control gain, F (t) is the auxiliary variable,
is the first derivative of F (t),
is the first derivative of b and is,
the first derivative of τ.
Further, the adaptive supercoiled extended state observer is represented as:
in the formula (I), the compound is shown in the specification,
is an observer variable, K1、K2To observer gain, K1、K2Are all positive fixed diagonal arrays,
as an auxiliary variable, the auxiliary variable expression is as follows:
K1＝diag(K11,K12,K13,K14,K15,K16)
K2＝diag(K21,K22,K23,K24,K25,K26)
in the formula (I), the compound is shown in the specification,
the expression of i ═ 1,2,3,4,5,6 is as follows:
in the formula, mu1i,μ2iAre all normal numbers, i is 1,2,3,4,5,6,
estimating an error for an observer;
the adaptation law is represented as:
in the formula (I), the compound is shown in the specification,
K1i(t) are all adaptive variables, c1i、c2i、c3i、HiAre all control parameters and are positive numbers.
Further, the second-order bufferless nonsingular integral terminal sliding mode surface is expressed as:
wherein λ is a positive number, and β ∈ R6×6Is a diagonal matrix, s is a sliding mode surface function, sigma is an auxiliary variable,
for the control parameter, d τ is the integration operator.
Further, the control law of the second-order buffeting-free nonsingular integral terminal sliding mode surface is expressed as:
τ＝τ1+τ2
in the formula (I), the compound is shown in the specification,
in the formula, k4For switching term gain, normal, k6Is a positive number,/1And l2In order to control the parameters of the device,
is an estimated value of the observer state variable,
is tau2The first derivative of (d), phi are integral operators,
is composed of
The first derivative of (a);
the self-adaptive law of the second-order buffeting-free nonsingular integral terminal sliding mode surface is expressed as follows:
in the formula, k5Is a normal number.
The invention has the beneficial effects that:
the algorithm improves a discontinuous time invariant control method, ensures the continuity of a control law by designing a second-order buffeting-free nonsingular integral terminal sliding mode controller, and can obtain required steady-state precision within limited time. The convergence algorithm can converge to a stable state within a limited time, the pose error can keep better stability after converging to zero, the convergence speed is high, the change of the controller is more gentle, the curve is smoother, and the convergence speed and the robustness of the controller are superior to those of the existing controller in the error convergence process. Compared with the existing controller, the controller has the advantages that the convergence time is shortened by 47%, and in response curves of the vertical speed, the yaw rate and the pitch angle rate, the convergence time is shortened by 25% compared with the existing controller.
Drawings
FIG. 1 is a conceptual diagram of a benthic AUV 1;
FIG. 2 is a conceptual diagram of a benthic AUV 2;
FIG. 3 is a conceptual diagram of a benthic AUV of FIG. 3;
FIG. 4 is a schematic view of a submersible AUV;
FIG. 5 is a graph of AUV longitudinal tracking error response;
FIG. 6 is a graph of AUV lateral tracking error response;
FIG. 7 is a graph of AUV vertical tracking error response;
FIG. 8 is a AUV pitch angle tracking error response graph;
FIG. 9 is a graph of AUV yaw angle tracking error response;
FIG. 10 is a graph of AUV longitudinal velocity response;
FIG. 11 is a graph of AUV lateral velocity response;
FIG. 12 is a graph of AUV vertical velocity response;
FIG. 13 is an AUV yaw rate response graph;
fig. 14 is an AUV pitch rate response plot.
Detailed Description
It should be noted that, in the present invention, the embodiments disclosed in the present application may be combined with each other without conflict.
The first embodiment is as follows: the present embodiment is specifically described with reference to fig. 1, fig. 2, fig. 3, and fig. 4, and a benthic AUV weak buffeting integral sliding mode point stabilization control method based on an extended state observer according to the present embodiment includes the following steps:
the method comprises the following steps: establishing a benthonic AUV motion equation, and constructing a benthonic AUV error model according to the benthonic AUV motion equation;
step two: constructing a benthonic AUV point stabilized tracking error model according to the benthonic AUV error model;
step three: designing a self-adaptive supercoiled extended state observer;
step four: constructing a second-order buffeting-free nonsingular integral terminal sliding mode surface;
step five: and designing a controller according to a benthonic AUV point stabilized tracking error model, a self-adaptive supercoiled extended state observer and a second-order buffeting-free nonsingular integral terminal sliding mode surface.
Related Key technology
The kinematic and kinetic equations of benthic AUV are expressed in Newton-Euler equations based on rigid body motion in fluids as proposed by Fossen (Debitto P A. fuzzy logic for depth control of infinite undersea vessels. Proeekings of Symposium of Autonomus Underwater vessel Technology [ J ].1994: 233-241.):
where M is a mass inertia matrix, η [ ξ n ζ φ θ ψ ]]ΤRepresenting six-degree-of-freedom position and posture in three-dimensional space when the benthonic AUV moves under a fixed coordinate system, and upsilon ═ u v w p q r]ΤRepresenting the speed and angular velocity in three-dimensional space when moving under a carrier coordinate systemThe degree of the magnetic field is measured,
when representing the benthonic AUV, fixing a coordinate transformation matrix between a coordinate system and a carrier coordinate system;
a Coriolis matrix containing additional mass items and a centripetal force matrix;
is a fluid damping matrix;
the restoring force and restoring moment vector generated by the gravity and buoyancy acting on the bentable AUV.
The control force and moment vector quantity generated when the benthonic AUV actuator operates;
the disturbance vector caused by the external interference.
The external disturbances experienced by an AUV in the ocean are quite complex and have a significant impact on the dynamics and control performance of the underwater vehicle. The method considers model uncertainty and ocean current disturbance, considers the model uncertainty and the ocean current disturbance as a disturbance lumped term, and considers feasible mathematical expression forms of the disturbance lumped term.
Sliding mode control: sliding Mode Control (SMC) is also called variable structure control, and from the aspect of control characteristics, sliding mode control belongs to a nonlinear control method, and the control strategy is different from other controls in that the "structure" of a system is not fixed, but can be purposefully and continuously changed according to the current state of the system in a dynamic process, so that the system is forced to move according to a state track of a predetermined "sliding mode". The control law designed based on the sliding mode control method is usually discontinuous, and the sliding mode control has the advantages of fast output response, simple engineering application, strong robustness and the like.
And (3) expanding the state observer: the disturbance action suffered by the control system is expanded into a new state variable, the new state variable is observed and approximated by using a feedback mechanism, and the expanded state observer does not need to measure the disturbance action or know a specific model of the disturbance, so that the method is widely applied to engineering practice. For the underwater robot control system with the characteristics of strong coupling and nonlinearity, the finite time supercoiled extended state observer can carry out online observation on the total disturbance of the system, and the method is a method for effectively solving the problem of unknown total disturbance in the system.
Parameter definition: m is a mass inertia matrix; eta ═ ξ n ζ phi psi]ΤThe six-degree-of-freedom position and attitude value of the benthonic AUV under the fixed coordinate system; etad＝[ξd nd ζd φd θd ψd]ΤThe six-degree-of-freedom position and attitude expected value of the benthonic AUV under a fixed coordinate system; etaeIs the position tracking error; omega is an auxiliary state variable; υ ═ u v w p q r]ΤThe speed and the angular velocity quantity under the motion coordinate system are obtained; r (eta) is a conversion matrix between a fixed coordinate system and a motion coordinate system; c (upsilon) is a Coriolis force and centripetal force matrix of a rigid body; d (upsilon) is a hydrodynamic damping matrix; g (η) is a force vector and a moment vector generated by gravity and buoyancy; tau is the control force and moment generated by the propulsion system; tau isdExternal interference; z is an observer system auxiliary variable;
observing the observer system; f is a comprehensive interference item;
the observed value of the comprehensive interference item is obtained;
adapting parameters for the controller; s is a sliding mode surface function;
the key steps of the invention patent are as follows: the invention designs a self-adaptive buffeting-free non-singular integral sliding mode controller based on an AUV point stabilization control error model to solve the problem of benthic AUV point stabilization control. In the controller design, firstly, an adaptive supercoiled extended state observer is adopted to eliminate the influence of external interference and model parameter uncertainty on a control system, then a new second-order bufferless nonsingular integral sliding mode function is designed, an AUV point stabilizing control law is designed based on the sliding mode function, and a self-adaptive method is adopted to eliminate the first order derivative of disturbance in second-order sliding mode control. The designed controller proves the limited time convergence performance through the Lyapunov stability theory. Finally, simulation tests prove that the designed controller has better control performance compared with the existing controller.
By adopting the method, the benthonic AUV motion control system can realize point stabilization control in a limited time under the condition of external interference, and a good expected effect is achieved.
Benthonic AUV motion system model
The formula (1) is used for establishing a benthonic AUV motion equation considering external interference
Where M is a mass inertia matrix, η [ ξ n ζ φ θ ψ ]]ΤRepresenting six-degree-of-freedom position and posture in three-dimensional space when the benthonic AUV moves under a fixed coordinate system, and upsilon ═ u v w p q r]ΤRepresenting the velocity and angular velocity in three-dimensional space when moving in the carrier coordinate system,
when representing the benthonic AUV, fixing a coordinate transformation matrix between a coordinate system and a carrier coordinate system;
a Coriolis matrix containing additional mass items and a centripetal force matrix;
is a fluid damping matrix;
restoring force and restoring moment vectors generated by the action of gravity and buoyancy on the bentable AUV;
the control force and moment vectors are generated when the benthonic AUV actuator operates;
the disturbance vector caused by the external interference. For the AUV motion mathematical model (2), the model uncertainty is represented by inertia uncertainty, hydrodynamic coefficient uncertainty and uncertainty of gravity and buoyancy, namely the values of M, C (upsilon), D (upsilon) and g (eta) matrixes are not completely accurate. Model uncertainty is typically expressed in the form:
in the formula, C (ν), D (ν), and g (η) represent actual values of model parameters.
And substituting the model parameter uncertainty model (3) into the AUV motion mathematical model (2) to obtain:
in the formula (I), the compound is shown in the specification,
AUV motion mathematical model reference formula (4) considering external time-varying interference and model uncertainty, in the form:
in the formula (I), the compound is shown in the specification,
and a comprehensive interference item representing superposition of model parameter uncertainty and external time-varying interference, and the form is as follows:
in the formula (I), the compound is shown in the specification,
representing model parametersPerturbation portions of numbers, and all with unknown boundaries; tau isd(t) represents an external time-varying disturbance.
Assume that 1: the invention assumes that the external interference is taudThe boundary is existed, the boundary is unknown, and the first derivative thereof is existed, namely the following relation is satisfied:
in the formula (I), the compound is shown in the specification,
is an unknown positive number.
Definition variable d (t) RM-1τd(t) from τd(t) and
is known as the boundedness of d (t) and
also with boundaries, the boundary conditions being unknown, i.e. satisfying the formula
In the formula (I), the compound is shown in the specification,
is an unknown positive number.
Assume 2: defining variables
P represents a model parameter in the model, wherein the superposition term is animated, and a boundary exists in P, and the first derivative of P with respect to time also exists in the boundary, and the boundary is unknown, namely the following relation is satisfied:
in the formula (I), the compound is shown in the specification,
are all unknown positive numbers.
Point-stabilized control error model
For the convenience of the controller design of the invention, on the basis of the benthonic AUV error model (5), the model needs to be further deformed, and a new state variable is defined firstly:
ω＝R(η)υ (6)
in the formula (I), the compound is shown in the specification,
deriving from (6):
the benthonic AUV motion mathematical model can be converted into the following form through formulas (5), (6) and (7):
defining the benthonic AUV point stabilized tracking error variable as follows:
ηe＝η-ηd
in the formula (I), the compound is shown in the specification,
indicating that the AUV is in the desired pose,
and (3) converting the AUV point stabilization control problem into an error convergence problem by establishing an error model in a vertical (8) form. The basic goal of the control law design of the invention is to make the pose error etaeCan converge to zero within a limited time and maintain a steady state.
For omegaeThe formula is derived:
thus, the AUV three-dimensional point stabilized control error model is expressed as follows:
in the formula (I), the compound is shown in the specification,
b＝R(η)M-1；
and the comprehensive interference item represents the superposition of the external time-varying interference and the uncertainty of the model parameter.
From hypotheses 1 and 2, the synthetic interference f (t) is bounded, and the boundary unknown, whose first derivative with respect to time is also bounded, i.e., satisfies the following relationship:
in the formula, Dm、δmAre all unknown positive numbers. The deviation variables are defined as follows:
in the formula, deltamTo represent
Is determined by the actual value of the unknown boundary,
represents deltamIs determined by the estimated value of (c),
to represent
Is estimated. The invention can be realized by an adaptive control method during the design of the controller
The finite time of (c) converges.
Design of self-adaptive supercoiled extended state observer
The self-adaptive supercoiled extended state observer is designed to carry out on-line observation on the comprehensive interference and eliminate the influence of the comprehensive interference on the stability of a control system.
The method comprises the following steps: the observer auxiliary state variable z is defined according to the (10) AUV mathematical model, of the form:
z＝ωe+Ληe (11)
wherein z is [ z ]1,z2,z3,z4,z5,z6]T；
Is a positive fixed constant diagonal matrix.
Taking the derivative with respect to time for (11):
let G (η, ν, t) f (η, ν, t) + Λ ωeEquation (12) can be expressed as:
step two: taking the integrated interference term f (t) in equation (9) as an extended state variable, equation (9) can be extended to:
in the formula (I), the compound is shown in the specification,
representing the derivative of the extended state variable f (t) with respect to time.
Will be used in the design of a supercoiled state observer.
Step three: the observer state variable error model is defined as follows:
in the formula (I), the compound is shown in the specification,
is an estimate of the observer state variable,
representing the observer state variable error.
The state variable error based on (15) defines a supercoiled disturbance observer of the form:
in the formula, K1、K2Is the observer gain, which is a positive fixed diagonal matrix, K1、K2、
The expression is as follows:
K1＝diag(K11,K12,K13,K14,K15,K16)
K2＝diag(K21,K22,K23,K24,K25,K26)
in the formula，
The expression of i ═ 1,2,3,4,5,6 is as follows:
in the formula, mu1i,μ2iAll of (i ═ 1,2,3,4,5, and 6) are normal numbers.
K1i,K2i(i ═ 1,2,3,4,5,6) is updated in real time through an adaptive law, so that the disturbance observer achieves a better convergence effect, and the adaptive law is designed as follows:
in the formula, c1i、c2i、c3i、HiAre all known positive numbers.
For the extended state system (15), the observer state variable error is adaptively modified by the gain of the generalized supercoiled extended state observer (17) of (16)
Can converge to zero in a finite time.
Second-order buffeting-free sliding mode controller design
Based on a better buffeting eliminating effect of a second-order slip form, the invention provides a novel second-order buffeting-free nonsingular integral terminal slip form controller which is applied to AUV point stabilization control.
Designing a new second-order integral sliding mode function form as follows:
wherein λ is a known positive number, and β ∈ R6×6Known as diagonal matrix.
The following is derived from equation (18):
in order to enable the control system (9) to reach the sliding mode switching surface s equal to 0 within a limited time and then converge to an origin along the sliding mode surface within the limited time, a second-order sliding mode function in the form of a formula (18) is adopted, and a control law is designed as follows:
τ＝τ1+τ2 (20)
in the formula (I), the compound is shown in the specification,
in the formula, k4Is the switching term gain, which is a normal number. k is a radical of6Is a known positive number.
The equation (23) proves that the actual control law is continuous and smooth by integrating the differential control input containing the sign function, and no high-frequency switching term exists, so that the buffeting problem in the traditional sliding mode control is eliminated. The second-order buffeting-free terminal sliding mode controller provided by the invention is added with the integral term, so that the fast convergence can be realized, and a good control effect can be obtained.
The second-order integral sliding mode function based on the form of the formula (18) can generate a first derivative of comprehensive disturbance after derivation, and in order to eliminate the influence of the uncertain term, an adaptive law form of the following form is designed:
in the formula, k5Known as normal.
The adaptive law enables approximation of the first derivative of the synthetic disturbance with respect to time.
Theoretical basis
Benthonic AUV motion system model
The formula (1) is used for establishing a benthonic AUV motion equation considering external interference
Where M is a mass inertia matrix, η [ ξ n ζ φ θ ψ ]]ΤRepresenting six-degree-of-freedom position and posture in three-dimensional space when the benthonic AUV moves under a fixed coordinate system, and upsilon ═ u v w p q r]ΤRepresenting the velocity and angular velocity in three-dimensional space when moving in the carrier coordinate system,
when representing the benthonic AUV, fixing a coordinate transformation matrix between a coordinate system and a carrier coordinate system;
a Coriolis matrix containing additional mass items and a centripetal force matrix;
is a fluid damping matrix;
restoring force and restoring moment vectors generated by the action of gravity and buoyancy on the bentable AUV;
the control force and moment vectors are generated when the benthonic AUV actuator operates;
the disturbance vector caused by the external interference. For the AUV motion mathematical model (2), the model uncertainty is represented by inertia uncertainty, hydrodynamic coefficient uncertainty and uncertainty of gravity and buoyancy, namely the values of M, C (upsilon), D (upsilon) and g (eta) matrixes are not completely accurate. Model uncertainty is typically expressed in the form:
in the formula, C (ν), D (ν), and g (η) represent actual values of model parameters.
Substituting the model parameter uncertainty model (26) into the AUV motion mathematical model (25) yields:
in the formula (I), the compound is shown in the specification,
AUV motion mathematical model reference equation (27) considering external time-varying interference and model uncertainty, in the form:
in the formula (I), the compound is shown in the specification,
and a comprehensive interference item representing superposition of model parameter uncertainty and external time-varying interference, and the form is as follows:
in the formula (I), the compound is shown in the specification,
representing the perturbed part of the model parameters, and all having unknown boundaries; tau isd(t) represents an external time-varying disturbance.
Assume that 1: the invention assumes that the external interference is taudThe boundary is existed, the boundary is unknown, and the first derivative thereof is existed, namely the following relation is satisfied:
in the formula (I), the compound is shown in the specification,
is an unknown positive number.
Definition variable d (t) RM-1τd(t) from τd(t) and
is known as the boundedness of d (t) and
also with boundaries, the boundary conditions being unknown, i.e. satisfying the formula
In the formula (I), the compound is shown in the specification,
is an unknown positive number.
Assume 2: defining variables
P represents a model parameter in the model, wherein the superposition term is animated, and a boundary exists in P, and the first derivative of P with respect to time also exists in the boundary, and the boundary is unknown, namely the following relation is satisfied:
in the formula (I), the compound is shown in the specification,
are all unknown positive numbers.
Point-stabilized control error model
For the design of the controller, the model needs to be further deformed on the basis of the benthonic AUV error model (28), and a new state variable is defined firstly:
ω＝R(η)υ (29)
in the formula (I), the compound is shown in the specification,
deriving (29) as:
the benthonic AUV motion mathematical model can be converted into the following form through formulas (28), (29) and (30):
defining the benthonic AUV point stabilized tracking error variable as follows:
ηe＝η-ηd
in the formula (I), the compound is shown in the specification,
indicating that the AUV is in the desired pose,
and converting the AUV point stabilization control problem into an error convergence problem by establishing an error model in a vertical (31) form. The basic goal of the control law design of the invention is to make the pose error etaeCan converge to zero within a limited time and maintain a steady state.
For omegaeThe formula is derived:
thus, the AUV three-dimensional point stabilized control error model is expressed as follows:
in the formula (I), the compound is shown in the specification,
b＝R(η)M-1；
From hypotheses 1 and 2, the synthetic interference f (t) is bounded, and the boundary unknown, whose first derivative with respect to time is also bounded, i.e., satisfies the following relationship:
in the formula, Dm、δmAre all unknown positive numbers. The deviation variables are defined as follows:
in the formula, deltamTo represent
Is determined by the actual value of the unknown boundary,
represents deltamIs determined by the estimated value of (c),
to represent
Is estimated. The invention can be realized by an adaptive control method during the design of the controller
The finite time of (c) converges.
Theorem of finite time convergence
Consider the following control system:
it is assumed that there is a continuous differentiable function V (x) and an open set
Let Lyapunov function V (x) satisfy the following relation:
wherein, omega is more than 0 and less than 1, and lambda is positive number. Then, from
Starting from any point as a starting position, V (x) can reach V (x) 0 in a limited time, and the convergence time meets the following relation:
defining a vector
If x represents a two-norm of x, then x satisfies the following relationship:
||x||≤|x|
design of self-adaptive supercoiled extended state observer
The self-adaptive supercoiled extended state observer is designed to carry out on-line observation on the comprehensive interference and eliminate the influence of the comprehensive interference on the stability of a control system.
The method comprises the following steps: an observer auxiliary state variable z is defined according to the AUV mathematical model (32), of the form:
z＝ωe+Ληe (34)
wherein z is [ z ]1,z2,z3,z4,z5,z6]T；
Taking the derivative with respect to time for (34):
let G (η, ν, t) f (η, ν, t) + Λ ωeEquation (34) can be expressed as:
step two: taking the integrated interference term f (t) in equation (33) as the extended state variable, equation (9) can be extended to:
in the formula (I), the compound is shown in the specification,
representing the derivative of the extended state variable f (t) with respect to time.
Will be used in the design of a supercoiled state observer.
Step three: the observer state variable error model is defined as follows:
in the formula (I), the compound is shown in the specification,
is an estimate of the observer state variable,
representing the observer state variable error.
The supercoiled disturbance observer of the form is defined based on the state variable error of (38):
in the formula, K1、K2Is the observer gain, which is a positive fixed diagonal matrix, K1、K2、
The expression is as follows:
K1＝diag(K11,K12,K13,K14,K15,K16)
K2＝diag(K21,K22,K23,K24,K25,K26)
in the formula (I), the compound is shown in the specification,
the expression is as follows:
in the formula, mu1i,μ2iAll of (i ═ 1,2,3,4,5, and 6) are normal numbers.
K1i,K2i(i ═ 1,2,3,4,5,6) is updated in real time through an adaptive law, so that the disturbance observer achieves a better convergence effect, and the adaptive law is designed as follows:
in the formula, c1i、c2i、c3i、HiAre all known positive numbers.
For extended state systems (34), the observer state variable error is adaptively scaled by a generalized supercoiled extended state observer of (39) and gain of (40)
Can converge to zero in a finite time. The process of identification is described in the literature (Guerrero J A, Torres J, Creuze V, et al]Ocean Engineering,2020,200: 107080.). The interference observer adopted by the invention introduces adaptive gain, so that the control system has better robustness to external interference and perturbation of model parameters, meanwhile, the requirement on interference prior knowledge is relaxed, and the interference boundary is not necessary information for the controller any more, thus having good control effect on processing complex interference or interference with larger amplitude.
Second-order buffeting-free sliding mode controller design
Based on a better buffeting eliminating effect of a second-order slip form, the invention provides a novel second-order buffeting-free nonsingular integral terminal slip form controller which is applied to AUV point stabilization control.
Designing a new second-order integral sliding mode function form as follows:
wherein λ is a known positive number, and β ∈ R6×6Known as diagonal matrix.
The following is derived from equation (41):
in order to enable the control system (32) to reach the sliding mode switching surface s equal to 0 within a limited time and then converge to an origin along the sliding mode surface within the limited time, a second-order sliding mode function in the form of a formula (41) is adopted, and a control law is designed as follows:
τ＝τ1+τ2 (43)
in the formula, k4Is the switching term gain, which is a normal number. k is a radical of6Is a known positive number.
Equation (46) proves that the actual control law is continuous and smooth by integrating the differential control input containing the sign function, and no high-frequency switching term exists, so that the buffeting problem in the traditional sliding mode control is eliminated. The second-order buffeting-free terminal sliding mode controller provided by the invention is added with the integral term, so that the fast convergence can be realized, and a good control effect can be obtained.
The second-order integral sliding mode function based on the form of the formula (41) can generate a first derivative of comprehensive disturbance after derivation, and in order to eliminate the influence of the uncertain term, an adaptive law form of the following form is designed:
in the formula, k5Known as normal.
The adaptive law enables approximation of the first derivative of the synthetic disturbance with respect to time.
The limited time convergence of the designed controller is proved by the Lyapunov stability theory, and the proving process is divided into the following two steps:
(1) the consistent bounded stability of the closed-loop system is proved, so that the bounded property of the adaptive error variable is proved;
(2) the finite time convergence of the sliding-mode variable sigma is demonstrated.
To verify consistent bounded convergence of the controller of the present invention, a Lyapunov function of the form:
deriving (48) as:
in the formula (I), the compound is shown in the specification,
(49) the transformation can be as follows:
bringing (28) and (38) into (50) to obtain:
bringing equations (39) and (40) into (51) results:
the generalized supercoiled disturbance observer proposed by the formulas (34), (35) can be used for a finite time T1Realizing effective approximation to comprehensive interference F (T), i.e. when T > T1When the temperature of the water is higher than the set temperature,
therefore, equation (52) can be transformed into:
substituting (41) into (53) to obtain:
analytically available, V1＞0，
V is bounded, estimation error
Is consistent and ultimately bounded. Thus, it can be assumed that there is a positive constant
So that the inequality
This is true.
To demonstrate the system's finite time convergence, a lyapunov function of the form:
deriving (55) as:
substituting (38), (39), (40) and (41) into (56) to obtain:
in the formula (I), the compound is shown in the specification,
only the appropriate positive number k needs to be selected6Value of (a), guarantee k6＞δmThen p can be ensuredk＞0。
According to the finite time convergence theorem, the sliding mode variable sigma can be converged to zero in finite time, and the convergence time meets the following requirements:
the controller designed by the invention can solve the problem of stabilizing control of the benthonic AUV point under the condition of considering external unknown interference and model parameter uncertainty, ensures that the benthonic AUV can realize accurate fixed-point hovering when sailing to the offshore bottom, and lays a foundation for accurate setting and smooth completion of monitoring tasks.
Comparison with the prior art solution
In the research of point stabilization control of the AUV, in order to meet the control requirement of benthic AUV point stabilization, a great deal of work has been done by the predecessors, besides the method mentioned in the algorithm of the present invention, schemes based on ordinary sliding mode control, discontinuous time-invariant control, and the like are also available.
Scheme based on common sliding mode control
The sliding mode control method has a good control effect on processing a nonlinear system with uncertain model parameters and external interference, but the sliding mode control usually introduces a switching term in the input of the sliding mode control to cause discontinuous control variables to generate a buffeting phenomenon. In a nonlinear system, discontinuity can excite high-frequency characteristics, weaken the control effect and even directly cause an uncontrollable state of the system, which is an inevitable problem in the conventional sliding mode control. A more common method of attenuating buffeting is to introduce boundary layer functions. The boundary layer method has good effect on inhibiting buffeting, but the method has high requirement on boundary layer width selection, the increase of system variable steady-state error can be caused by larger boundary layer, and the buffeting effect can not be obviously reduced by narrower boundary layer (Xu J, Kang X, Chen X. turbulent object based stabilizing and sizing mode dynamic configuration for UUV under wave disturbance [ C ]. Control and Decision reference 2016: 6345-. The document (Wan L, Chen G, Sheng M, et al. adaptive damping-free damping-mode control for full-order nonlinear Systems with unbounded damping and model uncategorized [ J ]. International Journal of Advanced fibrous Systems,2020,17(3): 172988142092529.) proposes a new adaptive full-order slip-mode controller without buffeting, which obtains a continuous smooth control law by integrating the differential control law with a sign function, thus well avoiding the influence of buffeting, the document (Mondal S, Mass C. adaptive controlled polar slip-mode controller for fibrous Systems [ J ]. 351. 20146. the problem of the second-order integral control is also well solved by integrating the differential control law with a sign function, thus obtaining a second-order slip-mode controller with continuous buffeting. Based on the better buffeting eliminating effect of the second-order slip form, the invention provides a novel second-order buffeting-free nonsingular integral terminal slip form controller, which is applied to AUV point stabilization control and can obtain a better control effect.
Scheme based on discontinuous time invariant control
Time invariant feedback controllers of under-actuated surface vessels are designed by a Reyhanogli (Paliotta C, Lefeber E, Pettersen K Y, Pinto J, Costa M.Transmission Tracking and Path Following for extracting marked minerals [ J ]. IEEE Transactions on Control System technology.2019,27:1423 + 1437.) by a sigma transformation method; aguiar (Reyhanoglu M.Control and stability of an understated surface vessel [ C ] Proceedings of the 35th IEEE Conference on Decision and Control,1996, 3:2371 and 2376.) and the like, use coordinate transformation to solve the problem of surface ballast Control of under-driven AUVs. The AUV point stabilizing controller is designed by adopting a discontinuous time-invariant control method, the design process is relatively simple, but the designed control law is discontinuous, the requirement of global asymptotic stability of a control system is difficult to ensure, and the AUV point stabilizing controller is difficult to be applied to actual engineering.
The algorithm improves a discontinuous time invariant control method, ensures the continuity of a control law by designing a second-order buffeting-free nonsingular integral terminal sliding mode controller, and can obtain required steady-state precision within limited time.
Simulation test
The performance of the AUV point stabilizing controller under the conditions of considering external interference and model uncertainty is verified through a reasonably designed simulation test, the self-adaptive buffeting-free integral terminal sliding mode controller designed by the invention is marked as an ACFIMC controller, the test model adopts an AUV six-degree-of-freedom model established in step (32), and the model parameters refer to a table 1. The simulation parameter settings in the ACFIMC controller designed by the invention are shown in the table 2.
TABLE 1 submersible AUV model parameters
In the simulation test, the initial position of the AUV is set to be [ [1,1,1,1,1,1 ] 1 (0) ]]ΤDesired target point set to ηd＝[0,0.5,2,0.5,0.5,0.5]ΤAdaptive law initial value set to
Model uncertainty and external interference in simulation test are shown in a formula (57).
The simulation test adopts a self-adaptive second-order terminal sliding mode controller (of an unknown automatic water vehicle with a parameter modeling and utilizing Lyapunov functions [ C ]. Proceedings of the 40th IEEE Conference on Decision and Control,2001, 5:4178 and 4183.) as a comparison controller to verify the Control effect of the sliding mode Control method designed by the invention, wherein the comparison controller is marked as an ASOTMC controller, and the ASOTMC controller is in a form of a formula (58). The simulation test results are shown in fig. 5 to 14.
TABLE 2 ACFIMC controller parameter settings
Fig. 5 to 9 show AUV pose error response curves. As can be seen from fig. 5 to 9, both controllers can converge to a stable state within a limited time, and the pose error can maintain good stability after converging to zero, but the convergence speeds of both controllers are significantly different. In the initial phase of the initial movement of the AUV, the ACFIMC controller converges faster than the astmc controller, and the ACFIMC controller is shorter than the astmc controller in the time when the error converges to zero in each direction. In the error convergence curve, the convergence curves of the two controllers are overshot, but the ASOTMC fluctuation amplitude is larger than that of the ACFIMC controller when the error converges to a stage close to zero, which reflects that the ACFIMC controller is more sensitive to the output change of an actuator than that of the ASOTMC controller, and has a good early braking effect. When the error converges to zero, the ASOTMC error response curve has less jitter, the ACFIMC controller changes more smoothly, and the curve is smoother. In summary, the convergence speed and robustness of the ACFIMC are better than those of the astmc controller in the error convergence process.
Fig. 10 to 14 are speed response curves of the AUV point stabilization control. As can be seen from fig. 10 to 14, the speeds of both controllers converge to the steady state within a limited time, but the convergence speed of the ACFIMC controller is significantly better than that of the astomc controller. In the longitudinal and transverse speed response curves, the convergence time of the ACFIMC controller is reduced by 47% compared with the convergence time of the ASOTMC controller, and in the response curves of the vertical speed, the yaw rate and the pitch rate, the convergence time of the ACFIMC controller is reduced by 25% compared with the convergence time of the ASOTMC controller. In the speed convergence response curves in all directions, when the speed is converged to a near-steady state, the ASOTMC controller fluctuates, the curve change of the ACFIMC controller is smooth, and the output of the ACFIMC controller actuator is stable. In summary, in the speed response curve, the convergence speed and robustness of the ACFIMC controller are better than those of the ASOTMC controller.
It should be noted that the detailed description is only for explaining and explaining the technical solution of the present invention, and the scope of protection of the claims is not limited thereby. It is intended that all such modifications and variations be included within the scope of the invention as defined in the following claims and the description.
Claims (4)
1. A benthonic AUV weak buffeting integral sliding mode point stabilizing control method based on an extended state observer comprises the following steps:
the method comprises the following steps: establishing a benthonic AUV motion equation, and constructing a benthonic AUV error model according to the benthonic AUV motion equation;
step two: constructing a benthonic AUV point stabilized tracking error model according to the benthonic AUV error model;
step three: designing a self-adaptive supercoiled extended state observer;
step four: constructing a second-order buffeting-free nonsingular integral terminal sliding mode surface;
step five: designing a controller according to a benthonic AUV point stabilized tracking error model, a self-adaptive supercoiled extended state observer and a second-order buffeting-free nonsingular integral terminal sliding mode surface;
the method is characterized in that the second-order buffeting-free nonsingular integral terminal sliding mode surface is expressed as follows:
wherein λ is a positive number, and β ∈ R6×6Is a diagonal matrix, s is a sliding mode surface function, sigma is an auxiliary variable,
for the control parameters, d τ is the integral operator,
is etaeFirst derivative of, ηeIn order to be able to determine the position tracking error,
can be used as a benthonicThe control force and moment vector generated when the AUV actuator operates;
the control law of the second-order buffeting-free nonsingular integral terminal sliding mode surface is expressed as follows:
τ＝τ1+τ2
in the formula (I), the compound is shown in the specification,
in the formula, k4For switching term gain, normal, k6Is a positive number,/1And l2In order to control the parameters of the device,
is an estimated value of the observer state variable,
is tau2The first derivative of (d), phi are integral operators,
is composed of
F (η, ν, t) is an auxiliary variable;
the self-adaptive law of the second-order buffeting-free nonsingular integral terminal sliding mode surface is expressed as follows:
in the formula, k5Is a normal number, b is a control gain,
is the first derivative of b and is,
is an observer variable, δmIs composed of
Is determined by the actual value of the unknown boundary,
is deltamIs determined by the estimated value of (c),
is the first derivative of s.
2. The benthonic AUV weak buffeting integral sliding mode point stabilization control method based on the extended state observer as recited in claim 1, wherein the benthonic AUV motion equation is expressed as:
where M is a mass inertia matrix, η [ [ ξ n ζ φ θ ψ [ ]]ΤWhen a benthonic AUV moves under a fixed coordinate system, the position and the posture of six degrees of freedom in a three-dimensional space are divided into upsilon [ uv w p q r ═ v]ΤThe speed and the angular speed in the three-dimensional space when moving under the carrier coordinate system,
is a coordinate transformation matrix between a fixed coordinate system and a carrier coordinate system when the benthonic AUV moves on a horizontal plane,
for the nominal values of the parameters of the model,
the control force and the moment vector generated when the benthonic AUV actuator operates,
is a comprehensive interference item formed by superposing model parameter uncertainty and external time-varying interference,
perturbation values of model parameters, τd(t) is the external time-varying interference,
is the first derivative of v and,
comprehensive trunk for superposing model parameter uncertainty and external time-varying interferenceThe items of interference are displayed on the screen,
the first derivative of η.
3. The method according to claim 2, wherein the benthonic AUV weak buffeting integral sliding mode point stabilized control method based on the extended state observer is characterized in that the benthonic AUV point stabilized tracking error model is expressed as:
in the formula (I), the compound is shown in the specification,
as an auxiliary variable, the number of variables,
is omegaeThe first derivative of (a) is,
is omegaeThe second derivative of (a) is,
is etaeFirst derivative of, ηeIn order to be able to determine the position tracking error,
the first derivative of the rotation matrix is represented,
a second derivative representing the desired position;
b＝R(η)M-1；
the above-mentioned
The following relationship is satisfied:
||F(t)||＜Dm
Dmactual value of unknown boundary, δ, of F (t)mIs composed of
Is determined by the actual value of the unknown boundary,
is deltamIs determined by the estimated value of (c),
is composed of
B is the control gain, F (t) is the auxiliary variable,
is the first derivative of F (t),
is a first order of bThe derivative(s) of the signal(s),
the first derivative of τ.
4. The extended state observer-based benthic AUV weak buffeting integral sliding mode point stabilization control method according to claim 3, wherein the adaptive supercoiled extended state observer is represented as:
wherein G (eta, upsilon, t),
Is an observer variable, K1、K2To observer gain, K1、K2Are all positive definite diagonal matrix, K1、K2、
As an auxiliary variable, the auxiliary variable expression is as follows:
K1＝diag(K11,K12,K13,K14,K15,K16)
K2＝diag(K21,K22,K23,K24,K25,K26)
in the formula (I), the compound is shown in the specification,
the expression is as follows:
in the formula, mu1i,μ2iAre all normal numbers, i is 1,2,3,4,5,6,
estimating an error for an observer;
the adaptation law is represented as:
in the formula (I), the compound is shown in the specification,
K1i(t) are all adaptive variables, c1i、c2i、c3i、HiAre all control parameters and are positive numbers.
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