CN114296449B - Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control - Google Patents

Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control Download PDF

Info

Publication number
CN114296449B
CN114296449B CN202111514616.7A CN202111514616A CN114296449B CN 114296449 B CN114296449 B CN 114296449B CN 202111514616 A CN202111514616 A CN 202111514616A CN 114296449 B CN114296449 B CN 114296449B
Authority
CN
China
Prior art keywords
fixed time
unmanned
surface vehicle
unmanned surface
tracking
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202111514616.7A
Other languages
Chinese (zh)
Other versions
CN114296449A (en
Inventor
刘海涛
王志成
田雪虹
李永卓
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guangdong Ocean University
Original Assignee
Guangdong Ocean University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Guangdong Ocean University filed Critical Guangdong Ocean University
Priority to CN202111514616.7A priority Critical patent/CN114296449B/en
Publication of CN114296449A publication Critical patent/CN114296449A/en
Application granted granted Critical
Publication of CN114296449B publication Critical patent/CN114296449B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Landscapes

  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention discloses a method based on fixed time H ∞ The fast track control method for the unmanned surface vehicle track includes the following steps: s1, establishing a water surface unmanned ship control system comprising a kinematics and dynamics model; s2, building a water surface unmanned ship trajectory tracking error model based on a kinematics and dynamics model; s3, designing a fixed time extended state observer based on the kinematics and dynamics of the unmanned surface vehicle; s4, establishing fixed time H ∞ A controller; s5, tracking error model based on unmanned surface vehicle trajectory, fixed time extended state observer and fixed time H ∞ The controller design assists the controller to establish a dynamic system; s6, designing fixed time H based on dynamic system ∞ And tracking the controller by the track, and analyzing the stability. The invention not only improves the robustness of the unmanned surface vehicle control system, but also ensures that the convergence time of the system does not depend on the initial value of the system, and the system has higher stability on the premise of ensuring the rapid convergence of the tracking error.

Description

Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control
Technical Field
The invention belongs to the technical field of unmanned surface vehicle control, and particularly relates to a method for controlling unmanned surface vehicle based on fixed time H ∞ A rapid tracking control method for a controlled water surface unmanned ship track.
Background
With the rapid rise of many marine activities including military reconnaissance, environmental monitoring, rescue at sea and submarine passage inspection, the problem of trajectory tracking control of unmanned surface vessels has become a hot spot in research nowadays. The core work of the method is to design a control law and explore a control method, so that the track tracking of the ship is more accurate in a stable state. However, since wind, wave and ocean current have important effects on the speed and maneuverability of a ship, how to achieve fast and accurate trajectory tracking is a big challenge for the controller.
In the current water surface unmanned ship controller, the uncertainty of ship model parameters and the complex and variable disturbance of marine environment bring huge influence on the stability of the system. The PID (proportional-integral-derivative) control commonly used in the research controller does not need an accurate system model and has acceptable control performance under most conditions, but the traditional PID control has the problems of weak anti-interference capability, slow control speed, complex parameter setting and the like, the parameter setting depends on multiple trial and error and abundant parameter adjusting experience support under common conditions, and even when the parameter is adjusted to a better control effect under the current system state, the time-varying external environment interference can also cause great influence on the control effect.
At present, aiming at the problems of uncertainty of parameters of the unmanned surface vehicle and disturbance of marine environment, a common control method is to design a robust controller or adopt a neural network to approach the lumped disturbance of a system, and design an effective track tracking control law, so that the unmanned surface vehicle can track a set expected track from an initial state to complete a specified task, and ensure the global consistency and gradual stability of track tracking errors in a short time, thereby realizing the requirement of high-precision rapid deployment operation in a specified area. However, the operation of the neural network is complex and the online calculation speed is limited, which results in some unavoidable problems, such as slow adjustment speed of the controller, low control accuracy, inability to achieve convergence within a limited time, and the like. In actual engineering, the complex marine environment has a great influence on the accuracy of the speed sensor, so that the state information of the controller is not easy to acquire.
Therefore, a global fast and stable water surface unmanned ship system control method is designed in a fixed time aiming at the actual marine environment, so that the system has higher stability on the premise of ensuring fast convergence of tracking errors, and the method becomes a problem to be solved urgently in the industry.
Disclosure of Invention
To solve at least one of the above problems, the present invention provides a method for determining a fixed time H ∞ Controlled waterA fast track control method for unmanned surface vehicle.
The purpose of the invention is realized by the following technical scheme:
the invention provides a method based on fixed time H ∞ The fast track control method for the unmanned surface vehicle track comprises the following steps:
s1, establishing a water surface unmanned ship control system comprising a kinematics and dynamics model;
s2, building a water surface unmanned ship trajectory tracking error model based on a kinematics and dynamics model;
s3, designing a fixed time extended state observer based on the kinematics and dynamics of the unmanned surface vehicle;
s4, establishing fixed time H ∞ A controller;
s5, tracking error model based on unmanned surface vehicle trajectory, fixed time extended state observer and fixed time H ∞ The controller design assists the controller to establish a dynamic system;
s6, designing fixed time H based on dynamic system ∞ And tracking the controller by the track, and analyzing the stability.
As a further improvement, in the step S1, the step of establishing the surface unmanned ship controller including the kinematics and dynamics model includes the following steps:
s11, establishing a kinematics and dynamics model of the unmanned surface vehicle;
s12, carrying out coordinate transformation on the kinematics and dynamics model of the unmanned surface vehicle;
and S13, carrying out parameter uncertainty and time-varying interference processing on the unmanned surface vehicle control system on the kinematics and dynamics model of the unmanned surface vehicle.
And S14, obtaining the expected track of the kinematics and dynamic model of the unmanned surface vehicle.
As a further improvement, in the step S2, building a surface unmanned ship trajectory tracking error model based on kinematics and dynamics models, including the following steps:
s21, defining track tracking errors of the unmanned surface vehicle and speed errors of the unmanned surface vehicle in a fixed coordinate system and obtaining the tracking error dynamics of the unmanned surface vehicle;
and S22, combining the step S13 and the step S14 to rewrite the tracking error dynamic of the unmanned surface boat.
As a further improvement, in the step S3, designing a fixed-time extended state observer based on the surface unmanned vehicle controller and the surface unmanned vehicle trajectory tracking error model includes the following steps:
s31, designing a fixed time extended state observer, and then defining the observation error of the observer;
and S32, further designing the fixed-time extended state observer according to the defined observation error.
As a further improvement, in the step S4, the fixed time H is established ∞ A controller comprising the steps of:
s41, defining a closed loop system comprising a causal dynamic compensator;
s42, the closed loop system analyzed and defined by the theorem proving technology is stable in global fixed time, and the causal dynamic compensator is a global fixed time H ∞ And a controller.
As a further improvement, in the step S5, based on the unmanned surface vehicle trajectory tracking error model, the fixed time extended state observer and the fixed time H ∞ The controller design assists the controller to establish a dynamic system, and comprises the following steps:
s51, according to the steps S22, S32 and S42, the tracking error dynamics of the unmanned surface vehicle is converted within fixed time;
s52, introducing an auxiliary controller and defining a tracking error variable;
and S53, combining the tracking error dynamics of the unmanned surface vehicle and the defined tracking error variable to establish a dynamic system.
As a further improvement, in the step S6, the fixed time H is designed based on the dynamic system ∞ A trajectory tracking controller and performing stability analysis, comprising the steps of:
s61, defining an auxiliary function for realizing the stability of the dynamic system in a fixed time;
s62, defining a performance vector in the dynamic system;
s63, designing a fixed time H based on the fixed time extended state observer according to the auxiliary function and the performance vector ∞ A trajectory tracking controller policy;
s64, based on fixed time H ∞ The trajectory tracking controller strategy utilizes theorem proving techniques to analyze that a surface drone is able to track a desired trajectory in a fixed time and independent of the initial state of the surface drone.
As a further improvement, in the step S11, a kinematic and dynamic model of the surface unmanned boat is established as follows:
Figure BDA0003406385640000031
wherein n represents a three-degree-of-freedom pose vector of the water surface unmanned ship in a horizontal plane under a geodetic coordinate system, y represents a course angle, R (psi) represents a coordinate conversion matrix between the geodetic coordinate system and a ship body coordinate system, R represents a real number, v represents a speed and an angular velocity vector of the water surface unmanned ship in the horizontal plane under the ship body coordinate system,
Figure BDA0003406385640000041
representing the velocity and angular velocity vector of the unmanned surface vehicle under a geodetic coordinate system,
Figure BDA0003406385640000042
representing the acceleration and angular acceleration vectors of the unmanned surface vehicle in a ship body coordinate system, M being an inertia matrix, C (v) being a Coriolis centripetal force matrix, D (v) being a fluid damping matrix, an upper corner mark T representing the transposition of the matrix, tau being a control input vector of the unmanned surface vehicle, and w (T) being time-varying disturbance caused by stormy waves and ocean current sea environment.
As a further improvement, in the step S21, the water surface unmanned ship tracking error dynamics is obtained as follows:
Figure BDA0003406385640000043
wherein, n is e Tracking error of unmanned surface vehicle trajectory, v e Is the speed error v of the unmanned surface vehicle under a fixed coordinate system d And the expected values of the speed and the angular speed of the unmanned surface vehicle in the horizontal plane under the ship body coordinate system are shown.
As a further improvement, in step S31, the observation error of the fixed-time extended state observer is defined as follows:
Figure BDA0003406385640000044
wherein, mu ═ R (psi) v, chi is the lumped disturbance of the unmanned surface vehicle control system,
Figure BDA0003406385640000045
is the observed value of n and is,
Figure BDA0003406385640000046
is the observed value of mu, and the measured value of mu,
Figure BDA0003406385640000047
the observed value of x is the value of x,
Figure BDA0003406385640000048
are both estimated error values.
The invention provides a method based on fixed time H ∞ The fast track control method for the unmanned surface vehicle track includes the following steps: s1, establishing a water surface unmanned ship control system comprising a kinematics and dynamics model; s2, building a water surface unmanned ship trajectory tracking error model based on a kinematics and dynamics model; s3, designing a fixed time extended state observer based on the kinematics and dynamics of the unmanned surface vehicle; s4, establishing fixed time H ∞ A controller; s5, tracking error model based on unmanned surface vehicle trajectory, fixed time extended state observer and fixed time H ∞ The controller design assists the controller to establish a dynamic system; s6, designing fixed time H based on dynamic system ∞ And tracking the controller by the track, and analyzing the stability. The invention is in H ∞ Further research is carried out on the basis of control, the designed fixed time extended state observer is used for estimating state information and lumped disturbance of the system, the actual application requirements of engineering are met better, and the established fixed time H ∞ The whole closed-loop system of the controller realizes global stability in fixed time, the convergence rate and stability of tracking control are greatly improved, the robustness of the water surface unmanned ship control system is improved, the convergence time of the system does not depend on the initial value of the system, and the system has higher stability on the premise of ensuring the quick convergence of tracking errors.
Drawings
The invention is further illustrated by means of the attached drawings, but the embodiments in the drawings do not constitute any limitation to the invention, and for a person skilled in the art, other drawings can be obtained on the basis of the following drawings without inventive effort.
FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 is a schematic representation of the kinematic and kinetic model of the present invention.
FIG. 3 is a schematic diagram of the expected trajectory and the actual trajectory of the kinematic and kinetic models of the present invention.
FIG. 4 is a schematic diagram of the present invention illustrating the tracking of a surge trajectory; in the figure, x is the longitudinal position coordinate of the unmanned surface vehicle in a geodetic coordinate system, and x d And (4) obtaining the expected longitudinal position coordinates of the unmanned surface vehicle under the geodetic coordinate system.
FIG. 5 is a schematic diagram of the present invention illustrating the tracking of a swaying trajectory; in the figure, y is the transverse position coordinate of the unmanned surface vehicle in a geodetic coordinate system, and y d And (4) obtaining the expected transverse position coordinates of the unmanned surface vehicle under the geodetic coordinate system.
FIG. 6 is a schematic view of the heading trajectory tracking of the present invention; in the figure, psi is the heading angle psi d Is the desired heading angle.
FIG. 7 illustrates the surging direction velocity estimation of the present inventionA situation schematic diagram; in the figure, u is a longitudinal actual speed coordinate of the unmanned surface vehicle under a hull coordinate system,
Figure BDA0003406385640000051
and longitudinally estimating a speed coordinate for the unmanned surface vehicle under a ship body coordinate system.
FIG. 8 is a schematic diagram of the estimation of the yaw rate according to the present invention; in the figure, v is the actual speed coordinate of the water surface unmanned ship swaying under the ship body coordinate system,
Figure BDA0003406385640000052
and estimating a speed coordinate for the swaying of the unmanned surface vehicle under the hull coordinate system.
FIG. 9 is a schematic view of the heading direction velocity estimation of the present invention; in the figure, r is the actual speed coordinate of the unmanned surface vehicle in the heading direction under the ship body coordinate system,
Figure BDA0003406385640000053
and estimating a speed coordinate for the heading direction of the unmanned surface vehicle under the ship body coordinate system.
FIG. 10 is a schematic view of a surge direction control input according to the present invention; in the figure, τ u The control input is the longitudinal control input of the unmanned surface vehicle along the coordinate system of the ship body.
FIG. 11 is a schematic view of the present invention illustrating a yaw direction control input; in the figure, τ v The control input is the horizontal control input of the unmanned surface vehicle along the ship body coordinate system.
FIG. 12 is a schematic view of yaw direction control inputs of the present invention; in the figure,. tau. r The control input of the unmanned surface vehicle along the heading direction of the ship body coordinate system is realized.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following detailed description of the present invention is provided with reference to the accompanying drawings and specific embodiments, and it is to be noted that the embodiments and features of the embodiments of the present application can be combined with each other without conflict.
The embodiment of the invention provides a method based on fixed time H ∞ The method for controlling the rapid tracking of the unmanned surface vehicle track as shown in fig. 1 comprises the following steps:
s1, establishing a water surface unmanned ship control system comprising a kinematics and dynamics model, comprising the following steps:
s11, establishing a kinematics and dynamics model of the unmanned surface vehicle, and combining the kinematics and dynamics model with the model shown in FIG. 2, as follows:
Figure BDA0003406385640000061
wherein n is [ x, y, ψ ═ x, y, ψ] T The three-degree-of-freedom position and posture vector of the water surface unmanned boat in the horizontal plane under a geodetic coordinate system Xe-Oe-Ye is shown, x and y respectively represent longitudinal and transverse position coordinates of the water surface unmanned boat under a geodetic coordinate system Xb-Ob-Yb, and psi represents a course angle; r (psi) represents a coordinate transformation matrix representing the coordinate system between the geodetic coordinate system and the hull coordinate system, R (psi) E R 3×3 R represents a real number; v ═ u, v, r] T V represents the velocity and angular velocity vector of the unmanned surface vehicle in the horizontal plane under the hull coordinate system,
Figure BDA0003406385640000062
is the first derivative of n and is,
Figure BDA0003406385640000063
representing the velocity and angular velocity vector of the unmanned surface vehicle under a geodetic coordinate system;
Figure BDA0003406385640000064
is the first derivative of v and is,
Figure BDA0003406385640000065
representing the acceleration and angular acceleration vectors of the unmanned surface vehicle under a ship body coordinate system; m is an inertia matrix; c (v) is a coriolis centripetal force matrix; d (v) is a fluid damping matrix; the superscript T represents the transpose of the matrix; τ ═ τ [ τ ] u ，τ v ，τ r ] T Inputting a vector for the control of the unmanned surface vehicle system; w (t) is the wave and ocean current seaTime-varying disturbances caused by the marine environment; wherein the transformation matrix R (ψ) satisfies the following properties:
Figure BDA0003406385640000071
wherein R is -1 Is the inverse of the R matrix and,
Figure BDA0003406385640000072
is the first derivative of R;
Figure BDA0003406385640000073
is an antisymmetric matrix.
S12, defining μ ═ R (ψ) v, and coordinate-converting the kinematics and dynamics model of the surface unmanned boat as follows:
Figure BDA0003406385640000074
where, mu is an auxiliary variable,
Figure BDA0003406385640000075
is the first derivative of μ; m -1 Is the inverse of the M matrix; f (n, μ) is a simplified matrix; f (n, mu) ═ S (R) mu-R (psi) M -1 (C (v) + D (v)) v; considering the parameter uncertainty of the model of the surface unmanned ship system, f (n, mu) can be expressed as follows:
f(n,μ)＝f 0 (n, mu) +. DELTA.f (formula 4)
Wherein f is 0 The (n, mu) is a nominal value form containing uncertainty items in the water surface unmanned ship control system, and the delta f is an uncertainty part of the water surface unmanned ship control system, and the specific mathematical expression form is as follows:
Figure BDA0003406385640000076
wherein, C 0 (v) Nominal value, D, representing the Coriolis centripetal force matrix 0 (v) Representative flowNominal values of the bulk damping matrix,. DELTA.C (v) representing the uncertainty values of the Coriolis centripetal force matrix,. DELTA.D (v) representing the uncertainty values of the fluid damping matrix.
S13, after the surface unmanned ship control system parameter uncertainty and the time-varying interference processing are carried out on the kinematics and dynamics model of the surface unmanned ship, the kinematics and dynamics model of the surface unmanned ship is as follows:
Figure BDA0003406385640000077
wherein χ ═ Δ f (n, μ) + w (t) is regarded as the lumped disturbance of the unmanned surface vessel.
S14, obtaining the expected track of the water surface unmanned boat kinematics and dynamic model as follows:
Figure BDA0003406385640000081
wherein n is d ＝[x d ,y d ,ψ d ] T Representing the expected value x of the three-degree-of-freedom position and posture of the unmanned surface vehicle in the horizontal plane under the geodetic coordinate system d Is the expected value of x, y d Is the desired value of y,. psi d A desired value of ψ;
Figure BDA0003406385640000082
and
Figure BDA0003406385640000083
are each n d First and second derivatives of; v. of d ＝[u d ,v d ,r d ] T Representing the expected values of the speed and the angular speed of the unmanned surface vehicle in the horizontal plane under the ship body coordinate system, u d Is the expected value of u, v d Is a desired value of v, r d Is the desired value of r;
Figure BDA0003406385640000084
is v d Is the first derivative.
S2, building a water surface unmanned ship trajectory tracking error model based on kinematics and dynamics models, and comprising the following steps:
s21, definition of n e ＝n-n d ，v e ＝v-v d The obtained water surface unmanned ship tracking error dynamics is as follows:
Figure BDA0003406385640000085
in the formula, n e Representing the track tracking error of the unmanned surface vehicle in a geodetic coordinate system; v. of e Representing the speed error of the unmanned surface vehicle in a ship body coordinate system;
Figure BDA0003406385640000086
is n e Is the first derivative;
Figure BDA0003406385640000087
is v e The first derivative of (a).
S22, definition x 1 ＝n e ，
Figure BDA0003406385640000088
The overwrites of the water surface unmanned ship tracking error dynamics with reference to equation 6 of step S13 and equation 7 of step S14 are as follows:
Figure BDA0003406385640000089
wherein x is 1 Representing the track tracking error of the unmanned surface vehicle under a geodetic coordinate system; x is the number of 2 Is x 1 The first derivative of (a).
S3, designing a fixed time extended state observer based on the kinematics and dynamics of the unmanned surface vehicle, and comprising the following steps:
s31, designing a fixed time extended state observer, and defining the observation error as follows:
Figure BDA0003406385640000091
wherein,
Figure BDA0003406385640000092
is an estimate of n;
Figure BDA0003406385640000093
is an estimate of μ;
Figure BDA0003406385640000094
is an estimate of χ;
Figure BDA0003406385640000095
are both estimated error values.
S32, further designing the fixed-time extended state observer according to the defined observation error and equation 6 as follows:
Figure BDA0003406385640000096
wherein,
Figure BDA0003406385640000097
is that
Figure BDA0003406385640000098
The first derivative of (a);
Figure BDA0003406385640000099
is that
Figure BDA00034063856400000910
The first derivative of (a);
Figure BDA00034063856400000911
is that
Figure BDA00034063856400000912
The first derivative of (a);
Figure BDA00034063856400000913
Figure BDA00034063856400000914
is the first derivative of χ d Represents a positive real number; sgn represents a sign function, and a suitable gain coefficient k of the state observer is selected i (i ═ 1,2,3) and l i (i ═ 1,2,3), such that 1 PMatrix sum 2 PThe matrix is a Hurwitz matrix, so that n, mu and chi can be at a fixed time T 0 Inside is respectively covered
Figure BDA00034063856400000915
And
Figure BDA00034063856400000916
and (6) estimating.
Figure BDA00034063856400000917
Convergence time satisfaction
Figure BDA00034063856400000918
Wherein r is 1 Represents a simplified matrix and satisfies r 1 ＝λ min (Q 1 )/λ max (Ω 1 )；r 2 Represents a simplified matrix and satisfies r 2 ＝λ min (Q 2 )/λ max (Ω 2 )；
Figure BDA00034063856400000919
Normal number
Figure BDA00034063856400000921
Q 1 ,Q 2 ,Ω 1 ,Ω 2 Are all non-singular, symmetric and positive definite matrices. In addition, the parameter matrices of the complaints satisfy
Figure BDA00034063856400000920
S4, establishing fixed time H ∞ A controller comprising the steps of:
s41, definition 1: consider a closed loop system including a causal dynamics compensator as follows:
Figure BDA0003406385640000101
wherein x is a vector reflecting system state information, f (x) and g (x) both represent non-linear terms about x in a closed-loop system, xi (x) is a controller input vector of the system, w (x) is an unknown disturbance, Z is a performance vector, and w is external disturbance.
One causal dynamics compensator is as follows:
xi phi (x, t) (formula 15)
The causal dynamics compensator xi is a global fixed time H, if the following two conditions are fulfilled ∞ And a controller.
(1) When w is 0, the closed loop systems in equations 14 and 15 are globally fixed-time stable;
(2) given a real number γ >0, for all t 1 ＞t 0 And all non-linear perturbations if the output z and initial state x (t) are produced by w 0 ) 0 satisfies the following inequality including a definite integral:
Figure BDA0003406385640000102
wherein z (t) represents a vector of performance functions over time t; w (t) represents a perturbation term with respect to time t; then L of the closed loop system in equations 14 and 15 2 The gain is less than or equal to γ.
S42, the closed loop system analytically defined by the theorem proving technology is stable in global fixed time, and the causal dynamic compensator is a global fixed time H ∞ And a controller.
Theorem 1: consider equation 9, assume thatNeighborhood of persons
Figure BDA0003406385640000103
Defines a function V (x) for which there is a real number c near the origin 1 ＞0，c 2 >0 and 0 < a 1 ＜1，a 2 > 1 so that:
(1) v (x) in U 0 Is a positive definite function;
(2)
Figure BDA0003406385640000104
wherein, c 1 、c 2 A convergence speed control coefficient; a is 1 、a 2 The control parameter is a fixed time convergence control parameter.
Then, the origin of closed-loop system 14 is locally fixed-time stable, and L of the system is 2 The gain is less than or equal to γ. If U is present 0 ＝R n And v (x) is radially unbounded (i.e., v (x) → + ∞when | | x | → + ∞), the origin of closed-loop system equation 14 is globally fixed-time stable.
And (3) proving that: as can be seen from definition 1, two conditions must be satisfied.
(1) When w is 0, the condition (2) in theorem 1 can be written as:
Figure BDA0003406385640000111
according to the theorem 1, the closed loop system formed by the equations 14 and 15 is stable in fixed time.
(2) When w ≠ 0, v (x) >0, then the following inequality holds:
Figure BDA0003406385640000112
satisfies the condition (2) in definition 1, and thus L of formula 15 is a closed ring system 2 The gain is less than or equal to gamma, and theorem 1 proves to be complete.
S5 unmanned ship rail based on water surfaceTrace tracking error model, fixed time extended state observer and fixed time H ∞ The controller design assists the controller to establish a dynamic system, and comprises the following steps:
s51, lemma 1 and of S42 according to formula 9 of step S22, formula 13 of S32 and
Figure BDA0003406385640000113
it can be known that at a fixed time T 0 The tracking error dynamics of the inner-conversion water surface unmanned ship are as follows:
Figure BDA0003406385640000114
wherein,
Figure BDA0003406385640000115
is that
Figure BDA0003406385640000116
The first derivative of (a) is,
Figure BDA0003406385640000117
the error estimation value of the track tracking of the unmanned surface vehicle in the geodetic coordinate system is obtained;
Figure BDA0003406385640000118
is that
Figure BDA0003406385640000119
The first derivative of (a).
S52, introducing an auxiliary controller
Figure BDA00034063856400001110
Defining tracking error variables
Figure BDA00034063856400001111
The following were used:
Figure BDA00034063856400001112
s53, combining the tracking error dynamic equation 19 of the surface unmanned ship and the defined tracking error variable equation 20 to establish a dynamic system as follows:
Figure BDA00034063856400001113
s6, designing fixed time H based on dynamic system ∞ And tracking the controller by the track, and analyzing the stability.
S61, defining an auxiliary function for realizing the stability of the dynamic system equation 21 in a fixed time as follows:
Figure BDA0003406385640000121
wherein,
Figure BDA0003406385640000122
representing an argument as a tracking error
Figure BDA0003406385640000123
The auxiliary function of (2);
Figure BDA0003406385640000124
representing an argument as a tracking error
Figure BDA0003406385640000125
The auxiliary function of (2); alpha, beta represent fixed time convergence control parameters and satisfy 0<a<1，β>1；p i (i＝1,2,3,4)＝diag{p i1 ,p i2 ,...,p in All positive definite diagonal matrixes represent auxiliary function control gain coefficients; sign function sign satisfies the relationship: sig a (·)＝sign(·)|·| a ,sig β (·)＝sign(·)|·| β 。
S62, a performance vector is defined in dynamic system equation 21 as follows:
Figure BDA0003406385640000126
wherein λ is 1 >0,λ 2 >0, each represents x 1 And
Figure BDA0003406385640000127
the weighting coefficient of (2).
S63, designing a fixed time H based on the fixed time extended state observer according to the auxiliary function and the performance vector ∞ The trajectory tracking controller strategy is as follows:
Figure BDA0003406385640000128
wherein,
Figure BDA0003406385640000129
is a secondary function
Figure BDA00034063856400001210
The first derivative of (a);
Figure BDA00034063856400001211
is a secondary function
Figure BDA00034063856400001212
The first derivative of (a); by selecting appropriate parameters, dynamic system equation 21 reaches steady state for a limited time and L of the closed loop system 2 The gain is less than or equal to γ.
S64, based on fixed time H ∞ The trajectory tracking controller strategy utilizes theorem to prove that the technology for analyzing the initial state of the unmanned surface vehicle can track the expected trajectory in a fixed time and does not depend on the unmanned surface vehicle, and the method specifically comprises the following steps:
theorem 2: when the unmanned surface vehicle tracks the expected track, factors such as system uncertainty, ocean environment disturbance and state immeasurability are considered, and the designed fixed time H-based track is designed ∞ The trajectory tracking controller strategy 24 can ensureThe unmanned surface vehicle tracks the expected track in fixed time, the error convergence time is independent of the initial state of the unmanned surface vehicle, and the upper bound T of the convergence time s The following were used:
T s ＝T 0 +T 1 (formula 25)
And (3) proving that: the evidence of reaching a stable phase within a fixed time is as follows:
will fix the time H ∞ Substituting the trajectory tracking controller policy equation 24 into the dynamic system equation 21 to obtain:
Figure BDA0003406385640000131
designing a Lyapunov function (Lyapunov function, namely V function):
Figure BDA0003406385640000132
combining equations 22, 24, and 26, deriving V yields:
Figure BDA0003406385640000133
defining a function H:
Figure BDA0003406385640000134
substituting equations 22, 26 and 28 into equation 29, a positive real number p is selected * Satisfy the following requirements
Figure BDA0003406385640000135
And p is * ＝min{p 0i Then one can get:
Figure BDA0003406385640000136
let σ be (1+ α)/2,1/2<σ<1,δ＝(1+β)/2,p 1min ＝min{p 1i },p 2min ＝min{p 2i },p 3min ＝min{p 3i }p 4min ＝min{p 4i },
Figure BDA0003406385640000141
Figure BDA0003406385640000142
According to the theory 1, the following results are obtained:
Figure BDA0003406385640000143
combining equations 29 and 31, one can obtain:
Figure BDA0003406385640000144
wherein,
Figure BDA0003406385640000145
all represent convergence rate control coefficients; both σ and δ represent fixed time convergence control parameters.
From theorem 1, it can be seen that the dynamic system equation 21 is globally stable for a fixed time, and from theorem 2, an upper bound of the convergence time can be calculated:
Figure BDA0003406385640000146
error known from fixed time convergence system theory
Figure BDA0003406385640000147
And
Figure BDA0003406385640000148
at a fixed time T 1 Internally converged to 0, combined with the convergence time T of the fixed-time extended state observer 0 According to the separation principle, the whole closed-loop system is at a fixed timeThe global stability is achieved and does not depend on the initial state of the system, and theorem 2 proves to be complete.
Further, theorem 1 in the proving step is specifically as follows:
if present
Figure BDA0003406385640000149
And
Figure BDA00034063856400001410
then for
Figure BDA00034063856400001411
The following inequalities are satisfied:
Figure BDA00034063856400001412
in the formula,
Figure BDA00034063856400001413
is a power term, x i Are positive and real.
Further, the theory 2 in the above-mentioned certification step is specifically as follows:
consider the following system:
Figure BDA0003406385640000151
wherein y is the system output value,
Figure BDA0003406385640000152
is the first derivative of y, y (0) is the initial value of the system state y at time 0, y 0 The system state is initialized at the time 0; b 1 、b 2 All are convergence rate control coefficients and satisfy b 1 >0，b 2 >0；q 1 、q 2 Control parameters for fixed time convergence and satisfy 0<q 1 <1，q 2 >1; the balance point of the system is stable in fixed time and has an upper bound T of convergence time max Can be calculated independently of the initial state as follows:
Figure BDA0003406385640000153
wherein, T max Is the upper bound of fixed time convergence.
Invention in H ∞ Further research is carried out on the basis of control, the designed fixed time extended state observer is used for estimating state information and lumped disturbance of a control system, the actual application requirements of engineering are met better, and the established fixed time H ∞ The whole closed-loop system of the controller realizes global stability in fixed time, the convergence rate and stability of tracking control are greatly improved, the robustness of the water surface unmanned ship control system is improved, the convergence time of the system does not depend on the initial value of the system, and the system has higher stability on the premise of ensuring the quick convergence of tracking errors.
In order to verify the effectiveness of the embodiment of the invention, a simulation experiment is carried out, which specifically comprises the following steps:
simulation experiment is carried out by combining a Cybership II (Saibo II) ship model to verify that the designed ship model is based on the fixed time H ∞ The effectiveness of the controlled water surface unmanned ship track rapid tracking control method is shown in the following table 1, wherein the parameters of the Cybership II ship model are shown in the following table.
TABLE 1
Figure BDA0003406385640000154
The parameter settings in the surface unmanned boat control system are as follows in table 2:
TABLE 2
Figure BDA0003406385640000161
The time-varying perturbation is as follows:
Figure BDA0003406385640000162
the reference trajectories are as follows:
Figure BDA0003406385640000163
the simulation results are shown in fig. 3-12, and the designed trajectory tracking controller is shown to enable the unmanned surface vehicle to accurately track the expected trajectory in about 5s, and has good robustness. It is clear that the proposed control scheme can guarantee that the convergence time is less than the maximum value and can be calculated independently of the substituted initial state.
In the description above, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore should not be construed as limiting the scope of the present invention.
In conclusion, although the present invention has been described with reference to the preferred embodiments, it should be noted that various changes and modifications can be made by those skilled in the art, and they should be included in the scope of the present invention unless they depart from the scope of the present invention.

Claims (8)

1. Based on fixed time H ∞ The fast track control method for the unmanned surface vehicle track is characterized by comprising the following steps:
s1, establishing a water surface unmanned ship control system comprising a kinematics and dynamics model;
s2, building a water surface unmanned ship trajectory tracking error model based on a kinematics and dynamics model;
s3, designing a fixed time extended state observer based on the kinematics and dynamics of the unmanned surface vehicle;
s4, establishing fixed time H ∞ A controller;
s5, tracking error model based on unmanned surface vehicle trajectory, fixed time extended state observer and fixed time H ∞ The controller design assists the controller to establish a dynamic system, and comprises the following steps:
s51, changing the tracking error dynamics of the unmanned surface vehicle within a fixed time:
Figure FDA0003709700680000011
wherein,
Figure FDA0003709700680000012
is that
Figure FDA0003709700680000013
The first derivative of (a) is,
Figure FDA0003709700680000014
is an error estimation value of track tracking of the unmanned surface vehicle under a geodetic coordinate system,
Figure FDA0003709700680000015
is that
Figure FDA0003709700680000016
The first derivative of (a) is,
Figure FDA0003709700680000017
is that
Figure FDA0003709700680000018
The first derivative of (a), R (psi) is a coordinate transformation matrix between a geodetic coordinate system and a ship body coordinate system, M is an inertia matrix, tau is a control input vector of a water surface unmanned ship control system, f 0 (n, mu) is in a nominal value form containing uncertain items in the water surface unmanned ship control system,
Figure FDA0003709700680000019
is an estimated value of chi, the chi is the lumped disturbance of the unmanned surface vehicle control system,
Figure FDA00037097006800000110
is n d Second derivative of, n d The expected value of the three-degree-of-freedom pose of the unmanned surface vehicle in the horizontal plane under the geodetic coordinate system is obtained;
s52, introducing an auxiliary controller
Figure FDA00037097006800000111
Defining tracking error variables
Figure FDA00037097006800000112
The following were used:
Figure FDA00037097006800000113
s53, combining the steps S51 and S52 to establish a dynamic system as follows:
Figure FDA00037097006800000114
wherein:
Figure FDA0003709700680000021
representing an argument as a tracking error
Figure FDA0003709700680000022
The auxiliary function of (2);
s6, designing fixed time H based on dynamic system ∞ A trajectory tracking controller and performing stability analysis, comprising the steps of:
s61, defining the auxiliary function for realizing the stability of the dynamic system of the step S53 in a fixed time as follows:
Figure FDA0003709700680000023
wherein,
Figure FDA0003709700680000024
representing an argument as a tracking error
Figure FDA0003709700680000025
α, β represent fixed time convergence control parameters and satisfy 0<a<1，β>1；p i (i＝1,2,3,4)＝diag{p i1 ,p i2 ,...,p in All positive definite diagonal matrixes represent auxiliary function control gain coefficients, and the sign function sign satisfies the relation: sig a (·)＝sign(·)|·| a ,sig β (·)＝sign(·)|·| β ；
S62, defining a performance vector in the dynamic system of step S53 as follows:
Figure FDA0003709700680000026
wherein λ is 1 >0,λ 2 >0, each represents
Figure FDA0003709700680000027
And
Figure FDA0003709700680000028
the weighting coefficient of (2);
s63, designing a fixed time H infinity trajectory tracking controller strategy based on the fixed time extended state observer according to the auxiliary function of the step S61 and the performance vector of the step S62 as follows:
Figure FDA0003709700680000029
wherein the superscript T represents the transpose of the matrix,
Figure FDA00037097006800000210
is a secondary function
Figure FDA00037097006800000211
The first derivative of (a) is,
Figure FDA00037097006800000212
is a secondary function
Figure FDA00037097006800000213
Is given as a real number;
s64, analyzing that the unmanned surface vehicle can track the expected track in a fixed time and is independent of the initial state of the unmanned surface vehicle by utilizing a theorem proving technology based on a fixed time H infinity track tracking controller strategy.
2. Fixed time base H according to claim 1 ∞ The method for controlling the rapid tracking of the trajectory of the unmanned surface vehicle is characterized in that in the step S1, the step of establishing the unmanned surface vehicle controller comprising a kinematics and dynamics model comprises the following steps:
s11, establishing a kinematics and dynamics model of the unmanned surface vehicle;
s12, carrying out coordinate transformation on the kinematics and dynamics model of the unmanned surface vehicle;
s13, carrying out parameter uncertainty and time-varying interference processing on the kinematics and dynamics model of the unmanned surface vehicle;
and S14, obtaining the expected track of the kinematics and dynamic model of the unmanned surface vehicle.
3. Fixed time base H according to claim 2 ∞ The controlled water surface unmanned ship track rapid tracking control method is characterized in that in the step S2, a water surface unmanned ship track tracking error model is built based on a kinematics and dynamics model, and the method comprises the following steps:
s21, defining track tracking errors of the unmanned surface vehicle and speed errors of the unmanned surface vehicle in a fixed coordinate system and obtaining the tracking error dynamics of the unmanned surface vehicle;
and S22, combining the step S13 and the step S14 to rewrite the tracking error dynamic of the unmanned surface boat.
4. Fixed time base H according to claim 3 ∞ The controlled water surface unmanned ship track rapid tracking control method is characterized in that in the step S3, a fixed time extended state observer is designed based on a water surface unmanned ship controller and a water surface unmanned ship track tracking error model, and the method comprises the following steps:
s31, designing a fixed time extended state observer and defining the observation error of the observer;
and S32, further designing the fixed-time extended state observer according to the defined observation error.
5. Fixed time base H according to claim 4 ∞ The method for controlling the rapid tracking of the trajectory of the unmanned surface vehicle is characterized in that in the step S4, fixed time H is established ∞ A controller comprising the steps of:
s41, defining a closed loop system containing a causal dynamic compensator;
s42, the closed loop system analytically defined by the theorem proving technology is stable in global fixed time, and the causal dynamic compensator is a global fixed time H ∞ And a controller.
6. Fixed time base H according to claim 2 ∞ The method for controlling the rapid tracking of the trajectory of the unmanned surface vehicle is characterized in that in the step S11, a kinematics and dynamics model of the unmanned surface vehicle is established as follows:
Figure FDA0003709700680000041
wherein n represents the water of the unmanned surface vehicle in the geodetic coordinate systemThree-degree-of-freedom pose vector in a plane, psi represents a course angle, R represents a real number, v represents the velocity and angular velocity vector of the unmanned surface vessel in the horizontal plane under a vessel body coordinate system,
Figure FDA0003709700680000042
representing the velocity and angular velocity vector of the unmanned surface vehicle under a geodetic coordinate system,
Figure FDA0003709700680000043
representing the acceleration and angular acceleration vectors of the unmanned surface vehicle in a hull coordinate system, wherein C (v) is a Coriolis centripetal force matrix, D (v) is a fluid damping matrix, and w (t) is time-varying disturbance caused by storms and ocean current marine environments.
7. Fixed time base H according to claim 3 ∞ The controlled water surface unmanned ship track rapid tracking control method is characterized in that in the step S21, the following dynamic states of the tracking error of the water surface unmanned ship are obtained:
Figure FDA0003709700680000044
wherein n is e Tracking error of unmanned surface vehicle trajectory, v e Is the speed error v of the unmanned surface vehicle under a fixed coordinate system d And the expected values of the speed and the angular speed of the unmanned surface vehicle in the horizontal plane under the ship body coordinate system are shown.
8. Fixed time base H according to claim 4 ∞ The method for controlling the rapid tracking of the trajectory of the unmanned surface vehicle is characterized in that in the step S31, the observation error of the fixed-time extended state observer is designed and defined as follows:
Figure FDA0003709700680000045
wherein, mu ═ R (psi) nu,
Figure FDA0003709700680000046
is the observed value of n and is,
Figure FDA0003709700680000047
is the observed value of mu, and the measured value of mu,
Figure FDA0003709700680000048
the observed value of x is the value of x,
Figure FDA0003709700680000049
are both estimated error values.
CN202111514616.7A 2021-12-13 2021-12-13 Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control Active CN114296449B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111514616.7A CN114296449B (en) 2021-12-13 2021-12-13 Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111514616.7A CN114296449B (en) 2021-12-13 2021-12-13 Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control

Publications (2)

Publication Number Publication Date
CN114296449A CN114296449A (en) 2022-04-08
CN114296449B true CN114296449B (en) 2022-08-02

Family

ID=80966912

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111514616.7A Active CN114296449B (en) 2021-12-13 2021-12-13 Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control

Country Status (1)

Country Link
CN (1) CN114296449B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115951693B (en) * 2022-12-14 2023-08-29 广东海洋大学 Robust track tracking control method for under-actuated underwater robot
CN117193303B (en) * 2023-09-18 2024-09-17 哈尔滨理工大学 Multi-unmanned-ship formation control method based on fixed-time extended state observer

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6064997A (en) * 1997-03-19 2000-05-16 University Of Texas System, The Board Of Regents Discrete-time tuning of neural network controllers for nonlinear dynamical systems
CN110879599A (en) * 2019-12-12 2020-03-13 大连海事大学 Fixed time formation control method based on finite time disturbance observer
CN112965371A (en) * 2021-01-29 2021-06-15 哈尔滨工程大学 Water surface unmanned ship track rapid tracking control method based on fixed time observer
CN112965375A (en) * 2021-02-02 2021-06-15 大连海事大学 Multi-unmanned-boat formation control method based on fixed-time terminal sliding mode

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6064997A (en) * 1997-03-19 2000-05-16 University Of Texas System, The Board Of Regents Discrete-time tuning of neural network controllers for nonlinear dynamical systems
CN110879599A (en) * 2019-12-12 2020-03-13 大连海事大学 Fixed time formation control method based on finite time disturbance observer
CN112965371A (en) * 2021-01-29 2021-06-15 哈尔滨工程大学 Water surface unmanned ship track rapid tracking control method based on fixed time observer
CN112965375A (en) * 2021-02-02 2021-06-15 大连海事大学 Multi-unmanned-boat formation control method based on fixed-time terminal sliding mode

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
Robust Finite-time Convergent Trajectory Tracking Control for Unmanned Surface Vehicle;Haitao Liu等;《2019 Chinese Automation Congress (CAC)》;20200213;全文 *
基于扰动观测的无人水下航行器复合航迹跟踪控制研究;刘厶源等;《中国博士学位论文全文数据库 工程科技Ⅱ辑》;20181215;全文 *
欠驱动UUV级联自适应目标跟踪控制方法研究;王宏健等;《高技术通讯》;20141115(第11期);全文 *
高性能欠驱动水面机器人的有限时间跟踪控制;刘海涛等;《应用科学学报》;20160331;全文 *

Also Published As

Publication number Publication date
CN114296449A (en) 2022-04-08

Similar Documents

Publication Publication Date Title
Sun et al. Leader-follower formation control of underactuated surface vehicles based on sliding mode control and parameter estimation
CN114047773B (en) Underwater ore collection robot backstepping sliding mode self-adaptive attitude control method based on extended state observer
Zheng et al. Output-constrained tracking control of an underactuated autonomous underwater vehicle with uncertainties
Shen et al. Dynamic surface control for tracking of unmanned surface vessel with prescribed performance and asymmetric time-varying full state constraints
CN112965371B (en) Water surface unmanned ship track rapid tracking control method based on fixed time observer
CN114296449B (en) Water surface unmanned ship track rapid tracking control method based on fixed time H-infinity control
Yang et al. A recurrent neural network based fuzzy sliding mode control for 4-DOF ROV movements
CN112068440B (en) AUV recovery butt joint power positioning control method based on model prediction control
CN111650832A (en) Method for tracking and controlling mechanical foot posture of underwater multi-foot walking robot
CN108089589A (en) A kind of underwater robot attitude control method
Zhang et al. A novel event-triggered robust neural formation control for USVs with the optimized leader–follower structure
CN108170151A (en) The adaptive motion control device and its method of a kind of underwater robot
Tang et al. Adaptive fuzzy nonlinear integral sliding mode control for unmanned underwater vehicles based on ESO
CN105955034A (en) Offset-free trajectory tracking prediction control method for disturbed hypersonic aircraft
He et al. Flight and vibration control of flexible air-breathing hypersonic vehicles under actuator faults
Li et al. Underactuated multi-AUV robust formation control based on virtual leader
CN113848887A (en) Under-actuated unmanned ship trajectory tracking control method based on MLP method
Gao et al. Offset-free trajectory tracking control for hypersonic vehicle under external disturbance and parametric uncertainty
Wang et al. Robust trajectory tracking control of underactuated surface vehicles with prescribed performance
Sun et al. Adaptive nonlinear relative motion control of quadrotors in autonomous shipboard landings
Joukhadar et al. Advanced UAVs nonlinear control systems and applications
Wang et al. Tracking control with input saturation and full-state constraints for surface vessels
Zhang et al. Adaptive output feedback control for trajectory tracking of AUV in wave disturbance condition
Ma et al. Trajectory tracking control for autonomous underwater vehicle with disturbances and input saturation based on contraction theory
Miao et al. PECLOS path-following control of underactuated AUV with multiple disturbances and input constraints

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant