CN110618606B - Under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under combined interference - Google Patents

Under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under combined interference Download PDF

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CN110618606B
CN110618606B CN201910938266.3A CN201910938266A CN110618606B CN 110618606 B CN110618606 B CN 110618606B CN 201910938266 A CN201910938266 A CN 201910938266A CN 110618606 B CN110618606 B CN 110618606B
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魏延辉
蒋志龙
贺佳林
***强
马博也
牛家乐
刘东东
姜瑶瑶
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Abstract

The invention discloses an under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under combined interference. Firstly, establishing a kinematics and dynamics model of the AUV, and establishing a track tracking error model based on a Serret-Frenet coordinate system; according to the error model, considering the situation without interference, respectively designing track tracking backstepping sliding mode controllers of a horizontal plane and a vertical plane to realize a track tracking function; on the basis, the working state of the system under the condition of composite interference is considered, and a self-adaptive fuzzy logic system is added on the original controller, so that the anti-interference capability of the system is improved. So as to realize the trace tracking control of the under-actuated AUV under the condition of external complex interference. The method can identify the under-actuated AUV composite interference, and provides a reference scheme with the advantages of self-adaption, strong robustness and the like for the accurate control of the trajectory tracking of the underwater robot.

Description

Under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under combined interference
Technical Field
The invention relates to the field of track tracking control of underwater robots, in particular to a backstepping self-adaptive fuzzy sliding mode control method which can enable an AUV to stably track a preset track under compound interference.
Background
The ocean is a vital resource treasury on the earth, and the ocean gradually becomes an object of the key development of human beings due to the imminent exhaustion of land resources. According to the detection of human beings, a large amount of fossil fuels, metal deposits and biological resources exist in the ocean, and the ocean is a treasure place capable of carrying out transportation and wave power generation. In recent years, mankind has accelerated the pace of ocean development, which is an important area of research and development in various countries. However, the marine environment is special compared with the land, the underwater environment is very severe, and factors such as underwater pressure, temperature, illumination and the like can be greatly changed along with the increase of water depth. Due to the danger and complexity of the submarine environment, manned Underwater operation is very dangerous, so that the research of a high-technology unmanned Underwater detector and an intelligent Underwater robot (Autonomous Underwater Vehicle) as a high-tech ocean detection carrier are urgently required, the research and development of an AUV are products under the background of the era and are organic combination of science and technology and information. At present, a plurality of AUVs of different models are put into use successively, and the application of the AUV plays a great role in human development and ocean utilization. The AUV can explore underwater resources, collect marine samples, observe marine life, explore submarine topography, and the like.
The intelligent underwater robot can be divided into three categories according to whether the input number is matched with the controlled degree of freedom: the system comprises a fully-driven underwater robot, an over-driven underwater robot and an under-driven underwater robot. In consideration of saving cost and reducing weight, the invention adopts the under-actuated AUV for research, the under-actuated AUV is an underwater robot with the dimension of control input less than the degree of freedom of a body, the under-actuated AUV has the advantages of high system reliability, low energy consumption, high system propulsion efficiency and the like, and has great effect in the fields of marine exploration, hydrological investigation, target detection, biological sampling and the like. However, the under-actuated AUV system has strong coupling, the model has nonlinearity and time-varying property, the model parameters have uncertainty, and the under-actuated AUV is easily influenced by external interference. Therefore, the quality of the design of the control algorithm determines the quality of the AUV trajectory tracking performance.
At present, most of research on AUV control at home and abroad is based on a controller designed according to a nominal model, the self dynamic characteristics of the under-actuated AUV are ignored, and the influence of external interference and parameter uncertainty is not considered.
Disclosure of Invention
Aiming at the prior art, the technical problem to be solved by the invention is to provide an under-actuated AUV (autonomous underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under the composite interference, which can self-adaptively identify the composite interference and inhibit the influence of the interference, so that a system stably tracks and has the characteristic of strong robustness.
In order to solve the technical problem, the under-actuated AUV backstepping self-adaptive fuzzy sliding-mode control method under the composite interference comprises the following steps of:
step 1: setting an expected trajectory, an initial position and a speed of the AUV, and establishing a dynamic model and a kinematic model of a vertical plane and a horizontal plane of the AUV;
step 2: establishing a trajectory tracking error model based on a Serret-Frenet coordinate system;
and step 3: constructing a backstepping sliding mode controller for the horizontal plane and the vertical plane respectively by using the trajectory tracking error model and the dynamic model, and acquiring controller outputs under the horizontal plane and the vertical plane respectively;
and 4, step 4: and (3) designing a self-adaptive backstepping sliding mode fuzzy controller on the basis of the controller in the step (3), adding a self-adaptive fuzzy control system, and realizing the under-actuated AUV trajectory tracking control under the composite interference.
The invention also includes:
1. the dynamic model in the step 1 comprises a horizontal plane dynamic model and a vertical plane dynamic model, wherein the horizontal plane dynamic model meets the following requirements:
Figure BDA0002222165810000021
the vertical plane dynamics model satisfies:
Figure BDA0002222165810000022
the kinematic model in the step 1 comprises a horizontal plane kinematic model and a vertical plane kinematic model, wherein the horizontal plane kinematic model satisfies the following conditions:
Figure BDA0002222165810000023
the vertical surface kinematics model satisfies:
Figure BDA0002222165810000024
where m represents the actual mass of the AUV in motion,
Figure BDA0002222165810000031
representing the projection of the acceleration on three axes of motion, x, respectivelyg、yg、zgRespectively representing the components of the gravitational acceleration in the x, y, z directions, Ix、Iy、IzRepresenting the moment of inertia in the x, y, z axes, m11，m22，m33Additional mass and coriolis force for the longitudinal, lateral and heading of the AUV; x represents the thrust to which the simplified AUV is subjected; n represents the yaw moment to which the simplified AUV is subjected; xuu，Xu|u|，Yvv，Yv|v|，Nrr，Nr|r|The viscous damping coefficient between the AUV and the water environment when the AUV translates and rotates in x, y and z axes is shown, and is a positive number.
2. The trajectory tracking error model in the step 2 comprises a horizontal plane trajectory tracking error model and a vertical plane trajectory tracking error model, wherein the horizontal plane trajectory tracking error model satisfies the following conditions:
Figure BDA0002222165810000032
wherein psieFor course angle tracking error, psie＝ψ-ψP，
Figure BDA0002222165810000033
Is the derivative of the course angle error, Up is the speed of movement of the reference point along the reference track, τe、neRespectively representing the tracking errors of the tracking points in the tangential direction and the normal direction of the tracking track; r and rpRespectively representing along the z-axis and pointing UpAngular velocity of the direction;
wherein the vertical plane trajectory tracking error model satisfies:
Figure BDA0002222165810000034
wherein theta iseIndicating a pitch tracking error.
3. Step 3, the backstepping sliding mode controller comprises a horizontal surface backstepping sliding mode longitudinal speed controller, a horizontal surface backstepping sliding mode course controller and a vertical surface backstepping sliding mode trim angle controller;
wherein, the horizontal plane backstepping sliding mode longitudinal speed controller satisfies:
Figure BDA0002222165810000035
the horizontal surface backstepping sliding mode course controller meets the following requirements:
Figure BDA0002222165810000036
the vertical surface backstepping sliding mode pitch angle controller meets the following requirements:
Figure BDA0002222165810000041
4. step 4 the adaptive backstepping sliding mode fuzzy controller comprises: a horizontal plane backstepping self-adaptive fuzzy sliding mode longitudinal speed controller, a horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller and a vertical plane backstepping self-adaptive fuzzy sliding mode pitch angle controller;
wherein, the horizontal plane backstepping self-adaptive fuzzy sliding mode longitudinal speed controller meets the following requirements:
Figure BDA0002222165810000042
the horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller meets the following requirements:
Figure BDA0002222165810000043
the vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller meets the following requirements:
Figure BDA0002222165810000044
wherein
Figure BDA0002222165810000045
Is the output of the fuzzy logic system and,
Figure BDA0002222165810000046
is the output of the fuzzy logic system and,
Figure BDA0002222165810000047
disturbance terms for fuzzy logic systems, S1＝u-udH and beta each represent a real number having a positive value, z1＝ψ-ψd，
Figure BDA0002222165810000048
The index numbers of the subscripts indicate the representation of the parameters in the different controllers.
The invention has the beneficial effects that: the method comprises the steps of generating an error variable, designing a backstepping sliding mode controller under the condition of no interference by utilizing the error variable and a dynamic model, realizing stable tracking of the AUV, further adding composite interference, adding a fuzzy logic system, designing a self-adaptive backstepping sliding mode fuzzy controller, and realizing accurate control of the trajectory tracking of the AUV under the composite interference. Compared with the prior art, the method has the advantages of more accurate tracking effect, no buffeting, better composite interference suppression and higher stability.
Drawings
Fig. 1 is an AUV coordinate system reference diagram.
Fig. 2 is a flow chart of adaptive backstepping sliding mode fuzzy control.
Fig. 3 is a structure diagram of adaptive backstepping sliding mode fuzzy control.
FIG. 4 is a horizontal backstepping sliding mode control trajectory tracking diagram.
FIG. 5 is a vertical surface backstepping sliding mode control trajectory tracking diagram.
Fig. 6 is a graph of horizontal circular trajectory tracking under the composite interference.
Fig. 7 is a graph of vertical circular trajectory tracking under a compound disturbance.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
The invention discloses an under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding mode control method under combined interference. Firstly, establishing a kinematics and dynamics model of the AUV, and establishing a track tracking error model based on a Serret-Frenet coordinate system; according to the error model, considering the situation without interference, respectively designing track tracking backstepping sliding mode controllers of a horizontal plane and a vertical plane to realize a track tracking function; on the basis, the working state of the system under the condition of composite interference is considered, and a self-adaptive fuzzy logic system is added on the original controller, so that the anti-interference capability of the system is improved. The trajectory tracking control of the under-actuated AUV under the condition of external composite interference is realized. The method can identify the under-actuated AUV composite interference, and provides a reference scheme with the advantages of self-adaption, strong robustness and the like for the accurate control of the trajectory tracking of the underwater robot.
The specific technical scheme is as follows:
an under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding-mode control method under compound interference comprises the following contents:
step 1, setting initial conditions and an expected track of an AUV, and establishing a dynamics and kinematics model of a vertical plane and a horizontal plane of the AUV;
step 2, establishing a track tracking error model based on a Serret-Frenet coordinate system;
step 3, constructing a backstepping sliding mode control controller for the horizontal plane and the vertical plane respectively by using the error variable and the AUV dynamic model, and acquiring controller outputs under the horizontal plane and the vertical plane respectively to realize under-actuated AUV trajectory tracking control under the condition of no interference;
and 4, adding a self-adaptive fuzzy control system to the trajectory tracking controller under the undisturbed control to realize the identification and inhibition of the compound interference and weaken the buffeting of the sliding mode. And the under-actuated AUV trajectory tracking control under the composite interference is realized.
The mathematical model of the AUV is as follows:
the horizontal plane kinematic equation is:
Figure BDA0002222165810000051
the vertical plane kinematic equation is:
Figure BDA0002222165810000052
the horizontal plane kinetic equation is:
Figure BDA0002222165810000061
the vertical plane kinetic equation is:
Figure BDA0002222165810000062
wherein: m is11，m22，m33Additional mass and coriolis force for the longitudinal, lateral and heading of the AUV;
AUV propulsion directionIs in the X-axis direction, X and Y are thrust of AUV along the X-coordinate axis and the Y-coordinate axis, N represents torque along the z-axis direction, and X isuu，Xu|u|，Yvv，Yv|v|，Nrr，Nr|r|The viscous damping coefficients of the AUV and the water environment during translation and rotation of the axis x, y and z are positive numbers;
the AUV horizontal plane trajectory tracking error equation is as follows:
Figure BDA0002222165810000063
the AUV vertical plane trajectory tracking error equation is as follows:
Figure BDA0002222165810000064
the backstepping sliding mode controller comprises:
horizontal surface backstepping sliding mode longitudinal speed controller:
Figure BDA0002222165810000065
horizontal surface backstepping sliding mode course controller
Figure BDA0002222165810000066
Vertical surface backstepping sliding mode trim angle controller
Figure BDA0002222165810000067
The backstepping self-adaptive fuzzy sliding mode controller comprises the following steps:
horizontal plane backstepping self-adaptive fuzzy sliding mode longitudinal speed controller
Figure BDA0002222165810000071
Horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller design
Figure BDA0002222165810000072
Vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller design
Figure BDA0002222165810000073
The specific implementation mode of the invention also comprises:
implementation 1: fig. 2 is a flow chart of adaptive backstepping sliding mode fuzzy control, and the implementation process is as follows:
step 1, establishing a dynamics and kinematics model of a vertical plane and a horizontal plane of the AUV;
step 2, establishing a track tracking error model based on a Serret-Frenet coordinate system;
step 3, constructing a backstepping sliding mode control controller for the horizontal plane and the vertical plane respectively by using the error variables and the dynamic model, and acquiring controller outputs under the horizontal plane and the vertical plane respectively to realize under-actuated AUV (autonomous underwater vehicle) trajectory tracking control under the condition of no interference;
and 4, adding a self-adaptive fuzzy control system to the trajectory tracking controller under the undisturbed control to realize the identification and inhibition of the compound interference and weaken the buffeting of the sliding mode. And the under-actuated AUV trajectory tracking control under the composite interference is realized.
Implementation 2: as shown in fig. 3, it can be seen that the fuzzy sliding mode controller mainly includes a fuzzy sliding mode controller, an adaptive backstepping controller and a control object. The invention establishes the kinematics and dynamics model of AUV:
the horizontal plane kinematic equation is:
Figure BDA0002222165810000074
the vertical plane kinematic equation is:
Figure BDA0002222165810000075
the horizontal plane kinetic equation is:
Figure BDA0002222165810000081
the vertical plane kinetic equation is:
Figure BDA0002222165810000082
then, a tracking error model is established under a Serret-Frenet coordinate system:
the AUV horizontal plane trajectory tracking error equation is as follows:
Figure BDA0002222165810000083
the AUV vertical plane trajectory tracking error equation is as follows:
Figure BDA0002222165810000084
implementation 3: designing a self-adaptive backstepping controller:
horizontal surface backstepping sliding mode longitudinal speed controller:
Figure BDA0002222165810000085
horizontal surface backstepping sliding mode course controller
Figure BDA0002222165810000086
Vertical surface backstepping sliding mode longitudinal inclination angle controller
Figure BDA0002222165810000087
Fig. 4 and 5 are obtained by applying this controller to the control target in embodiment 1. Fig. 4 is a graph of circular trajectory tracking in the horizontal plane, and fig. 5 is a graph of sinusoidal trajectory tracking in the vertical plane. The simulation assumes the same initial conditions, does not consider external interference, and the expected speed of AUV is udThe circle and the sine curve are respectively selected as the tracks to be tracked, and the initial state of the AUV is v (0) ═ r (0) ═ 0, and u (0) ═ 0.08 m/s. As can be seen from fig. 4 and 5, the horizontal plane trajectory tracking controller and the PID controller designed by the present invention can better track the target trajectory without external interference. The backstepping sliding mode controller can track the upper target track relatively more quickly, and the PID controller has larger offset in the early period; the backstepping sliding mode controller can achieve better tracking effect than the traditional PID under the condition of no interference.
Implementation 4: on the basis of implementation 3, the adaptive backstepping sliding mode fuzzy controller is designed as follows:
horizontal surface backstepping self-adaptive fuzzy sliding mode longitudinal speed controller
Figure BDA0002222165810000091
Horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller design
Figure BDA0002222165810000092
Vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller design
Figure BDA0002222165810000093
Wherein
Figure BDA0002222165810000094
Is the output of the fuzzy logic system and,
Figure BDA0002222165810000095
is the output of the fuzzy logic system and,
Figure BDA0002222165810000096
disturbance terms for fuzzy logic systems, S1＝u-udH and beta each represent a real number having a positive value, z1＝ψ-ψd，
Figure BDA0002222165810000097
The index numbers of the subscripts indicate the representation of the parameters in the different controllers.
The controller is acted on the control object in the embodiment 2, and the compound interference is added to simulate the horizontal plane. The simulation assumes the same initial conditions and the desired speed of AUV is ud1m/s and the initial state of the AUV is u (0) 0.08m/s, v (0) r (0) 0, ψ (0) 0, ξ (0) η (0) 0,
Figure BDA0002222165810000098
and respectively selecting a circle and a straight line as the tracks to be tracked. In addition, model parameter estimates
Figure BDA0002222165810000099
And
Figure BDA00022221658100000910
initial value is set to 0, and external interference estimated value
Figure BDA00022221658100000911
And
Figure BDA00022221658100000912
the initial value is also set to 0 and it is assumed that the under-actuated AUV is subjected to [3N 3N 3N/m]Selecting the parameters of the controller as the horizontal plane path tracking control parameters in the table 2
Figure BDA00022221658100000913
(1) The parametric equation for the circular trajectory is:
Figure BDA0002222165810000101
as shown in fig. 6, which is a tracking curve of a horizontal plane circular trajectory under the combined interference, it can be known from fig. 6 that both the back-step sliding mode controller and the back-step adaptive fuzzy sliding mode controller can track the circular trajectory well, but the back-step adaptive fuzzy sliding mode controller has a relatively better tracking effect.
Implementation 5: under the controller of the embodiment 4, the tracking simulation of the vertical plane is continued. The simulation assumes the same initial conditions and the desired speed of AUV is ud1m/s, and the initial state of the AUV is u (0) ═ 0.06m/s, w (0) ═ q (0) ═ 0, θ (0) ═ 0, ξ (0) ═ ζ (0) ═ 0,
Figure BDA0002222165810000102
and respectively selecting a sine curve and a straight line as the tracks to be tracked. In addition, model parameter estimation values
Figure BDA0002222165810000103
And
Figure BDA0002222165810000104
is set to 0, and the external interference estimate is set to
Figure BDA0002222165810000105
And
Figure BDA0002222165810000106
the initial value is also set to 0 and it is assumed that the under-actuated AUV is subjected to [2N 2N 2N/m]The parameters of the selected controller are shown in table 3.
TABLE 3 vertical plane Path tracking control parameters
Figure BDA0002222165810000107
(1) The parametric equation for sinusoidal trajectory is:
Figure BDA0002222165810000108
as shown in fig. 7, which is a compound disturbance lower vertical sinusoidal track tracking curve, it can be seen that both controllers can track sinusoidal tracks well, but the backstepping sliding mode controller generates large buffeting. And the adaptive backstepping sliding mode fuzzy control can stably track under the composite interference.
The specific implementation mode of the invention also comprises the following steps:
step 1, establishing a dynamics and kinematics model of a vertical plane and a horizontal plane of the AUV;
step 2, a track tracking error model based on a Serret-Frenet coordinate system is solved to calculate a virtual control law;
step 3, constructing a backstepping sliding mode control controller for the horizontal plane and the vertical plane respectively by using the error variable and the virtual control law, and acquiring controller outputs under the horizontal plane and the vertical plane respectively to realize under-actuated AUV (autonomous underwater vehicle) trajectory tracking control under the condition of no interference;
and 4, adding a self-adaptive fuzzy control system to the trajectory tracking controller under the undisturbed control to realize the identification and inhibition of the compound interference and weaken the buffeting of the sliding mode. And the under-actuated AUV trajectory tracking control under the composite interference is realized.
TABLE 1 Underwater robot 6 degree of freedom motion identifier
Figure BDA0002222165810000111
The mathematical model of the AUV is (AUV six degrees of freedom motion identifier is shown in table 1):
the horizontal plane kinematic equation is:
Figure BDA0002222165810000112
where m represents the actual mass of the AUV in motion,
Figure BDA0002222165810000113
respectively representing the projections of the acceleration on the three axes of motion,
xg、yg、zgrespectively representing the components of the gravitational acceleration in the x, y, z directions, Ix、Iy、IzRepresenting the moment of inertia in the x, y, z axes. The same applies below.
The vertical plane kinematic equation is:
Figure BDA0002222165810000114
the horizontal plane kinetic equation is:
Figure BDA0002222165810000115
the vertical plane kinetic equation is:
Figure BDA0002222165810000121
wherein: m is11，m22，m33Additional mass and coriolis force for the longitudinal, lateral and heading of the AUV;
x represents the thrust to which the simplified AUV is subjected;
n represents the yaw moment to which the simplified AUV is subjected;
Xuu，Xu|u|，Yvv，Yv|v|，Nrr，Nr|r|the viscous damping coefficients are all positive numbers;
the AUV horizontal plane trajectory tracking error equation is as follows:
Figure BDA0002222165810000122
wherein: psieFor course angle tracking error, psie＝ψ-ψP，
Figure BDA0002222165810000123
Is the derivative of the course angle error, Up is the speed of movement of the reference point along the reference track, τe、neRespectively representing the tracking error of the tracking point in the tangential direction and the normal direction of the tracking track, wherein the AUV vertical plane track tracking error equation is as follows:
Figure BDA0002222165810000124
wherein theta iseIndicating pitch tracking error
Horizontal surface backstepping sliding mode longitudinal speed controller:
Figure BDA0002222165810000125
wherein h is1Denotes a positive constant, S1Surface for representing sliding form
Horizontal surface backstepping sliding mode course controller
Figure BDA0002222165810000126
Wherein c is1、h2Is a constant, S2Is a slip-form surface and is characterized in that,
vertical surface backstepping sliding mode trim angle controller
Figure BDA0002222165810000127
Horizontal surface backstepping self-adaptive fuzzy sliding mode longitudinal speed controller
Figure BDA0002222165810000131
Horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller design
Figure BDA0002222165810000132
Vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller design
Figure BDA0002222165810000133
Wherein the content of the first and second substances,
Figure BDA0002222165810000134
to represent the input to the fuzzy system, h and β each represent a real number with a positive value. The index numbers of the subscripts indicate the representation of the parameters in the different controllers.

Claims (2)

1. An under-actuated AUV (autonomous Underwater vehicle) backstepping self-adaptive fuzzy sliding-mode control method under combined interference is characterized by comprising the following steps of:
step 1: setting an expected trajectory, an initial position and a speed of the AUV, and establishing a dynamic model and a kinematic model of a vertical plane and a horizontal plane of the AUV;
step 2: establishing a track tracking error model based on a Serret-Frenet coordinate system, wherein the track tracking error model comprises a horizontal plane track tracking error model and a vertical plane track tracking error model, and the horizontal plane track tracking error model meets the following requirements:
Figure FDA0003526564150000011
wherein psieFor course angle tracking error, psie＝ψ-ψP，
Figure FDA0003526564150000012
Is the derivative of the course angle tracking error, Up is the speed of movement of the reference point along the reference track, τe、neRespectively representing the tracking errors of the tracking points in the tangential direction and the normal direction of the tracking track; r and rpRespectively representing along the z-axis and pointing UpAngular velocity of the direction;
wherein the vertical plane trajectory tracking error model satisfies:
Figure FDA0003526564150000013
wherein theta iseRepresenting a pitch tracking error;
and step 3: constructing a backstepping sliding mode controller for the horizontal plane and the vertical plane respectively by utilizing the trajectory tracking error model and the dynamic model, and acquiring controller outputs under the horizontal plane and the vertical plane respectively, wherein the backstepping sliding mode controller comprises a horizontal plane backstepping sliding mode longitudinal speed controller, a horizontal plane backstepping sliding mode course controller and a vertical plane backstepping sliding mode pitch angle controller;
wherein, the horizontal plane backstepping sliding mode longitudinal speed controller satisfies:
Figure FDA0003526564150000014
the horizontal surface backstepping sliding mode course controller meets the following requirements:
Figure FDA0003526564150000015
the vertical surface backstepping sliding mode pitch angle controller meets the following requirements:
Figure FDA0003526564150000016
and 4, step 4: designing a self-adaptive backstepping sliding mode fuzzy controller on the basis of the controller in the step 3, adding a self-adaptive fuzzy control system, and realizing under-actuated AUV (autonomous underwater vehicle) trajectory tracking control under the composite interference; the adaptive backstepping sliding mode fuzzy controller comprises: a horizontal plane backstepping self-adaptive fuzzy sliding mode longitudinal speed controller, a horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller and a vertical plane backstepping self-adaptive fuzzy sliding mode pitch angle controller;
wherein, the horizontal plane backstepping self-adaptive fuzzy sliding mode longitudinal speed controller meets the following requirements:
Figure FDA0003526564150000021
the horizontal plane backstepping self-adaptive fuzzy sliding mode course angle controller meets the following requirements:
Figure FDA0003526564150000022
the vertical surface backstepping self-adaptive fuzzy sliding mode pitch angle controller meets the following requirements:
Figure FDA0003526564150000023
wherein
Figure FDA0003526564150000024
Is the output of the fuzzy logic system and,
Figure FDA0003526564150000025
is the output of the fuzzy logic system and,
Figure FDA0003526564150000026
disturbance terms for fuzzy logic systems, S1＝u-udH and beta each represent a real number having a positive value, z1＝ψ-ψd，
Figure FDA0003526564150000027
The index numbers of the subscripts indicate the representation of the parameters in the different controllers.
2. The under-actuated AUV (autonomous Underwater vehicle) backstepping adaptive fuzzy sliding-mode control method under the combined interference according to claim 1, characterized in that:
the dynamic model in the step 1 comprises a horizontal plane dynamic model and a vertical plane dynamic model, wherein the horizontal plane dynamic model meets the following requirements:
Figure FDA0003526564150000028
the vertical plane dynamics model satisfies:
Figure FDA0003526564150000029
the kinematic model in the step 1 comprises a horizontal plane kinematic model and a vertical plane kinematic model, wherein the horizontal plane kinematic model satisfies the following conditions:
Figure FDA0003526564150000031
the vertical surface kinematics model satisfies:
Figure FDA0003526564150000032
where m represents the actual mass of the AUV in motion,
Figure FDA0003526564150000033
respectively representing the linear acceleration of the AUV along the x-axis direction, the linear acceleration along the y-axis direction and the linear acceleration along the z-axis direction, xg、yg、zgRespectively representing the components of the gravitational acceleration in the x, y, z directions, Ix、Iy、IzDenotes the moment of inertia of the x, y, z axes, m11，m22，m33Additional mass and coriolis force for the longitudinal, lateral and heading of the AUV; x represents the thrust to which the simplified AUV is subjected; n represents the yaw moment to which the simplified AUV is subjected; xuu，Xu|u|，Yvv，Yv|v|，Nrr，Nr|r|And the viscous damping coefficients of the AUV and the water environment during translation and rotation of the AUV on the x axis, the y axis and the z axis are positive numbers.
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