CN113820956B - High-speed AUV motion control method - Google Patents

High-speed AUV motion control method Download PDF

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CN113820956B
CN113820956B CN202111393837.3A CN202111393837A CN113820956B CN 113820956 B CN113820956 B CN 113820956B CN 202111393837 A CN202111393837 A CN 202111393837A CN 113820956 B CN113820956 B CN 113820956B
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郭军军
连文康
范彦福
顾建军
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Abstract

本发明公开了一种高速自主水下机器人（AUV，Autonomous Underwater Vehicle）运动控制方法，该方法通过将径向基神经网络和边界层法融入到传统滑模控制中，以提高AUV在高速运动时的控制精度，并有效抑制控制系统的抖振。本发明所涉及的高速AUV运动控制方法包括高速AUV运动模型的简化和运动控制方法的设计，相比于传统的AUV模型简化方法，在模型化简时加入了自适应变化的参数模型，使得所建立的模型更接近实际情况；相比于传统的AUV滑模控制方法，本发明在滑模控制中加入了径向基神经网络的补偿，并通过边界层法对滑模的切换面进行改善，使得滑模控制系统可以保持较高的控制精度并抑制抖振。

Figure 202111393837

The invention discloses a motion control method for a high-speed autonomous underwater vehicle (AUV, Autonomous Underwater Vehicle). The method integrates the radial basis neural network and the boundary layer method into the traditional sliding mode control, so as to improve the high-speed motion of the AUV. control accuracy, and effectively suppress the chattering of the control system. The high-speed AUV motion control method involved in the present invention includes the simplification of the high-speed AUV motion model and the design of the motion control method. The established model is closer to the actual situation; compared with the traditional AUV sliding mode control method, the present invention adds the compensation of the radial basis neural network in the sliding mode control, and improves the switching surface of the sliding mode through the boundary layer method. The sliding mode control system can maintain high control accuracy and suppress chattering.

Figure 202111393837

Description

一种高速AUV运动控制方法A high-speed AUV motion control method

技术领域technical field

本发明涉及自主水下机器人（AUV, Autonomous Underwater Vehicle）控制领域，尤其涉及一种高速AUV运动控制方法。The invention relates to the field of autonomous underwater vehicle (AUV, Autonomous Underwater Vehicle) control, in particular to a high-speed AUV motion control method.

背景技术Background technique

自主水下机器人（Autonomous Underwater Vehicle，简称AUV）是探索海洋空间的有力工具之一，AUV在军事海洋技术、油田勘测、海底打捞、管路检修、海底勘测等领域获得越来越广泛的应用。然而，传统的水下机器人普遍具有航速较低、环境适应能力不强等方面的问题，围绕深海快速应急搜探、水下环境快速评估等迫切需求，探索高速AUV的运动控制方法是研究的重要方向。Autonomous Underwater Vehicle (AUV) is one of the powerful tools for exploring ocean space. AUV has been widely used in military marine technology, oil field survey, seabed salvage, pipeline maintenance, seabed survey and other fields. However, traditional underwater robots generally have problems such as low speed and poor environmental adaptability. Focusing on urgent needs such as rapid emergency search in deep sea and rapid assessment of underwater environment, it is important to explore motion control methods for high-speed AUVs. direction.

PID控制（Proportion Integration Differentiation Control）、反步法控制（Back Stepping Control）、模糊控制（Fuzzy Control）、滑模控制（Sliding ModeControl）、神经网络控制（Neural Networks Control）等是当今AUV常用的一些控制方法，而近年来，深度学习（Deep Learning）在控制领域的应用也极大地推动了控制技术的发展。PID控制只能适用于一些AUV弱机动下的简单控制，但它对环境参数变化敏感，整定优化比较麻烦；反步法控制依赖于精确的数学模型，但此类新型高速AUV的精确模型很难获得；滑模变结构控制虽具有响应速度快的特点，但是其容易引起抖振；模糊控制器依赖于先验知识；神经网络控制虽然具有很强的非线性逼近能力，但是其网络层数以及每层的节点数较难确定；深度学习具有强大的复杂非线性建模能力，但是其训练耗时，模型正确性验证复杂且麻烦。PID control (Proportion Integration Differentiation Control), Back Stepping Control (Back Stepping Control), Fuzzy Control (Fuzzy Control), Sliding Mode Control (Sliding Mode Control), Neural Networks Control (Neural Networks Control) are some of the controls commonly used in today's AUVs In recent years, the application of deep learning in the field of control has also greatly promoted the development of control technology. PID control can only be applied to simple control under weak maneuvering of some AUVs, but it is sensitive to changes in environmental parameters, making tuning and optimization more troublesome; backstepping control relies on accurate mathematical models, but it is difficult to accurately model such new high-speed AUVs Obtained; although the sliding mode variable structure control has the characteristics of fast response, it is easy to cause chattering; the fuzzy controller depends on the prior knowledge; although the neural network control has a strong nonlinear approximation ability, its network layers and The number of nodes in each layer is difficult to determine; deep learning has powerful complex nonlinear modeling capabilities, but its training is time-consuming, and the model correctness verification is complex and troublesome.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于针对现有技术的不足，提供一种高速AUV运动控制方法。The purpose of the present invention is to provide a high-speed AUV motion control method aiming at the deficiencies of the prior art.

本发明的目的是通过以下技术方案来实现：一种高速AUV运动控制方法，包括以下步骤：The object of the present invention is to realize through the following technical solutions: a kind of high-speed AUV motion control method, comprises the following steps:

（1）通过多项式拟合得到系统参数和航速的函数关系，根据函数关系得到高速AUV简化运动模型；将航速作为高速AUV简化运动模型的输入；(1) The functional relationship between the system parameters and the speed is obtained by polynomial fitting, and the simplified motion model of the high-speed AUV is obtained according to the functional relationship; the speed is used as the input of the simplified motion model of the high-speed AUV;

（2）选择径向基神经网络，定义滑模函数，设计滑模控制律和自适应律，基于边界层法计算滑模面切换函数，对滑模控制律进行改进；(2) Select radial basis neural network, define sliding mode function, design sliding mode control law and adaptive law, calculate sliding mode surface switching function based on boundary layer method, and improve sliding mode control law;

（3）利用步骤（2）得到的改进后的滑模控制律对高速AUV进行运动控制。(3) Using the improved sliding mode control law obtained in step (2) to control the motion of the high-speed AUV.

进一步地，步骤（1）中高速AUV简化运动模型具体为：Further, the simplified motion model of the high-speed AUV in step (1) is specifically:

Figure 634249DEST_PATH_IMAGE001
Figure 634249DEST_PATH_IMAGE001

其中，设

Figure 791692DEST_PATH_IMAGE002
，设
Figure 758511DEST_PATH_IMAGE003
，
Figure 123633DEST_PATH_IMAGE004
为AUV的纵向速度，
Figure 651435DEST_PATH_IMAGE005
为垂向速度，
Figure 2782DEST_PATH_IMAGE006
为纵倾角度，
Figure 948742DEST_PATH_IMAGE007
为纵倾角速度，
Figure 94552DEST_PATH_IMAGE008
为深度值，
Figure 876695DEST_PATH_IMAGE009
为纵倾力矩，
Figure 625208DEST_PATH_IMAGE010
为艉舵舵角，
Figure 566619DEST_PATH_IMAGE011
为正数，
Figure 522811DEST_PATH_IMAGE012
、
Figure 916884DEST_PATH_IMAGE013
为AUV的水动力系数，取
Figure 734667DEST_PATH_IMAGE014
，
Figure 999426DEST_PATH_IMAGE015
为海水密度，
Figure 627985DEST_PATH_IMAGE016
为高速AUV的长度，
Figure 509353DEST_PATH_IMAGE017
和
Figure 130827DEST_PATH_IMAGE018
为多项式系数。Among them, let
Figure 791692DEST_PATH_IMAGE002
,Assume
Figure 758511DEST_PATH_IMAGE003
,
Figure 123633DEST_PATH_IMAGE004
is the longitudinal speed of the AUV,
Figure 651435DEST_PATH_IMAGE005
is the vertical speed,
Figure 2782DEST_PATH_IMAGE006
is the pitch angle,
Figure 948742DEST_PATH_IMAGE007
is the pitch angular velocity,
Figure 94552DEST_PATH_IMAGE008
is the depth value,
Figure 876695DEST_PATH_IMAGE009
is the pitch moment,
Figure 625208DEST_PATH_IMAGE010
is the stern rudder angle,
Figure 566619DEST_PATH_IMAGE011
is a positive number,
Figure 522811DEST_PATH_IMAGE012
,
Figure 916884DEST_PATH_IMAGE013
is the hydrodynamic coefficient of AUV, take
Figure 734667DEST_PATH_IMAGE014
,
Figure 999426DEST_PATH_IMAGE015
is the density of sea water,
Figure 627985DEST_PATH_IMAGE016
is the length of the high-speed AUV,
Figure 509353DEST_PATH_IMAGE017
and
Figure 130827DEST_PATH_IMAGE018
are polynomial coefficients.

进一步地，步骤（2）中所述的滑模函数基于稳定性理论得到，具体为：Further, the sliding mode function described in step (2) is obtained based on the stability theory, specifically:

Figure 781251DEST_PATH_IMAGE019
Figure 781251DEST_PATH_IMAGE019

其中，

Figure 548088DEST_PATH_IMAGE020
为正数，
Figure 41386DEST_PATH_IMAGE021
为误差。in,
Figure 548088DEST_PATH_IMAGE020
is a positive number,
Figure 41386DEST_PATH_IMAGE021
for error.

进一步地，步骤（2）中所述的滑模控制律为：Further, the sliding mode control law described in step (2) is:

Figure 76338DEST_PATH_IMAGE022
Figure 76338DEST_PATH_IMAGE022

其中，

Figure 722214DEST_PATH_IMAGE023
，
Figure 286051DEST_PATH_IMAGE024
、
Figure 266645DEST_PATH_IMAGE025
为正数，
Figure 105288DEST_PATH_IMAGE026
为目标值；in,
Figure 722214DEST_PATH_IMAGE023
,
Figure 286051DEST_PATH_IMAGE024
,
Figure 266645DEST_PATH_IMAGE025
is a positive number,
Figure 105288DEST_PATH_IMAGE026
is the target value;

所述自适应律为：

Figure 844486DEST_PATH_IMAGE027
The adaptive law is:
Figure 844486DEST_PATH_IMAGE027

其中，

Figure 969437DEST_PATH_IMAGE028
，
Figure 47114DEST_PATH_IMAGE029
为俯仰角，
Figure 564815DEST_PATH_IMAGE030
为高斯基函数的输出，
Figure 44337DEST_PATH_IMAGE031
为水动力系数，
Figure 605769DEST_PATH_IMAGE032
为神经网络的权值；in,
Figure 969437DEST_PATH_IMAGE028
,
Figure 47114DEST_PATH_IMAGE029
is the pitch angle,
Figure 564815DEST_PATH_IMAGE030
is the output of the Gaussian function,
Figure 44337DEST_PATH_IMAGE031
is the hydrodynamic coefficient,
Figure 605769DEST_PATH_IMAGE032
is the weight of the neural network;

进一步地，步骤（2）中所述的滑模面切换函数为：Further, the sliding mode surface switching function described in step (2) is:

Figure 905163DEST_PATH_IMAGE033
Figure 905163DEST_PATH_IMAGE033

式中，

Figure 459510DEST_PATH_IMAGE034
为符号函数，
Figure 793539DEST_PATH_IMAGE035
为自然常数，
Figure 525872DEST_PATH_IMAGE036
为正数。In the formula,
Figure 459510DEST_PATH_IMAGE034
is a symbolic function,
Figure 793539DEST_PATH_IMAGE035
is a natural constant,
Figure 525872DEST_PATH_IMAGE036
is a positive number.

进一步地，所述步骤（3）具体为：将期望深度和反馈深度作差得到深度误差，将该深度误差输入滑模函数进行滑模控制，并利用径向基神经网络和边界层法对滑模控制律进行改进，通过滑模控制律得到输出舵角，高速AUV通过舵角改变深度，完成反馈控制。Further, the step (3) is specifically as follows: the difference between the desired depth and the feedback depth is obtained to obtain a depth error, the depth error is input into the sliding mode function for sliding mode control, and the radial basis neural network and the boundary layer method are used to control the sliding mode. The mode control law is improved, the output rudder angle is obtained through the sliding mode control law, and the high-speed AUV changes the depth through the rudder angle to complete the feedback control.

本发明的有益效果在于，本发明通过对滑模的切换函数用

Figure 578142DEST_PATH_IMAGE037
进行替换，在保证系统的强鲁棒性的情况下，有效削弱滑模控制系统的抖振，提高了控制算法的实用性。本发明的方法中，通过径向基神经网络对滑模控制的补偿，能够有效地抑制高速AUV在高速机动时内外部扰动的影响，从而保证高速AUV在不同航速下的控制精度，提高了系统的工作性能。The beneficial effect of the present invention is that the present invention uses the switching function of the sliding mode to
Figure 578142DEST_PATH_IMAGE037
It can effectively weaken the chattering of the sliding mode control system and improve the practicability of the control algorithm while ensuring the strong robustness of the system. In the method of the present invention, the compensation of the sliding mode control by the radial basis neural network can effectively suppress the influence of the internal and external disturbances of the high-speed AUV during high-speed maneuvering, thereby ensuring the control accuracy of the high-speed AUV at different speeds and improving the system. work performance.

为了实现对高速AUV的运动控制，本发明通过将径向基神经网络和非线性切换面应用到滑模变结构控制（SMC, Sliding Mode Control）的方式，对AUV控制系统进行改善，以达到削弱系统抖振、提高运动控制精度的目的。In order to realize the motion control of the high-speed AUV, the present invention improves the AUV control system by applying the radial basis neural network and the nonlinear switching surface to the sliding mode variable structure control (SMC, Sliding Mode Control). The purpose of system chattering and improving motion control accuracy.

附图说明Description of drawings

图1是高速AUV定深控制工作原理示意图；Figure 1 is a schematic diagram of the working principle of high-speed AUV fixed depth control;

图2是高速AUV以10节航速下潜时算法改进前后的深度对比示意图；Figure 2 is a schematic diagram of the depth comparison before and after the algorithm improvement when the high-speed AUV dives at a speed of 10 knots;

图3是高速AUV以10节航速下潜时算法改进前后的舵角对比示意图。Figure 3 is a schematic diagram of the rudder angle comparison before and after the algorithm improvement when the high-speed AUV dives at a speed of 10 knots.

具体实施方式Detailed ways

以下结合附图和实施例对本发明作进一步说明。本发明提供了一种高速AUV运动控制方法，具体包括以下步骤：The present invention will be further described below with reference to the accompanying drawings and embodiments. The invention provides a high-speed AUV motion control method, which specifically includes the following steps:

（1）通过多项式拟合得到系统参数和航速的函数关系，根据函数关系得到高速AUV简化运动模型；以航速作为高速AUV简化运动模型的输入。具体为：(1) The functional relationship between the system parameters and the speed is obtained by polynomial fitting, and the simplified motion model of the high-speed AUV is obtained according to the functional relationship; the speed is used as the input of the simplified motion model of the high-speed AUV. Specifically:

图1为高速AUV惯性坐标系和载体坐标系示意图，对高速AUV的动力学模型进行简化。在不同航速下对高速AUV进行深度控制，AUV按照深度进行机动时，假定纵向速度

Figure 906486DEST_PATH_IMAGE038
由推力系统单独提供并能够保持为稳定数值，则可设纵向速度
Figure 485235DEST_PATH_IMAGE038
为常数，忽略横摇的影响，则有
Figure 529414DEST_PATH_IMAGE039
，
Figure 177302DEST_PATH_IMAGE040
为正数，
Figure 699550DEST_PATH_IMAGE038
为纵向航速，
Figure 867227DEST_PATH_IMAGE041
为垂向航速，
Figure 816728DEST_PATH_IMAGE042
为纵倾角。假设高速AUV的外形结构左右对称，上下近似对称，高速AUV在高速运动情况下，与纵向速度
Figure 453377DEST_PATH_IMAGE038
相比垂荡运动速度
Figure 779316DEST_PATH_IMAGE041
要小很多，不妨将垂荡运动速度
Figure 801499DEST_PATH_IMAGE041
看成一个小扰动，假设
Figure 295803DEST_PATH_IMAGE043
。Figure 1 is a schematic diagram of the high-speed AUV inertial coordinate system and the carrier coordinate system, which simplifies the dynamic model of the high-speed AUV. Depth control of high-speed AUVs at different speeds, when AUV maneuvers according to depth, the longitudinal speed is assumed
Figure 906486DEST_PATH_IMAGE038
Provided by the thrust system alone and can be maintained at a stable value, the longitudinal speed can be set
Figure 485235DEST_PATH_IMAGE038
is a constant, ignoring the effect of rolling, there is
Figure 529414DEST_PATH_IMAGE039
,
Figure 177302DEST_PATH_IMAGE040
is a positive number,
Figure 699550DEST_PATH_IMAGE038
is the longitudinal speed,
Figure 867227DEST_PATH_IMAGE041
is the vertical speed,
Figure 816728DEST_PATH_IMAGE042
is the pitch angle. Assuming that the shape structure of the high-speed AUV is symmetrical from left to right, and approximately symmetrical up and down, the high-speed AUV is in high-speed motion with the longitudinal speed.
Figure 453377DEST_PATH_IMAGE038
Compared to heave motion speed
Figure 779316DEST_PATH_IMAGE041
Much smaller, might as well set the heave motion speed
Figure 801499DEST_PATH_IMAGE041
as a small disturbance, suppose
Figure 295803DEST_PATH_IMAGE043
.

所述垂直面运动简化的动力学模型如下：The simplified dynamic model of the vertical plane motion is as follows:

Figure 809961DEST_PATH_IMAGE044
Figure 809961DEST_PATH_IMAGE044

其中，

Figure 798645DEST_PATH_IMAGE002
，
Figure 816280DEST_PATH_IMAGE045
，设
Figure 982950DEST_PATH_IMAGE046
为内外部的扰动为建模模型不确定性带来的影响，
Figure 718825DEST_PATH_IMAGE038
为AUV的纵向速度，
Figure 511200DEST_PATH_IMAGE041
为垂向速度，
Figure 383341DEST_PATH_IMAGE042
为纵倾角度，
Figure 479168DEST_PATH_IMAGE007
为纵倾角速度，
Figure 702339DEST_PATH_IMAGE008
为深度值，
Figure 32826DEST_PATH_IMAGE047
为纵倾力矩，
Figure 25053DEST_PATH_IMAGE010
为艉舵舵角，
Figure 799105DEST_PATH_IMAGE011
为正数，
Figure 103047DEST_PATH_IMAGE048
、
Figure 112592DEST_PATH_IMAGE049
为AUV的水动力系数，它们与速度
Figure 598806DEST_PATH_IMAGE038
的函数关系可以通过多项式拟合得到，可取
Figure 137234DEST_PATH_IMAGE050
，其中
Figure 459631DEST_PATH_IMAGE038
为高速AUV的纵向速度，
Figure 7287DEST_PATH_IMAGE015
为海水密度，
Figure 583893DEST_PATH_IMAGE051
为高速AUV的长度，
Figure 683436DEST_PATH_IMAGE052
和
Figure 368496DEST_PATH_IMAGE018
为多项式系数；
Figure 93744DEST_PATH_IMAGE053
同理。本实施例中，取
Figure 915069DEST_PATH_IMAGE054
、
Figure 185514DEST_PATH_IMAGE055
、
Figure 92290DEST_PATH_IMAGE056
、
Figure 857115DEST_PATH_IMAGE057
和
Figure 798526DEST_PATH_IMAGE058
。in,
Figure 798645DEST_PATH_IMAGE002
,
Figure 816280DEST_PATH_IMAGE045
,Assume
Figure 982950DEST_PATH_IMAGE046
For the influence of internal and external disturbances on the uncertainty of the modeling model,
Figure 718825DEST_PATH_IMAGE038
is the longitudinal speed of the AUV,
Figure 511200DEST_PATH_IMAGE041
is the vertical speed,
Figure 383341DEST_PATH_IMAGE042
is the pitch angle,
Figure 479168DEST_PATH_IMAGE007
is the pitch angular velocity,
Figure 702339DEST_PATH_IMAGE008
is the depth value,
Figure 32826DEST_PATH_IMAGE047
is the pitch moment,
Figure 25053DEST_PATH_IMAGE010
is the stern rudder angle,
Figure 799105DEST_PATH_IMAGE011
is a positive number,
Figure 103047DEST_PATH_IMAGE048
,
Figure 112592DEST_PATH_IMAGE049
are the hydrodynamic coefficients of the AUV, which are related to the speed
Figure 598806DEST_PATH_IMAGE038
The functional relationship of can be obtained by polynomial fitting, it is desirable to
Figure 137234DEST_PATH_IMAGE050
,in
Figure 459631DEST_PATH_IMAGE038
is the longitudinal speed of the high-speed AUV,
Figure 7287DEST_PATH_IMAGE015
is the density of sea water,
Figure 583893DEST_PATH_IMAGE051
is the length of the high-speed AUV,
Figure 683436DEST_PATH_IMAGE052
and
Figure 368496DEST_PATH_IMAGE018
is the polynomial coefficient;
Figure 93744DEST_PATH_IMAGE053
The same is true. In this embodiment, take
Figure 915069DEST_PATH_IMAGE054
,
Figure 185514DEST_PATH_IMAGE055
,
Figure 92290DEST_PATH_IMAGE056
,
Figure 857115DEST_PATH_IMAGE057
and
Figure 798526DEST_PATH_IMAGE058
.

（2）选择径向基神经网络，定义滑模面，计算神经网络自适应率，计算滑模面切换函数，设计滑模控制律和自适应律；具体包括：(2) Select the radial basis neural network, define the sliding mode surface, calculate the neural network adaptation rate, calculate the sliding mode surface switching function, and design the sliding mode control law and adaptive law; the details include:

（2.1）选择径向基神经网络：(2.1) Select radial basis neural network:

由于径向基神经网络（RBF神经网络）有无限逼近的能力，采用RBF神经网络逼近

Figure 239871DEST_PATH_IMAGE046
，网络输入取
Figure 633944DEST_PATH_IMAGE059
，网络输出为：
Figure 700994DEST_PATH_IMAGE060
，则有：
Figure 355967DEST_PATH_IMAGE061
，其中，
Figure 109159DEST_PATH_IMAGE062
。Since the radial basis neural network (RBF neural network) has infinite approximation ability, the RBF neural network is used for approximation.
Figure 239871DEST_PATH_IMAGE046
, the network input takes
Figure 633944DEST_PATH_IMAGE059
, the network output is:
Figure 700994DEST_PATH_IMAGE060
, then there are:
Figure 355967DEST_PATH_IMAGE061
,in,
Figure 109159DEST_PATH_IMAGE062
.

（2.2）定义滑模函数：(2.2) Define the sliding mode function:

为了减少控制器参数的个数，提高参数调节效率。基于Hurwitz稳定性理论，设Hurwitz判据的特征方程为：

Figure 865894DEST_PATH_IMAGE063
，其中
Figure 831576DEST_PATH_IMAGE064
为Laplace算子，即要求多项式
Figure 606634DEST_PATH_IMAGE065
的特征值实部为负。不妨取
Figure 530727DEST_PATH_IMAGE066
，即
Figure 13573DEST_PATH_IMAGE067
，取
Figure 173159DEST_PATH_IMAGE068
即可满足Hurwitz的要求，其中
Figure 678090DEST_PATH_IMAGE069
，
Figure 648451DEST_PATH_IMAGE070
，
Figure 97887DEST_PATH_IMAGE071
，
Figure 936530DEST_PATH_IMAGE072
，
Figure 669868DEST_PATH_IMAGE073
为正数。则滑模函数可表示为：
Figure 935765DEST_PATH_IMAGE074
，其中
Figure 138076DEST_PATH_IMAGE021
为误差。In order to reduce the number of controller parameters and improve the efficiency of parameter adjustment. Based on the Hurwitz stability theory, the characteristic equation of the Hurwitz criterion is set as:
Figure 865894DEST_PATH_IMAGE063
,in
Figure 831576DEST_PATH_IMAGE064
is the Laplace operator, which requires a polynomial
Figure 606634DEST_PATH_IMAGE065
The real part of the eigenvalues is negative. may wish to take
Figure 530727DEST_PATH_IMAGE066
,Right now
Figure 13573DEST_PATH_IMAGE067
,Pick
Figure 173159DEST_PATH_IMAGE068
can satisfy Hurwitz's requirements, where
Figure 678090DEST_PATH_IMAGE069
,
Figure 648451DEST_PATH_IMAGE070
,
Figure 97887DEST_PATH_IMAGE071
,
Figure 936530DEST_PATH_IMAGE072
,
Figure 669868DEST_PATH_IMAGE073
is a positive number. Then the sliding mode function can be expressed as:
Figure 935765DEST_PATH_IMAGE074
,in
Figure 138076DEST_PATH_IMAGE021
for error.

（2.3）设计滑模控制律和自适应律：(2.3) Design sliding mode control law and adaptive law:

根据李雅普诺夫函数（Lyapunov函数）

Figure 514831DEST_PATH_IMAGE075
，和步骤（2.2）定义的滑模函数设滑模控制律为：According to the Lyapunov function (Lyapunov function)
Figure 514831DEST_PATH_IMAGE075
, and the sliding mode function defined in step (2.2) Let the sliding mode control law be:

Figure 869720DEST_PATH_IMAGE076
Figure 869720DEST_PATH_IMAGE076

其中，

Figure 306517DEST_PATH_IMAGE077
，
Figure 996125DEST_PATH_IMAGE024
、
Figure 910991DEST_PATH_IMAGE025
为正数，
Figure 884501DEST_PATH_IMAGE078
为目标值。in,
Figure 306517DEST_PATH_IMAGE077
,
Figure 996125DEST_PATH_IMAGE024
,
Figure 910991DEST_PATH_IMAGE025
is a positive number,
Figure 884501DEST_PATH_IMAGE078
is the target value.

设计自适应律为：

Figure 492200DEST_PATH_IMAGE079
The design adaptive law is:
Figure 492200DEST_PATH_IMAGE079

其中，

Figure 403524DEST_PATH_IMAGE080
，
Figure 731868DEST_PATH_IMAGE081
为俯仰角，
Figure 185983DEST_PATH_IMAGE082
为高斯基函数的输出，
Figure 823638DEST_PATH_IMAGE031
为水动力系数，
Figure 737105DEST_PATH_IMAGE083
为神经网络的权值。in,
Figure 403524DEST_PATH_IMAGE080
,
Figure 731868DEST_PATH_IMAGE081
is the pitch angle,
Figure 185983DEST_PATH_IMAGE082
is the output of the Gaussian function,
Figure 823638DEST_PATH_IMAGE031
is the hydrodynamic coefficient,
Figure 737105DEST_PATH_IMAGE083
are the weights of the neural network.

基于上述滑模控制律和自适应律的控制器设计，其系统稳定性可简单证明如下：Based on the controller design of the above sliding mode control law and adaptive law, the system stability can be simply proved as follows:

基于李雅普诺夫稳定性得：Based on the Lyapunov stability, we get:

Figure 259353DEST_PATH_IMAGE084
Figure 259353DEST_PATH_IMAGE084

设N为

Figure 692609DEST_PATH_IMAGE085
的最大值，则
Figure 376531DEST_PATH_IMAGE086
，取
Figure 13180DEST_PATH_IMAGE087
，则
Figure 339119DEST_PATH_IMAGE088
，系统李雅普诺夫稳定。Let N be
Figure 692609DEST_PATH_IMAGE085
the maximum value, then
Figure 376531DEST_PATH_IMAGE086
,Pick
Figure 13180DEST_PATH_IMAGE087
,but
Figure 339119DEST_PATH_IMAGE088
, the system is Lyapunov stable.

（2.4）利用边界层法设计滑模面切换函数，对滑模控制律进行改进：(2.4) The sliding mode surface switching function is designed by using the boundary layer method, and the sliding mode control law is improved:

在传统滑模控制中边界层的切换函数为符号函数

Figure 361302DEST_PATH_IMAGE034
，其不连续性易造成系统的抖振现象。为了削弱传统滑模控制的抖振现象，利用边界层法对步骤（2.3）设计的滑模控制律进行改进，采用具有光滑连续特性的非线性函数（即滑模面切换函数）
Figure 873184DEST_PATH_IMAGE089
代替符号函数
Figure 387342DEST_PATH_IMAGE034
，k为正数，用于调节非线性函数
Figure 376026DEST_PATH_IMAGE037
在零点附近的切换速度，可以改善切换特性。则替换后控制律为：The switching function of the boundary layer in traditional sliding mode control is a sign function
Figure 361302DEST_PATH_IMAGE034
, and its discontinuity is easy to cause the chattering phenomenon of the system. In order to weaken the chattering phenomenon of traditional sliding mode control, the boundary layer method is used to improve the sliding mode control law designed in step (2.3), and a nonlinear function with smooth continuous characteristics (ie sliding mode surface switching function) is used.
Figure 873184DEST_PATH_IMAGE089
Substitute symbolic functions
Figure 387342DEST_PATH_IMAGE034
, k is a positive number, used to adjust the nonlinear function
Figure 376026DEST_PATH_IMAGE037
The switching speed around the zero point can improve the switching characteristics. Then the control law after replacement is:

Figure 128082DEST_PATH_IMAGE090
Figure 128082DEST_PATH_IMAGE090

其中，

Figure 560331DEST_PATH_IMAGE091
，
Figure 296206DEST_PATH_IMAGE024
、
Figure 823002DEST_PATH_IMAGE025
为正数，
Figure 537886DEST_PATH_IMAGE092
为目标值。in,
Figure 560331DEST_PATH_IMAGE091
,
Figure 296206DEST_PATH_IMAGE024
,
Figure 823002DEST_PATH_IMAGE025
is a positive number,
Figure 537886DEST_PATH_IMAGE092
is the target value.

（3）利用步骤（2）得到的改进后的滑模控制律对高速AUV进行运动控制：(3) Use the improved sliding mode control law obtained in step (2) to control the motion of the high-speed AUV:

参照附图1为本发明方案中高速AUV定深控制工作原理的示意图。Referring to FIG. 1, it is a schematic diagram of the working principle of the high-speed AUV depth control in the solution of the present invention.

将期望深度和反馈深度作差得到深度误差，将该深度误差输入滑模函数进行滑模控制，并利用径向基神经网络（RBF神经网络）和边界层法对滑模控制律进行改进，通过滑模控制律（即舵角控制律）得到输出舵角，高速AUV通过舵角改变深度。最后输出实际深度，实现负反馈控制过程。The depth error is obtained by making the difference between the expected depth and the feedback depth, and the depth error is input into the sliding mode function for sliding mode control. The radial basis neural network (RBF neural network) and the boundary layer method are used to improve the sliding mode control law. The sliding mode control law (ie, the rudder angle control law) obtains the output rudder angle, and the high-speed AUV changes the depth through the rudder angle. Finally, the actual depth is output to realize the negative feedback control process.

为了验证本发明方法的有效性，假定高速AUV 10节航速(5.145米/秒)下潜到10米，验证本发明基于径向基神经网络的滑模控制方法（改进后）和传统滑模控制方法（改进前）在提高控制精度方面的有效性，如图2和图3所示，可以看出基于本发明的思路改进后稳态误差减小，控制精度提高，抖振被有效削弱。In order to verify the effectiveness of the method of the present invention, it is assumed that the high-speed AUV dives at a speed of 10 knots (5.145 m/s) to 10 meters, and the sliding mode control method (after improvement) based on the radial basis neural network of the present invention and the traditional sliding mode control method of the present invention are verified. The effectiveness of the method (before the improvement) in improving the control accuracy is shown in Figures 2 and 3. It can be seen that after the improvement based on the idea of the present invention, the steady-state error is reduced, the control accuracy is improved, and the chattering is effectively weakened.

综上所述，本发明通过对滑模的切换函数用

Figure 124725DEST_PATH_IMAGE037
进行替换，在保证系统的强鲁棒性的情况下，有效削弱滑模控制系统的抖振，提高了控制算法的实用性。本发明的方法中，通过径向基神经网络对滑模控制的补偿，能够有效地抑制高速AUV在高速机动时内外部扰动的影响，从而保证高速AUV在不同航速下的控制精度，提高了系统的工作性能。本发明利用基于径向基神经网络的滑模控制方法，对高速AUV在不同航速、不同负载情况下进行深度控制，实现在不同任务下的深度机动。In summary, the present invention uses the switching function of the sliding mode to
Figure 124725DEST_PATH_IMAGE037
It can effectively weaken the chattering of the sliding mode control system and improve the practicability of the control algorithm while ensuring the strong robustness of the system. In the method of the present invention, the compensation of the sliding mode control by the radial basis neural network can effectively suppress the influence of the internal and external disturbances of the high-speed AUV during high-speed maneuvering, thereby ensuring the control accuracy of the high-speed AUV at different speeds and improving the system. work performance. The invention utilizes the sliding mode control method based on the radial basis neural network to perform deep control of the high-speed AUV under different speed and load conditions, and realizes deep maneuvering under different tasks.

Claims (1)

1.一种高速AUV运动控制方法，其特征在于，包括以下步骤：1. a high-speed AUV motion control method, is characterized in that, comprises the following steps: （1）通过多项式拟合得到系统参数和航速的函数关系，根据函数关系得到高速AUV简化运动模型；将航速作为高速AUV简化运动模型的输入；(1) The functional relationship between the system parameters and the speed is obtained by polynomial fitting, and the simplified motion model of the high-speed AUV is obtained according to the functional relationship; the speed is used as the input of the simplified motion model of the high-speed AUV; 所述高速AUV简化运动模型具体为：The high-speed AUV simplified motion model is specifically:
Figure DEST_PATH_IMAGE001
Figure DEST_PATH_IMAGE001
 其中，设
Figure 737103DEST_PATH_IMAGE002
，设
Figure DEST_PATH_IMAGE003
，
Figure 202719DEST_PATH_IMAGE004
为AUV的纵向速度，
Figure DEST_PATH_IMAGE005
为垂向速度，
Figure 759865DEST_PATH_IMAGE006
为纵倾角度，
Figure DEST_PATH_IMAGE007
为纵倾角速度，
Figure 576511DEST_PATH_IMAGE008
为深度值，
Figure DEST_PATH_IMAGE009
为纵倾力矩，
Figure 110261DEST_PATH_IMAGE010
为艉舵舵角，
Figure DEST_PATH_IMAGE011
为正数，
Figure 695963DEST_PATH_IMAGE012
、
Figure DEST_PATH_IMAGE013
为AUV的水动力系数，取
Figure 922545DEST_PATH_IMAGE014
，
Figure DEST_PATH_IMAGE015
为海水密度，
Figure 725022DEST_PATH_IMAGE016
为高速AUV的长度，
Figure DEST_PATH_IMAGE017
和
Figure 62463DEST_PATH_IMAGE018
为多项式系数；Among them, let
Figure 737103DEST_PATH_IMAGE002
,Assume
Figure DEST_PATH_IMAGE003
,
Figure 202719DEST_PATH_IMAGE004
is the longitudinal speed of the AUV,
Figure DEST_PATH_IMAGE005
is the vertical speed,
Figure 759865DEST_PATH_IMAGE006
is the pitch angle,
Figure DEST_PATH_IMAGE007
is the pitch angular velocity,
Figure 576511DEST_PATH_IMAGE008
is the depth value,
Figure DEST_PATH_IMAGE009
is the pitch moment,
Figure 110261DEST_PATH_IMAGE010
is the stern rudder angle,
Figure DEST_PATH_IMAGE011
is a positive number,
Figure 695963DEST_PATH_IMAGE012
,
Figure DEST_PATH_IMAGE013
is the hydrodynamic coefficient of AUV, take
Figure 922545DEST_PATH_IMAGE014
,
Figure DEST_PATH_IMAGE015
is the density of sea water,
Figure 725022DEST_PATH_IMAGE016
is the length of the high-speed AUV,
Figure DEST_PATH_IMAGE017
and
Figure 62463DEST_PATH_IMAGE018
is the polynomial coefficient; （2）选择径向基神经网络，定义滑模函数，设计滑模控制律和自适应律，基于边界层法计算滑模面切换函数，对滑模控制律进行改进；(2) Select radial basis neural network, define sliding mode function, design sliding mode control law and adaptive law, calculate sliding mode surface switching function based on boundary layer method, and improve sliding mode control law; 所述的滑模函数基于稳定性理论得到，具体为：The sliding mode function is obtained based on the stability theory, specifically:
Figure DEST_PATH_IMAGE019
Figure DEST_PATH_IMAGE019
 其中，
Figure 502671DEST_PATH_IMAGE020
为正数，
Figure DEST_PATH_IMAGE021
为误差；in,
Figure 502671DEST_PATH_IMAGE020
is a positive number,
Figure DEST_PATH_IMAGE021
for error; 所述的滑模控制律为：The sliding mode control law is:
Figure 900155DEST_PATH_IMAGE022
Figure 900155DEST_PATH_IMAGE022
 其中，
Figure DEST_PATH_IMAGE023
，
Figure 927279DEST_PATH_IMAGE024
、
Figure DEST_PATH_IMAGE025
为正数，
Figure 802831DEST_PATH_IMAGE026
为目标值；in,
Figure DEST_PATH_IMAGE023
,
Figure 927279DEST_PATH_IMAGE024
,
Figure DEST_PATH_IMAGE025
is a positive number,
Figure 802831DEST_PATH_IMAGE026
is the target value; 所述自适应律为：
Figure DEST_PATH_IMAGE027
The adaptive law is:
Figure DEST_PATH_IMAGE027
 其中，
Figure 363125DEST_PATH_IMAGE028
，
Figure DEST_PATH_IMAGE029
为俯仰角，
Figure 931510DEST_PATH_IMAGE030
为高斯基函数的输出，
Figure DEST_PATH_IMAGE031
为水动力系数，
Figure 678886DEST_PATH_IMAGE032
为神经网络的权值；in,
Figure 363125DEST_PATH_IMAGE028
,
Figure DEST_PATH_IMAGE029
is the pitch angle,
Figure 931510DEST_PATH_IMAGE030
is the output of the Gaussian function,
Figure DEST_PATH_IMAGE031
is the hydrodynamic coefficient,
Figure 678886DEST_PATH_IMAGE032
is the weight of the neural network; 所述的滑模面切换函数为：The sliding mode surface switching function is:
Figure DEST_PATH_IMAGE033
Figure DEST_PATH_IMAGE033
 式中，
Figure 139822DEST_PATH_IMAGE034
为符号函数，
Figure DEST_PATH_IMAGE035
为自然常数，
Figure 289043DEST_PATH_IMAGE036
为正数；In the formula,
Figure 139822DEST_PATH_IMAGE034
is a symbolic function,
Figure DEST_PATH_IMAGE035
is a natural constant,
Figure 289043DEST_PATH_IMAGE036
is a positive number; （3）利用步骤（2）得到的改进后的滑模控制律对高速AUV进行运动控制；具体为：将期望深度和反馈深度作差得到深度误差，将该深度误差输入滑模函数进行滑模控制，并利用径向基神经网络和边界层法对滑模控制律进行改进，通过滑模控制律得到输出舵角，高速AUV通过舵角改变深度，完成反馈控制。(3) Use the improved sliding mode control law obtained in step (2) to control the motion of the high-speed AUV; specifically, the depth error is obtained by taking the difference between the expected depth and the feedback depth, and the depth error is input into the sliding mode function for sliding mode The sliding mode control law is improved by using radial basis neural network and boundary layer method. The output rudder angle is obtained through the sliding mode control law, and the high-speed AUV changes the depth through the rudder angle to complete the feedback control.
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