WO2022242633A1 - 一种吊舱式无人艇航向控制方法 - Google Patents
一种吊舱式无人艇航向控制方法 Download PDFInfo
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- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/0206—Control of position or course in two dimensions specially adapted to water vehicles
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- the invention relates to the technical field of ship course control, in particular to a method for controlling the course of a pod-type unmanned boat.
- the control system of unmanned boats has problems such as nonlinearity, instability, and even unpredictable strong external disturbances in complex waters except for the influence of the hull itself, which will lead to large-angle Phenomena such as yaw and abnormal navigation trajectory or loss of control require targeted research on related controls.
- the pod-propelled unmanned boat has better maneuverability and higher propulsion efficiency, which can reduce the lack of rudder devices, save ship space, and increase the flexibility of ship construction. Therefore, it is very necessary to design a flexible, efficient and suitable course keeping controller for unmanned boats in inland waters, so as to realize the stability and efficiency of autonomous navigation of pod-type unmanned boats.
- PID control The existing technology is to use PID control.
- This control method has limitations.
- the output of the controlled object is related to the function mapping of the control output. It is very limited for linear time-invariant systems.
- PID control needs to consider the dynamics of the execution link to prevent excessive Saturation, and even time delay.
- PID control needs to increase the monitoring link, so there are problems such as low efficiency and long optimization cycle, and the goal of real-time tracking of course deviation cannot be achieved.
- the present invention provides a pod-type unmanned boat course control method, which can greatly reduce the delay problem, the control method is simple, the efficiency is high, and the unmanned boat course control accuracy is improved, which can meet the requirements of complex waters in inland rivers. Requirements for course deviation control of unmanned boats under navigational conditions.
- the present invention adopts the following technical solutions:
- a heading control method for a pod type unmanned boat comprising the following steps:
- the present invention proposes a simple and effective control method for the deviation problem existing in the course control of the existing pod-type unmanned boat, which adopts equivalent iterative sliding mode control, and can control the state of the pod-type unmanned boat in the process of maneuvering Changes are adjusted in real time to achieve fast and stable course control, improve the accuracy of the course control of the unmanned boat, and improve the time delay problem existing in the existing PID control;
- Fig. 1 is the flow chart of a kind of pod type unmanned boat course control method of the present invention
- Fig. 2 is the plane motion variable diagram of the pod type unmanned boat of the present invention
- Fig. 3 is a block diagram of the structure of the pod type unmanned boat of the present invention.
- Fig. 4 is the equivalent iterative sliding mode heading control simulation model diagram of the pod type unmanned boat of the present invention.
- Fig. 5 is the equivalent iterative sliding mode heading control simulation result figure of the pod type unmanned boat of the present invention.
- Fig. 5 (1) is the 45 ° unmanned boat heading change curve graph (horizontal axis represents time variation under no interference , the vertical axis represents the change of heading angle)
- Fig. 5 (2) is the 45 ° unmanned boat pod steering angle change curve without interference (the horizontal axis represents the time change, and the vertical axis represents the change of the pod steering angle)
- Fig. 5 (3) is the 45° voyage trajectory curve of the unmanned boat without interference (the horizontal axis represents the distance traveled along the X axis, and the vertical axis represents the distance traveled along the Y axis).
- Figure 5(4) is 45° under the interference of wind and waves
- Figure 5(5) is the change curve of the steering angle of the unmanned boat pod at 45° under wind and wave interference (horizontal axis represents the time change, the vertical axis represents the pod steering angle change)
- Figure 5(6) is the 45° unmanned boat navigation trajectory curve under the interference of wind and waves (the horizontal axis represents the sailing distance along the X axis, and the vertical axis represents the distance along the Y axis). axis sailing distance);
- a kind of pod type unmanned boat course control method of the present invention comprises the following steps:
- step S1 the force analysis is carried out on the three-degree-of-freedom plane motion of the pod-type unmanned boat, the horizontal drift and the yaw, and the influence of the steering angle rotation characteristics of the pod on the heading of the unmanned boat is considered (that is, according to the pod cabin steering angle steering characteristics), to obtain the force and moment generated by the pod-type unmanned boat along the x-axis, y-axis and z-axis; combine the obtained force and moment generated by the pod-type unmanned boat with the MMG ship separation type mathematics
- the model formula is to establish the ship motion mathematical model of the pod type unmanned boat.
- step S1 includes the following sub-steps:
- Sub-step S101 researching the motion of the unmanned vessel on the sea surface with three degrees of freedom, establishing three coordinate systems: the inertial coordinate system (earth coordinate system), the horizontal appendage coordinate system (plane motion coordinate system) and the appendage coordinate system (movement coordinate system). coordinate system) to analyze the force of the unmanned boat.
- the inertial coordinate system earth coordinate system
- the horizontal appendage coordinate system plane motion coordinate system
- the appendage coordinate system movement coordinate system
- Sub-step S102 in the motion coordinate system, specify the forward velocity u along the x-axis direction, the traversing velocity v along the y-axis direction and the yaw angular velocity r around the z-axis, as shown in Table 1, each axis
- Table 1 each axis
- Table 1 The relationship between the total external force and moment and the forces and moments of each part is:
- the subscript H represents the viscous hydrodynamic force and moment on the ship; the subscript P represents the thrust and torque on the propeller; the subscript R represents the rudder force and moment on the ship, and wave and wind represent the resistance of waves and wind.
- the unmanned boat using the pod propulsion system cancels the traditional paddle-rudder structure, considering the thrust of the pod propeller and the influence of the lateral force, then according to the force between the pod and the hull of the unmanned boat It can be decomposed into the hydrodynamic force on the ship itself and the ship pod.
- the maneuvering motion equation of the pod-type unmanned boat the mathematical model of the MMG (Maneuvering Mathematical Model Group) ship separation motion is corrected as shown in formulas (2) and (3):
- X, Y, and N are the longitudinal force, lateral force and yaw moment of the unmanned boat; Pod is the thrust and moment of the pod propeller; wave and wind are the resistance of waves and wind; m is the weight of the unmanned boat, m x , m y is the additional mass in the direction of x-axis and y-axis; u, v, r are the speed, traversing speed and angular velocity of the ship in motion; I ZZ is the moment of inertia of O X- axis; J zz is the direction of z-axis The additional moment of inertia on ; x 0 , y 0 are the original coordinates of the ship.
- Sub-step S103 under the same rotation angle, the pod propeller produces greater lateral force and gyroscopic moment than the traditional rudder, and the pod propeller rotates around the axis, and its pod rod, propeller and its wake flow together Rotating, the thrust and lateral force coefficients in the pod propeller depend on the pod's local drift angle ⁇ Pod , deflection angle ⁇ Pod and advance speed ratio J Pod .
- the force analysis of the propulsion of the unmanned boat pod is shown in Figure 2, and the calculation formula of the force and moment generated by the pod installed on the unmanned boat along the x-axis, y-axis and z-axis direction is shown in (4):
- the forces and moments generated in the directions of x, y and z axes are the longitudinal thrust, lateral thrust and turning moment, where: t Pod is propeller thrust derating coefficient; T p is pod thruster thrust; ⁇ HPod is the lateral force coefficient induced by the pod; Q is the lateral force of the pod; x HPod is the longitudinal coordinate of the action point of the pod-hull lateral force coefficient; x Pod is the pod Longitudinal coordinate of the center of pressure.
- Sub-step S104 according to the force and moment formulas generated by the pod installed on the unmanned boat along the x, y and z-axis directions obtained in sub-step S103, a mathematical model of the movement of the pod-type unmanned boat is established.
- step S2 according to the heading control system of the pod-type unmanned boat, the wind and wave disturbance, the pod propulsion motor and the thrust torque are modeled accordingly.
- step S2 includes the following sub-steps:
- Sub-step S201 according to the composition block diagram of the pod-type unmanned boat shown in Figure 3, the wind and wave force will cause the unmanned boat to deviate from the course and cause difficulty in maneuvering in the inland waters. Maneuverability of manboat in wind and waves, establish mathematical model of wind and wave disturbance.
- the wind pressure and moment acting on the UAV are:
- ⁇ a is the air density
- a f is the orthographic projection area on the waterline of the unmanned boat
- a s is the side projection area on the waterline
- L oa is the total length of the unmanned boat
- C wx , C wy , C wn Respectively, the wind pressure coefficient in the x and y directions and the wind pressure moment coefficient around the z axis.
- ⁇ is fluid density
- L boat length
- a wave amplitude
- ⁇ wavelength
- ⁇ wave direction angle
- C dx , C dy , C dn are test coefficients.
- Sub-step S202 according to the influence of the speed and thrust torque of the pod propulsion motor on the steering angle and steering angular velocity of the unmanned boat, establish the pod propulsion motor and thrust torque models.
- the propulsion motor and steering torque of the pod By controlling the propulsion motor and steering torque of the pod, the course deviation of the unmanned boat is adjusted under the premise of ensuring the uniform motion of the unmanned boat.
- Sub-step S203 according to the wind pressure and moment formula and wave pressure and moment formula of the unmanned boat combined with pod thrust torque and steering angle control, establish a pod-type unmanned boat heading motion mathematical model.
- step S3 the principle of the equivalent iterative sliding mode course control is to establish a sliding mode feedback control law based on the error between the actual course angle and the expected course angle of the pod-type unmanned boat, and combine the control of the steering angle The formula obtains the steering angle command for the next step.
- step S3 compare the set heading angle with the output feedback heading angle to obtain the heading angle deviation and heading angle deviation rate of the unmanned boat, and use the equivalent iterative sliding mode algorithm to determine the heading angle deviation and heading angle deviation rate of the unmanned boat The steering angle command for the next step.
- step S3 includes the following sub-steps:
- Sub-step S301 compare the feedback course angle of the unmanned boat with the set expected course angle, calculate the course deviation e, and the course deviation conversion rate
- sub-step S302 the sliding mode control design is carried out using the saturation function, and the saturation function is a nonlinear tangent function, and the formula is:
- step S303 the equivalent iterative sliding mode is used to optimize the course deviation, and the steering angle command for the next step is obtained to realize the course control of the pod-type unmanned boat, and the course deviation sliding mode is constructed as follows:
- the output value of the equivalent iterative sliding mode control algorithm is the steering angle ⁇ . Construct the functional relationship between the "sliding mode surface" and the steering angle, and combine the strict boundedness of the saturation function, the formula (8) is modified as follows:
- Sub-step S304 using the "sliding mode surface" feedback value s2 for an easy - to-implement sliding mode feedback control law:
- the controlled steering angle command is:
- ⁇ E is the steering angle adjusted by the equivalent iterative sliding mode control
- ⁇ is the actual steering angle
- T E is the time constant
- s 2 is the established "sliding mode surface" feedback value
- K p , ⁇ are the equivalent Iterative sliding mode control adjustment coefficient.
- the Lyapunov function is constructed as:
- N Pod -(1+ ⁇ HPod (x HPod /x Pod ))x Pod Qcos( ⁇ )+x Pod sin( ⁇ ) (15)
- step S4 the course deviation control adjustment is performed through the equivalent iterative sliding mode algorithm, and the steering angle command is calculated by PWM to drive the brushless DC motor and the digital steering gear, and the unmanned vehicle is controlled according to the steering angle command. The next sailing movement of the boat.
- the MALTAB/SIMULINK simulation is carried out with the existing single-blade pod type unmanned boat with a length of 1.8 meters as the research object, and compared with the PID control algorithm comparing.
- the relevant parameters of the unmanned vehicle are shown in Table 2.
- the disturbance is set as wind wave disturbance, the wind speed is 20m/s, the wind direction angle is 20°, the wave height is 5m/s, and the wave direction is 20°.
- Fig. 4 is the pod of the present invention Simulation model diagram of the equivalent iterative sliding mode heading control of the UAV.
- Figure 5 shows the comparison results of the two. From the comparison of Figure 5(1) and Figure 5(4), it can be seen that under the condition of no interference and wind and wave interference Under this condition, the equivalent iterative sliding mode control has low overshoot and strong stability. From the comparison of Figure 5(2) and Figure 5(5), it can be seen that under the condition of no disturbance and wind and wave disturbance, the steering angle of the pod is limited to within 35°, and the equivalent iterative sliding mode control ratio PID control is used to turn to The 45° heading takes a short time and can avoid large buffeting. From the comparison of Fig. 5(3) and Fig.
- the equivalent iterative sliding mode control can overcome the disturbance and maintain the stability of the heading angle and navigation trajectory.
- the equivalent iterative sliding mode control can be used to adjust the state changes in the pod-type unmanned boat in real time, realize fast and stable heading control, and improve the accuracy of the heading control of the unmanned boat.
- the delay problem existing in the existing PID control is improved.
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Abstract
本发明公开了一种吊舱式无人艇航向控制方法，包括以下步骤：S1、对吊舱式无人艇进行受力分析，根据吊舱转向角转向特性，建立吊舱式无人艇的船舶运动数学模型；S2、根据所述船舶运动数学模型，建立吊舱式无人艇航向运动数学模型；S3、根据所述航向运动数学模型，采用等效迭代滑模算法对无人艇的航向角进行控制；S4、通过PWM计算得出下一转向角指令，根据所述的转向角指令控制无人艇下一步的航行运动。本发明的控制方法可大幅度减少时延性问题，控制方式简单，效率高，并且提高无人艇航向控制精度，能够满足内河复杂水域通航条件下无人艇对航向偏差控制的要求。
Description
本申请要求于2021年5月17日提交中国专利局、申请号为202110533417.4、发明名称为“一种吊舱式无人艇航向控制方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
本发明涉及船舶航向控制技术领域，特别是涉及一种吊舱式无人艇航向控制方法。
无人艇控制系统作为一种典型的欠驱动系统，在复杂水域中除了船体本身因素影响，其控制系统存在非线性、不稳定性，甚至存在不可预测的强外部干扰等问题，将导致大角度偏航以及航行轨迹异常或失控等现象，需要对其相关控制进行针对性研究。另外，采用吊舱式推进的无人艇对比传统的螺旋桨推进的无人艇，其机动性较好、推进效率较高，可减少无方向舵装置，节省船舶空间，增加船舶建造的灵活性。所以十分有必要设计一个灵活高效且适合内河水域中无人艇航向保持控制器，实现吊舱式无人艇自主航行的稳定性及高效性。
现有的技术是使用PID控制，该控制方法具有局限性，其被控对象输出与控制输出的函数映射有关，对于线性时不变系统很受限制，PID控制需考虑执行环节的动态，防止过饱和，甚至存在时延性。对于内河水域环境，PID控制要增加监测环节，则效率低、优化周期长等问题，无法达到实时跟进航向偏差的目标。
发明内容
本发明为解决上述问题，提供了一种吊舱式无人艇航向控制方法，可大幅度减少时延性问题，控制方式简单，效率高，并且提高无人艇航向控制精度，能够满足内河复杂水域通航条件下无人艇对航向偏差控制的要求。
为实现上述目的，本发明采用如下技术方案：
一种吊舱式无人艇航向控制方法，包括以下步骤：
S1、对吊舱式无人艇进行受力分析，根据吊舱转向角转向特性，建立吊舱式无人艇的船舶运动数学模型；
S2、根据所述船舶运动数学模型，建立吊舱式无人艇航向运动数学模型；
S3、根据所述航向运动数学模型，采用等效迭代滑模算法对无人艇的航向角进行控制；
S4、通过PWM计算得出下一转向角指令，根据所述的转向角指令控制无人艇下一步的航行运动。
本发明的有益效果是：
1.本发明针对现有吊舱式无人艇航向控制存在的偏差问题提出一种简单有效的控制方法，其采用等效迭代滑模控制，能够对吊舱式无人艇操纵过程中的状态变化进行实时调节，实现快速、稳定的航向控制，提高了无人艇航向控制的精度，且改善了现有PID控制存在的时延性问题；
2.通过推导的吊舱推力与力矩的公式，进一步改善船舶分离模型存在的转向角偏差问题。
说明书附图
此处所说明的附图用来提供对本发明的进一步理解，构成本发明的一部分，本发明的示意性实施例及其说明用于解释本发明，并不构成对本发明的不当限定。在附图中：
图1为本发明的一种吊舱式无人艇航向控制方法的流程图；
图2为本发明的吊舱式无人艇平面运动变量图；
图3为本发明的吊舱式无人艇所受力的构成框图；
图4为本发明的吊舱式无人艇等效迭代滑模航向控制仿真模型图；
图5为本发明的吊舱式无人艇等效迭代滑模航向控制仿真结果图；其中，图5(1)为无干扰下45°的无人艇航向变化曲线图(横轴表示时间变化，纵轴表示航向角变化)、图5(2)为无干扰下45°的无人艇吊舱转向角变化曲线图(横轴表示时间变化，纵轴表示吊舱转向角变化)、图5(3)为无干扰下45°的无人艇航行轨迹曲线图(横轴表示沿X轴航行距离，纵 轴表示沿Y轴航行距离)、图5(4)为风、浪干扰下45°的无人艇航向变化曲线图(横轴表示时间变化，纵轴表示航向角变化)、图5(5)为风、浪干扰下45°的无人艇吊舱转向角变化曲线图(横轴表示时间变化，纵轴表示吊舱转向角变化)，图5(6)为风、浪干扰下45°的无人艇航行轨迹曲线图(横轴表示沿X轴航行距离，纵轴表示沿Y轴航行距离)；
图5中的附图标记为：
1-PID控制的航向仿真曲线；2-等效迭代滑模控制的航向仿真曲线；3-设定的航向角度曲线。
下面结合具体实施例对本发明的技术方案作进一步的详细说明。
如图1所示，本发明的一种吊舱式无人艇航向控制方法，包括以下步骤：
S1、对吊舱式无人艇进行受力分析，根据吊舱转向角转向特性，建立吊舱式无人艇的船舶运动数学模型。
S2、根据所述船舶运动数学模型，建立吊舱式无人艇航向运动数学模型。
S3、根据所述航向运动数学模型，采用等效迭代滑模算法对无人艇的航向角进行控制。
S4、通过PWM计算得出下一转向角指令，根据所述的转向角指令控制无人艇下一步的航行运动。
具体的，在步骤S1中，对吊舱式无人艇前进、横漂和艏摇三自由度平面运动进行受力分析，考虑吊舱转向角转动特性对无人艇航向的影响(即根据吊舱转向角转向特性)，获得吊舱式无人艇沿x轴、y轴和z轴所产生的力和力矩；将获得的吊舱式无人艇产生的力和力矩结合MMG船舶分离型数学模型公式，建立所述吊舱式无人艇的船舶运动数学模型。
进一步的，所述步骤S1包括以下子步骤：
子步骤S101，研究无人艇在海面上三自由度的运动，建立三种坐标系：惯性坐标系(大地坐标系)、水平附体坐标系(平面运动坐标系)和附体坐标系(运动坐标系)，对无人艇进行受力分析。
子步骤S102，在运动坐标系中，规定沿x轴方向为前进速度u，沿y轴方向为横移速度v和绕z轴转动的艏摇角速度r，具体如表1所示，则各轴的合外力和合力矩与各个部分力和力矩的关系为：
其中下标H表示船舶所受到的粘性流体动力及力矩；下标P表示螺旋桨所受到的推力及转矩；下标R表示船舶所受到的舵力及力矩，wave和wind表示波浪和风的阻力。
表1 三自由度无人艇运动状态
采用吊舱式推进系统的无人艇，取消了传统的桨-舵结构，综合考虑吊舱推进器的推力以及侧向力的影响，那么根据无人艇吊舱与船体之间的受力情况可分解为船舶本身与船舶吊舱所受到的水动力。根据吊舱式无人艇的操纵运动方程，对MMG(Maneuvering Mathematical ModelGroup)船舶分离型运动数学模型进行修正如公式(2)、(3)所示：
其中X、Y、N为无人艇纵向力、横向力以及艏摇力矩；Pod表示为 吊舱推进器的推力及力矩；wave、wind表示波浪和风的阻力；m为无人艇重量，m
x，m
y为x轴、y轴方向的附加质量；u，v，r为船运动中的速度、横移速度和转首角速度；I
ZZ为O
X轴的惯性矩；J
zz为z轴方向上的附加惯性力矩；x
0，y
0为船舶原始坐标。
子步骤S103，在相同的转角下，吊舱式推进器比传统的方向舵产生更大的侧向力和陀螺力矩，而且吊舱推进器绕轴旋转，其吊舱杆与螺旋桨及其尾流一同旋转，则吊舱推进器中的推力和侧向力系数取决于吊舱的局部漂角β
Pod、偏转角δ
Pod及进速比J
Pod。对无人艇吊舱推进进行受力分析如图2所示，进一步得到无人艇安装的吊舱沿x轴、y轴和z轴方向产生的力和力矩计算公式如(4)所示：
其中x、y轴和z轴方向产生的力和力矩为纵向的推力、侧向推力及回转力矩，式中：t
Pod为螺旋桨推力减额系数；T
p为吊舱推进器推力；δ为吊舱推进器的转向角；α
HPod为吊舱诱导的侧向力系数；Q为吊舱的侧向力；x
HPod为吊舱-船体侧向力系数作用点的纵向坐标；x
Pod为吊舱压力中心的纵向坐标。
子步骤S104，根据子步骤S103获得的无人艇安装的吊舱沿x、y轴以及z轴方向产生的力和力矩公式，建立吊舱式无人艇的运动数学模型。
在步骤S2中，根据吊舱式无人艇航向控制系统，并对风、浪干扰以及吊舱推进电机及推力转矩进行相应建模。
具体的，所述步骤S2包括以下子步骤：
子步骤S201，根据图3所示的吊舱式无人艇所受力的构成框图，无人艇在内河水域中，风、浪力作用会导致其偏离航向而引起操纵困难，因此，研究无人艇在风、浪中的操纵性能，建立风、浪干扰力的数学模型。
作用在无人艇的风压力和力矩为：
其中，ρ
a为空气密度；A
f为无人艇水线上的正投影面积；A
s为水线上的侧投影面积；L
oa为无人艇的总长；C
wx，C
wy，C
wn分别为x，y方向的风压力系数及绕z轴的风压力矩系数。
求规定波流场中的压力，忽略产生波运动的能量压力项，即高阶小量
计算波浪漂移力和力矩，以二阶波浪漂移力和力矩进行计算。
则作用在无人艇的浪压力和力矩为：
式中，ρ为流体密度，L为艇长，a为波幅，λ为波长，ψ为浪向角，C
dx、C
dy、C
dn为试验系数。
子步骤S202，根据吊舱推进电机的转速和推力转矩对无人艇的转向角和转向角速度的影响，建立吊舱推进电机和推力转矩模型。通过控制吊舱推进电机和转向力矩，保证无人艇匀速运动的前提下，对无人艇进行航向偏差调节。
子步骤S203，根据所述的无人艇的风压力和力矩公式和浪压力和力矩公式结合吊舱推力转矩及转向角控制，建立吊舱式无人艇航向运动数学模型。
所述的步骤S3中，等效迭代滑模航向控制的原理是基于吊舱式无人艇的实际航向角和期望航向角之间的误差进行建立滑模反馈控制律，并结合转向角的控制公式得到下一步转向角指令。
在步骤S3中，对比设定的航向角与输出反馈的航向角得到无人艇航向角偏差、航向角偏差率，采用等效迭代滑模算法根据无人艇航向角偏差与航向角偏差率确定下一步的转向角指令。
具体的，所述步骤S3包括以下子步骤：
子步骤S301，将无人艇的反馈航向角与设定的期望航向角进行对比，计算出航向偏差e，航向偏差变换率
利用如下公式得到航向偏差：
e＝ψ
d-ψ，式中ψ
d为期望航向角，ψ为实时反馈艏向。
利用如下公式得到航向偏差变换率：
子步骤S302，采用饱和函数对其进行滑模控制设计，令饱和函数为非线性正切函数，公式为：
根据公式(7)可知：当x→0时，其函数斜率比较大，随着x值得逐渐增加，斜率逐渐减小并趋近于零，所以其饱和函数满足操纵运动中降低转向角偏差，并保持稳定航行的约束要求。
步骤S303，采用等效迭代滑模优化航向偏差，得到下一步的转向角指令，实现吊舱式无人艇的航向控制，构建航向偏差滑动模态为：
由于航向控制是对转向角的控制，则等效迭代滑模控制算法其输出值为转向角δ。构建“滑模面”与转向角之间的函数关系，并结合饱和函数的严格有界性，对公式(8)进行修正为：
当s
2→0时，s
1→0。为了满足系统有效到达“滑模面”，对s
2进行镇 定控制，保证s
2收敛速度快于s
1，保证参数k
4≥k
2。
子步骤S304，将“滑模面”反馈值s
2用于易于实现的滑模反馈控制律：
结合转向角的控制公式：
得控制的转向角指令为：
δ
E＝δ-T
E(k
ps
2+εsgn(s
2))k
p,ε∈R
+ (11)
其中，δ
E为等效迭代滑模控制调节输出的转向角，δ为实际转向角，T
E为时间常数，s
2为所建立的“滑模面”反馈值，K
p，ε为等效迭代滑模控制调节系数。
以下，基于李雅普诺夫稳定理论以及吊舱式无人艇的运动数学模型，评估航向偏差e在滑模控制下的稳定性：
构建李雅普诺夫函数为：
对上方公式进行求导得：
根据公式(9)和公式(13)，对s
2进一步展开得：
根据无人艇运动数学模型，可知
为δ的二阶导，不为零。右航向
其中r为绕z轴转动的角速度，公式中与舵角有关的只有N
Pod，所以
取决于
根据N
Pod的公式为：
N
Pod＝-(1+α
HPod(x
HPod/x
Pod))x
PodQcos(δ)+x
Podsin(δ) (15)
因为当无人艇在航行过程中，其
所以
取决于
和s2，基于公式得：
因此，根据李雅普诺夫稳定性定理，可以看出航向偏差e在滑模控制下是渐进稳定的。
在步骤S4中，通过等效迭代滑模算法进行航向偏差控制调节，将所述的转向角指令通过PWM运算，从而驱动无刷直流电机和数字舵机，根据所述的转向角指令控制无人艇下一步的航行运动。
为了验证本发明提出的吊舱式无人艇航向控制方法的控制效果，以现有首尾长度为1.8米的单桨吊舱式无人艇为研究对象进行MALTAB/SIMULINK仿真，并与PID控制算法进行对比。验证时，无人艇相关参数如表2所示，设定扰动为风浪干扰，设定风速为20m/s，风向角为20°，波高为5m/s，波向为20°。
表2 无人艇的主要设计参数
在MALTAB中进行等效迭代滑模航向控制程序编写，并与MALTAB/SIMULINK中吊舱式无人艇航向运动数学模型结合，得出无人艇航向运动仿真结果，图4为本发明的吊舱式无人艇等效迭代滑模航向控制仿真模型图。
该仿真与航向PID控制算法进行了对比研究，图5绘示出了二者的对比结果图，由图5(1)和图5(4)的对比可以看出，在无干扰下以及风浪干扰下，采用等效迭代滑模控制的超调量低、稳定性强。由图5(2)和图5(5)的对比可以看出，在无干扰下以及风浪干扰下，吊舱转向角限制在35°范围内，采用等效迭代滑模控制比PID控制转到45°航向所用时间短，并且能够避免大幅度抖振现象。由图5(3)和图5(6)的对比可以看出，在无干扰下以及风浪干扰下，采用等效迭代滑模控制能够克服干扰保持航向角和航行轨迹的稳定。综上所述，采用等效迭代滑模控制，能够对吊舱式无人艇操纵过程中的状态变化进行实时调节，实现快速、稳定的航向控制，提高了无人艇航向控制的精度，且改善了现有PID控制存在的时延性问题。
以上内容仅为本发明的技术思想，不能以此限定本发明的保护范围，凡是按照本发明提出的技术思想，在技术方案基础上所做的任何改动，均落入本发明权利要求书的保护范围之内。
Claims (6)
- 一种吊舱式无人艇航向控制方法，其特征在于，包括以下步骤：S1、对吊舱式无人艇进行受力分析，根据吊舱转向角转向特性，建立吊舱式无人艇的船舶运动数学模型；S2、根据所述船舶运动数学模型，建立吊舱式无人艇航向运动数学模型；S3、根据所述吊舱式无人艇航向运动数学模型，采用等效迭代滑模算法对无人艇的航向角进行控制；S4、通过PWM计算得出下一转向角指令，根据所述的转向角指令控制无人艇下一步的航行运动。
- 根据权利要求1所述的吊舱式无人艇航向控制方法，其特征在于，在步骤S1中，对吊舱式无人艇的前进、横漂和艏摇三自由度平面运动进行受力分析，根据吊舱转向角转向特性，获得吊舱式无人艇沿x轴、y轴和z轴所产生的力和力矩；将获得的吊舱式无人艇产生的力和力矩结合船舶分离型数学模型公式，建立所述吊舱式无人艇的船舶运动数学模型。
- 根据权利要求2所述的吊舱式无人艇航向控制方法，其特征在于，所述步骤S1包括以下子步骤：子步骤S101、建立三种坐标系：惯性坐标系、水平附体坐标系和附体坐标系，以对无人艇进行受力分析；子步骤S102、在所述的附体坐标系中，规定沿x轴方向为前进速度u，沿y轴方向为横移速度v和绕z轴转动的艏摇角速度r，具体如表1所示，则各轴的合外力和合力矩与各个部分力和力矩的关系如公式(1)所示：
其中下标H表示船舶所受到的粘性流体动力及力矩；下标P表示螺旋桨所受到的推力及转矩；下标R表示船舶所受到的舵力及力矩，wave和wind表示波浪和风的阻力；表1三自由度无人艇运动状态
根据吊舱式无人艇的操纵运动方程，对分离型船舶运动数学模型进行修正，如公式(2)、(3)所示：
其中X、Y、N为无人艇纵向力、横向力以及艏摇力；wave、wind表示波浪和风的阻力；m为无人艇重量，m x，m y为x轴、y轴方向的附 加质量；u，v，r为船运动中的速度、横移速度和转首角速度；I ZZ为O X轴的惯性矩；J zz为z轴方向上的附加惯性力矩；x 0，y 0为船舶原始坐标；子步骤S103、对吊舱式推进器进行受力分析得到无人艇安装的吊舱沿x、y轴以及z轴方向产生的力和力矩，计算公式如(4)所示：
其中x轴、y轴和z轴方向产生的力和力矩为纵向的推力、侧向推力及回转力矩，式中：Pod表示为吊舱推进器的推力，t Pod为螺旋桨推力减额系数；T p为吊舱推进器推力；δ为吊舱推进器的转向角；α HPod为吊舱诱导的侧向力系数；Q为吊舱的侧向力；x HPod为吊舱—船体侧向力系数作用点的纵向坐标；x Pod为吊舱压力中心的纵向坐标；子步骤S104、根据子步骤S103获得的无人艇安装的吊舱沿x、y轴以及z轴方向产生的力和力矩公式，建立吊舱式无人艇的船舶运动数学模型。 - 根据权利要求1所述的吊舱式无人艇航向控制方法，其特征在于，步骤S2包括以下子步骤：子步骤S201、建立风、浪干扰力的数学模型：作用在无人艇的风压力和力矩为：
公式(5)中，ρ a为空气密度；A f为无人艇水线上的正投影面积；A s为水线上的侧投影面积；L oa为无人艇的总长；C wx，C wy，C wn分别为x，y方向的风压力系数及绕z轴的风压力矩系数；求规定波流场中的压力，忽略产生波运动的能量压力项，即高阶小量计算波浪漂移力和力矩，以二阶波浪漂移力和力矩进行计算，
则作用在无人艇的浪压力和力矩为：
公式(6)中，ρ为流体密度，L为艇长，a为波幅，λ为波长，ψ为浪向角，C dx、C dy、C dn为试验系数；子步骤S202、根据吊舱推进电机的转速和推力转矩对无人艇的转向角和转向角速度的影响，建立吊舱推进电机和推力转矩模型；子步骤S203、根据所述的无人艇的风压力和力矩公式和浪压力和力矩公式结合吊舱推力转矩及转向角控制，建立吊舱式无人艇航向运动数学模型。 - 根据权利要求1所述的吊舱式无人艇航向控制方法，其特征在于，步骤S3包括以下子步骤：子步骤S301、将无人艇的反馈航向角与设定的期望航向角进行对比，计算出航向偏差e，航向偏差变换率
利用如下公式得到航向偏差：e＝ψ d-ψ，式中ψ d为期望航向角，ψ为实时反馈艏向；利用如下公式得到航向偏差变换率：式中
为期望航向角和反馈艏向角随时间的变换率；
子步骤S302、采用饱和函数对其进行滑模控制设计，令饱和函数为非线性正切函数，公式为：
根据公式(7)可知：当x→0时，其函数斜率比较大，随着x值得逐渐增加，斜率逐渐减小并趋近于零；子步骤S303、采用等效迭代滑模优化航向偏差，得到下一步的转向角指令：构建航向偏差滑动模态为：
由于航向控制是对转向角的控制，则等效迭代滑模控制算法其输出值为转向角δ；构建“滑模面”与转向角之间的函数关系，并结合饱和函数的严格有界性，对公式(8)进行修正为：
当s 2→0时，s 1→0；为了满足系统有效到达“滑模面”，对s 2进行镇 定控制，保证s 2收敛速度快于s 1，保证参数k 4≥k 2；子步骤S304、将“滑模面”反馈值s 2用于滑模反馈控制律：
结合转向角的控制公式：得控制的转向角指令为：
δ E＝δ-T E(k ps 2+εsgn(s 2)) k p,ε∈R + (11)式(11)中，δ E为等效迭代滑模控制调节输出的转向角，δ为实际转向角，T E为时间常数，s 2为所建立的“滑模面”反馈值，K p，ε为等效迭代滑模控制调节系数。 - 根据权利要求5所述的吊舱式无人艇航向控制方法，其特征在于：转向角约束为：-35°≤δ≤35°，转向速率约束为：
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| CN117270391A (zh) * | 2023-09-25 | 2023-12-22 | 大连海事大学 | 一种面向网箱巡检的转筒帆助航船自适应触发控制方法 |
| CN117270391B (zh) * | 2023-09-25 | 2024-04-30 | 大连海事大学 | 一种面向网箱巡检的转筒帆助航船自适应触发控制方法 |
| CN117762152A (zh) * | 2024-02-22 | 2024-03-26 | 陕西欧卡电子智能科技有限公司 | 无人船矢量入库控制方法、系统、无人船及可读存储介质 |
| CN117762152B (zh) * | 2024-02-22 | 2024-05-10 | 陕西欧卡电子智能科技有限公司 | 无人船矢量入库控制方法、系统、无人船及可读存储介质 |
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| CN113341953B (zh) | 2022-08-26 |
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