CN109116838B - Automatic berthing auxiliary control method for small ship - Google Patents

Abstract

An automatic mooring assistance control method for small boats is proposed, starting from a complete mathematical description of the boat's motion, introducing a simplified control-oriented model, identifying the physical parameters of the system through a grey-box model, which are then used to tune nested loops Parameters that control the architecture. The control algorithm is studied to achieve two main modes of operation: semi-automatic mode and position-holding mode. In semi-autonomous mode, the boat is manually guided to a parking space, while the controller helps the user maintain course and position by removing disturbances (e.g. wind, waves). In position hold mode, the controller maintains the vessel's position and heading within the port.

Description

A kind of automatic parking assistance control method for small boats

technical field

The invention relates to the field of automatic berthing control of ships, in particular to an auxiliary control method for automatic berthing of small ships.

Background technique

In marine and marine engineering, the technical advantages of using automated systems to maintain a vessel's position by means of actuators have been recognized since the 1960s. In general, most strategies are aimed at large ships or offshore platforms. The use of electronic equipment for control purposes in small ships is expanding, which means that some special problems of small ships can also be solved and solved by automatic control, one of the most important problems is how to carry out parking operations in ports.

Similar parking assist work proposed by domestic and foreign scholars, in which the heading is controlled only when the propeller is used (without the rudder). Specifically, a constant thrust is given according to the distance between the ship and the port without considering the sway control, this control method is used in the positioning holding strategy of small ships, the reference position is maintained by using longitudinal thrusters to compensate for wind disturbances, Not considering the sway control and the heading is not controlled, there is a big technical flaw. For the automatic berthing technology of small-scale ships, there is a large technical gap.

SUMMARY OF THE INVENTION

An automatic parking assist control method for small boats is proposed, starting from a complete mathematical description of the boat's motion,

A simplified control-oriented model is introduced to identify the physical parameters of the system through a grey-box model, which is then used to tune the parameters of the nested loop control architecture. The control algorithm is studied to achieve two main modes of operation: semi-automatic mode and position-holding mode. In semi-autonomous mode, the boat is manually guided to a parking space, while the controller works by removing disturbances such as wind,

waves) to help the user maintain heading and position. In position hold mode, the controller maintains the vessel's position and heading within the port. It mainly includes the following steps:

Step 1, 3 degrees of freedom mathematical model modeling

The motion model of the ship is described by a 6-DOF system. The symbols used are as follows: x is the pitch displacement, y is the sway displacement, z is the heave displacement, φ is the roll angle, θ is the pitch angle, and ψ is the bow angle. Specifically, x, y and z describe the position of the ship, while φ, θ and ψ represent the orientation.

The following assumptions are introduced to simulate the physical system:

)，横摇运动和纵摇运动被忽略；1) It is assumed that the longitudinal and transverse center of the ship is stable (i.e.

), the roll and pitch motions are ignored;

2) Ignore the heave motion under the assumption of z≈0;

3) Since the seaport is in a "closed" environment, the effect of waves (ie high frequency motion) is ignored, so the impact of waves on mooring maneuverability is small;

4) According to the maneuvering theory, the interaction between the ship and environmental disturbances (wind and ocean waves) is described by the viscous friction equation;

5) ignore the dynamics of the actuators as they are usually much faster than the dynamics of the boat;

6) The mass distribution of the ship is uniform and symmetrical about the xz plane;

7) The maximum speed achievable in port is 3 knots, hydrostatics and hydrodynamics are neglected.

The model used to describe the low-frequency motion of the ship on the horizontal plane can be simplified as a three-degree-of-freedom model, and the three-degree-of-freedom mathematical model is related to the reference frame fixed on the ship, that is, the hull coordinate system {1}. The state of the ship can be described by the vector x = [x yψ] ^T , which represents the surge, sway and yaw motions in the hull coordinate system {1}. The state vector x can be described in a ground-fixed reference frame {e}.

The forces acting on the boat are as follows:

1) The thrust generated by the thruster. These can be simplified to three (virtual) thrusters located in the center of gravity (CG). The input force f _x in the longitudinal direction, the input force f _y in the transverse direction and the τ in the yaw direction are all applied to the center of gravity.

2) Hydrodynamics (due to wind and water) _Fxc , _Fxw in longitudinal direction and _Fyc , _Fyw in transverse direction. The strength and direction of wind and current are defined on the ground coordinate system {e} and then projected onto the hull coordinate system {1}.

The mathematical model is as follows:

和

分别是纵荡和横荡加速度，

是艏摇角加速度，

是艏摇角速度，M是质量，J是惯性矩，K_ψ是地转偏向力向心系数，b_xw(t)，b_xc(t)，b_yw(t)和分别是中心(CG)与中心点(CP)之间的时变距离，即流体动力的作用点。下标w表示“风”，而下标c表示“水流”。where the equations are obtained by calculating the lateral and longitudinal balance of forces and the balance of moments with respect to the z-axis. In (1), f _x , f _y and τ are the inputs to the model,

and

are the surge and sway accelerations, respectively,

is the yaw angular acceleration,

is the yaw angular velocity, M is the mass, J is the moment of inertia, K _ψ is the centripetal coefficient of the geostrophic deflection force, b _xw (t), b _xc (t), b _yw (t) and are the center (CG) and The time-varying distance between the center points (CP), the point of action of the hydrodynamic force. The subscript w means "wind" and the subscript c means "water flow".

In {1}, the moment generated by the hydrodynamic force acting longitudinally is denoted by τ _x =b _xw F _xw +b _xc F _xc , and the moment generated by the hydrodynamic force acting laterally is denoted by τ _y =b _yw F _yw +b _yc F _yc . Since the length of the hull of a small ship is more than three times the width, τ _y >>τ _x , the center point is located on the longitudinal axis of the ship, resulting in b _xw (t)=0, b _xc (t)=0.

b _yc (t) and b _yw (t) will be treated as constants and their values will be incorporated into the gain and time constant of the transfer function used in the grey box identification process.

Fluid dynamics can be defined as

in

其中

为流体动力系数，ρ_c和ρ_w分别是空气和水的密度，而

是流体/接触表面。The hydrodynamic derivative is expressed as

in

are the hydrodynamic coefficients, ρ _c and ρ _w are the densities of air and water, respectively, and

is the fluid/contact surface.

The three-degree-of-freedom state-space model can be written as:

是状态向量，

是干扰向量，u＝[f_x f_y τ]^T是输入向量，y是输出向量。in

is the state vector,

is the interference vector, u=[f _x f _y τ] ^T is the input vector, and y is the output vector.

确定)，惯性力(f_x，f_y，τ)与实际推力之间的关系可写为：The boat is equipped with two lateral propellers producing f _v1 and f _v2 , and two stern thrusters producing f _u = f _u1 + f _u2 (while the direction is determined by the rudder angle

determined), the relationship between the inertial force (f _x , f _y , τ) and the actual thrust can be written as:

Finally, the motion of the ship with the ground coordinate system {e} as the reference frame can be expressed as:

[XY Ψ] ^T = R(ψ)[xy ψ] ^T (6)

where R is the rotation matrix.

Step 2. Control model design

也就是

Consider the point of action defined by the constant velocity, i.e.

that is

The linear dynamics of the ship are obtained by linearizing the nonlinear model (4) for the considered steady-state conditions, correlating the three input resultant forces with the three output velocities. The final model can be written in compact form as

矩阵A，B，F和C的计算方法如下in,

Matrices A, B, F and C are calculated as follows

The input-output model is implemented by applying the Laplacian operator to a linearized state-space model. δy(t) can be expressed as

δy(t)=G(s)δu(t)+H(s)δd(t) (10)

in,

Since the control system is designed to approach the port at low speed, the rudder angle has little effect on the yaw motion:

(传递函数

和

可以忽略不计)；1)

(Transfer Function

and

can be ignored);

可以忽略不计)；2) The center point coincides with the center (

can be ignored);

3)

和

是一阶传递函数。The model is simplified as follows: where K _PP and K _PROP represent the constant terms of the maximum thrust along the longitudinal and transverse directions, respectively, com _i represents the actual command signal of the actuator, and

and

is the first-order transfer function.

Step 3. Gray box identification

The grey box identification procedure consists of three steps:

1) Identify the gain and time constant of the transfer function for the control model;

2) Determine the gain term from resultant force to ship speed;

3) Identify the physical parameters of the model.

的过程如下：Identify transfer functions associated with longitudinal motion

The process is as follows:

First, the linearized model equation is rewritten as

是com_x和

之间的增益，

是

和

之间的增益，

是纵荡运动的时间常数。其次，时间常数

是通过输出估算的。第三，风速和纵荡速度

之间的传递函数的增益是从所有推进器关闭的测试中识别。最后，执行器的指令与横荡速度之间的传递函数的增益通过相对于

的最小化代价函数来计算

is com _x and

gain between,

Yes

and

gain between,

is the time constant of the surging motion. Second, the time constant

is estimated from the output. Third, wind speed and surge speed

The gain in transfer function between is identified from tests with all thrusters turned off. Finally, the gain of the transfer function between the actuator's command and the sway speed is determined by relative to

to minimize the cost function of

之间的增益。例如，考虑纵荡运动。使用公式

来合外力增益和纵荡运动的时间常数的关系为

类似地，对于横荡运动，可以表示为

The transfer function describes the dynamic relationship between thruster command and boat speed. Then, calculate the resultant force and the speed of the boat

gain between. For example, consider surging motion. use formula

The relationship between the external force gain and the time constant of the surging motion is

Similarly, for sway motion, it can be expressed as

Since the mass is known, the gain can be obtained by transforming the basic formula into

where a is the distance between the lateral thrusters and the center of gravity.

和纵荡时间常数

相对于流体动态导数K_xc和K_xw是线性的，所以线性系统可以在操作条件(

和

)下使用最小二乘法来定义Also note that since the gain

and the surge time constant

The derivatives K _xc and K _xw are linear with respect to the fluid dynamics, so the linear system can be

and

) using the least squares method to define

Similarly, the hydrodynamic derivatives K _yc and K _yw of the sway motion can also be calculated.

Step four, control system system design

The automatic park assist system operates in semi-automatic mode or holds position. The control structure is designed to cascade two loops per degree of freedom, the inner velocity loop is dedicated to the semi-automatic mode, and the positioning mode is implemented by the outer position loop.

The setpoint of the inner speed loop can be provided in two different ways: in position hold mode, the speed setpoint is given by the position regulator, and in semi-automatic mode, the speed setpoint is set by the user via the joystick . The command variables of the control system are the gears of the propulsion unit and the lateral propeller. The propulsion was used to control the sway motion as the vessel reached the maximum speed allowed near the port (3 knots) with the gears triggered, and the lateral propellers were used to control the sway and yaw motion at low speeds.

1) Considering (7), the coordinate transformation block transforms the variables to be used from the ground coordinate system to the hull coordinate system;

2) The position regulator module is implemented by three proportional regulators, which generate reference setpoints for the internal speed loop (the closed-loop bandwidth is about 0.001Hz, and the phase margin is about 80°);

3) The speed regulator module is implemented by three proportional-integral regulators, which are regulated based on the transfer function of the control-oriented model, and the vessel motion is decoupled (closed-loop bandwidth is about 0.01Hz, and the phase margin is about 90 °);

4) The splitter module converts the output of the speed controller into the instructions of the available actuators;

5) The PWM module generates pulses of variable length to control the on/off of the thrusters and adjust the thrust.

This method has the following effects and advantages:

The physical parameters of the automatic mooring model are identified through the grey box and then used to tune the parameters of the nested loop control architecture. Contains two main modes of operation: semi-automatic mode and position hold mode. In semi-automatic mode,

The boat is manually guided to a parking space, while the controller helps the user maintain course and position by removing disturbances (eg wind, waves). In the position hold mode, the controller maintains the position and heading of the ship in the port, and can implement sway control,

Compensation for wind and wave disturbance through reference position has better control performance and control accuracy.

Description of drawings

Figure 1 is a schematic diagram of inertial coordinate system and force

Figure 2 is a block diagram of the linear system

Figure 3 shows the architecture of the control system

Figure 4 is a block diagram of the control system

Detailed ways

Step 1, 3 degrees of freedom mathematical model modeling

The motion of the boat is described by a 6-DOF system. The symbols used are as follows: x is the pitch displacement, y is the sway displacement, z is the heave displacement, φ is the roll angle, θ is the pitch angle, and ψ is the bow angle. Specifically, x, y and z describe the position of the ship, while φ, θ and ψ represent the orientation.

The following assumptions are introduced to simulate the physical system to obtain a model that is both simple and reliable:

)，横摇运动和纵摇运动被忽略。1) It is assumed that the longitudinal and transverse center of the ship is stable (i.e.

), the roll and pitch motions are ignored.

2) Ignore the heave motion under the assumption of z≈0;

3) Since the seaport is in a "closed" environment, the effect of waves (ie high frequency motion) is ignored, so the impact of waves on mooring maneuverability is small;

4) According to the motor mechanism, use the viscous friction equation to describe the interaction between the ship and environmental disturbances (wind and waves);

5) ignore the dynamics of the actuators as they are usually much faster than the dynamics of the boat;

6) The mass distribution of the ship is uniform and symmetrical about the xz plane;

7) The maximum speed achievable in port is 3 knots, hydrostatics and hydrodynamics are neglected.

The model used to describe the low-frequency motion of the ship on the horizontal plane can be simplified as a three-degree-of-freedom model, and the three-degree-of-freedom mathematical model is related to the reference frame fixed on the ship, that is, the hull coordinate system {1}. The state of the ship can be described by the vector x = [x yψ] ^T , which represents the surge, sway and yaw motions in the hull coordinate system {1}. The state vector x can be described in a ground-fixed reference frame {e}.

The force acting on the ship is shown in Figure 1, and the coordinate system X _e Y _e is the ground coordinate system:

1) The thrusters generate thrust. These can be simplified to three (virtual) thrusters located in the center of gravity (CG) such that the resultant input force f _x along the longitudinal direction x ₁ , the resultant input force f _y along the transverse direction y ₁ and the resultant moment along the yaw direction τ is all applied to the center of gravity.

2) Hydrodynamics (due to wind and water) _Fxc , _Fxw in longitudinal direction and _Fyc , _Fyw in transverse direction. The strength and direction of wind and current are defined on the ground coordinate system {e} and then projected onto the hull coordinate system {1}.

The mathematical model is as follows:

和

分别是纵荡和横荡加速度，

是艏摇角加速度，

是艏摇角速度，M是质量，J是惯性矩，K_ψ是地转偏向力向心系数，b_xw(t)，b_xc(t)，b_yw(t)和分别是中心(CG)与中心点(CP)之间的时变距离，即流体动力的作用点。下标w表示“风”，而下标c表示“水流”。V_w和V_c分别是代表风和水流的矢量，

和

分别表示在地面坐标系下风和水流相对于横坐标的偏角。where the equations are obtained by calculating the lateral and longitudinal balance of forces and the balance of moments with respect to the z-axis. In (1), f _x , f _y and τ are the inputs to the model,

and

are the surge and sway accelerations, respectively,

is the yaw angular acceleration,

is the yaw angular velocity, M is the mass, J is the moment of inertia, K _ψ is the centripetal coefficient of the geostrophic deflection force, b _xw (t), b _xc (t), b _yw (t) and are the center (CG) and The time-varying distance between the center points (CP), the point of action of the hydrodynamic force. The subscript w means "wind" and the subscript c means "water flow". _Vw and _Vc are the vectors representing wind and current, respectively,

and

respectively represent the declination angle of the wind and current relative to the abscissa in the ground coordinate system.

In {1}, the moment generated by the hydrodynamic force acting longitudinally is denoted by τ _x =b _xw F _xw +b _xc F _xc , and the moment generated by the hydrodynamic force acting laterally is denoted by τ _y =b _yw F _yw +b _yc F _yc . Since the length of the hull of a small ship is more than three times the width, τ _y >>τ _x , the center point is located on the longitudinal axis of the ship, resulting in b _xw (t)=0, b _xc (t)=0.

b _yc (t) and b _yw (t) will be treated as constants and their values will be incorporated into the gain and time constant of the transfer function used in the grey box identification process.

Fluid dynamics can be defined as

in

其中

为流体动力系数，ρ_c和ρ_w分别是空气和水的密度，而

是流体/接触表面。The hydrodynamic derivative is expressed as

in

are the hydrodynamic coefficients, ρ _c and ρ _w are the densities of air and water, respectively, and

is the fluid/contact surface.

The three-degree-of-freedom state-space model can be written as:

是状态向量，

是干扰向量，u＝[f_xf_yτ]^T是输入向量，y是输出向量。in

is the state vector,

is the interference vector, u=[f _x f _y τ] ^T is the input vector, and y is the output vector.

确定)，惯性力(f_x，f_y，τ)与实际推力之间的关系可写为：The boat is equipped with two lateral propellers producing f _v1 and f _v2 , and two stern thrusters producing f _u1 and f _u2 , f _u = f _u1 + f _u2 (while the direction is determined by the rudder angle

determined), the relationship between the inertial force (f _x , f _y , τ) and the actual thrust can be written as:

Finally, the motion of the ship with the ground coordinate system {e} as the reference frame can be expressed as:

[XY Ψ] ^T = R(ψ)[xy ψ] ^T (6)

where R is the rotation matrix.

Step 2. Control model design

也就是

Consider the point of action defined by the constant velocity, i.e.

that is

The linear dynamics of the ship are obtained by linearizing the nonlinear model (4) for the considered steady-state conditions, correlating the three input resultant forces with the three output velocities. The final model can be written in compact form as

矩阵A，B，F和C的计算方法如下in,

Matrices A, B, F and C are calculated as follows

The input-output model is implemented by applying the Laplacian operator to a linearized state-space model. δy(t) can be expressed as

δy(t)=G(s)δu(t)+H(s)δd(t) (10)

in,

Since the control system is designed to approach the port at low speed, the rudder angle has little effect on the yaw motion:

(传递函数

和

可以忽略不计)；1)

(Transfer Function

and

can be ignored);

可以忽略不计)；2) The center point coincides with the center (

can be ignored);

3)

和

是一阶传递函数。

和

分别为风带来的噪声扰动。δf_x、δf_y和δτ分别为沿着纵向、横向和艏摇方向的三个输入合力。

和

分别为三个输出速度。The simplified model is shown in Figure 2: where K _PP and K _PROP represent the constant term of the maximum thrust along the longitudinal and lateral directions, respectively, com _i represents the command signal of the actual actuator, and com _x1 and com _x2 represent the command signal of the stern thruster, respectively , com _stern and com _bow represent the command signals of the two lateral thrusters near the stern and the bow respectively, com _fx is the combined command signal in the longitudinal direction, com _fy is the combined command signal in the lateral direction, and com _τ is the combined command signal in the yaw direction ,

and

is the first-order transfer function.

and

are the noise disturbances caused by wind, respectively. δf _x , δf _y and δτ are the three input resultant forces along the longitudinal, lateral and yaw directions, respectively.

and

three output speeds respectively.

Step 3. Gray box identification

The grey box identification procedure consists of three steps:

1) Identify the gain and time constant of the transfer function for the control model;

2) Determine the gain term from resultant force to ship speed;

3) Identify the physical parameters of the model.

的过程如下：Identify transfer functions associated with longitudinal motion

The process is as follows:

First, the linearized model equation is rewritten as

是com_x和

之间的增益，

是

和

之间的增益，

是纵荡运动的时间常数。其次，时间常数

是通过输出估算的。第三，风速和纵荡速度

之间的传递函数的增益是从所有推进器关闭的测试中识别。最后，执行器的指令与横荡速度之间的传递函数的增益通过相对于

的最小化代价函数来计算

is com _x and

gain between,

Yes

and

gain between,

is the time constant of the surging motion. Second, the time constant

is estimated from the output. Third, wind speed and surge speed

The gain in transfer function between is identified from tests with all thrusters turned off. Finally, the gain of the transfer function between the actuator's command and the sway speed is determined by relative to

to minimize the cost function of

之间的增益。例如，考虑纵荡运动。使用公式

来合外力增益和纵荡运动的时间常数的关系为

类似地，对于横荡运动，可以表示为

The transfer function describes the dynamic relationship between thruster command and boat speed. Then, calculate the resultant force and the speed of the boat

gain between. For example, consider surging motion. use formula

The relationship between the external force gain and the time constant of the surging motion is

Similarly, for sway motion, it can be expressed as

Since the mass is known, the gain can be obtained by transforming the basic formula into

where a is the distance between the lateral thrusters and the center of gravity.

和纵荡时间常数

相对于流体动态导数K_xc和K_xw是线性的，所以线性系统可以在操作条件(

和

)下使用最小二乘法来定义Also note that since the gain

and the surge time constant

The derivatives K _xc and K _xw are linear with respect to the fluid dynamics, so the linear system can be

and

) using the least squares method to define

Similarly, the hydrodynamic derivatives K _yc and K _yw of the sway motion can also be calculated.

Step four, control system system design

The automatic park assist system operates in semi-automatic mode or holds position. The control structure is designed to cascade two loops per degree of freedom, as shown in Figure 3. The inner velocity loop is dedicated to the semi-automatic mode, while the positioning mode is implemented through the outer position loop. P ^* is the reference input signal for gear control, and P is the output gear control signal. V _JOY is the speed reference signal of the joystick, and V _REG is the speed reference signal of the position regulator. R _Y (s), G _Y (s) and G _P (s) are transfer functions.

和

分别为沿着纵向、横向和艏摇方向速度参考设定值。

和

分别为沿着纵向、横向和艏摇方向速度实际值。

和

为速度调节器的输入信号。F_x、F_y和T_ψ为速度调节器输出的合力和合力矩。com_pp,su和com_pp,dx为分离器输出的用于船尾推进器的控制指令，com_PROD,stern和com_PROD,bow分别为用于靠近船尾和靠近船首的两个侧向推进器的控制指令。com^PWM _pp,su、com^PWM _pp,dx、com^PWM _PROD,stern和com^PWM _PROD,bow为脉宽调制输出的可变长度脉冲，以控制四个推进器的开关和推力大小。The setpoint of the inner speed loop can be provided in two different ways: in position hold mode, the speed setpoint is given by the position regulator, and in semi-automatic mode, the speed setpoint is set by the user via the joystick . The command variables of the control system are the gears of the propulsion unit and the lateral propeller. The propulsion was used to control the sway motion as the vessel reached the maximum speed allowed near the port (3 knots) with the gears triggered, and the lateral propellers were used to control the sway and yaw motion at low speeds. The block diagram of the control system is shown in Figure 4. Considering (7), the coordinate transformation block transforms the variables to be used from the ground coordinate system to the hull coordinate system; LAT ^* , LONG ^* and ψ ^* are the reference position references along the longitudinal, lateral and yaw directions in the ground coordinate system value. LAT, LONG and ψ are the actual position values along the longitudinal, lateral and yaw directions in the ground coordinate system. e _LAT , e _LONG and e _ψ are the variables along the longitudinal, lateral and yaw directions in the ground coordinate system. e _xlong , e _ylat and e _ψ are the variables along the longitudinal, lateral and yaw directions in the hull coordinate system, respectively.

and

They are the speed reference setting values along the longitudinal, lateral and yaw directions, respectively.

and

are the actual speed along the longitudinal, lateral and yaw directions, respectively.

and

It is the input signal of the speed regulator. F _x , F _y and T _ψ are the resultant force and resultant torque output by the speed regulator. com _pp,su and com _pp,dx are the control commands for the stern thruster output by the splitter, com _{PROD, stern} and com _PROD,bow are the control commands for the two side thrusters near the stern and near the bow respectively instruction. com ^PWM _pp,su , com ^PWM _pp,dx , com ^PWM _PROD,stern and com ^PWM _PROD,bow are variable-length pulses output by PWM to control the on-off and thrust of the four thrusters.

1) The position regulator module is implemented by three proportional regulators, which generate reference setpoints for the internal speed loop (the closed-loop bandwidth is about 0.001Hz, and the phase margin is about 80°);

2) The speed regulator module is implemented by three proportional-integral regulators, which are regulated based on the transfer function of the control-oriented model, and the vessel motion is decoupled (closed-loop bandwidth is about 0.01Hz, and the phase margin is about 90 °);

3) The splitter module converts the output of the speed controller into instructions for the available actuators;

4) The PWM module generates pulses of variable length to control the on/off of the thrusters and adjust the thrust.

Claims (1)

1. An automatic berthing auxiliary control method for a small-sized ship, characterized by comprising the steps of:

step one, three-degree-of-freedom motion mathematical model modeling

The motion model of the vessel is described by a 6-degree-of-freedom system, using the notation: x is the surge displacement, y is the surge displacement, z is the heave displacement, phi is the roll angle, theta is the surge angle, psi is the bow angle; x, y and z describe the position of the vessel, and phi, theta and psi denote directions;

the following assumptions were introduced to simulate a physical system:

1) assuming that the vessel is longitudinally and transversely centre-stabilized, i.e.

Roll and pitch motions are ignored;

2) ignoring the heave motion under the assumption that z ≈ 0;

3) because the harbor is in a closed environment, the high-frequency motion of the ship caused by waves is ignored, and the influence of sea waves on the mooring maneuverability is small;

4) according to dynamics, the viscous friction equation is used for describing the interaction between the ship and environmental disturbance caused by wind and sea waves;

5) neglecting the dynamics of the actuators, they are generally much faster than the dynamics of the ship;

6) the mass distribution of the vessel is uniform and symmetrical about the xz plane;

7) the maximum speed which can be reached in the port is 3 sections, and the fluid statics and the fluid mechanics are ignored;

the model for describing the low-frequency motion of the ship on the horizontal plane is simplified into a three-degree-of-freedom motion mathematical model, and the three-degree-of-freedom motion mathematical model is related to a reference system fixed on the ship, namely a ship body coordinate system {1 }; the state of the ship can be determined by the state vector x ═ x y ψ]^TDescribing the vector, the vector represents the surging, swaying and yawing motion on the ship body coordinate system {1 }; the state vector x is inDescribed in the ground-fixed reference frame { e };

the forces acting on the vessel are as follows:

1) the thrust generated by the propeller is reduced to three propellers at the center of gravity, the input force f along the longitudinal direction_xInput force f in the transverse direction_yAnd τ along the heading direction is all applied to the center of gravity;

2) hydrodynamic forces F in the longitudinal direction due to wind and water_xc、F_xwAnd F in the transverse direction_yc、F_ywThe strength and direction of wind and water flow are defined on a ground coordinate system { e }, and then projected on a ship body coordinate system {1 }; the mathematical model is as follows:

obtaining an equation by calculating the lateral and longitudinal balance of forces and the balance of moments with respect to the z-axis; in (1), f_x,f_yAnd tau is the input to the model,

and

respectively surging acceleration and surging acceleration,

is the acceleration of the yaw angle,

is the yaw rate, M is the mass, J is the moment of inertia, K_ψIs the centripetal coefficient of the rotary deflection force, b_xw(t)，b_xc(t)，b_yw(t)，b_yc(t) are the time varying distances between the vessel's center of gravity and the vessel's center point, respectively; wherein the subscript x denotes the vessel surge direction, y denotes the vessel heading direction, w denotes the force induced by sea waves, c denotes the force induced by sea currentsMeaning, (t) means that the quantity is not a fixed constant, but a time variable;

the moment produced by the hydrodynamic force acting longitudinally in {1} is denoted by τ_x＝b_xwF_xw+b_xcF_xcRepresenting the moment produced by hydrodynamic forces acting transversely by τ_y＝b_ywF_yw+b_ycF_ycRepresents; the length of the small-sized ship body is more than three times of the width, tau_y＞＞τ_xWith the centre point lying on the longitudinal axis of the vessel, thus generating b_xw(t)＝0,b_xc(t)＝0；

b_yc(t) and b_yw(t) will be considered as constants, their values will be incorporated into the gain and time constants of the transfer function used in the gray box identification process;

fluid power can be defined as

Wherein

The hydrodynamic derivative is expressed as

Where i ═ { x, y }, j ═ w, c }

Is the hydrodynamic coefficient, p_cAnd ρ_wDensity of air and water, respectively, and

is a fluid contact surface;

the state space model of three degrees of freedom can be written as follows:

wherein

Is a vector of the states of the memory cells,

is an interference vector, u ═ f_xf_yτ]^TIs the input vector, y is the output vector;

the ship being equipped with two lateral propellers for producing f_v1And f_v2And two stern thrusters generate f_u＝f_u1+f_u2Is influenced by the rudder angle theta, and the inertial force (f)_x，f_yτ) versus actual thrust can be written as:

the motion of the vessel with reference to the ground coordinate system { e } can be expressed as:

[X Y Ψ]^T＝R(ψ)[x y ψ]^T (6)

wherein R is a rotation matrix;

step two, controlling model design

Considering the point of action defined by constant velocity, i.e.

That is to say

The linear dynamics of the ship are obtained by linearizing a non-linear model (4) taking into account the steady-state conditions, associating three input resultant forces with three output speeds, the final model being written in the form

Wherein,

the matrices A, B, F and C are calculated as follows

The input-output model is implemented by applying the Laplacian to a linearized state space model, δ y (t) can be expressed as

δy(t)＝G(s)δu(t)+H(s)δd(t) (10)

Wherein,

the control system is designed to be close to a port at a low speed, and the influence of a rudder angle on yawing motion is small:

1)

i.e. transfer function

And

neglect;

2) the centre point coinciding with the centre, i.e.

Neglect;

3)θ＝0；

the model is simplified as follows: wherein K_PPAnd K_PROPA constant term, com, representing the maximum thrust in the longitudinal and transverse directions, respectively_iRepresenting the actual actuator command signals, and

and

is a first order transfer function;

step three, ash box identification

The gray box identification procedure consists of three steps:

1) identifying gains and time constants of a control model-oriented transfer function;

2) determining a gain term from resultant force to watercraft speed;

3) identifying physical parameters of the model;

identifying a transfer function associated with longitudinal motion

The process of (2) is as follows:

the linearized model equation is rewritten as

Is com_xAnd

the gain of the first amplifier is larger than the gain of the second amplifier,

is that

And

the gain of the first amplifier is larger than the gain of the second amplifier,

is the time constant of the surging motion; time constant

Estimated by the output; wind speed and surging speed

The gain of the transfer function between is identified from the test that all thrusters were shut down; gain through the transfer function between command and yaw rate of the actuator relative to

To calculate a minimum cost function of

The transfer function describes the dynamic relation between the propeller command and the ship speed, and the resultant force and the ship speed are calculated

A gain in between; considering surging motion, using formulas

The relationship between the gain of the external force and the time constant of the surging motion is

For a swaying motion, it can be expressed as

The quality is known and the gain can be transformed by transforming the basic formula into

a is the distance between the lateral thruster and the centre of gravity;

gain of

And surge time constant

Derivative with respect to fluid dynamics K_xcAnd K_xwIs linear, using the least squares method under the operating conditions (

And

) Linear system of lower definition

Calculating hydrodynamic derivatives K of the swaying motion_ycAnd K_yw；

Step four, designing a control system

The automatic parking auxiliary system runs or is positioned and maintained in a semi-automatic mode, the control structure is designed to cascade two loops for each degree of freedom, an internal speed loop is specially used for the semi-automatic mode, and a positioning mode is realized through an external position loop;

the set point for the inner ring velocity ring can be provided in two different ways: in the position hold mode, the speed set point is given by the position regulator, while in the semi-automatic mode, the speed set point is set by the user through the joystick; the control output of the control system is the gear of the propulsion device and the lateral propeller; the propulsion device is used for controlling the surging movement, the maximum speed of the ship which is allowed to reach the vicinity of a port under the condition of gear contact is three sections, and the lateral propeller is used for controlling the surging and yawing movement at low speed;

1) considering (7), the coordinate transformation block transforms variables to be used from the ground coordinate system to the hull coordinate system;

2) the position regulator module is implemented by three proportional regulators which generate reference setpoints for the inner velocity loop; the closed loop bandwidth is about 0.001Hz and the phase margin is about 80 °;

3) the speed regulator module is realized by three proportional-integral regulators, the regulators are used for regulating based on a transfer function of a control guidance model, and the ship motion is decoupled; closed loop bandwidth is about 0.01Hz and phase margin is about 90 °;

4) the separator module converts the output of the speed controller into an instruction of an available actuator;

5) the pulse width modulation module generates pulses of variable length to control the on/off of the propeller and adjust thrust.

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