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

Automatic berthing auxiliary control method for small ship Download PDF

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Publication number
CN109116838B
CN109116838B CN201810329931.4A CN201810329931A CN109116838B CN 109116838 B CN109116838 B CN 109116838B CN 201810329931 A CN201810329931 A CN 201810329931A CN 109116838 B CN109116838 B CN 109116838B
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ship
motion
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gain
vessel
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CN109116838A (en
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王旭阳
高迪驹
周宇
刘涵
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Shanghai Maritime University
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Shanghai Maritime University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • 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

Abstract

An automatic berthing auxiliary control method for small ships is proposed, starting from a complete mathematical description of the ship's movements, introducing a simplified control-oriented model, recognizing the physical parameters of the system by means of a grey-box model, and then using them to adjust the parameters of a nested loop control architecture. The control algorithm was studied to achieve two main modes of operation: a semi-automatic mode and a position-keeping mode. In semi-autonomous mode, the boat is manually guided to the parking space, while the controller helps the user maintain heading and position by excluding disturbances (e.g., wind, waves). In the position-keeping mode, the controller keeps the position and heading of the vessel within the port.

Description

Automatic berthing auxiliary control method for small ship
Technical Field
Relates to the field of automatic berthing control of ships, in particular to an automatic berthing auxiliary control method for small ships.
Background
In oceans and marine engineering, the technical advantages of using automated systems to maintain the position of vessels by actuators have been recognized since the 60's of the 20 th century. In general, most strategies are for large vessels or ocean platforms. The use of electronic equipment for control purposes in small vessels is expanding, which means that some special problems of small vessels can also be solved and solved by automatic control, one of the most important being how to perform parking operations in ports.
Similar parking assistance work has been proposed by foreign and domestic scholars, where heading is controlled only when a propeller is used (no rudder). In particular, this control method is used for a positioning maintenance strategy for small ships, giving a constant thrust depending on the distance between the ship and the port, irrespective of the roll control and uncontrolled course, the reference position being maintained by using longitudinal thrusters to compensate for wind disturbances, presents a great technical drawback. For the automatic ship berthing technology of small-scale ships, a great technical blank exists.
Disclosure of Invention
An automatic mooring assistance control method for small ships is proposed, starting from a complete mathematical description of the ship's movements,
a simplified control-oriented model is introduced, physical parameters of the system are identified through a gray box model, and then the physical parameters are used for adjusting parameters of the nested loop control architecture. The control algorithm was studied to achieve two main modes of operation: a semi-automatic mode and a position-keeping mode. In semi-automatic mode, the boat is manually guided to the parking space, while the controller operates by eliminating disturbances (e.g., wind, etc.),
Waves) to help the user maintain heading and position. In the position-keeping mode, the controller keeps the position and heading of the vessel within the port. The method mainly comprises the following steps:
step one, 3 degree of freedom mathematical model modeling
The motion model of the vessel is described by a 6 degree of freedom system. The symbols used are as follows: 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 yaw angle. Specifically, x, y, and z describe the position of the vessel, and φ, θ, and ψ represent directions.
The following assumptions were introduced to simulate a physical system:
1) assuming that the vessel is longitudinally and transversely center stabilized (i.e., the vessel is transversely centered and stabilized)
Figure BDA0001627669730000011
) Roll and pitch motions are ignored;
2) ignoring the heave motion under the assumption that z ≈ 0;
3) because the harbour is in a "closed" environment, the influence of waves (i.e. high frequency motion) is neglected, so that the influence of waves on the maneuverability of the mooring is small;
4) according to the theory of maneuvering, the viscous friction equation is used for describing the interaction between the ship and environmental disturbance (wind and sea waves);
5) the dynamics of the actuators are neglected because 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 achievable at port is 3 knots and the hydrostatic and hydrodynamic are negligible.
The model for describing the low-frequency motion of the ship on the horizontal plane can be simplified into a three-degree-of-freedom model, and the three-degree-of-freedom 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 vector x ═ x y ψ]TTo illustrate, the vector represents the surge, sway and yaw motions in the hull coordinate system {1 }. The state vector x may be described on a ground-based fixed reference frame { e }.
The forces acting on the vessel are as follows:
1) the propeller generates thrust. These can be reduced to three (virtual) thrusters located in the Center of Gravity (CG). Input force f in longitudinal directionxInput force f in the transverse directionyAnd τ along the heading direction is all applied to the center of gravity.
2) Hydrodynamic forces (due to wind and water) F in the longitudinal directionxc、FxwAnd F in the transverse directionyc、Fyw. The strength and direction of wind and water flow are defined on the ground coordinate system { e } and then projected onto the hull coordinate system {1 }.
The mathematical model is as follows:
Figure BDA0001627669730000021
where the equations are obtained by calculating the lateral and longitudinal balance of the forces and the balance of the moments with respect to the z-axis. In (1), fx,fyAnd tau is the input to the model,
Figure BDA0001627669730000022
and
Figure BDA0001627669730000023
respectively surging acceleration and surging acceleration,
Figure BDA0001627669730000024
is the acceleration of the yaw angle,
Figure BDA0001627669730000025
is the yaw rate, M is the mass, J is the moment of inertia, KψIs the centripetal coefficient of the rotary deflection force, bxw(t)，bxc(t)，bywAnd (t) are the time-varying distances between the Center (CG) and the Center Point (CP), respectively, i.e. the points of action of the fluid power. Subscript w represents "wind" and subscript c represents "water flow".
The moment produced by the hydrodynamic force acting longitudinally in {1} is denoted by τx＝bxwFxw+bxcFxcRepresenting the moment produced by hydrodynamic forces acting transversely by τy＝bywFyw+bycFycAnd (4) showing. Since the length of the hull of a small ship is more than three times the width, tauy>>τxWith the centre point lying on the longitudinal axis of the vessel, thus generating bxw(t)＝0,bxc(t)＝0。
byc(t) and byw(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
Figure BDA0001627669730000031
Wherein
Figure BDA0001627669730000032
The hydrodynamic derivative is expressed as
Figure BDA0001627669730000033
Wherein
Figure BDA0001627669730000034
In order to be the coefficient of the fluid dynamics,ρcand ρwDensity of air and water, respectively, and
Figure BDA0001627669730000035
is the fluid/contact surface.
The state space model of three degrees of freedom can be written as follows:
Figure BDA0001627669730000036
wherein
Figure BDA0001627669730000037
Is a vector of the states of the memory cells,
Figure BDA0001627669730000038
is an interference vector, u ═ fx fy τ]TIs the input vector and y is the output vector.
The ship being equipped with two lateral propellers for producing fv1And fv2And two stern thrusters generate fu＝fu1+fu2(simultaneous steering by rudder angle)
Figure BDA00016276697300000311
Determination), inertial force (f)x，fyτ) versus actual thrust can be written as:
Figure BDA0001627669730000039
finally, 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)
Figure BDA00016276697300000310
where R is a rotation matrix.
Step two, controlling model design
Considering the point of action defined by constant velocity, i.e.
Figure BDA0001627669730000041
That is to say
Figure BDA0001627669730000042
The linear dynamics of the ship are obtained by linearizing a non-linear model (4) taking into account steady-state conditions, correlating three input resultant forces with three output speeds. The final model can be written in compact form as follows
Figure BDA0001627669730000043
Wherein the content of the first and second substances,
Figure BDA0001627669730000044
the matrices A, B, F and C are calculated as follows
Figure BDA0001627669730000045
The input-output model is implemented by applying the laplacian operator to the linearized state space model. δ y (t) can be expressed as
δy(t)＝G(s)δu(t)+H(s)δd(t) (10)
Wherein the content of the first and second substances,
Figure BDA0001627669730000046
Figure BDA0001627669730000047
because the control system is designed to be close to the port at low speed, the rudder angle has little influence on the yawing motion:
1)
Figure BDA0001627669730000048
(transfer function)
Figure BDA0001627669730000049
And
Figure BDA00016276697300000410
negligible);
2) the center point coincides with the center (
Figure BDA00016276697300000411
Negligible);
3)
Figure BDA00016276697300000414
the model is simplified as follows: wherein KPPAnd KPROPA constant term, com, representing the maximum thrust in the longitudinal and transverse directions, respectivelyiRepresenting the actual actuator command signals, and
Figure BDA00016276697300000412
and
Figure BDA00016276697300000413
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) physical parameters of the model are identified.
Identifying a transfer function associated with longitudinal motion
Figure BDA0001627669730000051
The process of (2) is as follows:
first, the linearized model equation is rewritten as
Figure 100002_DEST_PATH_FDA0001680987740000049
Figure BDA0001627669730000053
Is comxAnd
Figure BDA0001627669730000054
the gain of the first amplifier is larger than the gain of the second amplifier,
Figure BDA0001627669730000055
is that
Figure BDA0001627669730000056
And
Figure BDA0001627669730000057
the gain of the first amplifier is larger than the gain of the second amplifier,
Figure BDA0001627669730000058
is the time constant of the surging motion. Second, time constant
Figure BDA0001627669730000059
Is estimated by the output. Third, wind speed and surging speed
Figure BDA00016276697300000510
The gain of the transfer function between is identified from the test that all thrusters were shut down. Finally, the gain of the transfer function between the command of the actuator and the yaw rate is determined by the relative relationship
Figure BDA00016276697300000511
To calculate a minimum cost function of
Figure BDA00016276697300000512
The transfer function describes the dynamic relationship between propeller commands and the speed of the ship. Then, the sum of the resultant forces is calculatedSpeed of ship
Figure BDA00016276697300000513
Figure BDA00016276697300000514
The gain in between. Consider, for example, a surging motion. Using the formula
Figure BDA00016276697300000515
The relationship between the gain of the external force and the time constant of the surging motion is
Figure BDA00016276697300000516
Similarly, for a swaying motion, it can be expressed as
Figure BDA00016276697300000517
Since the mass is known, the gain can be transformed by transforming the basic formula into
Figure BDA00016276697300000518
Where a is the distance between the lateral thruster and the centre of gravity.
It is also noted that due to the gain
Figure BDA0001627669730000061
And surge time constant
Figure BDA0001627669730000062
Derivative with respect to fluid dynamics KxcAnd KxwIs linear, so a linear system can be operated under conditions of (A)
Figure BDA0001627669730000063
And
Figure BDA0001627669730000064
) Is defined using the least squares method
Figure BDA0001627669730000065
Similarly, the hydrodynamic derivative K of the swaying motion can also be calculatedycAnd Kyw。
Step four, designing a control system
The automatic parking assist system operates in a semi-automatic mode or position maintenance. The control structure is designed to cascade two loops per degree of freedom, the inner speed loop being dedicated to the semi-automatic mode, and the positioning mode being realized by the outer 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 command variables of the control system are the propulsion device and the gear of the lateral propeller. The propulsion device is used to control the surge motion because the ship reaches the maximum speed allowed near the port (3 knots) with gear activation and the side propellers are used to control the roll and yaw motion at low speeds.
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 that generate reference settings for the inner velocity loop (closed loop bandwidth about 0.001Hz, phase margin about 80 °);
3) the speed regulator module is implemented by three proportional integral regulators which regulate based on the transfer function of the control guidance model, the vessel motion is decoupled (closed loop bandwidth about 0.01Hz, phase margin 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.
The method has the following effects and advantages:
the physical parameters of the automatic mooring model are identified by the grey boxes and then used to adjust the parameters of the nested loop control architecture. Two main modes of operation are involved: a semi-automatic mode and a position-keeping mode. In the semi-automatic mode, the user may,
the boat is manually guided to the parking space, and the controller helps the user to maintain heading and position by excluding disturbances (e.g., wind, waves). In the position keeping mode, the controller keeps the position and the heading of the ship in the harbor, can implement the swing control,
the disturbance of wind and sea waves is compensated through the reference position, and the control performance and the control precision are better.
Drawings
FIG. 1 is a diagram of an inertial coordinate system and a force-bearing principle
FIG. 2 is a block diagram of a linear system
FIG. 3 is a control system architecture diagram
FIG. 4 is a block diagram of a control system
Detailed Description
Step one, 3 degree of freedom mathematical model modeling
The motion of the vessel is described by a 6 degree of freedom system. The symbols used are as follows: 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 yaw angle. Specifically, x, y, and z describe the position of the vessel, and φ, θ, and ψ represent directions.
The following assumptions were introduced to simulate a physical system to obtain a simple and reliable model:
1) assuming that the vessel is longitudinally and transversely center stabilized (i.e., the vessel is transversely centered and stabilized)
Figure BDA0001627669730000071
) The roll motion and pitch motion are ignored.
2) Ignoring the heave motion under the assumption that z ≈ 0;
3) because the harbour is in a "closed" environment, the influence of waves (i.e. high frequency motion) is neglected, so that the influence of waves on the maneuverability of the mooring is small;
4) according to the mechanics, the viscous friction equation is used to describe the interaction between the ship and the environmental disturbance (wind and sea waves);
5) the dynamics of the actuators are neglected because 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 achievable at port is 3 knots and the hydrostatic and hydrodynamic are negligible.
The model for describing the low-frequency motion of the ship on the horizontal plane can be simplified into a three-degree-of-freedom model, and the three-degree-of-freedom 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 vector x ═ x y ψ]TTo illustrate, the vector represents the surge, sway and yaw motions in the hull coordinate system {1 }. The state vector x may be described on a ground-based fixed reference frame { e }.
The forces acting on the vessel are shown in fig. 1, coordinate system XeYeAs a ground coordinate system:
1) the propeller generates thrust. These can be simplified to three (virtual) thrusters located in the Center of Gravity (CG) so that along the longitudinal direction x1Input resultant force fxIn the transverse direction y1Input resultant force fyAnd resultant moment τ in the heading direction is all applied to the center of gravity.
2) Hydrodynamic forces (due to wind and water) F in the longitudinal directionxc、FxwAnd F in the transverse directionyc、Fyw. The strength and direction of wind and water flow are defined on the ground coordinate system { e } and then projected onto the hull coordinate system {1 }.
The mathematical model is as follows:
Figure BDA0001627669730000081
where the equations are obtained by calculating the lateral and longitudinal balance of the forces and the balance of the moments with respect to the z-axis. In (1), fx,fyAnd tau is the input to the model,
Figure BDA0001627669730000082
and
Figure BDA0001627669730000083
respectively surging acceleration and surging acceleration,
Figure BDA0001627669730000084
is the acceleration of the yaw angle,
Figure BDA0001627669730000085
is the yaw rate, M is the mass, J is the moment of inertia, KψIs the centripetal coefficient of the rotary deflection force, bxw(t)，bxc(t)，bywAnd (t) are the time-varying distances between the Center (CG) and the Center Point (CP), respectively, i.e. the points of action of the fluid power. Subscript w represents "wind" and subscript c represents "water flow". VwAnd VcAre vectors representing wind and water flow respectively,
Figure BDA0001627669730000086
and
Figure BDA0001627669730000087
respectively representing the wind and current declination angles relative to the abscissa under the ground coordinate system.
The moment produced by the hydrodynamic force acting longitudinally in {1} is denoted by τx＝bxwFxw+bxcFxcRepresenting the moment produced by hydrodynamic forces acting transversely by τy＝bywFyw+bycFycAnd (4) showing. Since the length of the hull of a small ship is more than three times the width, tauy>>τxWith the centre point lying on the longitudinal axis of the vessel, thus generating bxw(t)＝0,bxc(t)＝0。
byc(t) and byw(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
Figure BDA0001627669730000088
Wherein
Figure BDA0001627669730000091
The hydrodynamic derivative is expressed as
Figure BDA0001627669730000092
Wherein
Figure BDA0001627669730000093
Is the hydrodynamic coefficient, pcAnd ρwDensity of air and water, respectively, and
Figure BDA0001627669730000094
is the fluid/contact surface.
The state space model of three degrees of freedom can be written as follows:
Figure BDA0001627669730000095
wherein
Figure BDA0001627669730000096
Is a vector of the states of the memory cells,
Figure BDA0001627669730000097
is an interference vector, u ═ fxfyτ]TIs the input vector and y is the output vector.
The ship being equipped with two lateral propellers for producing fv1And fv2And two stern thrusters generate fu1And fu2， fu＝fu1+fu2(simultaneous steering by rudder angle)
Figure BDA00016276697300000914
Determination), inertial force (f)x，fyTau) and the actual thrust can beWrite as:
Figure BDA0001627669730000098
finally, 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)
Figure BDA0001627669730000099
where R is a rotation matrix.
Step two, controlling model design
Considering the point of action defined by constant velocity, i.e.
Figure BDA00016276697300000910
That is to say
Figure BDA00016276697300000911
The linear dynamics of the ship are obtained by linearizing a non-linear model (4) taking into account steady-state conditions, correlating three input resultant forces with three output speeds. The final model can be written in compact form as follows
Figure BDA00016276697300000912
Wherein the content of the first and second substances,
Figure BDA00016276697300000913
the matrices A, B, F and C are calculated as follows
Figure BDA0001627669730000101
The input-output model is implemented by applying the laplacian operator to the linearized state space model. δ y (t) can be expressed as
δy(t)＝G(s)δu(t)+H(s)δd(t) (10)
Wherein the content of the first and second substances,
Figure BDA0001627669730000102
Figure BDA0001627669730000103
because the control system is designed to be close to the port at low speed, the rudder angle has little influence on the yawing motion:
1)
Figure BDA0001627669730000104
(transfer function)
Figure BDA0001627669730000105
And
Figure BDA0001627669730000106
negligible);
2) the center point coincides with the center (
Figure BDA0001627669730000107
Negligible);
3)
Figure BDA00016276697300001015
model simplification as shown in fig. 2: wherein KPPAnd KPROPA constant term, com, representing the maximum thrust in the longitudinal and transverse directions, respectivelyiCommand signal, com, representing the actual actuatorx1And comx2Respectively representing command signals, com, of stern thrusterssternAnd combowCommand signals, com, representing two lateral thrusters, respectively, close to the stern and the bowfxFor combining command signals in the longitudinal direction, comfyFor combining command signals in transverse direction, comτFor the heading direction and the command signal,
Figure BDA0001627669730000108
Figure BDA0001627669730000109
and
Figure BDA00016276697300001010
is a first order transfer function.
Figure BDA00016276697300001011
And
Figure BDA00016276697300001012
respectively noise disturbances caused by the wind. δ fx、δfyAnd δ τ are the resultant of the three inputs along the longitudinal, lateral and yaw directions, respectively.
Figure BDA00016276697300001013
And
Figure BDA00016276697300001014
three output speeds, respectively.
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) physical parameters of the model are identified.
Identifying a transfer function associated with longitudinal motion
Figure BDA0001627669730000111
The process of (2) is as follows:
first, the linearized model equation is rewritten as
Figure 223675DEST_PATH_FDA0001680987740000049
Figure BDA0001627669730000113
Is comxAnd
Figure BDA0001627669730000114
the gain of the first amplifier is larger than the gain of the second amplifier,
Figure BDA0001627669730000115
is that
Figure BDA0001627669730000116
And
Figure BDA0001627669730000117
the gain of the first amplifier is larger than the gain of the second amplifier,
Figure BDA0001627669730000118
is the time constant of the surging motion. Second, time constant
Figure BDA00016276697300001118
Is estimated by the output. Third, wind speed and surging speed
Figure BDA0001627669730000119
The gain of the transfer function between is identified from the test that all thrusters were shut down. Finally, the gain of the transfer function between the command of the actuator and the yaw rate is determined by the relative relationship
Figure BDA00016276697300001110
To calculate a minimum cost function of
Figure BDA00016276697300001111
The transfer function describes the dynamic relationship between propeller commands and the speed of the ship. Then, the resultant force and the ship speed are calculated
Figure BDA00016276697300001112
Figure BDA00016276697300001113
The gain in between. Consider, for example, a surging motion. Using the formula
Figure BDA00016276697300001114
The relationship between the gain of the external force and the time constant of the surging motion is
Figure BDA00016276697300001115
Similarly, for a swaying motion, it can be expressed as
Figure BDA00016276697300001116
Since the mass is known, the gain can be transformed by transforming the basic formula into
Figure BDA00016276697300001117
Where a is the distance between the lateral thruster and the centre of gravity.
It is also noted that due to the gain
Figure BDA0001627669730000121
And surge time constant
Figure BDA0001627669730000122
Derivative with respect to fluid dynamics KxcAnd KxwIs linear, so a linear system can be operated under conditions of (A)
Figure BDA0001627669730000123
And
Figure BDA0001627669730000124
) Is defined using the least squares method
Figure BDA0001627669730000125
Similarly, the yaw may also be calculatedHydrodynamic derivative of motion KycAnd Kyw。
Step four, designing a control system
The automatic parking assist system operates in a semi-automatic mode or position maintenance. The control structure is designed to cascade two loops per degree of freedom as shown in fig. 3. The inner velocity loop is dedicated to the semi-autonomous mode, while the positioning mode is implemented by the outer position loop. P*Is a reference input signal for gear control, and P is an output gear control signal. VJOYFor the velocity of the joystick given a signal, VREGA signal is given for the speed of the position regulator. RY(s)、GY(s) and GP(s) is the transfer function.
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 command variables of the control system are the propulsion device and the gear of the lateral propeller. The propulsion device is used to control the surge motion because the ship reaches the maximum speed allowed near the port (3 knots) with gear activation and the side propellers are used to control the roll and yaw motion at low speeds. The control system block diagram is shown in fig. 4. Considering (7), the coordinate transformation block transforms variables to be used from the ground coordinate system to the hull coordinate system; LAT*、LONG*And psi*Reference values for reference positions along the longitudinal direction, the transverse direction and the yawing direction under a ground coordinate system. LAT, LONG, and ψ are actual position values in the longitudinal, lateral, and yaw directions in the ground coordinate system. e.g. of the typeLAT、eLONGAnd eψAre the variables in the longitudinal, transverse and yaw directions under the ground coordinate system. e.g. of the typexlong、eylatAnd eψRespectively the variables along the longitudinal direction, the transverse direction and the yawing direction in the hull coordinate system.
Figure BDA0001627669730000126
Figure BDA0001627669730000131
And
Figure BDA0001627669730000132
reference set values for the velocity in the longitudinal direction, the transverse direction and the heading direction, respectively.
Figure BDA0001627669730000133
And
Figure BDA0001627669730000134
actual values of velocity in the longitudinal direction, the transverse direction and the heading direction, respectively.
Figure BDA0001627669730000135
And
Figure BDA0001627669730000136
is the input signal of the speed regulator. Fx、FyAnd TψThe resultant force and resultant moment output for the speed regulator. compp,suAnd compp,dxControl commands for stern thrusters, com, output for the decouplerPROD,sternAnd comPROD,bowControl commands for two lateral thrusters close to the stern and close to the bow, respectively. comPWM pp,su、comPWM pp,dx、comPWM PROD,sternAnd comPWM PROD,bowThe variable length pulse is output by pulse width modulation to control the on-off and the thrust of the four propellers.
1) The position regulator module is implemented by three proportional regulators that generate reference settings for the inner velocity loop (closed loop bandwidth about 0.001Hz, phase margin about 80 °);
2) the speed regulator module is implemented by three proportional integral regulators which regulate based on the transfer function of the control guidance model, the vessel motion is decoupled (closed loop bandwidth about 0.01Hz, phase margin about 90 °);
3) the separator module converts the output of the speed controller into an instruction of an available actuator;
4) the pulse width modulation module generates pulses of variable length to control the on/off of the propeller and adjust 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.
Figure FDA0003219932760000011
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 directionxInput force f in the transverse directionyAnd 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 waterxc、FxwAnd F in the transverse directionyc、FywThe 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:
Figure FDA0003219932760000012
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), fx,fyAnd tau is the input to the model,
Figure FDA0003219932760000021
and
Figure FDA0003219932760000022
respectively surging acceleration and surging acceleration,
Figure FDA0003219932760000023
is the acceleration of the yaw angle,
Figure FDA0003219932760000024
is the yaw rate, M is the mass, J is the moment of inertia, KψIs the centripetal coefficient of the rotary deflection force, bxw(t)，bxc(t)，byw(t)，byc(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 τx＝bxwFxw+bxcFxcRepresenting the moment produced by hydrodynamic forces acting transversely by τy＝bywFyw+bycFycRepresents; the length of the small-sized ship body is more than three times of the width, tauy＞＞τxWith the centre point lying on the longitudinal axis of the vessel, thus generating bxw(t)＝0,bxc(t)＝0；
byc(t) and byw(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
Figure FDA0003219932760000025
Wherein
Figure FDA0003219932760000026
The hydrodynamic derivative is expressed as
Figure FDA0003219932760000027
Where i ═ { x, y }, j ═ w, c }
Figure FDA0003219932760000028
Is the hydrodynamic coefficient, pcAnd ρwDensity of air and water, respectively, and
Figure FDA0003219932760000029
is a fluid contact surface;
the state space model of three degrees of freedom can be written as follows:
Figure FDA00032199327600000210
wherein
Figure FDA0003219932760000031
Is a vector of the states of the memory cells,
Figure FDA0003219932760000032
is an interference vector, u ═ fxfyτ]TIs the input vector, y is the output vector;
the ship being equipped with two lateral propellers for producing fv1And fv2And two stern thrusters generate fu＝fu1+fu2Is influenced by the rudder angle theta, and the inertial force (f)x，fyτ) versus actual thrust can be written as:
Figure FDA0003219932760000033
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)
Figure FDA0003219932760000034
wherein R is a rotation matrix;
step two, controlling model design
Considering the point of action defined by constant velocity, i.e.
Figure FDA0003219932760000035
That is to say
Figure FDA0003219932760000036
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
Figure FDA0003219932760000037
Wherein the content of the first and second substances,
Figure FDA0003219932760000038
the matrices A, B, F and C are calculated as follows
Figure FDA0003219932760000039
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 content of the first and second substances,
Figure FDA0003219932760000041
Figure FDA0003219932760000042
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)
Figure FDA0003219932760000043
i.e. transfer function
Figure FDA0003219932760000044
And
Figure FDA0003219932760000045
neglect;
2) the centre point coinciding with the centre, i.e.
Figure FDA0003219932760000046
Neglect;
3)θ＝0；
the model is simplified as follows: wherein KPPAnd KPROPA constant term, com, representing the maximum thrust in the longitudinal and transverse directions, respectivelyiRepresenting the actual actuator command signals, and
Figure FDA0003219932760000047
and
Figure FDA0003219932760000048
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
Figure FDA0003219932760000049
The process of (2) is as follows:
the linearized model equation is rewritten as
Figure DEST_PATH_FDA0001680987740000049
Figure FDA00032199327600000411
Is comxAnd
Figure FDA00032199327600000412
the gain of the first amplifier is larger than the gain of the second amplifier,
Figure FDA00032199327600000413
is that
Figure FDA00032199327600000414
And
Figure FDA00032199327600000415
the gain of the first amplifier is larger than the gain of the second amplifier,
Figure FDA00032199327600000416
is the time constant of the surging motion; time constant
Figure FDA00032199327600000417
Estimated by the output; wind speed and surging speed
Figure FDA00032199327600000418
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
Figure FDA0003219932760000051
To calculate a minimum cost function of
Figure FDA0003219932760000052
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
Figure FDA0003219932760000053
A gain in between; considering surging motion, using formulas
Figure FDA0003219932760000054
The relationship between the gain of the external force and the time constant of the surging motion is
Figure FDA0003219932760000055
For a swaying motion, it can be expressed as
Figure FDA0003219932760000056
The quality is known and the gain can be transformed by transforming the basic formula into
Figure FDA0003219932760000057
a is the distance between the lateral thruster and the centre of gravity;
gain of
Figure FDA0003219932760000058
And surge time constant
Figure FDA0003219932760000059
Derivative with respect to fluid dynamics KxcAnd KxwIs linear, using the least squares method under the operating conditions (
Figure FDA00032199327600000510
And
Figure FDA00032199327600000511
) Linear system of lower definition
Figure FDA00032199327600000512
Calculating hydrodynamic derivatives K of the swaying motionycAnd Kyw；
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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