CN110333658B - An underactuated ship heading control method with input constraints and drift angle compensation - Google Patents

Abstract

The invention proposes an underactuated ship heading control method with input constraints and drift angle compensation. Based on the backstepping control algorithm, the hyperbolic tangent function is introduced to convert the discontinuous input saturation function into a continuous function, and the bow is adjusted by the adaptive law. The external disturbance in the yaw direction is estimated, and the proposed heading control algorithm can make the underactuated ship sail along the set heading while maintaining a small control input torque, and the motion control performance is greatly improved.

Description

An underactuated ship heading control method with input constraints and drift angle compensation

technical field

The invention relates to the field of ship control, in particular to an underactuated ship course control method with input constraints and drift angle compensation.

Background technique

With the increasing density of maritime traffic, the problem of how to better realize the ship heading control has attracted more and more scholars' attention. Most conventional ships in real life are usually underactuated systems, that is, only one control input controls motion in both yaw and yaw directions. The existence of drift angle is usually ignored in heading control, but the actual drift angle is not zero, which will make the ship's actual motion direction and the expected heading different by a drift angle. If no correction is made, the heading control performance will be reduced. Input saturation is a common phenomenon in the actual control system. Any actuator has a certain executable range. Once the input exceeds the limit value, it will affect the operation of the actuator, resulting in reduced system performance, affecting the control effect, and long-term Maintaining an excessively large control input also increases rudder losses.

SUMMARY OF THE INVENTION

The present invention proposes an underactuated ship course controller with input constraints and drift angle compensation. Based on the backstep control algorithm, the hyperbolic tangent function is introduced to convert the discontinuous input saturation function into a continuous function, and the bow is controlled by the adaptive law. The external disturbance in the yaw direction is estimated, and the proposed heading control algorithm can make the underactuated ship sail along the set heading while maintaining a small control input torque, and the motion control performance is greatly improved.

It mainly includes the following steps:

Step 1. Establish a mathematical model of the ship;

The motions in the heave, roll and pitch directions are ignored, and the dynamic model of the underactuated ship with two degrees of freedom in the yaw and yaw directions can be summarized as follows:

是实际的控制输入，

是饱和执行器的输出，τ_M为控制输入约束的界值。where _{r is the yaw frequency, ur and v r are} the relative surge and sway speeds of the ship relative to the hull coordinate system; ψ represents the actual heading angle of the ship, for _i =11, 22, 33, the parameter mi represents the ship system inertia, d _i is the hydrodynamic damping in yaw, surge and sway, ω _r and ω _v are external disturbances with unknown bounds in the yaw and sway directions, respectively;

is the actual control input,

is the output of the saturated actuator, and τ _M is the boundary value of the control input constraint.

Step 2. Introduce the hyperbolic tangent function to convert the control input saturation constraint into a continuous function;

来近似饱和函数的非线性部分，如下所示Introduce the hyperbolic tangent function

to approximate the nonlinear part of the saturation function as follows

定义为两部分，即So will

is defined in two parts, namely

为逼近误差，假设其有界，则式(1)可以改写如下：in

In order to approximate the error, assuming that it is bounded, equation (1) can be rewritten as follows:

有界，所以假设Δ≤σ，定义

为σ的估计值，其估计误差为

c为正常数，φ为辅助信号。in

is bounded, so assuming Δ≤σ, the definition

is the estimated value of σ, and its estimated error is

c is a positive number, and φ is an auxiliary signal.

Step 3, issue the desired heading command, that is, set the desired heading angle ψ _d ;

Step 4. Consider the influence of the current on the drift angle, calculate the drift angle β, and use the drift angle to compensate the desired heading angle ψ _d ;

where ur and v _r are the actual sway and _surge velocities of the ship relative to the hull coordinate system, respectively, and v _c and β _c are the wave velocity and azimuth angle relative to the geodetic coordinate system, which can be obtained by combining the above formulas

ψ _da = ψ _d -β (7)

Step 5. Design the heading control algorithm;

Combine step 4 to introduce new variables for state transition

z ₁ =∫ψdt- _∫ψda dt (8)

z ₂ =ψ-ψ _da -α ₁ (9)

z ₃ =r-α ₂ (10)

where z _i , i=1, 2, 3, 4 are auxiliary variables, and α _i , i=1, 2, 3 represent the virtual stabilization function, as follows

α ₁ =-k ₁ z ₁ (12)

Wherein the constants k ₁ >0, k ₂ >0, k ₃ >0, υ >0;

为Design Adaptive Law

for

where the constant γ _f >0;

Then the auxiliary signal φ is

where the constant k ₄ >0.

Step 6. The control system executes the instruction, updates the heading angle ψ, the yaw angle frequency r and the sway speed v _r in real time, and goes to step 4 .

This method has the following effects and advantages:

By introducing the hyperbolic tangent function to approximate the control input saturation constraint, it satisfies the requirement that all functions can be derivable in the design of the backstepping method, and combines the adaptive law to estimate the disturbance in the yaw direction. The method of the method of heading control makes the system reach a stable state in a short time, the heading output error is greatly reduced, and at the same time, the control input torque is kept small, and the control performance is effectively improved.

Description of drawings

Figure 1 is a schematic diagram of the course control of the ship's uncompensated drift angle

FIG. 2 is a schematic diagram of the heading control after the drift angle compensation of the present invention

Detailed ways

The present invention proposes an underactuated ship heading control method with input constraints and drift angle compensation. The hyperbolic tangent function is introduced to convert the discontinuous input saturation function into a continuous function, and the adaptive law is used to control the external disturbance in the yaw direction. Estimated, combined with backstepping to design a complete heading controller, including the following steps:

Step 1. Establish a mathematical model of the ship;

The motions in the heave, roll and pitch directions are ignored, and the dynamic model of the underactuated ship with two degrees of freedom in the yaw and yaw directions can be summarized as follows:

是实际的控制输入，

是饱和执行器的输出，τ_M为控制输入约束的界值。where _{r is the yaw frequency, ur and v r are} the relative surge and sway speeds of the ship relative to the hull coordinate system; ψ represents the actual heading angle of the ship, for _i =11, 22, 33, the parameter mi represents the ship system inertia, d _i is the hydrodynamic damping in yaw, surge and sway, ω _r and ω _v are external disturbances with unknown bounds in the yaw and sway directions, respectively;

is the actual control input,

is the output of the saturated actuator, and τ _M is the boundary value of the control input constraint.

Step 2. Introduce the hyperbolic tangent function to convert the control input saturation constraint into a continuous function;

来近似饱和函数的非线性部分，如下所示Introduce the hyperbolic tangent function

to approximate the nonlinear part of the saturation function as follows

定义为两部分，即So will

is defined in two parts, namely

为逼近误差，假设其有界，则式(1)可以改写如下：in

In order to approximate the error, assuming that it is bounded, equation (1) can be rewritten as follows:

有界，所以假设Δ≤σ，定义

为σ的估计值，其估计误差为

c为正常数，φ为辅助信号。in

is bounded, so assuming Δ≤σ, the definition

is the estimated value of σ, and its estimated error is

c is a positive number, and φ is an auxiliary signal.

Step 3, issue the desired heading command, that is, set the desired heading angle ψ _d ;

Step 4. Consider the influence of the current on the drift angle, calculate the drift angle β, and use the drift angle to compensate the desired heading angle ψ _d ;

where ur and v _r are the actual sway and _surge velocities of the ship relative to the hull coordinate system, respectively, and v _c and β _c are the current velocity and azimuth angle relative to the geodetic coordinate system, which can be obtained by combining the above formulas

ψ _da = ψ _d -β (7)

Step 5. Design the heading control algorithm;

Combine step 4 to introduce new variables for state transition

z ₁ =∫ψdt- _∫ψda dt (8)

z ₂ =ψ-ψ _da -α ₁ (9)

z ₃ =r-α ₂ (10)

where z _i , i=1, 2, 3, 4 are auxiliary variables, and α _i , i=1, 2, 3 represent virtual stabilization functions, as follows

α ₁ =-k ₁ z ₁ (12)

Wherein the constants k ₁ >0, k ₂ >0, k ₃ >0, υ >0;

为Design Adaptive Law

for

where the constant γ _f >0;

Then the auxiliary signal φ is

where the constant k ₄ >0.

Step 6. The control system executes the instruction, updates the heading angle ψ, the yaw angle frequency r and the sway speed v _r in real time, and goes to step 4 .

Claims (1)

1. an underactuated ship heading control method with input constraint and drift angle compensation, is characterized in that: Step 1. Establish a mathematical model of the ship; The motions in the heave, roll and pitch directions are ignored, and the dynamic model of the underactuated ship with two degrees of freedom in the yaw and yaw directions can be summarized as follows:

where _{r is the yaw frequency, ur and v r are} the relative surge and sway speeds of the ship relative to the hull coordinate system; ψ represents the actual heading angle of the ship, for _i =11, 22, 33, the parameter mi represents the ship system inertia, d _i is the hydrodynamic damping in yaw, surge and sway, ω _r and ω _v are external disturbances with unknown bounds in the yaw and sway directions, respectively;

is the actual control input,

is the output of the saturated actuator, and τ _M is the boundary value of the control input constraint; Step 2. Introduce the hyperbolic tangent function to convert the control input saturation constraint into a continuous function; Hyperbolic tangent function

to approximate the nonlinear part of the saturation function as follows

So will

is defined in two parts, namely

in

In order to approximate the error, assuming that it is bounded, equation (1) can be rewritten as follows:

in

is bounded, so assuming Δ≤σ, the definition

is the estimated value of σ, and its estimated error is

c is a positive number, φ is an auxiliary signal; Step 3, issue the desired heading command, that is, set the desired heading angle ψ _d ; Step 4. Consider the influence of the current on the drift angle, calculate the drift angle β, and use the drift angle to compensate the desired heading angle ψ _d ;

where u and v are the actual surge and sway velocities of the ship relative to the hull coordinate system, respectively, and v _c and β _c are the wave velocity and azimuth angle relative to the geodetic coordinate system, which can be obtained by combining the above formulas ψ _da = ψ _d -β (7) Step 5. Design the heading control algorithm; Combine step 4 to introduce new variables for state transition z ₁ =∫ψdt- _∫ψda dt (8) z ₂ =ψ-ψ _da -α ₁ (9) z ₃ =r-α ₂ (10)

where z _i , i=1, 2, 3, 4 are auxiliary variables, and α _i , i=1, 2, 3 represent virtual stabilization functions, as follows α ₁ =-k ₁ z ₁ (12)

Wherein the constants k ₁ >0, k ₂ >0, k ₃ >0, υ >0; Design Adaptive Law

for

where the constant γ _f >0; Then the auxiliary signal φ is

where the constant k ₄ >0; Step 6. The control system executes the instruction, updates the heading angle ψ, the yaw angle frequency r and the sway speed v _r in real time, and goes to step 4 .

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