Energy balance based variable-radius bilge keel buoy roll control method and system

Abstract

The present application relates to a kind of energy balance-based variable-radius bilge keel buoy swing control method and system, belong to buoy motion control technical field, including the following steps: S1, the swing angle of buoy is collected in real time, swing angular velocity;S2, according to swing angular velocity, obtain real-time swing kinetic energy;S3, according to the desired motion state of buoy, set target swing kinetic energy;S4, according to the difference between target swing kinetic energy and real-time swing kinetic energy, based on energy balance relationship dynamic solution bilge target radius;S5, if the absolute value of difference is greater than or equal to the preset dead zone threshold, then adjust the current radius of bilge to target radius;If difference or its absolute value is less than the preset dead zone threshold, then maintain the current radius of bilge unchanged.The present application changes system damping by adjusting bilge radius in real time, so that buoy swing kinetic energy always approaches the preset target value, solves the problem that existing fixed-radius bilge cannot adjust buoy motion state according to real-time sea conditions.

Description

Technical Field

[0001] This invention relates to the field of buoy motion control technology, specifically to a method and system for controlling the swaying of a variable radius bilge keel buoy based on energy balance. Background Technology

[0002] When buoys operate at sea, wave action causes them to sway. Bilge keels, due to their simple structure, lack of external power, and ease of maintenance, have been used to control this buoy swaying motion. Currently, most buoy bilge keels use fixed-radius keels, providing a fixed damping torque. The limitations of fixed-radius bilge keels are as follows: at low sea states, the buoy's sway amplitude is small, and the damping provided by the fixed bilge keel is relatively excessive, inhibiting the buoy's necessary movement, which reduces energy capture efficiency for wave energy buoys; at high sea states, the damping provided by the fixed bilge keel is relatively insufficient, unable to effectively suppress large buoy swaying, potentially damaging high-precision instruments. Therefore, fixed-radius bilge keels cannot adapt to real-time changes in sea states.

[0003] Although some retractable bilge keel technologies have been disclosed in the marine industry, such as the Chinese invention patent application CN105438414A entitled "A Bilge Keel" which discloses a clamshell-type opening and closing structure, and the Chinese invention patent application CN106394822A entitled "A Ship Retractable Bilge Keel Device Using Guide Rails" which discloses a retractable structure, they mainly adopt switch-type control, with only two states: deployed and retracted. It is difficult to achieve continuous and fine adjustment of damping, and the control logic depends on the speed, which is not suitable for the working mode of zero-speed anchored buoys.

[0004] Therefore, there is an urgent need for a control method that can continuously and adaptively adjust the bilge keel damping according to the real-time motion state of the buoy, so as to achieve precise control of the swaying motion under different task requirements. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this invention is to provide a variable radius bilge keel buoy sway control method and system based on energy balance. It changes the system damping by adjusting the bilge keel radius in real time, so that the buoy sway kinetic energy always approaches the preset target value, thereby realizing real-time matching between the buoy motion state and the wave input power.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a variable radius bilge keel buoy sway control method based on energy balance, comprising the following steps: S1. Real-time acquisition of the buoy's swing angle and swing angular velocity; S2. Obtain the real-time swaying kinetic energy based on the swaying angular velocity; S3. Set the target sway kinetic energy according to the desired motion state of the buoy; S4. Based on the difference between the target swaying kinetic energy and the real-time swaying kinetic energy, dynamically calculate the target radius of the bilge keel based on the energy balance relationship; S5. If the difference is positive, the current radius of the bilge keel is increased to the target radius to improve damping energy consumption; if the difference is negative, the current radius of the bilge keel is decreased to the target radius to reduce damping energy consumption.

[0007] Preferably, in step S1, if the absolute value of the sway angle exceeds a preset angle threshold or the absolute value of the sway angular velocity exceeds a preset angular velocity threshold, the current radius of the bilge keel is forcibly adjusted to the maximum allowable radius, and the subsequent adjustment actions of the current control cycle are terminated.

[0008] Preferably, in step S2, the formula for calculating the real-time oscillation kinetic energy based on the oscillation angular velocity is as follows: ; in, For real-time swing kinetic energy, Let be the total moment of inertia of the buoy's oscillation. ω represents the angular velocity of the swing.

[0009] Preferably, in step S4, the formula for dynamically calculating the target radius of the bilge keel based on the energy balance relationship is: ; in, For the target diameter of the bilge keel, The current radius of the bilge keel. The difference between the target sway kinetic energy and the real-time sway kinetic energy. The damping coefficient of the bilge keel is... The angular velocity of the swing. The sampling period.

[0010] Preferably, the formula for expressing the damping coefficient of the bilge keel is: ; in, The number of bilge keel segments, The density of seawater, The drag coefficient, The arc length of a single arc segment. The thickness of the bilge keel.

[0011] Preferably, in step S5, a dead zone threshold is set. If the difference is positive and greater than or equal to the dead zone threshold, the current radius of the bilge keel is increased to the target radius to improve damping energy consumption. If the difference is negative and its absolute value is greater than or equal to the dead zone threshold, the current radius of the bilge keel is decreased to the target radius to reduce damping energy consumption. If the difference or its absolute value is less than the dead zone threshold, the current radius of the bilge keel is kept unchanged.

[0012] Preferably, in step S5, the formula for determining the dead zone threshold is: ; in, Dead zone threshold, This is the dead zone coefficient. The kinetic energy of the swing towards the target This is the minimum dead zone width.

[0013] The present invention also provides a variable radius bilge keel buoy sway control system based on energy balance, comprising: Attitude sensor, used to collect the buoy's sway angle and sway angular velocity in real time; The controller is used to obtain the real-time swaying kinetic energy based on the swaying angular velocity, and to calculate the target radius of the bilge keel based on the difference between the preset target swaying kinetic energy and the real-time swaying kinetic energy, according to the energy balance relationship. A variable radius bilge keel actuator is used to receive the adjustment radius command issued by the controller and adjust the current radius of the bilge keel to the target radius.

[0014] Preferably, the controller is configured such that: when the difference is positive, the controller sends an increase radius command to the variable radius bilge keel actuator; when the difference is negative, the controller sends a decrease radius command to the variable radius bilge keel actuator.

[0015] Preferably, the controller is configured to: when the difference is positive and greater than or equal to a preset dead zone threshold, the controller sends an increase radius command to the variable radius bilge keel actuator; when the difference is negative and its absolute value is greater than or equal to the preset dead zone threshold, the controller sends a decrease radius command to the variable radius bilge keel actuator.

[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention collects the buoy's angular velocity in real time, calculates the buoy's real-time angular energy of oscillation, sets a target angular energy of oscillation according to application requirements, and adaptively adjusts the bilge keel radius by comparing the two values. Specifically, if the angular energy is insufficient, the bilge keel retracts to release the motion; if the angular energy is excessive, it extends to suppress the motion. This invention eliminates the need for a wave meter, allows for the traceability of most parameters, reducing calibration reliance, and sets the target motion state according to different application requirements. It has advantages such as all-sea-state adaptability, precise and controllable motion state, fewer calibration parameters, and numerical robustness. It is suitable for various scenarios such as high-precision instrument roll reduction and wave energy buoy motion control, solving the problem that existing fixed-radius bilge keels cannot adjust the buoy's motion state according to real-time sea conditions. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on the drawings described below without creative effort.

[0018] Figure 1 This is a flowchart of an energy balance-based variable radius bilge keel buoy sway control method according to an embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram of the buoy swing motion and control closed loop according to an embodiment of the present invention.

[0020] Figure 3 This is a diagram illustrating the composition of a variable radius bilge keel buoy swaying control system based on energy balance, according to an embodiment of the present invention.

[0021] Figure 4 This is a time-varying curve of the simulated rocking angle in Python, representing an embodiment of the present invention.

[0022] Figure 5 This is a time-varying curve of the bilge keel radius simulated using Python, according to an embodiment of the present invention.

[0023] Figure 6 This is a time-varying curve of the kinetic energy of a rocking motion simulated using Python, according to an embodiment of the present invention.

[0024] Figure 7 This is a time-varying curve of the sway angle in a MATLAB simulation of an embodiment of the present invention.

[0025] Figure 8 This is a MATLAB simulation of the time-varying radius of the bilge keel, according to an embodiment of the present invention.

[0026] Figure 9 This is a time-varying curve of the kinetic energy of a rocking motion, as simulated in MATLAB according to an embodiment of the present invention.

[0027] Reference numerals: 1. Controller, 2. Encoder, 3. Bike keel, 4. Attitude sensor. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. To make the above features and advantages of this invention more apparent and understandable, specific embodiments are provided below with reference to the accompanying drawings for detailed description.

[0029] like Figures 1 to 3 As shown, some embodiments of the present invention provide a method for controlling the swaying of a variable radius bilge keel buoy based on energy balance, comprising the following steps: S1. Real-time acquisition of the buoy's swing angle angular velocity of the swing ; S2, based on the angular velocity of the swing. To obtain real-time swing kinetic energy ; S3. Set the target sway kinetic energy according to the desired motion state of the buoy. ; S4. Based on the target's swing kinetic energy With real-time swing kinetic energy The difference The target radius of the bilge keel is dynamically calculated based on the energy balance relationship. ; S5, if the difference It is a positive value, that is This indicates the real-time swaying kinetic energy. Greater than the target swing kinetic energy This increases the current radius of the bilge keel. To the target radius To improve damping energy dissipation; if the difference It is a negative value, that is This indicates the real-time swaying kinetic energy. Less than the target swing kinetic energy This reduces the current radius of the bilge keel. To the target radius This is to reduce damping energy consumption.

[0030] In one embodiment of the present invention, in step S1, the buoy performs a swaying motion, and the buoy's sway angle is collected and output in real time by an attitude sensor. angular velocity of the swing To protect the buoy, the radial extension radius R of the bilge keel can be set within the range defined by the mechanism. , [Infinitely variable adjustment.] After the attitude sensor collects data, the controller first determines whether the motion exceeds a safety threshold. If the sway angle... absolute value Exceeding the preset angle threshold Or the angular velocity of the oscillation absolute value Exceeding the preset angular velocity threshold ,Right now or Then the current radius of the bilge keel will be forcibly reduced. Adjust to the maximum allowable radius If the current control cycle is terminated, the subsequent adjustment actions will be terminated, meaning that subsequent energy balance control steps will not be executed; otherwise, subsequent steps will continue to be executed.

[0031] In one embodiment of the present invention, in step S2, based on the angular velocity of the swing... To obtain real-time swing kinetic energy The calculation formula is: ; in, For real-time swing kinetic energy, Let be the total moment of inertia of the buoy's oscillation. The angular velocity of the swing is abbreviated as . . Specifically, Moment of inertia of the buoy itself It can be directly given by a 3D model, while the moment of inertia of the attached water... It can be derived from the empirical formula for the moment of inertia of attached water.

[0032] In one embodiment of the present invention, in step S4, the formula for dynamically calculating the target radius of the bilge keel based on the energy balance relationship is as follows: ; in, For the target diameter of the bilge keel, The current radius of the bilge keel. The difference between the target sway kinetic energy and the real-time sway kinetic energy. The sampling period is The damping coefficient of the bilge keel is... ω represents the angular velocity of the swing.

[0033] The specific derivation of the above formula is as follows: First, establish the bilge keel damping model: According to the Morison equation, the force on the bilge keel mainly depends on the drag term, i.e., the drag force. Where u is the fluid velocity. For a bilge keel of radius R, the total damping torque of n arc segments... for: ; in, The total damping moment is abbreviated as: , For drag force, Let be the radius of the bilge keel, and n be the number of bilge keel segments. The density of seawater, The drag coefficient, For bilge keel thickness, The arc length of a single arc segment. ω represents the angular velocity of the swing.

[0034] Define the bilge keel damping coefficient The formula for expressing it is: ; in, The number of bilge keel segments, The density of seawater, The drag coefficient, The arc length of a single arc segment. The thickness of the bilge keel.

[0035] Therefore, the corresponding instantaneous power dissipation of the bilge keel for: ; in, For the instantaneous power dissipation of the bilge keel, For the total damping torque, The damping coefficient of the bilge keel is... For the bilge keel radius, ω represents the angular velocity of the swing.

[0036] Then, the energy balance solution for the bilge keel radius: To control the buoy's motion, the target sway kinetic energy is first set according to the desired motion state. , representing the desired intensity of the buoy's swaying motion. The difference between the real-time swaying kinetic energy and the target swaying kinetic energy is defined as: ; in, The difference is abbreviated as , For real-time swing kinetic energy, The kinetic energy of the swing towards the target.

[0037] Let the average power change required to compensate for the kinetic energy difference within one sampling period be... Therefore, the control law is: ; Solving for: ; in, For the target diameter of the bilge keel, The current radius of the bilge keel. The difference between the target sway kinetic energy and the real-time sway kinetic energy. The damping coefficient of the bilge keel is... The angular velocity of the swing. The sampling period.

[0038] when At that time, in the above control law When the radius approaches infinity, the controller does not perform radius adjustment and maintains the current radius. No change. The significance of this approach is clear: near the point of reversal in the sway, the damping torque itself approaches zero, and the direct impact of the adjustment radius on the instantaneous kinetic energy is negligible. Adjustment can be made again after the angular velocity recovers to the effective range.

[0039] In another embodiment of the present invention, to avoid frequent fine-tuning of the radius near the target value, a dead zone threshold is set in step S5. Dead zone threshold The formula for determining it is: ; in, Dead zone threshold, This is the dead zone coefficient. The kinetic energy of the swing towards the target This is the minimum dead zone width.

[0040] If the difference It is a positive value and is greater than or equal to the dead zone threshold. ,Right now Then increase the current radius of the bilge keel to the target radius. To improve damping energy dissipation; if the difference It is a negative value and its absolute value is greater than or equal to the dead zone threshold. ,Right now Then reduce the current radius of the bilge keel to the target radius. To reduce damping energy consumption; if the difference Or its absolute value is less than the dead zone threshold ,Right now or This indicates that the real-time swaying kinetic energy is within the allowable range near the target value, therefore the current radius of the bilge keel should be maintained. No change; radius adjustment will not be performed.

[0041] like Figures 1 to 3 As shown, some embodiments of the present invention also provide a variable radius bilge keel buoy swaying control system based on energy balance, comprising: Attitude sensor 4 is used to collect the buoy's sway angle in real time. angular velocity of the swing ; Controller 1, used to determine the angular velocity of the swing. Obtain real-time swing kinetic energy And according to the preset target swing kinetic energy With real-time swing kinetic energy The difference The target radius of the bilge keel was calculated based on the energy balance relationship. ; The variable radius bilge keel actuator is used to receive the radius adjustment command issued by the controller 1 and adjust the current radius of the bilge keel 3. Adjust to target radius .

[0042] The variable radius bilge keel actuator can employ an electric chuck structure, converting the motor's rotational motion into the radial motion of the chuck's jaws via a helical groove. The jaws then drive the bilge keel 3 to extend and retract, thereby changing the radius of the bilge keel 3. The motor is equipped with an encoder 2, which measures the current radius of the bilge keel 3. Of course, in other embodiments, the variable radius bilge keel actuator can also be a telescopic drive mechanism such as a cylinder, an electric cylinder, or an electric ball screw mechanism.

[0043] In one embodiment of the present invention, controller 1 is configured such that: when the difference It is a positive value, that is Then controller 1 sends an increase radius command to the variable radius bilge keel actuator; when the difference It is a negative value, that is Then controller 1 sends a radius reduction command to the variable radius bilge keel actuator.

[0044] In another embodiment of the present invention, controller 1 is configured such that: when the difference It is a positive value and is greater than or equal to the preset dead zone threshold. Then controller 1 sends an increase radius command to the variable radius bilge keel actuator; when the difference It is a negative value and its absolute value is greater than or equal to the preset dead zone threshold. Then controller 1 sends a radius reduction command to the variable radius bilge keel actuator.

[0045] This invention proposes to collect the buoy's oscillation angular velocity in real time, calculate the buoy's real-time oscillation kinetic energy, set a target oscillation kinetic energy according to application requirements, and adaptively adjust the bilge keel radius by comparing the two values. Specifically, if the oscillation kinetic energy is insufficient, the bilge keel retracts to release the motion; if the oscillation kinetic energy is excessive, the bilge keel extends to suppress the motion. This invention eliminates the need for a wave meter, allows for the traceability of most parameters to reduce calibration dependence, and sets the target motion state according to different application requirements. It is suitable for various scenarios such as high-precision instrument oscillation reduction and wave energy buoy motion control.

[0046] Experimental example: Taking a certain type of mooring buoy as an example, the parameter configuration is shown in Table 1: Table 1

[0047]

[0048] In this experimental example, the drag coefficient The damping coefficient is calculated using the Ikeda empirical formula. The formula it defines is used for real-time dynamic calculation: ; ; ; Solving for: ; in, For the swing angle The abbreviation of .

[0049] Simulation verification: To verify the numerical stability and tool independence of this invention, simulations were performed using two independent tools, Python (RK4 solver) and MATLAB (explicit Euler method), under the same parameter conditions.

[0050] Simulation conditions: Significant wave height Wave spectrum peak period Simulation duration Sampling period .

[0051] The simulation results are shown in Table 2.

[0052] Table 2

[0053]

[0054] Figures 4 to 6 The Python simulation results are shown: the yaw angle is... Fluctuating within a certain range, affected by the mechanical structure, the bilge keel radius is within and The radius continuously changes between values, exhibiting numerous intermediate values, thus verifying the continuous adjustment capability of the radius. The oscillating kinetic energy fluctuates around the target value, rapidly returning when it deviates from the target value, verifying the effectiveness of the control method of this invention. Figures 7 to 9 The results of the MATLAB simulation are shown, and they are consistent with those of the Python simulation.

[0055] The advantages of this invention are: (1) All sea state adaptive: Automatically adjusts the bilge keel radius according to real-time sway kinetic energy feedback to adapt to any sea state; (2) Precise and controllable motion state: By setting different target sway kinetic energies, the motion state of the buoy can be made closer to the desired value, which is suitable for various scenarios such as high-precision instrument platform sway reduction and wave energy acquisition motion control; (3) Fewer calibration parameters: The control parameters can be obtained directly from physical constants, design drawings and other relevant literature, which can greatly reduce the dependence on calibration; (4) Numerical robustness: The control law is based on the physical derivation of energy balance and Morison equation, and is verified by simulation using two independent tools, Python and MATLAB, and different solvers. It has numerical stability and tool independence.

[0056] This invention is applicable to application scenarios that require active adjustment of the intensity of buoy swaying according to different sea conditions and mission requirements, such as motion state control of wave energy buoys.

[0057] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0058] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0059] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for controlling the swaying of a variable radius bilge keel buoy based on energy balance, characterized in that, Includes the following steps: S1. Real-time acquisition of the buoy's swing angle and swing angular velocity; S2. Obtain the real-time swaying kinetic energy based on the swaying angular velocity; S3. Set the target sway kinetic energy according to the desired motion state of the buoy; S4. Based on the difference between the target swaying kinetic energy and the real-time swaying kinetic energy, dynamically calculate the target radius of the bilge keel based on the energy balance relationship; S5. If the difference is positive, the current radius of the bilge keel is increased to the target radius to improve damping energy consumption; if the difference is negative, the current radius of the bilge keel is decreased to the target radius to reduce damping energy consumption.

2. The method for controlling the oscillation of a variable radius bilge keel buoy based on energy balance according to claim 1, characterized in that, In step S1, if the absolute value of the sway angle exceeds a preset angle threshold or the absolute value of the sway angular velocity exceeds a preset angular velocity threshold, the current radius of the bilge keel is forcibly adjusted to the maximum allowable radius, and the subsequent adjustment actions of the current control cycle are terminated.

3. The method for controlling the oscillation of a variable radius bilge keel buoy based on energy balance according to claim 1, characterized in that, In step S2, the formula for calculating the real-time oscillation kinetic energy based on the oscillation angular velocity is as follows: ； in, For real-time swing kinetic energy, Let be the total moment of inertia of the buoy's oscillation. ω represents the angular velocity of the swing.

4. The method for controlling the oscillation of a variable radius bilge keel buoy based on energy balance according to claim 1, characterized in that, In step S4, the formula for dynamically calculating the target radius of the bilge keel based on the energy balance relationship is as follows: ； in, For the target diameter of the bilge keel, The current radius of the bilge keel. The difference between the target sway kinetic energy and the real-time sway kinetic energy. The damping coefficient of the bilge keel is... The angular velocity of the swing. The sampling period.

5. The method for controlling the oscillation of a variable radius bilge keel buoy based on energy balance according to claim 4, characterized in that, The formula for expressing the damping coefficient of the bilge keel is: ； in, The number of bilge keel segments, The density of seawater, The drag coefficient, The arc length of a single arc segment. The thickness of the bilge keel.

6. The method for controlling the oscillation of a variable radius bilge keel buoy based on energy balance according to claim 1, characterized in that, In step S5, a dead zone threshold is set. If the difference is positive and greater than or equal to the dead zone threshold, the current radius of the bilge keel is increased to the target radius to improve damping energy consumption. If the difference is negative and its absolute value is greater than or equal to the dead zone threshold, the current radius of the bilge keel is decreased to the target radius to reduce damping energy consumption. If the difference or its absolute value is less than the dead zone threshold, the current radius of the bilge keel is kept unchanged.

7. The method for controlling the oscillation of a variable radius bilge keel buoy based on energy balance according to claim 6, characterized in that, In step S5, the formula for determining the dead zone threshold is: ； in, Dead zone threshold, This is the dead zone coefficient. The kinetic energy of the swing towards the target This is the minimum dead zone width.

8. A variable radius bilge keel buoy sway control system based on energy balance, used to implement the variable radius bilge keel buoy sway control method based on energy balance as described in any one of claims 1 to 7, characterized in that, include: Attitude sensor, used to collect the buoy's sway angle and sway angular velocity in real time; The controller is used to obtain the real-time swaying kinetic energy based on the swaying angular velocity, and to calculate the target radius of the bilge keel based on the difference between the preset target swaying kinetic energy and the real-time swaying kinetic energy, according to the energy balance relationship. A variable radius bilge keel actuator is used to receive the adjustment radius command issued by the controller and adjust the current radius of the bilge keel to the target radius.

9. A variable radius bilge keel buoy swaying control system based on energy balance according to claim 8, characterized in that, The controller is configured such that when the difference is positive, the controller sends an increase radius command to the variable radius bilge keel actuator; when the difference is negative, the controller sends a decrease radius command to the variable radius bilge keel actuator.

10. A variable radius bilge keel buoy swaying control system based on energy balance according to claim 9, characterized in that, The controller is configured such that: when the difference is positive and greater than or equal to a preset dead zone threshold, the controller sends an increase radius command to the variable radius bilge keel actuator; when the difference is negative and its absolute value is greater than or equal to the preset dead zone threshold, the controller sends a decrease radius command to the variable radius bilge keel actuator.

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