An optimal control method for two pairs of controllable stabilizing fins

Abstract

The application discloses an optimal control method for two pairs of controllable stabilizing fins, and relates to the field of marine electromechanical auxiliary equipment.The method takes the rolling, pitching and heaving motion of a ship as input signals, and is used for multi-target control of two pairs of controllable stabilizing fins.The ship is a ship comprising two pairs of controllable stabilizing fins.The method comprises the following steps: a ship-mounted fin angle control system of the ship is inputted with the difference between the expected values of the heaving distance, the pitching angle and the rolling angle of the ship and the real-time detected heaving distance, the pitching angle and the rolling angle of the ship by a sensor, a control signal w is calculated according to the difference, the control signal w is optimized, and then the control signal w is outputted to the two pairs of controllable stabilizing fins.The two pairs of controllable stabilizing fins are adjusted through optimal fin angle control parameters K contained in the control signal w, so as to reduce the oscillation amplitude of the ship sailing.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of marine electromechanical auxiliary equipment, in particular to an optimal control method for two pairs of controllable stabilizing fins. BACKGROUND

[0002] Due to the unique lines and structure of the small waterplane ship, there is a longitudinal MUNK overturning moment at different speeds, which increases with the increase of the trim angle and changes with the speed oscillation, that is, the bow is buried at low speed and the bow is lifted at high speed; and the length of the ship body of the small waterplane ship is relatively short, and the bottom is designed as a flat bottom, so its stability is relatively poor, which is not conducive to sailing in large waves and wind waves, in addition, the speed of the small waterplane ship is generally fast, and high steering ability is required for flexible steering at high speed.

[0003] In order to improve its stability, the present application designs an optimal control algorithm for two pairs of controllable stabilizing fins of the small waterplane ship, so that the lateral stability and longitudinal stability of the ship body can be improved. For different sailing conditions, the position and angle of the stabilizing fins can be adjusted to realize the stability control of the ship body, so as to better adapt to complex marine environment and maritime task requirements. In addition, the use of two pairs of controllable stabilizing fins can realize the lateral and longitudinal control of the ship body, so as to realize the precise steering and steering of the ship body. SUMMARY

[0004] The purpose of the present application is to provide an optimal control method which can realize lateral and longitudinal control of the ship body by using two pairs of controllable stabilizing fins.

[0005] The technical solution of the present application is to provide an optimal control method for two pairs of controllable stabilizing fins, which is a multi-input multi-output control method suitable for the following kinematic control equation, taking the roll, pitch and heave motion of the ship including two pairs of controllable stabilizing fins as input signals for controlling the two pairs of controllable stabilizing fins, the method comprises:

[0006] The kinematic control equation of the ship is constructed, which is represented as:

[0007]

[0008] Where the state variable X = [x1 x2 x3 x4 x5 x6] matrix elements represent heave velocity, heave distance, pitch angular velocity, pitch angle, roll angular velocity and roll angle in turn, the control input u = [u1 u2 u3 u4] represents the fin angle of the four fins, Y represents the output variable of the system; A, B, C, D are the coefficient matrices of the state space model;

[0009] The ship includes a fin angle control system. The ship inputs the expected values ​​of the ship's heave distance, pitch angle and roll angle into the fin angle control system. The fin angle control system subtracts the expected values ​​from the current heave distance, pitch angle and roll angle detected by the sensor in real time, and calculates a control signal w based on the difference. The control signal w includes the optimal fin angle control parameter K. Optimizing it means satisfying the minimum performance index function J: J = ∑(X n 2 +u n 2 )Δt, the subscript n represents the nth sampling moment, and Δt is the sampling step size;

[0010] The minimization condition of the performance index function J is:

[0011] (A-BK) T P+P(A-BK)=-(Q+K T RK);

[0012] Where P is a real symmetric matrix, Q is the state weight matrix, R is the control input weight matrix, and the superscript T indicates matrix transpose;

[0013] After obtaining the optimal fin angle control parameter K through the above formula, the control signal w is obtained based on the optimal fin angle control parameter K. The control signal w is output to two pairs of controllable stabilizing fins. The two pairs of controllable stabilizing fins adjust themselves according to the optimal fin angle control parameter K to reduce the oscillation amplitude of the ship's navigation.

[0014] In any of the above technical solutions, further, in J=∑(X n 2 +u n 2 )Δt, and considering the infinite time regulator, the above formula is derived as follows:

[0015]

[0016] Using the optimal fin angle control parameter K and the state quantity X, the above formula can be expressed as:

[0017] In any of the above technical solutions, further, the method further includes: obtaining The original function:

[0018]

[0019] Since P is a real symmetric matrix, the above formula needs to satisfy:

[0020] (A-BK) T P+P(A-BK)=-(Q+KT RK);

[0021] The above formula is taken as a minimum condition of the performance index function J.

[0022] In any of the technical solutions above, further, the state weighting matrix Q and the control input weighting matrix R have the following values:

[0023]

[0024] In any of the technical solutions above, further, the real symmetric matrix P and the state weighting matrix Q satisfy the following relationship:

[0025] A T P+PA=-Q;

[0026] After the value of the state weighting matrix Q is obtained, the value of the real symmetric matrix P can be obtained.

[0027] In any of the technical solutions above, further, the mathematical model of the three-degree-of-freedom motion of the ship under the action of the fin angle force F fin is:

[0028]

[0029] From top to bottom, the modes of heave, pitch and roll are represented; wherein M is the displacement of the ship, I5 is the moment of inertia of the ship's center of gravity about the y-axis, I2 is the moment of inertia of the ship's center of gravity about the x-axis, F3 represents the heave disturbing moment of the ship, F5 represents the pitch disturbing moment of the ship, f2 represents the roll disturbing moment of the ship, ξ3 represents the heave displacement of the ship, ξ5 represents the pitch displacement of the ship, and ξ2 represents the roll displacement of the ship; by solving the parameters of the above mathematical model of the small waterplane area catamaran through the slice method, the added mass coefficient A ik , the damping coefficient B ik and the restoring force coefficient C ik of the ship motion can be obtained, wherein the subscript 3 represents the heave direction, the subscript 5 represents the pitch direction, and the subscript 2 represents the roll direction.

[0030] In any of the technical solutions above, further, the mathematical model of the three-degree-of-freedom motion of the ship under the action of the fin angle force F fin is written as a state space model and represented as:

[0031]

[0032] wherein:

[0033]

[0034] The state space model is multiplied by Z -1Then:

[0035]

[0036] Let A = Z -1 N, B = Z -1 H, then:

[0037]

[0038] Z is a quality parameter matrix, N is a kinematics parameter matrix, ξ is a motion state vector, the matrix H represents the matrix form of the force and torque generated by each pair of fins, the matrix elements in α = [α1α2α3α4] represent the front left, front right, rear left, and rear right fin angles in turn; the matrix elements in F = [F3F5F2] represent the wave disturbance force, the heave force moment, the pitch force moment, and the roll force moment that the ship receives in turn.

[0039] In any of the above technical solutions, further, the value of the control input u = [u1u2u3u4] is α = [α1α2α3α4].

[0040] The beneficial effects of the present application are:

[0041] The technical solution in the present application is a typical multiple-input multiple-output control, which overcomes the defects of previous anti-rolling fins that can only control single degree of freedom and single output, and can control the front and rear four fins with ship roll, pitch, and heave motion as input signals; in the process of obtaining control parameters, the controlled quantity is guaranteed to reach the balance point, and the system input consumption is minimized, which also meets the minimum performance index function, realizes the optimal control of the front and rear four fins, and greatly enhances the stability of the ship. BRIEF DESCRIPTION OF DRAWINGS

[0042] The above and additional aspects of the present application will become apparent and easy to understand from the following description of the embodiments, in conjunction with the accompanying drawings, in which:

[0043] Figure 1 is a schematic flowchart of an optimal control method for two pairs of controllable stabilizing fins according to an embodiment of the present application;

[0044] Figure 2 is a simulation result graph of an optimal control method for two pairs of controllable stabilizing fins according to an embodiment of the present application. DETAILED DESCRIPTION

[0045] In order to more clearly understand the above-mentioned purposes, features and advantages of the present application, the present application will be further described in detail below in conjunction with the drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0046] In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one skilled in the art that the present application can be practiced without the specific details set forth in this description. In other instances, well-known methods have not been described in detail in order to avoid obscuring the present application.

[0047] The motion mathematical model based on the coupling of the heave and pitch motion of the ship is:

[0048]

[0049] The first line of the formula represents the heave motion mode of the ship, and the second line of the formula represents the pitch motion mode of the ship; wherein M is the displacement of the ship, I5 is the moment of inertia of the ship's center of gravity about the y-axis, F3 represents the heave interference force moment of the ship, F5 represents the pitch interference force moment of the ship, ξ3 represents the heave displacement of the ship, and ξ5 represents the pitch displacement of the ship; by solving the parameters of the above motion mathematical model of the small waterplane area catamaran by the slice method, the added mass coefficient A ik , the damping coefficient B ik and the restoring force coefficient C ik of the ship motion can be obtained, i and k in the formula can be 3 or 5, 3 represents the heave direction, and 5 represents the pitch direction, for example, A 33 represents the heave added mass coefficient, B 35 represents the pitch damping coefficient in the heave direction.

[0050] The ship includes two pairs of controllable stabilizing fins, and the ship's roll and pitch deep motion do not affect each other, so the mathematical model of the three degrees of freedom motion of the ship under the action of the fin angle force F fin is:

[0051]

[0052] From top to bottom, the heave, pitch and roll motion modes are represented; wherein I2 is the moment of inertia of the ship's center of gravity about the x-axis, A 22 is the roll added mass coefficient, B 22 is the roll damping coefficient, C 22 is the roll restoring coefficient, and ξ2 represents the roll displacement of the ship, and F2 represents the interference roll force moment of the ship.

[0053] The above model is written as a state space model, which is:

[0054]

[0055] Wherein:

[0056]

[0057]

[0058] Multiply both sides of the state space model by Z -1 Then:

[0059]

[0060] Let A = Z -1 N, B = Z -1 H, then:

[0061]

[0062] Z is the mass parameter matrix, N is the kinematics parameter matrix, ξ is the motion state vector, the matrix H represents the matrix form of the force and moment generated by each pair of fins, and α = [α1α2α3α4] matrix elements represent the front left, front right, rear left, and rear right fin angles in turn. F = [F3F5F2] matrix elements represent the wave disturbance forces, heave force, pitch moment, and roll moment received by the ship in turn. As can be seen from the above formula, the model is a typical full state space equation disturbed by external sea waves.

[0063] The kinematics control equation of the ship is constructed, which is represented as:

[0064]

[0065] Wherein the matrix elements in the state variable X = [x1x2x3x4x5x6] represent the heave velocity, heave distance, pitch angular velocity, pitch angle, roll angular velocity, and roll angle in turn, the control input u = [u1u2u3u4] represents the fin angles of the four fins, let the value of the control input u = [u1u2u3u4] be α = [α1α2α3α4], Y represents the output variable of the system; A, B, C, and D are the coefficient matrices of the state space model, which are specifically represented as follows:

[0066] A is the state transition matrix, which describes the dynamic evolution relationship of the system state variables; B is the input matrix, which describes the influence of external input on the system state variables; C is the output matrix, which describes the relationship between the system state variables and the output variables; D is the direct transfer matrix, which describes the influence of external input directly on the output variables.

[0067] The embodiment provides an optimal control method for two pairs of controllable stabilization fins. The method is a multi-input multi-output control method suitable for the above model. Unlike the single degree of freedom and single output control of the roll damping fin in the past, the two pairs of stabilization fin control technology is a multi-objective control of the front and rear four fins taking the ship roll, pitch, and heave motion as input signals. It is a typical multi-input multi-output control and belongs to the difficulty in the control field, as shown in Figure 1 The method comprises the following steps.

[0068] The ship general control inputs the expected value of the ship heave distance, the pitch angle and the roll angle to the fin angle control system, and the difference between the expected value and the real-time detected ship heave distance, pitch angle and roll angle is input to the controller, the controller calculates and outputs the control signal w to the two pairs of controllable stabilizing fins, the two pairs of controllable stabilizing fins are adjusted through the optimal fin angle control parameter K contained in the control signal w, and the oscillation amplitude of the ship sailing is reduced.

[0069] The application is based on the establishment of an optimal control strategy under a state space model, and the optimal control is a linear quadratic integral problem. For a model controlled by a controller, the linear quadratic optimal control design is to design an optimized dynamic controller based on state space technology, and the objective function is a quadratic function of the state and the control input.

[0070] For the state quantity X=[x1 x2 x3 x4 x5 x6] and the control input u=[u1 u2 u3 u4], the control purpose should make the controlled quantity reach the balance point, and the system input consumption is minimized, which can be described as requiring to satisfy the performance index function J minimum in a period of time: J=∑(X n 2 +u n 2 )Δt, the subscript n represents the n th sampling time, and Δt is the sampling step.

[0071] In actual control, only some state quantities and input quantities are generally concerned, and the state weighting matrix Q and the control input weighting matrix R are usually added, and an infinite time regulator is considered, that is, the following formula is required to be minimum:

[0072]

[0073] In the application, the upper subscript T represents the matrix transpose, the control signal w contains the optimal fin angle control parameter K, and the above formula is expressed by using the optimal fin angle control parameter K and the state quantity X:

[0074] The original function of the integral is found:

[0075] Where P is a real symmetric matrix, and needs to satisfy:

[0076] (A-BK) T P+P(A-BK)=-(Q+K T RK);

[0077] Since the control target does not concern the heave velocity, the pitch angle velocity and the roll angle velocity, the corresponding positions of the state weighting matrix Q are Q 22 , Q 33 , Q 55The values ​​of matrices Q and R are set to zero and selected based on empirical data from ship model tests.

[0078] The determined state weight matrix Q and control input weight matrix R are respectively taken as follows:

[0079]

[0080] In addition, the above real symmetric matrix P and the state weight matrix Q satisfy this relationship: A T P+PA=-Q; after determining the state weight matrix Q, the real symmetric matrix P can be determined.

[0081] Through the above formula (A-BK) T P+p(A-BK)=-(Q+K T RK) can be used to obtain the optimal fin angle control parameter K.

[0082] In another embodiment of the present invention, an actual test was conducted using the optimal control method provided by the present invention, and the optimal fin angle control parameter K obtained is shown in Table 1 below:

[0083] Table 1 Optimal fin angle control parameter K

[0084]

[0085] Among them, the greater the speed and angular velocity gain, the faster the fin adjustment speed, and the greater the distance and angle gain, the greater the adjustment range of the fin.

[0086] like Figure 2 As shown in simulations and ship model tests, when the ship is sailing at 18 knots in a significant wave height of 1.5m, and applying stabilizing fin control, this set of control parameters, K, achieves excellent control effectiveness, with heave reduction exceeding 60%, pitch reduction exceeding 45%, and roll reduction exceeding 44%. Under these sea conditions, the maximum fin angle ranges from approximately 15° to 25°, never exceeding the maximum operating angle of 28°. This demonstrates that the optimal control algorithm for two pairs of controllable stabilizing fins designed in this invention is practical and effective in reducing roll, pitch, and heave for small waterplane area ships.

[0087] In summary, the present invention proposes an optimal control method for two pairs of controllable stabilizing fins. The method comprises: the ship inputs the expected values ​​of the ship's heave distance, pitch angle and roll angle into the fin angle control system carried by the ship, and subtracts the difference between the current heave distance, pitch angle and roll angle detected by the sensor in real time, and calculates a control signal w based on the difference. The control signal w includes the optimal fin angle control parameter K, which is optimized to meet the minimum performance index function J: J = ∑(X n 2 +u n 2 )Δt.

[0088] The minimum condition of the performance index function J is:

[0089] (A-BK) T P+P(A-BK)=-(Q+K T RK);

[0090] Wherein, P is a real symmetric matrix, Q is a state weighting matrix, and R is a control input weighting matrix.

[0091] After the optimal fin angle control parameter K is obtained through the above formula, the control signal w can be obtained, and the control signal w is output to the two pairs of controllable stable fins; the two pairs of controllable stable fins are adjusted according to the optimal fin angle control parameter K, so that the oscillation amplitude of the ship sailing is reduced.

[0092] The steps in the application can be adjusted in sequence, combined and deleted according to actual needs.

[0093] The units in the device of the application can be combined, divided and deleted according to actual needs.

[0094] Although the application has been disclosed in detail with reference to the drawings, it should be understood that the description is only exemplary and is not intended to limit the application of the application. The protection scope of the application is defined by the appended claims, and can include various modifications, modifications and equivalent solutions made to the application without departing from the protection scope and spirit of the application.

Claims

1. An optimal control method for two pairs of controllable stabilizing fins, the method being a multi-input multi-output control method adapted to the following kinematic control equations, taking the roll, pitch, and heave motions of a vessel including the two pairs of controllable stabilizing fins as input signals for controlling the two pairs of controllable stabilizing fins, characterized in that: The method comprises: The kinematic control equation of the ship is constructed as follows: The matrix elements in the state variable X = [x1 x2 x3 x4 x5 x6] represent the heave velocity, heave distance, pitch angular velocity, pitch angle, roll angular velocity, and roll angle, respectively; the control input u = [u1 u2 u3 u4] represents the fin angles of the four fins; Y represents the output variable of the system; A, B, C, and D are the coefficient matrices of the state space model; The vessel includes a fin angle control system, wherein the vessel inputs expected values ​​of the vessel's heave distance, pitch angle, and roll angle into the fin angle control system, and the fin angle control system subtracts the expected values ​​from the vessel's current heave distance, pitch angle, and roll angle detected in real time by sensors, and calculates a control signal w based on the difference. The control signal w includes an optimal fin angle control parameter K, which is optimized to meet the minimum performance index function J: J=∑(X n 2 +u n 2 )Δt, the subscript n represents the nth sampling moment, and Δt is the sampling step size; The minimization condition of the performance index function J is: (A-BK) T P+P(A-BK)=-(Q+K T RK); Where P is a real symmetric matrix, Q is the state weight matrix, R is the control input weight matrix, and the superscript T indicates matrix transpose; After the optimal fin angle control parameter K is obtained by the above formula, the control signal w is obtained based on the optimal fin angle control parameter K. The control signal w is output to two pairs of controllable stabilizing fins. The two pairs of controllable stabilizing fins adjust themselves according to the optimal fin angle control parameter K to reduce the oscillation amplitude of the ship's navigation.

2. The optimal control method for two pairs of controllable stabilizing fins according to claim 1, characterized in that: In J=∑(X n 2 +u n 2 )Δt, and considering the infinite time regulator, the above formula is derived as follows: Using the optimal fin angle control parameter K and the state quantity X, the above formula can be expressed as:

3. The optimal control method for two pairs of controllable stabilizing fins according to claim 2, characterized in that: The method further includes: obtaining The original function: Since P is a real symmetric matrix, the above formula needs to satisfy: (A-BK) T P+P(A-BK)=-(Q+K T RK); The above formula is used as the minimization condition of the performance index function J.

4. The optimal control method for two pairs of controllable stabilizing fins according to claim 3, characterized in that: The values ​​of the state weight matrix Q and the control input weight matrix R are as follows:

5. The optimal control method for two pairs of controllable stabilizing fins according to claim 4, characterized in that: The real symmetric matrix P and the state weighting matrix Q satisfy the following relationship: A T P+PA=-Q; After obtaining the value of the state weighted matrix Q, the value of the real symmetric matrix P can be obtained.

6. The optimal control method for two pairs of controllable stabilizing fins according to claim 1, characterized in that: The three-degree-of-freedom motion of the ship is affected by the fin angle F fin The mathematical model under the action is: From top to bottom, the heave, pitch, and roll motion modes are shown; Where M is the displacement of the ship, I5 is the moment of inertia of the ship's center of gravity about the y-axis, I2 is the moment of inertia of the ship's center of gravity about the x-axis, F3 represents the heave moment of the ship caused by wave interference, F5 represents the pitch moment of the ship caused by wave interference, F2 represents the roll moment of the ship caused by wave interference, ξ3 represents the heave displacement of the ship, ξ5 represents the pitch displacement of the ship, and ξ2 represents the roll displacement of the ship. By solving the parameters of the above mathematical model of the small waterplane area catamaran through the slicing method, the additional mass coefficient A generated by the ship's motion can be obtained. ik , damping coefficient B ik and the restoring coefficient C ik , subscript 3 indicates the heave direction, subscript 5 indicates the pitch direction, and subscript 2 indicates the roll direction.

7. The optimal control method for two pairs of controllable stabilizing fins according to claim 6, characterized in that: The three degrees of freedom motion of the ship is determined by the fin angle F fin The mathematical model under the action is written as a state space model: in: Multiply both sides of the state space model by Z -1 ,but: Let A = Z -1 N, B = Z -1 H, then: Z is the mass parameter matrix, N is the kinematic parameter matrix, ξ is the motion state vector, and the matrix H represents the matrix form of the forces and moments generated by each pair of fins. The matrix elements in α = [α1α2α3α4] represent the front left, front right, rear left, and rear right fin angles respectively; the matrix elements in F = [F3F5F2] represent the heave moment, pitch moment, and roll moment of the wave disturbance force acting on the ship respectively.

8. The optimal control method for two pairs of controllable stabilizing fins according to claim 7, characterized in that: The value of the control input u=[u1u2u3u4] is α=[α1α2α3α4].

Images