A ship longitudinal stability control method based on nonlinear modification of composite functions

Abstract

The present invention discloses a method for controlling the longitudinal stability of a ship based on nonlinear modification of a composite function. The method uses the error vector of the ship at the current moment and a closed-loop gain shaping algorithm to obtain an output matrix of a controller. Furthermore, based on the nonlinear modification method of the composite function, a transition matrix after the first layer of functions in the composite function and an input matrix of a mathematical model of the longitudinal motion of the ship after the second layer of functions in the composite function are sequentially obtained. Based on the mathematical model of the longitudinal motion of the ship, the actual value of the heave displacement and the actual value of the trim angle of the ship at the next moment are obtained to achieve control of the longitudinal stability of the ship. The present invention can effectively reduce the heave displacement and trim angle of the ship, significantly improve the robustness of the system, solve the problem of excessive overshoot, and simultaneously reduce control energy consumption, improve the robustness of the longitudinal motion of the ship under wave interference, and enhance the ship's anti-pitch roll capability under wave interference.

Description

Technical Field

[0001] The present invention relates to the technical field of ship control, and in particular to a ship longitudinal stability control method based on nonlinear modification of a composite function. Background Art

[0002] Ship motion control has long been a prominent research topic in shipbuilding and ocean engineering. Current research focuses primarily on heading maintenance, path tracking, and port entry and exit. Research on ship stability control is relatively limited. However, maintaining ship stability is crucial to ensuring safe navigation at sea amidst wind and wave disturbances. Ship stability control can be categorized into longitudinal and transverse stability control. Excessive longitudinal rolling, or severe pitching, can lead to engine stall, structural damage, seasickness, and other safety hazards. Severe ship pitching poses a significant safety hazard to both navigation and personnel. Pitching is primarily caused by irregular forces exerted between wind and waves and the hull, and these irregular forces cannot be eliminated at their source. Therefore, research on the control of longitudinal stability is of great significance. During an investigation aboard the Dalian Maritime University teaching vessel "Yukun," we observed that the vessel experienced severe pitching when disturbed by waves. To ensure safe navigation, minimizing longitudinal capsizing under wave disturbances and improving longitudinal stability is crucial.

[0003] Existing research on longitudinal anti-roll control for ships still suffers from issues such as excessive overshoot and high control energy consumption. This results in large pitch angles and heave displacements during longitudinal motion, which is detrimental to ensuring the ship's safe course. Summary of the Invention

[0004] The present invention discloses a ship longitudinal stability control method based on nonlinear modification of composite functions to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A ship longitudinal stability control method based on nonlinear modification of a composite function comprises the following steps:

[0007] S1: Establish a mathematical model of the longitudinal motion of the ship considering the interference of waves;

[0008] S2. Obtain the error vector of the ship at the current moment, and obtain the output matrix of the controller based on the closed-loop gain shaping algorithm;

[0009] The error vector of the ship includes a heave displacement error and a pitch angle error; the heave displacement error is the difference between the preset heave displacement and the actual heave displacement of the ship; the pitch angle error is the difference between the preset pitch angle and the actual pitch angle;

[0010] S3: According to the output matrix of the controller, based on the composite function nonlinear modification method, the expression of the first layer function in the composite function is obtained to obtain the transition matrix after the first layer function in the composite function acts on it, and then the expression of the second layer function in the composite function is obtained to obtain the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer function in the composite function acts on it;

[0011] S4: Based on the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer of functions in the composite function and the mathematical model of the longitudinal motion of the ship, the actual value of the heave displacement and the actual value of the longitudinal tilt angle of the ship at the next moment are obtained to achieve control of the longitudinal stability of the ship.

[0012] Furthermore, the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer function in the composite function is obtained as follows:

[0013]

[0014] Where: U represents the output matrix of the controller; U' represents the transition matrix after the first layer function in the composite function; f1() represents the first layer function in the composite function; λ is the gain coefficient of the bipolar function in the first layer function; f2() represents the second layer function in the composite function; a is the gain coefficient of U' in the second layer function; b is the gain coefficient of the inverse tangent function in the second layer function; U s It represents the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer of functions in the composite function acts on it.

[0015] Furthermore, the mathematical model of the longitudinal motion of the ship considering the interference of waves is established as follows:

[0016]

[0017] Where: h represents the heave displacement of the ship; represents the first-order derivative of h; represents the second derivative of h; θ is the trim angle of the ship; represents the first derivative of θ; represents the second-order derivative of θ; k hh’ ,k hh ,k hθ′ ,k hθ ,k θθ′ ,k θθ ,k θh′ ,k θh Both represent the hydrodynamic coefficient, which can express the interaction between waves and the hull; F h (t) is the wave disturbance force; M θ (t) is the wave disturbance torque; Fs (t) represents the force input to the mathematical model of the longitudinal motion of the ship; M s (t) represents the torque input to the mathematical model of the longitudinal motion of the ship; F w (t) represents the force generated by the wave disturbance; M w (t) represents the torque generated by the wave interference; α is the interference coefficient of the force generated by the wave interference; β is the interference coefficient of the torque generated by the wave interference; v(t) represents the approximate wave height; ξ is white noise; G ω (s) represents the wave transfer function; l represents the wave gain factor; s represents the Laplace operator; ω α represents the center frequency of the wave; θ represents the significant wave height.

[0018] Furthermore, the output matrix of the controller is obtained as follows:

[0019]

[0020] in,

[0021]

[0022] Where K c represents a linear controller; K 11 represents the controller acting on the heave displacement, K 22 represents the controller acting on the pitch angle; T 11 represents the heave displacement controller gain parameter; T 22 represents the gain parameter of the trim angle controller; s represents the Laplace operator; E represents the error vector of the ship; e h It represents the heave displacement error, that is, the difference between the preset heave displacement and the actual heave displacement of the ship, e θ represents the pitch angle error, that is, the difference between the preset pitch angle and the actual pitch angle; U represents the output matrix of the controller.

[0023] Furthermore, it also includes S5: based on the Taylor series expansion method, according to the expression of the first-level function in the composite function and the expression of the second-level function in the composite function, the steady-state error of the ship's longitudinal motion system, the ratio of the output of the ship's longitudinal motion system to the input matrix of the ship's longitudinal motion system, and the transfer function from the input matrix of the ship's longitudinal motion system to the input matrix of the mathematical model of the ship's longitudinal motion after the second-level function in the composite function are obtained, so as to evaluate the stability of the ship's longitudinal motion system, the dynamic performance of the ship's longitudinal motion system and the energy-saving effect of the system respectively.

[0024] Furthermore, the method used to obtain the steady-state error of the ship's longitudinal motion system, the ratio of the output of the ship's longitudinal motion system to the input matrix of the ship's longitudinal motion system, and the transfer function from the input matrix of the ship's longitudinal motion system to the input matrix of the ship's longitudinal motion mathematical model after the second layer of functions in the composite function are as follows:

[0025] First, expand the expressions of the first-level functions and the second-level functions in the composite function using Taylor series and retain them to the first order, and we get:

[0026]

[0027] The frequency of the ship's longitudinal motion system

[0028] but,

[0029] The steady-state error of the ship's longitudinal motion system is obtained as follows:

[0030]

[0031] Where: G represents the transfer function of the mathematical model of the ship's longitudinal motion; E ss (∞) represents the steady-state error when time approaches infinity; r represents the input matrix of the ship's longitudinal motion system; s is the Laplace operator; I represents the identity matrix; w represents the frequency of the ship's longitudinal motion system; K c represents a linear controller; T 11 represents the heave displacement controller gain parameter; T 22 represents the gain parameter of the pitch angle controller;

[0032] The ratio of the output matrix of the ship longitudinal motion system to the input matrix of the ship longitudinal motion system is obtained as follows:

[0033]

[0034] Where: y represents the output of the ship's longitudinal motion system, that is, the actual value of the ship's heave displacement and the actual value of the trim angle at the next moment;

[0035] The transfer function from the input matrix of the ship longitudinal motion system to the input matrix of the ship longitudinal motion mathematical model after the second layer function in the composite function is obtained as follows:

[0036]

[0037] Beneficial effect: The method for controlling the longitudinal stability of a ship based on the nonlinear modification of a composite function of the present invention is to obtain the output matrix of the controller based on the error vector of the ship at the current moment and the closed-loop gain shaping algorithm, and then obtain the transition matrix after the first layer function in the composite function and the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer function in the composite function based on the nonlinear modification method of the composite function in sequence, and obtain the actual value of the heave displacement and the actual value of the longitudinal tilt angle of the ship at the next moment according to the mathematical model of the longitudinal motion of the ship to achieve the control of the longitudinal stability of the ship. The present invention can effectively reduce the heave displacement and longitudinal tilt angle of the ship, significantly improve the robustness of the system, solve the problem of excessive overshoot, and at the same time reduce the control energy consumption, improve the robustness of the longitudinal motion of the ship under wave interference, and enhance the anti-pitch roll capability of the ship under wave interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0039] Figure 1 This is a flow chart of the ship longitudinal stability control method based on composite function nonlinear modification of the present invention;

[0040] Figure 2 This is a structural block diagram of a nonlinear modification method for a composite function according to an embodiment of the present invention;

[0041] Figure 3 This is a basic framework diagram of a ship longitudinal stability control method based on nonlinear modification of a composite function in an embodiment of the present invention;

[0042] Figure 4 It is a simulation design diagram of a composite function nonlinear feedback system in an embodiment of the present invention;

[0043] Figure 5a Schematic diagram of the heave displacement of a ship longitudinal roll stabilization control using a simple function nonlinearly modified with consideration of wave interference under ideal conditions in an embodiment of the present invention;

[0044] Figure 5b Schematic diagram of the trim angle of the ship longitudinal roll stabilization control using a simple function nonlinearly modified with consideration of wave interference under ideal conditions in an embodiment of the present invention;

[0045] Figure 6aSchematic diagram of the heave displacement of the ship longitudinal roll stabilization control using a composite function nonlinearly modified with consideration of wave interference under an ideal state in an embodiment of the present invention;

[0046] Figure 6b Schematic diagram of the trim angle of the ship longitudinal roll stabilization control using a composite function nonlinearly modified with consideration of wave interference under an ideal state in an embodiment of the present invention;

[0047] Figure 7a Schematic diagram of heave displacement of a ship longitudinal roll stabilization control using a simple function nonlinearly modified with consideration of wave interference and model perturbation in an embodiment of the present invention;

[0048] Figure 7b Schematic diagram of heave displacement of a ship longitudinal roll stabilization control using a simple function nonlinearly modified with consideration of wave interference and model perturbation in an embodiment of the present invention;

[0049] Figure 8a Schematic diagram of heave displacement of a ship longitudinal roll stabilization control using a composite function with nonlinear modification considering wave interference and model perturbation in an embodiment of the present invention;

[0050] Figure 8b Schematic diagram of the trim angle of the ship longitudinal roll stabilization control using the composite function nonlinear modification taking into account the wave interference and model perturbation in an embodiment of the present invention. DETAILED DESCRIPTION

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0052] This embodiment introduces a ship longitudinal stability control method based on nonlinear modification of composite functions, such as Figure 1-Figure 4 As shown, the following steps are included:

[0053] S1: Establish a mathematical model of the longitudinal motion of the ship considering the interference of waves;

[0054] Preferably, the mathematical model of longitudinal motion of the ship considering the interference of sea waves is established as follows:

[0055]

[0056] Where: h represents the heave displacement of the ship; represents the first-order derivative of h; represents the second derivative of h; θ is the trim angle of the ship; represents the first derivative of θ; represents the second-order derivative of θ; k hh’ ,k hh ,k hθ′ ,k hθ ,k θθ′ ,k θθ ,k θh′ ,k θh Both represent the hydrodynamic coefficient, which can express the interaction between waves and the hull; F h (t) is the wave disturbance force; M θ (t) is the wave disturbance torque; F s (t) represents the force input to the mathematical model of the longitudinal motion of the ship; M s (t) represents the torque input to the mathematical model of the longitudinal motion of the ship; F w (t) represents the force generated by the wave disturbance; M w (t) represents the torque generated by the wave interference; α is the interference coefficient of the force generated by the wave interference; β is the interference coefficient of the torque generated by the wave interference; v(t) represents the approximate wave height; ξ is white noise; G ω (s) represents the wave transfer function; l represents the wave gain factor; s represents the Laplace operator; ω α represents the center frequency of the wave; θ represents the significant wave height;

[0057] Specifically, in this embodiment, the heave displacement h and the pitch angle θ are taken as system outputs, and their control targets are set to 0 (meters) and 0 (degrees), respectively;

[0058] S2. Obtain the error vector of the ship at the current moment, and obtain the output matrix of the controller based on the closed-loop gain shaping algorithm;

[0059] The error vector of the ship includes a heave displacement error and a pitch angle error; the heave displacement error is the difference between the preset heave displacement and the actual heave displacement of the ship; the pitch angle error is the difference between the preset pitch angle and the actual pitch angle;

[0060] Specifically, in this embodiment, based on the error vector of the ship, a closed-loop gain shaping algorithm is used to design the controller to obtain the output matrix U of the controller. The closed-loop gain shaping algorithm is in the form of a PID controller. Formula (2) represents the PID controller, where the PID controller is a linear controller K designed by the third-order closed-loop gain shaping algorithm. c , and calculate the matrix U consisting of the controller output force and torque.

[0061] Preferably, the output matrix of the controller is obtained as follows:

[0062]

[0063] in,

[0064]

[0065] Where K c represents a linear controller; K 11 represents the controller acting on the heave displacement, K 22 represents the controller acting on the pitch angle; T 11 represents the heave displacement controller gain parameter; T 22 represents the gain parameter of the trim angle controller; s represents the Laplace operator; E represents the error vector of the ship; e h It represents the heave displacement error, that is, the difference between the preset heave displacement and the actual heave displacement of the ship, e θ represents the pitch angle error, that is, the difference between the preset pitch angle and the actual pitch angle; U represents the output matrix of the controller;

[0066] S3: According to the output matrix of the controller, based on the composite function nonlinear modification method, the expression of the first layer function in the composite function is obtained to obtain the transition matrix after the first layer function in the composite function acts on it, and then the expression of the second layer function in the composite function is obtained to obtain the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer function in the composite function acts on it;

[0067] Preferably, the input matrix of the mathematical model of longitudinal motion of the ship after the second layer function in the composite function is obtained as follows:

[0068] Specifically, the output matrix U of the controller in this embodiment is composed of the controller output force F(t) and the controller output torque M(t). The controller output matrix is ​​processed according to formula (3) as follows:

[0069]

[0070] Where: U represents the output matrix of the controller; U' represents the transition matrix after the first layer function in the composite function, and the composite function is composed of a bipolar function and an inverse tangent function; f1() represents the first layer function in the composite function; λ is the gain coefficient of the bipolar function in the first layer function; f2() represents the second layer function in the composite function; a is the gain coefficient of U' in the second layer function; b is the gain coefficient of the inverse tangent function in the second layer function; U sIt represents the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer of the composite function. Specifically, U is subjected to the function f1(U) to obtain U', and U' is subjected to the function f2(U') to obtain U s , by F s (t) and M s (t) constitutes, and finally U s As the input matrix of the mathematical model of ship longitudinal motion.

[0071] S4: According to the input matrix of the ship longitudinal motion mathematical model after the second layer function in the composite function, the U obtained by the nonlinear modification of the composite function is converted into s The data are transmitted to the mathematical model of the longitudinal motion of the ship to obtain the actual value of the heave displacement and the actual value of the longitudinal tilt angle of the ship at the next moment, so as to realize the control of the longitudinal stability of the ship.

[0072] Preferably, it also includes S5: based on the Taylor series expansion method, according to the expression of the first-level function in the composite function and the expression of the second-level function in the composite function, obtain the steady-state error of the ship's longitudinal motion system, the ratio of the output of the ship's longitudinal motion system to the input matrix of the ship's longitudinal motion system, and the transfer function from the input matrix of the ship's longitudinal motion system to the input matrix of the mathematical model of the ship's longitudinal motion after the second-level function in the composite function, so as to evaluate the stability of the ship's longitudinal motion system, the dynamic performance of the ship's longitudinal motion system and the energy-saving effect of the system respectively.

[0073] Specifically, in order to conveniently demonstrate the influence of the composite function nonlinear modification method of this embodiment on the performance of the ship longitudinal motion system, the Taylor series is used to expand formula (3) and retain it to the first order.

[0074]

[0075] The frequency of the ship's longitudinal motion system The following theoretical analysis is carried out:

[0076] The effect of this embodiment on the stability of the ship's longitudinal motion system, that is, on the steady-state error: For the convenience of analysis, the ship's longitudinal motion mathematical model is expressed as a matrix transfer function. According to the Laszlo transformation final value theorem, the steady-state error E of the system ss (∞) is expressed as:

[0077]

[0078] Where: G represents the transfer function of the mathematical model of the ship's longitudinal motion; E ss(∞) represents the steady-state error when time approaches infinity; r represents the input matrix of the ship's longitudinal motion system; s is the Laplace operator; I represents the identity matrix; w represents the frequency of the ship's longitudinal motion system; K c represents a linear controller; T 11 represents the heave displacement controller gain parameter; T 22 represents the gain parameter of the pitch angle controller;

[0079] Specifically, according to the above formula (5), it can be found that the output steady-state error E ss (∞) is 0, indicating that the nonlinear modification of the composite function has no additional effect on the steady state of the system.

[0080] This embodiment analyzes the impact of the system's dynamic performance: the ratio of the output of the ship's longitudinal motion system to the input matrix of the ship's longitudinal motion system is obtained as follows:

[0081]

[0082] Where: y represents the output of the ship's longitudinal motion system, that is, the actual value of the ship's heave displacement and the actual value of the trim angle at the next moment; ω represents the frequency of the ship's longitudinal motion system;

[0083] Specifically, since the frequency ω of the ship's longitudinal motion system is less than 1, according to the closed-loop gain shaping theory, the open-loop frequency characteristics of the system meet the high gain at low frequency and low gain at high frequency. Therefore, in the low-frequency range, Equation (6) is compared with the closed-loop transfer function of the standard feedback system GK c / (1+GK c ), the addition of ω has little effect on the dynamic performance of the system, indicating that the addition of the nonlinear modification of the composite function will not have a negative impact on the dynamic performance of the ship's longitudinal motion system; specifically, since the high frequency band has little effect on the dynamic performance of the system, it is not discussed in this embodiment.

[0084] The influence of this embodiment on the control output is the input matrix r of the ship longitudinal motion system to the input matrix U of the ship longitudinal motion mathematical model after the second layer function in the composite function. s The transfer function is:

[0085]

[0086] Equation (7) represents the transfer function from the system input to the controller output. The numerator in Equation (7) decays more significantly than the denominator. Since ω<1, adding ω reduces the value of the fraction, which in turn reduces the controller output. Therefore, nonlinear modification of the composite function can reduce the control output and achieve energy savings.

[0087] In one embodiment of the present invention, a simulation experiment was carried out using Matlab. The relevant parameters in the simulation were set as follows: the wave interference was set to level 4 sea state, the significant wave height θ generated by level 4 sea state ranged from (-3, 3), the wave gain factor l was 0.75, and the wave force and moment interference coefficient α was 1.71×10 5 , β=1.87×10 5 , the system gain is K0 = 3.25; the time constant T0 = 0.78. Controller parameters T 11 =T 22 =10 The nonlinear modification parameters of the composite function are set to a = 0.6, b = 0.5, and λ = 1.2. The simulation time is set to 300 s, and the simulation step size is 0.1.

[0088] The Dalian Maritime University teaching ship “Yukun” was used as the experimental object, and its parameters are shown in Table 1.

[0089] Table 1 Main parameters of Yukun wheel

[0090]

[0091] Specifically, this embodiment aims to take into account practical navigation and energy consumption during the control process, while simplifying the controller design. Considering the robustness of the closed-loop gain shaping algorithm and its simplified parameter tuning, and the fact that the composite function nonlinear modification can improve resistance to wave disturbances and model perturbations while further enhancing energy conservation compared to simple nonlinear modification, the two are combined to control the longitudinal stability of a ship. This controller achieves both desired longitudinal stability control performance and reduced performance consumption. Furthermore, considering the time lag characteristics of the actual control process, the model perturbations generated by time lag mitigation are added during simulations to produce simulation results more closely aligned with actual navigation. Under these circumstances, the ship longitudinal stability control algorithm based on the composite function nonlinear modification achieves lower energy consumption and better control performance than simple nonlinear modification. Simulations show that under ideal conditions and model perturbations, this embodiment can maintain longitudinal stability of a ship under wave disturbances, providing valuable insights for ship longitudinal stability control.

[0092] Specifically, in order to evaluate the energy consumption level of the algorithm proposed in this embodiment during the process of controlling the longitudinal stability of a ship, the performance index J is designed. h With J θ To express the energy consumption generated by controlling the heave displacement and pitch angle: Where t represents the simulation time, h(t) and θ(t) represent the functions of heave displacement and pitch angle changing with time. h With J θ They represent the energy consumption caused by heave displacement and pitch angle respectively.

[0093] The simulation results are shown in Figures 5 to 8 and Table 2. Figure 5a and Figure 5b These are all ship longitudinal stability control effects using simple function nonlinear modification under ideal conditions. Figure 6a and Figure 6b In order to calculate the control effect of ship longitudinal stability by using composite function nonlinear modification under ideal conditions without considering model perturbation, Figure 7a and Figure 7b It is the effect of ship longitudinal stability control using simple function nonlinear modification when considering model perturbation. Figure 8a and Figure 8b It is the effect of the ship's longitudinal stability control using a composite function nonlinear modification when considering model perturbations. The control targets for the trim angle and heave displacement are set to 0. As can be seen from the figure, in the ideal case of not considering model perturbations, the blue curve is the ship's heave displacement and trim angle under the action of level 4 wave interference. Without the controller, the maximum heave displacement of the Yukun is 8.5743m, the maximum trim angle is 7.8422°, and the performance consumption index J is 0. h With J θ The values ​​of 732.0476 and 642.2814 are 732.0476 and 642.2814 respectively. It can be seen that under the interference of level 4 waves, the Yukun has a serious capsizing tendency, which is extremely harmful to navigation safety. The red curve in Figure 5 is the result of the modification of a simple nonlinear function. At this time, the maximum deep displacement of the Yukun is 1.48m, the maximum pitch angle is 2.11°, and the performance consumption index J is 0. h With J θ 33.14 and 21.99 respectively. Although there is a certain effect on the longitudinal stability control of the ship, there are still large fluctuations. The red curve in Figure 6 shows the control effect after the control algorithm designed in this embodiment is introduced. Under the action of the nonlinear modification of the composite function, the maximum deep displacement of the Yukun ship is 0.1672m, the maximum longitudinal tilt angle is 0.0747°, and the performance consumption index J h With J θ They are 13.76 and 6.33 respectively. It can be seen that under the control algorithm proposed in this embodiment, the longitudinal motion of the Yukun ship is stable under level 4 wave interference, and the navigation safety is greatly improved.

[0094] When the delay link is added to generate the model perturbation, it can be seen from Figure 7 that under the effect of simple function modification, the divergence of the longitudinal motion of the ship is not controlled. However, according to Figure 8 and Table 2, under the effect of composite function nonlinear modification when the model is perturbed, the maximum heave displacement is 0.2216 and the maximum pitch angle is 0.07. h With J θThey are 14.45 and 6.45 respectively. It can be seen that under the influence of model perturbation, the nonlinear modification of the composite function can still keep the longitudinal motion of the ship stable with low energy consumption, indicating that the control algorithm designed in this embodiment has stronger robustness and can resist the influence of model perturbation.

[0095] Table 2 Performance indicators of various control algorithms under wave interference

[0096]

[0097] Specifically, simulations have shown that this embodiment performs well in controlling the longitudinal stability of ships under wave disturbances, reducing the ship's heave displacement and pitch angle, significantly improving the robustness of the system, and reducing control energy consumption. The robustness of the ship's longitudinal motion under wave disturbances has been successfully improved, and the ship's anti-pitch capability under wave disturbances has been enhanced. Considering model perturbations, the composite function nonlinear modification technology is more robust than the simple function nonlinear feedback technology, with the maximum pitch angle and heave displacement reduced by 1.04° and 1.26m, respectively. At the same time, the control energy consumption has been successfully reduced. Considering wave disturbances, the composite function nonlinear modification technology has better energy-saving effects than the simple function nonlinear feedback technology, with the control energy consumption performance indicators of the maximum pitch angle and heave displacement improved by 58.5% and 71.2%, respectively.

[0098] In summary, this embodiment combines the nonlinear modification of the composite function with the closed-loop gain shaping algorithm to achieve the purpose of strong robustness and low energy consumption, ultimately reducing the heave displacement and trim angle of the ship's longitudinal stability control while saving control energy consumption.

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A ship longitudinal stability control method based on nonlinear modification of composite functions, characterized in that: The steps include: S1: Establish a mathematical model of the longitudinal motion of the ship considering the interference of waves; S2. Obtain the error vector of the ship at the current moment, and obtain the output matrix of the controller based on the closed-loop gain shaping algorithm; The error vector of the ship includes a heave displacement error and a pitch angle error; the heave displacement error is the difference between the preset heave displacement and the actual heave displacement of the ship; the pitch angle error is the difference between the preset pitch angle and the actual pitch angle; S3: According to the output matrix of the controller, based on the composite function nonlinear modification method, the expression of the first layer function in the composite function is obtained to obtain the transition matrix after the first layer function in the composite function acts on it, and then the expression of the second layer function in the composite function is obtained to obtain the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer function in the composite function acts on it; S4: Based on the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer of functions in the composite function and the mathematical model of the longitudinal motion of the ship, the actual value of the heave displacement and the actual value of the longitudinal tilt angle of the ship at the next moment are obtained to achieve control of the longitudinal stability of the ship.

2. A ship longitudinal stability control method based on composite function nonlinear modification according to claim 1, characterized in that: The input matrix of the mathematical model of the longitudinal motion of the ship after the second layer of functions in the composite function is obtained as follows: Where: U represents the output matrix of the controller; U' represents the transition matrix after the first layer function in the composite function; f1() represents the first layer function in the composite function; λ is the gain coefficient of the bipolar function in the first layer function; f2() represents the second layer function in the composite function; a is the gain coefficient of U' in the second layer function; b is the gain coefficient of the inverse tangent function in the second layer function; U s It represents the input matrix of the mathematical model of the longitudinal motion of the ship after the second layer of functions in the composite function acts on it.

3. The ship longitudinal stability control method based on composite function nonlinear modification according to claim 1 is characterized in that: The mathematical model of the longitudinal motion of the ship considering the interference of sea waves is established as follows: Where: h represents the heave displacement of the ship; represents the first-order derivative of h; represents the second derivative of h; θ is the trim angle of the ship; represents the first derivative of θ; represents the second-order derivative of θ; k hh’ ,k hh ,k hθ′ ,k hθ ,k θθ′ ,k θθ ,k θh′ ,k θh Both represent hydrodynamic coefficients, which can represent the interaction between waves and the hull; F h (t) is the wave disturbance force; M θ (t) is the wave disturbance torque; F s (t) represents the force input to the mathematical model of the longitudinal motion of the ship; M s (t) represents the torque input to the mathematical model of the longitudinal motion of the ship; F w (t) represents the force generated by the wave disturbance; M w (t) represents the torque generated by the wave interference; α is the interference coefficient of the force generated by the wave interference; β is the interference coefficient of the torque generated by the wave interference; v(t) represents the approximate wave height; ξ is white noise; G ω (s) represents the wave transfer function; represents the wave gain factor; s represents the Laplace operator; ω α Indicates the center frequency of the wave; Indicates significant wave height.

4. A ship longitudinal stability control method based on composite function nonlinear modification according to claim 1, characterized in that: The output matrix of the controller is obtained as follows: in, Where K c represents a linear controller; K 11 represents the controller acting on the heave displacement, K 22 represents the controller acting on the pitch angle; T 11 represents the heave displacement controller gain parameter; T 22 represents the gain parameter of the trim angle controller; s represents the Laplace operator; E represents the error vector of the ship; e h It represents the heave displacement error, that is, the difference between the preset heave displacement and the actual heave displacement of the ship, e θ represents the pitch angle error, that is, the difference between the preset pitch angle and the actual pitch angle; U represents the output matrix of the controller.

5. The method for controlling longitudinal stability of a ship based on nonlinear modification of a composite function according to claim 1, characterized in that: It also includes S5: a method based on Taylor series expansion, according to the expression of the first-level function in the composite function and the expression of the second-level function in the composite function, to obtain the steady-state error of the ship's longitudinal motion system, the ratio of the output of the ship's longitudinal motion system to the input matrix of the ship's longitudinal motion system, and the transfer function from the input matrix of the ship's longitudinal motion system to the input matrix of the mathematical model of the ship's longitudinal motion after the second-level function in the composite function, so as to respectively evaluate the stability of the ship's longitudinal motion system, the dynamic performance of the ship's longitudinal motion system and the energy-saving effect of the system.

6. A ship longitudinal stability control method based on composite function nonlinear modification according to claim 5, characterized in that: The method used to obtain the steady-state error of the ship's longitudinal motion system, the ratio of the output of the ship's longitudinal motion system to the input matrix of the ship's longitudinal motion system, and the transfer function from the input matrix of the ship's longitudinal motion system to the input matrix of the ship's longitudinal motion mathematical model after the second layer of functions in the composite function are as follows: First, expand the expressions of the first-level functions and the second-level functions in the composite function using Taylor series and retain them to the first order, and we get: The frequency of the ship's longitudinal motion system but, The steady-state error of the ship's longitudinal motion system is obtained as follows: Where: G represents the transfer function of the mathematical model of the ship's longitudinal motion; E ss (∞) represents the steady-state error when time approaches infinity; r represents the input matrix of the ship's longitudinal motion system; s is the Laplace operator; I represents the identity matrix; w represents the frequency of the ship's longitudinal motion system; K c represents a linear controller; T 11 represents the heave displacement controller gain parameter; T 22 represents the gain parameter of the pitch angle controller; The ratio of the output matrix of the ship longitudinal motion system to the input matrix of the ship longitudinal motion system is obtained as follows: Where: y represents the output of the ship's longitudinal motion system, that is, the actual value of the ship's heave displacement and the actual value of the trim angle at the next moment; The transfer function from the input matrix of the ship longitudinal motion system to the input matrix of the ship longitudinal motion mathematical model after the second layer function in the composite function is obtained as follows:

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