Self-adaptive sliding mode ship trajectory tracking control method based on output redefinition

Abstract

The invention discloses a self-adaptive sliding mode ship trajectory tracking control method based on output redefinition, and the method comprises the steps: S1, building an under-actuated ship mathematical model, and redefining the position of the under-actuated ship mathematical model; s2, designing a position tracking error, and performing derivation on the position tracking error; s3, designing a first linear sliding mode surface and a second linear sliding mode surface according to the position tracking error and the tracking error after derivation; s4, designing longitudinal control force and yawing control torque of the ship based on the first linear sliding mode surface and the second linear sliding mode surface in combination with an adaptive technology; and S5, position tracking errors are adjusted through the longitudinal control force and the yawing control torque, convergence of the position tracking errors is achieved, and therefore trajectory tracking is achieved. According to the method, the under-actuated problem is solved by designing the ship longitudinal control force and the yawing control moment of the under-actuated ship mathematical model; and meanwhile, the position tracking error is adjusted through the longitudinal control force and the yawing control torque, so that the tracking error can be quickly converged, and trajectory tracking is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of ship trajectory tracking control, and in particular to an adaptive sliding mode ship trajectory tracking control method based on output redefinition. Background Art

[0002] With the development of science and technology, the demand for the development, transportation and exploration of marine resources is increasing. As an economical and effective tool, surface ships play a vital role in marine engineering. Trajectory tracking control is a typical control task in ship motion control. It enables surface ships to track the required reference trajectory, helps ship managers monitor the position of ships in real time, ensures the safe navigation of ships, and promotes the intelligent development of ships.

[0003] In practice, ships sailing at sea will be disturbed by the external environment, which is specifically manifested in the offset, speed change and shaking caused by the wind, waves and currents acting on the ships, which makes it difficult for ships to accurately track the expected trajectory. At the same time, most commercial ships sailing at sea are underactuated ships, lacking control input in the lateral direction, which further increases the difficulty of trajectory tracking. The current methods for dealing with underactuation include LOS guidance, derivative of the lateral velocity to obtain bow control input, etc., but the use of LOS requires the conversion of position geometry, which is cumbersome; and the derivative of the lateral velocity will result in a large amount of calculation and is relatively complicated. Therefore, there has been no simple and effective method to deal with the underactuation problem. At the same time, with the development of national strategies, the concept of energy conservation and carbon reduction has gradually become popular. Therefore, while meeting the actual requirements of ship trajectory tracking, how to reduce the control input and ensure navigation safety is also an urgent problem to be solved. Summary of the invention

[0004] The present invention provides an adaptive sliding mode ship trajectory tracking control method based on output redefinition to overcome the under-actuation problem of existing ship controllers and to solve the technical problem of how to reduce the control input and ensure navigation safety while meeting the actual requirements of ship trajectory tracking.

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

[0006] An adaptive sliding mode ship trajectory tracking control method based on output redefinition, the specific steps include:

[0007] S1: establishing a mathematical model of an underactuated ship, and redefining the position of the underactuated ship model using an output redefinition method;

[0008] S2: designing a position tracking error based on the position of the redefined underactuated ship mathematical model, and derivatizing the position tracking error to obtain a tracking error after the derivation;

[0009] S3: designing a first linear sliding surface and a second linear sliding surface according to the position tracking error and the derived tracking error;

[0010] S4: designing a ship longitudinal control force and a bow rolling control moment of an underactuated ship mathematical model based on the first linear sliding surface and the second linear sliding surface in combination with an adaptive technology;

[0011] S5: adjusting the position tracking error by means of the longitudinal control force and the yaw control torque so that the position tracking error converges, thereby achieving trajectory tracking.

[0012] Further, in S1, a mathematical model of an underactuated ship is established, and the position of the underactuated ship model is redefined using an output redefinition method. The mathematical model of the underactuated ship is expressed as:

[0013]

[0014] Where x, y, ψ are the longitudinal displacement, transverse displacement and heading angle of the ship respectively; u, v, r are the forward speed, drift speed and bow angular velocity of the ship in the appendage coordinate system respectively; τ u is the longitudinal control force of the ship, τ r is the yaw control torque; m 11 ,m 22 ,m 33 is the inertia parameter; d 11 ,d 22 ,d 33 is the hydrodynamic parameter; τ wu ,τ wv ,τ wr It is the disturbance caused by the external wind, current and waves acting on the ship;

[0015] The position of the underactuated ship model is redefined using an output redefinition method, and the position of the redefined underactuated ship mathematical model is:

[0016]

[0017] Where x1 and y1 are the longitudinal and transverse coordinates of the ship after redefinition, and l is the positive parameter to be designed.

[0018] Further, in S2, a position tracking error is designed based on the position of the redefined underactuated ship mathematical model, and the tracking error of the ship controller is derived to obtain the derived tracking error, including:

[0019] The designed position tracking error is:

[0020]

[0021] Among them, e x and e y is the longitudinal position error and the lateral position error; x d and d is the desired longitudinal position and the desired lateral position;

[0022] For e in formula (3), x and e y Taking the second derivative and combining equation (1) and equation (2), we can get:

[0023]

[0024] The formula (4) is transformed as follows:

[0025]

[0026] Where, the expressions of f(x) and f(y) are as shown in formula (6):

[0027]

[0028] Further, in S3, designing the first linear sliding surface and the second linear sliding surface according to the position tracking error and the derived tracking error includes:

[0029] The first linear sliding surface s1 is shown in formula (7):

[0030]

[0031] In the formula, λ1 is the positive parameter to be designed;

[0032] The second linear sliding surface s2 is shown in formula (8):

[0033]

[0034] In the formula, λ2 is the positive parameter to be designed.

[0035] Further, in S4, the process of designing the ship longitudinal control force and yaw control torque of the underactuated ship mathematical model based on the first linear sliding surface and the second linear sliding surface in combination with the adaptive technology is:

[0036] By taking the derivative of the first linear sliding surface and combining it with equation (5), we can obtain:

[0037]

[0038] By taking the derivative of the second linear sliding surface and combining it with equation (5), we can obtain:

[0039]

[0040] make The designed ship longitudinal control force τ is obtained u and the yaw control torque τ r , expressed as:

[0041]

[0042] In the formula, k1, k2, k3, k4 are the positive parameters to be designed. is the estimated value of μ1, is the estimated value of μ2, the design parameter and The adaptive laws are:

[0043]

[0044] In the formula, η1, η2, σ1, σ2 are positive design parameters.

[0045] Beneficial effects: The present invention redefines the position of the ship and designs the position tracking error, designs the first linear sliding surface and the second linear sliding surface according to the position tracking error and its derivative; designs the longitudinal control force and the bow roll control torque of the under-actuated ship mathematical model based on the first linear sliding surface and the second linear sliding surface and the adaptive technology to solve the under-actuated problem; at the same time, the position tracking error is adjusted by the longitudinal control force and the bow roll control torque to make the position error converge, thereby realizing trajectory tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces 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 creative labor.

[0047] Figure 1 It is a flow chart of the adaptive sliding mode ship trajectory tracking control method based on output redefinition in the present invention;

[0048] Figure 2 It is a design flow chart of an adaptive sliding mode ship trajectory tracking control method based on output redefinition in an embodiment of the present invention;

[0049] Figure 3 The expected trajectory and actual trajectory of the ship under the action of each control algorithm in the embodiment of the present invention;

[0050] Figure 4This is a diagram showing the convergence effect of the longitudinal position error in an embodiment of the present invention;

[0051] Figure 5 This is a diagram showing the convergence effect of the lateral position error in an embodiment of the present invention;

[0052] Figure 6 A longitudinal speed comparison diagram of various algorithms in an embodiment of the present invention;

[0053] Figure 7 A comparison diagram of lateral speeds of various algorithms in an embodiment of the present invention;

[0054] Figure 8 is a comparison diagram of the yaw angular velocity of various algorithms in the embodiment of the present invention;

[0055] Fig. 9 is a longitudinal control force input curve diagram in an embodiment of the present invention;

[0056] Fig.10 is a graph of the yaw control torque input in an embodiment of the present invention;

[0057] Fig.11 is a time history curve of the estimated value of the interference upper bound μ1 in an embodiment of the present invention;

[0058] Fig.12 FIG. 4 is a time history curve of the estimated value of the interference upper bound μ2 in an embodiment of the present invention. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] This embodiment provides an adaptive sliding mode ship trajectory tracking control method based on output redefinition, such as Figure 1 and Figure 2 As shown, the specific steps include:

[0061] S1: Establishing a mathematical model of an under-actuated ship, and redefining the position of the under-actuated ship model using an output redefinition method; In a specific embodiment, in S1, establishing a mathematical model of an under-actuated ship, and redefining the position of the under-actuated ship model using an output redefinition method, the mathematical model of the under-actuated ship is represented as:

[0062]

[0063] Where x, y, ψ are the longitudinal displacement, transverse displacement and heading angle of the ship respectively; u, v, r are the forward speed, drift speed and bow angular velocity of the ship in the appendage coordinate system respectively; τ u is the longitudinal control force of the ship, τ r is the yaw control torque; m 11 ,m 22 ,m 33 is the inertia parameter; d 11 ,d 22 ,d 33 is the hydrodynamic parameter; τ wu ,τ wv ,τ wr It is the disturbance caused by the external wind, current and waves acting on the ship;

[0064] In this embodiment, it is assumed that the external interference to the ship is time-varying interference and satisfies

[0065] |τ wu |≤D1,|τ wr |≤D2

[0066] Among them, D1 and D2 are interference τ wu ,τ wr The upper and lower bounds of are unknown and are both greater than 0.

[0067] The position of the underactuated ship model is redefined using an output redefinition method, and the position of the redefined underactuated ship mathematical model is:

[0068]

[0069] Where x1 and y1 are the longitudinal and transverse coordinates of the ship after redefinition, and l is the positive parameter to be designed.

[0070] S2: designing a position tracking error based on the position of the redefined underactuated ship mathematical model, and derivatizing the position tracking error to obtain a tracking error after the derivation;

[0071] In a specific embodiment, in S2, the position tracking error is designed based on the position of the redefined underactuated ship mathematical model, and the tracking error of the ship controller is derived to obtain the derived tracking error, including:

[0072] Assume that the desired trajectory of the ship (x d ,y d ) is smooth and has first- and second-order derivatives.

[0073] The designed position tracking error is:

[0074]

[0075] Among them, e x and e y is the longitudinal position error and the lateral position error; x d and d is the desired longitudinal position and the desired lateral position;

[0076] For e in formula (3), x and e y Taking the second derivative and combining equation (1) and equation (2), we can get:

[0077]

[0078] The formula (4) is transformed as follows:

[0079]

[0080] Where, the expressions of f(x) and f(y) are as shown in formula (6):

[0081]

[0082] S3: designing a first linear sliding surface and a second linear sliding surface according to the position tracking error and the derived tracking error;

[0083] In a specific embodiment, in S3, designing the first linear sliding surface and the second linear sliding surface according to the position tracking error and the derived tracking error includes:

[0084] The first linear sliding surface s1 is shown in formula (7):

[0085]

[0086] In the formula, λ1 is the positive parameter to be designed;

[0087] The second linear sliding surface s2 is shown in formula (8):

[0088]

[0089] In the formula, λ2 is the positive parameter to be designed.

[0090] S4: designing a ship longitudinal control force and a bow rolling control moment of an underactuated ship mathematical model based on the first linear sliding surface and the second linear sliding surface in combination with an adaptive technology;

[0091] In a specific embodiment, in S4, the process of designing the longitudinal control force and yaw control torque of the underactuated ship mathematical model based on the first linear sliding surface and the second linear sliding surface in combination with the adaptive technology is as follows:

[0092] By taking the derivative of the first linear sliding surface and combining it with equation (5), we can obtain:

[0093]

[0094] By taking the derivative of the second linear sliding surface and combining it with equation (5), we can obtain:

[0095]

[0096] make The designed ship longitudinal control force τ is obtained u and the yaw control torque τ r , expressed as:

[0097]

[0098] In the formula, k1, k2, k3, k4 are the positive parameters to be designed. is the estimated value of μ1, is the estimated value of μ2, the design parameter and The adaptive laws are:

[0099]

[0100] In the formula, η1, η2, σ1, σ2 are positive design parameters.

[0101] S5: adjusting the position tracking error by means of the longitudinal control force and the yaw control torque so that the position tracking error converges, thereby achieving trajectory tracking.

[0102] Specifically, in this embodiment, the stability of the designed control method is verified based on the Lyapunov function, and the process is:

[0103] Define the Lyapunov function, expressed as:

[0104]

[0105] In the formula,

[0106] By taking the derivative of both sides of equation (13) with respect to time and combining equations (8), (10), (11) and (12), we can obtain:

[0107]

[0108] According to Lemma 1: For any ε>0, there exists the following inequality:

[0109] 0≤|s|-stanh(s / ε)≤0.2785ε

[0110] In the formula, s is an arbitrary variable, ε is a positive design parameter;

[0111] We can get:

[0112] μ1|s1|-μ1s1tanh(s1)=μ1(|s1|-s1tanh(s1))≤0.2785μ1 (33)

[0113] In formula (14), there exists:

[0114]

[0115] because

[0116]

[0117] Substituting equations (15), (16) and (17) into equation (14), equation (14) is transformed into:

[0118]

[0119] In the formula,

[0120]

[0121] According to Lemma 2: Consider a system x = f(x), f(0) = 0, x∈R n , where f(x) is a continuous function. Assume that there exists a continuous Lyapunov function V: D→R that satisfies the following conditions: the Lyapunov function V is a positive definite function, and there exist real numbers ρ1>0, ρ2>0, θ l > 0 and an open-loop neighborhood near the origin, and satisfying Then the system can achieve finite time stability, and the stability time T r satisfy:

[0122]

[0123] Where V(0) is the initial value of the system V(x);

[0124] It can be seen that V can converge in a finite time, and time T r The following conditions are met:

[0125]

[0126] In this embodiment, in order to verify the effectiveness of the designed control scheme, a patrol ship named BAYCLASS of Singapore Customs is used as the simulation object for computer simulation experiments. The ship is 38m long and has a mass of m=1.18×10 5 kg, other parameters are m 11 =1.2×10 5 kg, m 22 =1.779×10 5 kg, m 33 =6.36×10 7 kg, d 11 =2.15×10 4 kg / s,d 22 =1.47×10 5 kg / s,d 33 =8.02×10 6 kg / s.

[0127] In the simulation experiment, the control scheme designed by the present invention is compared with the control scheme using the linear sliding surface, and the effect of the control strategy of the present invention when using different redefined lengths l is verified. In the simulation diagram, the trajectory under the control law used for comparison is set as the first group; the trajectory under the control law of the present invention is set as the second group; the effect of the control scheme of the present invention when l is 6 is set as the third group. The linear sliding surface, control law and adaptive law used for comparison are shown in equations (21), (22) and (23).

[0128]

[0129]

[0130] In order to simulate the sea conditions, the external time-varying disturbance is expressed by equation (24):

[0131]

[0132] Set the parameters χ = 2, c = 5, c1 = 2.4 × 10 5 , c2=2×10 7 , ε1=0.1,ε2=0.05,T r =0.1, λ1=1, λ2=1, k1=2, k2=0.7, k3=2, k4=0.4, l=4, η1=1×10 -2 ,η2=4×10 -2 ,η3=1500,η4=8.5×10 3 ,σ1=1×10 -7 ,σ2=1×10 -9 ,σ3=1×10 -6 ,σ4=1×10-8 .

[0133] Set the expected sine trajectory to x d =300sin(0.03t),y d =10t, and set the initial position and velocity of the ship to (x0; y0; ψ0; u0; v0; r0) = (40; 0; 0; 0.1; 0; 0).

[0134] Specifically, the simulation results are as follows: Figures 3 to 12 As shown, from Figure 3 It can be seen that under the action of different control strategies, the actual trajectory of the ship can track the expected trajectory. First, the first group is compared with the second group to highlight the effect of the control algorithm of the present invention compared with the comparison algorithm. Figure 4 and Figure 5 It can be seen that under the first control strategy, the longitudinal and lateral position errors of the ship can converge in about 25 seconds. However, under the second control strategy, the longitudinal and lateral position errors can converge in about 10 seconds, and the convergence speed has been significantly accelerated, 60% faster than the first group. Figure 6 , Figure 7 and Figure 8 It can be seen that the ship speed curves under the second group of algorithms fluctuate more violently than those under the first group, but they are not much different after stabilization. Fig. 9 and Fig.10 It can be seen that the control input of the second group is larger than that of the first group, but the control input of the third group is close to that of the first group. Therefore, it can be concluded that under the same control input, the trajectory tracking speed of the algorithm of the present invention is faster than that of the comparison algorithm.

[0135] Then, the second group is compared with the third group to highlight the effect of using different outputs to redefine the distance l. Figure 3 It can be seen that under the control strategy of the second group, the trajectory tracking rate is slightly faster than that of the third group, and the third group has some overshoot. Figures 4 to 8 In the study, there was almost no difference in the effects between the second and third groups; however, Fig. 9 and Fig.10It can be seen that the control input of the second group is larger than that of the third group. Therefore, it can be concluded that the adjustment of the output redefinition distance l can effectively change the trajectory tracking effect and control input, which is more suitable for the different needs of the ship during navigation. It can also be seen from equations (6) and (11) that the control input is related to l, which once again verifies the accuracy of the simulation results. It shows that the ship can achieve trajectory tracking under the action of this control method, and the size of l can be adjusted as required to obtain different control accuracies and control inputs, which is suitable for various scenarios. When the accuracy requirement is not high, l can be increased to obtain a smaller control input to achieve the purpose of energy saving.

[0136] Finally, from Fig.11 and Fig.12 It can be obtained that the adaptive law designed in the present invention can better estimate the external position disturbance μ i , i=1,2, thereby improving the tracking accuracy of the controller of the present invention.

[0137] Through the comparative simulation experiment between the above invention and the prior art, the beneficial effects brought by the present invention are summarized into the following two points:

[0138] (1) To solve the under-actuation problem of the ship, the present invention adopts an output redefinition method to re-output the initial position of the ship, so that the longitudinal control force τ appears when the second-order derivative of the tracking error is calculated. u and the yaw control torque τ r , by designing τ u and τ r Enables the ship to track the desired position.

[0139] (2) To address the problem of slow convergence, the controller is designed in combination with the finite time convergence theory, and a finite time term is added to accelerate the convergence rate of the error. An adaptive technique is used to estimate the upper bound of the external unknown disturbance, and the hyperbolic tangent function is used instead of the traditional sign function to eliminate jitter.

[0140] The present invention uses an adaptive sliding mode finite time ship trajectory tracking control algorithm based on output redefinition to realize ship trajectory tracking control, and theoretically proves that all error signals in the underactuated ship trajectory tracking control system can converge in a finite time under the action of this controller. By comparing with the effect of the comparative algorithm, it can be concluded that the algorithm proposed by the present invention can make the tracking error converge quickly. Theoretical analysis and simulation experimental results show that the feasibility of the adaptive sliding mode finite time ship trajectory tracking control algorithm based on output redefinition proposed by the present invention is confirmed.

[0141] 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned 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. An adaptive sliding mode ship trajectory tracking control method based on output redefinition, characterized in that: The specific steps include: S1: establishing a mathematical model of an underactuated ship, and redefining the position of the underactuated ship model using an output redefinition method; S2: designing a position tracking error based on the position of the redefined underactuated ship mathematical model, and derivatizing the position tracking error to obtain a tracking error after the derivation; S3: designing a first linear sliding surface and a second linear sliding surface according to the position tracking error and the derived tracking error; S4: designing a ship longitudinal control force and a bow rolling control moment of an underactuated ship mathematical model based on the first linear sliding surface and the second linear sliding surface in combination with an adaptive technology; S5: adjusting the position tracking error by means of the longitudinal control force and the yaw control torque so that the position tracking error converges, thereby achieving trajectory tracking.

2. The adaptive sliding mode ship trajectory tracking control method based on output redefinition according to claim 1 is characterized in that: In S1, a mathematical model of an underactuated ship is established, and the position of the underactuated ship model is redefined using an output redefinition method. The mathematical model of the underactuated ship is expressed as: Where x, y, ψ are the longitudinal displacement, transverse displacement and heading angle of the ship respectively; u, v, r are the forward speed, drift speed and bow angular velocity of the ship in the appendage coordinate system respectively; τ u is the longitudinal control force of the ship, τ r is the yaw control torque; m 11 ,m 22 ,m 33 is the inertia parameter; d 11 ,d 22 ,d 33 is the hydrodynamic parameter; τ wu ,τ wv ,τ wr It is the disturbance caused by the external wind, current and waves acting on the ship; The position of the underactuated ship model is redefined using an output redefinition method, and the position of the redefined underactuated ship mathematical model is: Where x1 and y1 are the longitudinal and transverse coordinates of the ship after redefinition, and l is the positive parameter to be designed.

3. The adaptive sliding mode ship trajectory tracking control method based on output redefinition according to claim 2 is characterized in that: In S2, a position tracking error is designed based on the position of the redefined underactuated ship mathematical model, and the tracking error of the ship controller is derived to obtain the derived tracking error, including: The designed position tracking error is: Among them, e x and e y is the longitudinal position error and the lateral position error; x d and d is the desired longitudinal position and the desired lateral position; For e in formula (3), x and e y Taking the second derivative and combining equation (1) and equation (2), we can get: The formula (4) is transformed as follows: Where, the expressions of f(x) and f(y) are shown in formula (6):

4. The adaptive sliding mode ship trajectory tracking control method based on output redefinition according to claim 3 is characterized in that: In S3, designing the first linear sliding surface and the second linear sliding surface according to the position tracking error and the derived tracking error includes: The first linear sliding surface s1 is shown in formula (7): In the formula, λ1 is the positive parameter to be designed; The second linear sliding surface s2 is shown in formula (8): In the formula, λ2 is the positive parameter to be designed.

5. The adaptive sliding mode ship trajectory tracking control method based on output redefinition according to claim 4 is characterized in that: In S4, the process of designing the longitudinal control force and the bow control torque of the underactuated ship mathematical model based on the first linear sliding surface and the second linear sliding surface in combination with the adaptive technology is as follows: By taking the derivative of the first linear sliding surface and combining it with equation (5), we can obtain: By taking the derivative of the second linear sliding surface and combining it with equation (5), we can obtain: make The designed ship longitudinal control force τ is obtained u and the yaw control torque τ r , expressed as: In the formula, k1, k2, k3, k4 are the positive parameters to be designed. is the estimated value of μ1, is the estimated value of μ2, the design parameter and The adaptive laws are: In the formula, η1, η2, σ1, σ2 are positive design parameters.

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