Pre-set performance control method for ship dynamic positioning system under saturation constraint

Abstract

The preset performance control method of a ship power positioning system under saturation constraint relates to the technical field of ship motion control. The preset performance control method of a ship power positioning system under saturation constraint is used to solve the problem that the existing ship power positioning system is difficult to simultaneously consider performance constraint and propeller saturation constraint. The preset performance control method of a ship power positioning system under saturation constraint constructs a system safety evaluation factor, so that when the state of the ship power positioning system exceeds a safety domain, an auxiliary variable and a compensation error are introduced, a controller of the ship power positioning system satisfying performance constraint while existing input saturation is obtained, and the preset performance control of the ship power positioning system is realized by using the controller.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of ship motion control. BACKGROUND

[0002] Compared with the traditional anchoring system, the dynamically positioned ship has the advantages of high maneuverability and precise positioning, and shows excellent performance in complex marine engineering. The dynamically positioned ship not only breaks through the depth limit, but also avoids the destructive impact on the seabed caused by anchoring, and thus becomes an ideal choice for performing complex tasks. This trend reflects the increasing demand for efficient and flexible ship technology in the field of marine resource development and marine engineering.

[0003] As a nonlinear system, the ship dynamic positioning system has various constraints in control, such as artificially added performance constraints and thruster saturation constraints, which are difficult to consider simultaneously. The existing preset performance control method of the ship dynamic positioning system mostly ignores the adjustment ability of the system itself when dealing with saturation constraints, and in some cases, the appearance of limited saturation may accelerate the convergence speed of the system. SUMMARY

[0004] In order to solve the problem that the existing ship dynamic positioning system is difficult to consider performance constraints and thruster saturation constraints simultaneously, the preset performance control method of the ship dynamic positioning system under saturation constraints based on BCFB (balanced command filter backstepping) is provided, which evaluates whether the ship dynamic positioning system is in a safe state by constructing a performance system safety evaluation factor, and then decides whether to compensate for input saturation.

[0005] The preset performance control method of the ship dynamic positioning system under saturation constraints comprises:

[0006] Constructing a system safety evaluation factor P f When the state of the ship dynamic positioning system exceeds the safety domain, auxiliary variables and compensation errors are introduced to obtain a controller that satisfies the performance constraints while the ship dynamic positioning system has input saturation, and the preset performance control of the ship dynamic positioning system is realized by using the controller;

[0007] The expression of the system safety evaluation factor P f is as follows:

[0008]

[0009] Wherein, Γ(t)=[ρ T (t)ρ(t)] / ||Q||, Q is a positive definite diagonal parameter matrix, ρ(t) is a performance function, Γ0(t)=δΓ(t), δ is a safety domain coefficient, V(t)=σ T Qσ, σ is a compensation error, Q is a positive definite diagonal parameter matrix;

[0010] The controller expression is:

[0011]

[0012] Where τ is the control input generated by the thruster, M, C, and D are the inertia matrix, Coriolis centripetal force matrix, and damping coefficient matrix of the ship's dynamic positioning system, respectively, R(ψ) is the transformation matrix between the northeast coordinate system and the hull coordinate system, and υ is the velocity vector of the ship in the hull coordinate system. For υ c The first derivative, υ c For the state of the command filter, s2 = υ - υ c σ1=s1-ξ1, where s1 is the trajectory tracking error of the ship's dynamic positioning system;

[0013] Auxiliary variables And it satisfies:

[0014]

[0015] k1, k2, and χ are all design parameters, and k1 > 0, k2 > 0, and -1 < χ < 0. α=R(ψ)(ξ2+υ s ), υ s Let Δτ be the velocity-order stable variable of the ship's dynamic positioning system, and let Δτ be the control error.

[0016] Furthermore, the performance function ρ(t) described above is a continuously smooth exponentially decaying function, expressed as:

[0017] ρ(t)=[ρ1(t),ρ2(t),ρ3(t)] T ,

[0018] ρ i (t)=(ρ i0 -ρ i∞ )exp(-λ i t)+ρ i∞ ,

[0019] Where i = 1, 2, 3, ρ i0 =ρ i (0)>ρ i∞ >0, ρ i (0) and ρ i∞ Representing ρ i The initial and infinite states of (t), λ i To determine the constant of the rate of decrease of the performance function, and we have λ i >0, where t is time.

[0020] Further, the above-mentioned safety domain Ω0is obtained according to the compensation error σ, and is expressed as:

[0021] Ω0= {σ: V(t)≤Γ0(t)},

[0022] where the compensation error σ2= s2- ξ2.

[0023] Further, the above-mentioned method for constructing a controller of a ship power positioning system satisfying performance constraints while input saturation exists comprises:

[0024] A continuous smooth exponential decay function is selected as a performance function ρ(t), and the performance function ρ(t) is used to constrain the performance boundary of the trajectory tracking error η e under the condition of input saturation;

[0025] An instruction filter is designed;

[0026] Based on the trajectory tracking error η e , the state υ c of the instruction filter and the velocity vector υ of the ship in the ship body coordinate system, an auxiliary variable ξ and a compensation error σ are constructed;

[0027] A system safety evaluation factor P f is designed, so that when the state of the ship power positioning system exceeds the safety domain, the auxiliary variable ξ and the compensation error σ can be introduced;

[0028] According to the instruction filter and the system safety evaluation factor P f , a controller of the ship power positioning system satisfying performance constraints while input saturation exists is constructed.

[0029] Further, the expression of the above-mentioned instruction filter is:

[0030]

[0031] υ c (0) = υ s (0),

[0032] wherein is a positive definite diagonal parameter matrix.

[0033] Further, the expression of the velocity order stability variable υ s of the above-mentioned ship power positioning system is:

[0034]

[0035] wherein η d is the expected position vector of the ship.

[0036] Further, the performance boundary expression of the trajectory tracking error η e is:

[0037] -ρ i (t)≤η ei (t)≤ρ i (t),

[0038] wherein i = 1, 2, 3, η e = [η e1 , η e2 , η e3 ] T = η - η d , η d is the desired position vector of the ship, and η is the position vector of the ship in the North-East coordinate system.

[0039] Further, the inertia matrix, the Coriolis centripetal force matrix, the damping coefficient matrix of the ship dynamic positioning system, and the conversion matrix expression between the North-East coordinate system and the ship coordinate system are as follows:

[0040]

[0041]

[0042] wherein is the heading angle of the ship in the North-East coordinate system, u, v and r are the surge velocity, sway velocity and yaw angle of the ship in the ship coordinate system, respectively.

[0043] The preset performance control device of the ship dynamic positioning system under saturation constraint, the preset performance control device comprises a processor and a memory, at least one instruction is stored in the memory, and the at least one instruction is loaded and executed by the processor to realize the preset performance control method of the ship dynamic positioning system under saturation constraint as described above.

[0044] A computer storage medium, at least one instruction is stored in the computer storage medium, and the at least one instruction is loaded and executed by the processor to realize the preset performance control method of the ship dynamic positioning system under saturation constraint as described above.

[0045] The preset performance control method of the ship dynamic positioning system under saturation constraint based on BCFB has the following beneficial effects relative to the prior art:

[0046] (1) The preset performance control method of the ship dynamic positioning system under saturation constraint based on BCFB has the following beneficial effects relative to the prior art:

[0047] (2) The application evaluates the safety of the ship dynamic positioning system under the influence of unstable factors such as propeller saturation by constructing a system safety evaluation factor, ensures the control performance of the ship dynamic positioning system while meeting the saturation constraint, improves the utilization efficiency of each propeller, and further improves the operation capacity of the ship.

[0048] In summary, the application is suitable for solving the problem that various performance constraints and propeller saturation constraints are difficult to be met simultaneously during the operation of the dynamic positioning ship, and ensures the stability of the ship dynamic positioning system while ensuring its control performance as much as possible. BRIEF DESCRIPTION OF DRAWINGS

[0049] Fig. 1 The preset performance control flowchart of the ship dynamic positioning system under the saturation constraint based on BCFB;

[0050] Fig. 2 The schematic diagram of the North-East coordinate system and the ship coordinate system;

[0051] Fig. 3 The schematic diagram of the invariant set Ω and the safe domain Ω0 of BCFB. DETAILED DESCRIPTION

[0052] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application. It should be noted that, in the case of no conflict, the embodiments in the application and the features in the embodiments can be combined with each other.

[0053] REFERENCE Figs. 1-3 To specifically describe the present embodiment, the preset performance control method of the ship dynamic positioning under the saturation constraint based on BCFB described in the present embodiment comprises:

[0054] First, the kinematics and dynamics models of the ship and the tracking error model are established; then a continuous smooth exponential decay function is selected to construct a performance function; subsequently, an instruction filter and a system safety evaluation factor are designed, and auxiliary variables are constructed to compensate for the influence of filter errors and propeller saturation on the ship dynamic positioning system; finally, a controller is designed to ensure that the ship dynamic positioning system meets the performance constraint while there is input saturation, and further ensure that the transient performance and steady-state performance constraints during the whole operation process of the ship are met.

[0055] The specific implementation steps are as follows:

[0056] First, the earth center is taken as the coordinate origin O E The North-East coordinate system XE Y E Z E ; with the ship's center of gravity as the coordinate origin O B Establish the ship coordinate system X B Y B Z B , as shown in the above coordinate system. Based on the above coordinate system, a three-degree-of-freedom dynamic positioning ship mathematical model considering input saturation is established, and the expression is as follows: Fig. 2

[0057]

[0058] where, and are the first-order derivatives of η and υ, respectively; is the position vector of the ship in the north-east coordinate system composed of position (x, y) and heading angle ψ ∈ [0, 2π]; is the velocity vector of the ship in the ship coordinate system composed of surge velocity u, sway velocity v and yaw r; respectively represent the inertia matrix, Coriolis centripetal force matrix and damping coefficient matrix of the ship's dynamic positioning system; is the transformation matrix between two coordinate systems satisfying R -1 (ψ) = R T (ψ) and ||R(ψ)|| = 1 properties; is the ocean environmental disturbance vector suffered by the ship, which is continuous and bounded. The specific forms of each parameter are as follows:

[0059]

[0060]

[0061] ω = [0.2sin(0.5t), 0.1sin(0.2t), 0.2sin(0.3t)] T ,

[0062] is the control input generated by the thruster, which includes force and torque, τ1, τ2, τ3 represent the longitudinal direction control force, lateral direction control force and heading direction control torque, respectively. In practice, due to the physical limitations of the thruster, the control force and torque will be subject to saturation nonlinearity, which is expressed as: sat(τ) = τ + Δτ, where is the control error between the expected output control force and torque and the actual output due to filtering error and thruster saturation, and the specific expression of the saturation function sat(τ) = [sat(τ1), sat(τ2), sat(τ3)] T is as follows: ​

[0063]

[0064] where i = 1, 2, 3, τ imax and τ imin denote the maximum and minimum control forces or moments that the ship's propeller can generate in the corresponding degree of freedom, respectively. In this implementation, τ imax = 680000, τ imin = -540000.

[0065] Secondly, to ensure that the ship meets the performance requirements of the task, a set of continuous and smooth exponential decay functions are selected as the performance functions:

[0066] ρ(t) = [ρ1(t), ρ2(t), ρ3(t)] T ,

[0067] ρ i (t) = (ρ i0 - ρ i∞ )exp(-λ i t) + ρ i∞ ,

[0068] where i = 1, 2, 3, ρ i0 = ρ i (0) > ρ i∞ > 0, ρ i (0) and ρ i∞ denote the initial and infinite states of ρ i (t), respectively; the constant λ i > 0 determines the rate of decline of the performance function, and t is time. In this implementation, the actual values are: ρ i0 = ρ i (0) = 20, ρ i∞ = 0.1 for i = 1, 2; ρ 30 = ρ i (0) = 1, ρ 3∞ = 0.01 for i = 3; and λ i = 0.05.

[0069] For t ≥ 0, given the continuous, bounded, and derivable partial derivatives of the desired position and heading of the ship and their initial states η0 = [0; 0; 0] and υ0 = [0; 0; 0], the trajectory tracking error of the ship's dynamic positioning system is The tracking error performance boundary in the presence of input saturation can be expressed as -ρ i (t) ≤ η ei (t) ≤ ρ i (t).

[0070] η d = [100cos(t / 100); 100sin(t / 100); 0],

[0071] η e = [η e1 ,η e2 ,η e3 ] T = η-η d .

[0072] Thirdly, the instruction filter is designed, and the auxiliary variables are constructed to compensate the influence of the filtering error and the thruster saturation on the ship dynamic positioning system.

[0073] Definition

[0074] wherein: denotes the state of the instruction filter.

[0075] The specific form of the instruction filter is designed as:

[0076]

[0077] υ c (0)=υ s (0),

[0078] wherein, is a positive definite diagonal parameter matrix, is the velocity order stable variable of the ship dynamic positioning system.

[0079] In order to compensate the influence of the filtering error υ f = υ c - υ s and the control error Δτ caused by the thruster saturation on the ship dynamic positioning system, the auxiliary variables υ and the compensation error Δτ are further constructed, and the specific form is as follows:

[0080]

[0081] wherein, k1>0, k2>0, -1<χ<0 are all design parameters, and the values of the embodiment are k 1i =2, k 2i =3, i∈{1,2,3}, χ=-0.5; P f is a system safety evaluation factor; α=R(ψ)(ξ2+υ s ) and satisfies:

[0082]

[0083] ​Further, the specific form of the speed stage stable variable υ of the ship power positioning system can be expressed as: s

[0084]

[0085] In the fourth step, a system safety evaluation factor P is designed to evaluate the influence of input saturation on the ship power positioning system.

[0086] According to the compensation error σ, an invariant set and a safety domain are defined.

[0087] The invariant set is Ω = {σ: V(t) = σ T Qσ ≤ Γ(t)}, where Γ(t) = [ρ T (t) ρ(t)] / ||Q||, is a positive definite diagonal parameter matrix. The invariant set Ω represents the feasible region of the state of the ship power positioning system.

[0088] The safety domain is Ω0 = {σ: V(t) ≤ Γ0(t)}, where Γ0(t) = δΓ(t) and 0 < δ < 1, and the safety domain coefficient δ is determined by human. In the embodiment, the safety domain coefficient δ = 0.5.

[0089] When the state of the ship power positioning system is in the safety domain Ω0, even if the propeller saturation occurs, it is considered that the ship power positioning system has a certain self-regulating ability, and thus the ship power positioning system is still considered to be safe. For the ship power positioning system with weak self-regulating ability, when the state of the ship power positioning system exceeds the safety domain Ω0, the system safety evaluation factor P f will play a role and drive the auxiliary variable to intervene, so as to finally ensure that the state of the ship power positioning system returns to the safety domain Ω0.

[0090] The specific form of the system safety evaluation factor P f is as follows:

[0091]

[0092] In the fifth step, a controller is designed to achieve the control target.

[0093]

[0094] The controller can ensure that the ship power positioning system meets the performance constraints while the input saturation exists.

[0095] ​Through MATLAB simulation, the trajectory tracking preset performance control method of the dynamic positioning ship under the saturation constraint based on BCFB can be obtained, the trajectory tracking preset performance control method can meet the performance constraint while considering input saturation, has strong flexibility and robustness, and can effectively improve the reliability and effectiveness of the operation of the dynamic positioning ship.

[0096] While the application has been described with reference to particular embodiments thereof, it should be understood that these are merely illustrative of the principles and applications of the application. It will thus be appreciated that numerous modifications can be made to the illustrative embodiments and that other arrangements can be devised without departing from the spirit and scope of the application as defined by the appended claims. It will be understood that the features described with reference to separate embodiments can be used in combination with features described elsewhere. It will be further understood that features described in relation to one embodiment can be used in other embodiments.

Claims

1. A preset performance control method for a ship dynamic positioning system under saturation constraints, characterized in that, include: Constructing system security assessment factors This allows the introduction of auxiliary variables and compensation errors when the ship's dynamic positioning system exceeds its safe range, thereby obtaining a controller that satisfies performance constraints while the ship's dynamic positioning system has input saturation. This controller is then used to achieve preset performance control of the ship's dynamic positioning system. The system security assessment factors The expression is: ， in, , It is a positive definite diagonal parameter matrix. For performance functions, , For the safety domain coefficient, , To compensate for errors, , It is a positive definite diagonal parameter matrix; The controller expression is: ， in, For the control input generated by the thruster, , and These are the inertial matrix, Coriolis centripetal force matrix, and damping coefficient matrix of the ship's dynamic positioning system, respectively. This is the transformation matrix between the northeast coordinate system and the ship's coordinate system. Let be the velocity vector of the ship in the ship's coordinate system. for The first derivative, This refers to the state of the instruction filter. , , , For the trajectory tracking error of the ship's dynamic positioning system; Auxiliary variables And satisfy: ， , and All are design parameters and have , , , , , For the velocity-order stable variable of the ship's dynamic positioning system, To control errors; The performance function It is a continuously smooth, exponentially decaying function, expressed as: ， ， in, , , and They represent The initial and infinite states, To determine the constant of the rate of decrease of the performance function and have , For time.

2. The preset performance control method for a ship dynamic positioning system under saturation constraints according to claim 1, characterized in that, The security domain Based on compensation error Obtained, represented as: ， Among them, compensation error .

3. The preset performance control method for a ship dynamic positioning system under saturation constraints according to claim 1 or 2, characterized in that, The method for constructing a controller for a ship dynamic positioning system that satisfies performance constraints while experiencing input saturation includes: A continuously smooth exponentially decaying function is chosen as the performance function. Using this performance function Trajectory tracking error under constraints with input saturation The performance boundary; Design instruction filters; Based on the trajectory tracking error The state of the instruction filter and the velocity vector of the ship in the hull coordinate system Constructing auxiliary variables and compensation error ; Design system safety assessment factors This allows the auxiliary variable to be introduced when the ship's dynamic positioning system exceeds its safe range. and compensation error ; Based on the instruction filter and system security assessment factors Construct a controller for a ship's dynamic positioning system that meets performance constraints while experiencing input saturation.

4. The preset performance control method for a ship dynamic positioning system under saturation constraints according to claim 3, characterized in that, The expression for the instruction filter is: ， ， in, It is a positive definite diagonal parameter matrix.

5. The preset performance control method for a ship dynamic positioning system under saturation constraints according to claim 4, characterized in that, The velocity-order stable variable of the ship dynamic positioning system The expression is: ， in, This is the desired position vector of the ship.

6. The preset performance control method for a ship dynamic positioning system under saturation constraints according to claim 3, characterized in that, The trajectory tracking error The performance boundary expression is: ， in, , , Let be the desired position vector of the ship. This is the position vector of the ship in the northeast coordinate system.

7. The preset performance control method for a ship dynamic positioning system under saturation constraints according to claim 1, characterized in that, The expressions for the inertial matrix, Coriolis centripetal force matrix, damping coefficient matrix, and transformation matrix between the northeast coordinate system and the hull coordinate system of the ship's dynamic positioning system are as follows: ， ， ， ， Among them, the bow angle of the ship in the northeast coordinate system, , and These are the ship's pitch speed, sway speed, and bow angle in the ship's coordinate system.

8. A preset performance control device for a ship dynamic positioning system under saturation constraints, characterized in that, The preset performance control device includes a processor and a memory, wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the preset performance control method for a ship dynamic positioning system under saturation constraints as described in any one of claims 1 to 7.

9. A computer storage medium, characterized in that, The computer storage medium stores at least one instruction, which is loaded and executed by a processor to implement the preset performance control method for a ship dynamic positioning system under saturation constraints as described in any one of claims 1 to 7.

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