Self-adaptive preset-time dynamic positioning control method for semi-submersible platform with input saturation

Abstract

The application discloses a semi-submersible platform adaptive preset time dynamic positioning control method with input saturation, which comprises the following steps: obtaining a three-degree-of-freedom motion model of the semi-submersible platform with input saturation; obtaining a conversion variable error according to a fixed time chimney boundary function and a fixed time tracking performance function; constructing a virtual controller according to the conversion variable error; constructing an adaptive law according to the virtual controller and obtaining a speed error vector according to the virtual controller; constructing an asymmetric saturation auxiliary system according to the three-degree-of-freedom motion model and a segmented input saturation limit, and constructing a final controller according to the speed error vector by combining the adaptive law. The problems that the controller with robust neural damping technology and the adaptive parameters cannot guarantee greater calculation load and more stable time when the ship model parameters change, and the system input saturation problem cannot be solved when the control input of the dynamic positioning ship is saturated to a certain limit are solved.

Description

Technical Field

[0001] This invention relates to the field of motion control research technology for semi-submersible platforms, and in particular to an adaptive preset time dynamic positioning control method for semi-submersible platforms with input saturation. Background Technology

[0002] The motion of a semi-submersible platform mainly relies on the forward thrust and yaw torque provided by several side thrusters distributed around it to adjust the platform's attitude to achieve the desired attitude. In the dynamic positioning control process of the SSP, firstly, the kinematic and dynamic models of the SSP are established; secondly, the error between the desired position and the current position of the platform is constructed; and simultaneously, considering issues such as model uncertainty, marine environmental disturbances, and actuator amplitude constraints, a nonlinear feedback control law for dynamic positioning of the SSP is designed. Finally, the actuators are driven according to the control signal to make the SSP reach the desired control state.

[0003] Among existing algorithms, a controller based on robust neural damping technology has been proposed. Let's denote this algorithm as Algorithm A. It designs the ship's dynamic positioning control law based on neural network approximation technology and constructs an adaptive law by compressing the neural network weights. However, while robust neural damping technology solves the system's uncertainty problem, updating the robust neural damping term and adaptive parameters requires a greater computational load when the appendage mass, moment of inertia, and hydrodynamic derivative in the ship's mathematical model increase, or when the initial error increases. This also exacerbates the overshoot of the control input. In reality, the thrust of a ship is limited, and the amplitude of the control input is objectively constrained by the mechanical structure and material reliability. When the control input overshoots to a certain limit, input saturation occurs, leading to instability in the control system and requiring more time and larger inputs to stabilize it.

[0004] Based on the above analysis, existing robust neural damping techniques have the following drawbacks:

[0005] (1) When the parameters of the ship model change, it cannot be guaranteed that the controller and adaptive parameters containing robust neural damping technology will not generate a larger computational load and more settling time.

[0006] (2) When the control input of a dynamically positioned vessel overshoots to a certain limit and reaches saturation, robust neural damping technology cannot handle the system input saturation problem. Summary of the Invention

[0007] This invention provides an adaptive preset time dynamic positioning control method for a semi-submersible platform with input saturation to overcome the above-mentioned technical problems.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] An adaptive preset-time dynamic positioning control method for a semi-submersible platform with input saturation specifically includes the following steps:

[0010] S1: Obtain a three-degree-of-freedom motion model of a semi-submersible platform with input saturation;

[0011] S2: Define the desired attitude and obtain the dynamic attitude error based on the three-degree-of-freedom motion model;

[0012] Construct a fixed-time tracking performance function and a fixed-time chimney boundary function;

[0013] The dynamic attitude error is transformed based on the fixed-time chimney boundary function and the fixed-time tracking performance function to obtain the transformed variable error.

[0014] S3: Based on neural network approximation technology, a virtual controller is constructed according to the three-degree-of-freedom motion model and the error of the transformed variables;

[0015] S4: Construct an adaptive law based on the virtual controller, and obtain the velocity error vector based on the virtual controller using dynamic surface control technology;

[0016] S5: Construct an asymmetric saturation auxiliary system based on a three-degree-of-freedom motion model and piecewise input saturation constraints;

[0017] S6: Based on the adaptive law and asymmetric saturation auxiliary system, the final controller is constructed according to the velocity error vector, so as to realize the adaptive preset time dynamic positioning control of the semi-submersible platform with input saturation according to the final controller.

[0018] Furthermore, the three-degree-of-freedom motion model of the semi-submersible platform with input saturation described in S1 is shown in Equation (1).

[0019]

[0020] In the formula: η=[x,y,ψ] T Let (x, y) represent the attitude vector of the semi-submersible platform (SSP) in the inertial coordinate system; ψ represents the heading angle; R(ψ) represents the velocity rotation matrix; ν = [u, v, r] T Let represent the velocity vector of the SSP in the attached coordinate system; u represent the forward velocity of the SSP; v represent the lateral drift velocity; r represent the bow roll angular velocity; M is the inertia matrix; N(ν)ν is the nonlinear derivative term including the added mass, added inertial torque, and hydrodynamics; τ w =[τ wu ,τ wv ,τ wr ] TThe vector represents the marine environmental disturbance, containing the disturbance forces and moments in the forward, drift, and yaw degrees of freedom of the SSP; τ represents the ideal control input under unsaturated conditions; τ re This represents the actual control input; and the three-degree-of-freedom control input force and torque should satisfy the piecewise input saturation constraint condition in formula (2), τ max ,τ min These represent the upper and lower limits of the SSP side thrust of a semi-submersible platform, respectively.

[0021] Furthermore, S2 specifically includes the following steps:

[0022] S21: Define the desired posture η d =[x d ,y d ,ψ d ] T The dynamic attitude error η is obtained based on the three-degree-of-freedom motion model. e =[xx d yy d ,ψ-ψ d ] T ;

[0023] S22: Construct a fixed-time tracking performance function and a fixed-time chimney boundary function;

[0024] The fixed-time chimney boundary function μ jν The expression is

[0025]

[0026] In the formula: η jν0 ,η jνT ,m j All represent positive adjustable parameters, and j = 1, 2, ν = u, v, r; T jν Indicates a preset time; μ 1ν =[μ 1u ,μ 1v ,μ 1r ] T With μ 2ν =[μ 2u ,μ 2v ,μ 2r ] T These represent the upper and lower boundaries during the error convergence process, respectively.

[0027] The fixed-time tracking performance function The expression is

[0028]

[0029] In the formula: k ν,T 0ν Indicates a positive adjustable parameter; T 0ν It is represented as a specified preset time;

[0030] S23: Perform error transformation on the dynamic attitude error based on the fixed-time tracking performance function to obtain the new error variable Υ(t).

[0031]

[0032] In the formula: η e Indicates η e (t) in short form; η e (0) represents the dynamic attitude error η. e The initial value of (t);

[0033] S24: Based on the fixed-time chimney boundary function μ jν The asymmetric performance constraint for obtaining the new error variable Υ(t) is as follows:

[0034] -μ 1ν (t)<Υ(t)<μ 2ν (t) (6)

[0035] S25: Introduce the intermediate variable transformation formula, and obtain the transformation variable error based on the new error variable Υ(t) and the asymmetric performance constraints;

[0036] The intermediate variable transformation formula is as follows:

[0037]

[0038] ρ(t)=(μ 1ν -μ 2ν ) / 2, Γ(t)=(μ 1ν +μ 2ν ) / 2 (9)

[0039] In the formula: The output of the intermediate variable transformation formula is represented by ρ(t) and Γ(t); ρ(t) and Γ(t) represent intermediate parameter variables.

[0040] The transformation variable error z1 is

[0041]

[0042] Furthermore, S3 specifically includes the following steps:

[0043] S31: Based on the three-degree-of-freedom motion model and the error of the transformed variable, obtain the dynamic equation of the derivative z1 of the error of the transformed variable, the expression of which is:

[0044]

[0045] In the formula: Φ(t) represents the intermediate parameter quantity, and

[0046] S32: Definition For the error derivative of the transformed variable The uncertainty term in the dynamic equation is approximated online by the nonlinear continuous function F1(η,A1) in the RBF-NNs approximation technique, and its expression is:

[0047]

[0048] In the formula: A1 represents the weight matrix; S1(η) represents the RBF basis function vector with Gaussian function form; S1 represents the abbreviation of S1(η); η represents the attitude vector and serves as the input vector for the nonlinear continuous function F1(η,A1); ε η This represents the approximation error term;

[0049] S33: Construct a virtual controller based on the transformation variable error z1 and step S32, and the expression of the virtual controller is:

[0050]

[0051] In the formula: k η =diag{k η1 k η2 k η3} represent the virtual controller parameters in the three degrees of freedom x, y, and ψ, respectively; a1 represents the positive design parameters; θ1 represents the adaptive parameters and θ1=||A1η|| 2 ; This represents an estimate of θ1.

[0052] Furthermore, S4 specifically includes the following steps:

[0053] S41: Construct an adaptive law based on the virtual controller, and the adaptive law is...

[0054]

[0055] Where: γ1, γ2, All represent positive adaptive design parameters; ν e This represents the velocity error vector to be solved;

[0056] Where the adaptive parameter θ2=||A2ν|| 2 Specifically, it is obtained by online approximating the nonlinear derivative term N(ν)ν in the three-degree-of-freedom motion model based on the nonlinear continuous function F2(ν,A2) in the RBF-NNs approximation technique, and its expression is:

[0057] N(ν)ν=F2(ν,A2)=S2(ν)A2ν+ε ν (15)

[0058] In the formula: F2(ν,A2) represents a nonlinear continuous function; A2 represents the weight matrix; S2(ν) represents the RBF basis function vector with Gaussian function form; ε ν This represents the approximation error term of the nonlinear derivative term;

[0059] S42: Based on dynamic surface control technology, the velocity error vector ν to be solved is obtained from the virtual controller. e ;

[0060] S421: A filter using dynamic surface control technology eliminates the complexity explosion problem of the control law caused by continuous differentiation of the virtual controller. The expression of the filter is:

[0061]

[0062] In the formula: t ν =diag{t u ,t v ,t r} is the time constant matrix; β ν This indicates that the output vector is the reference signal of velocity vector ν; β ν (0),α ν (0) represents β respectively. ν With α ν The initial value;

[0063] S422: Based on the output vector β ν Obtain the velocity error vector ν to be solved using the saturation correction signal. e Its expression is

[0064]

[0065] In the formula: Θ 12 ,Θ 22 This represents the saturation correction signal, and Θ 12 =[λ u12 ,λ v12 ,λ r12 ] T ,Θ 22 =[λ u22 ,λ v22 ,λ r22 ] T ;λ u12 ,λ v12 and λ r12 These represent the first-order correction signals in the three degrees of freedom; λ u22 ,λ v22 and λr22 These represent the second-order correction signals in the three degrees of freedom; I represents the unit vector; p1 and p2 represent positive saturation auxiliary parameters, and p1 > 0 and p2 > 0.

[0066] Furthermore, the asymmetric saturation auxiliary system used in S5 to obtain the saturation correction signal is expressed as follows:

[0067]

[0068] Where: G - (τ,τ min ),G + (τ,τ max ) indicates the amount of intermediate parameters.

[0069] Furthermore, in S6, based on the adaptive law and the asymmetric saturation auxiliary system, the final controller is constructed according to the velocity error vector, and its expression is:

[0070]

[0071] In the formula: k2=diag{k 21 ,k 22 ,k 23} represent the controller parameters in the three degrees of freedom u, v, and r respectively; σ2 and a2 represent positive design parameters.

[0072] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0073] (1) By combining the constructed fixed-time tracking performance function (FTTPF), the initial dynamic attitude error is transformed into an error form unaffected by initial conditions. Then, by combining the error transformation function, the system's transformed variable error is constructed, thereby confining the dynamic error to a greater extent within the boundaries. At the same time, when the system reaches the set preset time, the transformed variable error signal successfully and stably converges.

[0074] (2) The designed asymmetric saturation auxiliary system successfully solved the input saturation problem caused by the physical limitations of the ship's actuator. In addition, despite changes in ship model parameters and hydrodynamic derivatives, the asymmetric saturation auxiliary system can still solve the singularity problem caused by the input limitations of the actuator to the control system.

[0075] (3) The nonlinear terms in the SSP dynamic positioning system are approximated online by neural network approximation technology, and an adaptive law for actuator gain is designed by adaptive technology. Attached Figure Description

[0076] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0077] Figure 1 The flowchart shows the adaptive preset time dynamic positioning control method for a semi-submersible platform with input saturation according to the present invention.

[0078] Figure 2 This is a preset time control block diagram for a semi-submersible platform considering input saturation in this embodiment;

[0079] Figure 3 This is a schematic diagram of the inertial coordinate system and attached coordinate system of the SSP in this embodiment;

[0080] Figure 4 This is a comparison diagram of the planar motion trajectory simulation experiment in this embodiment;

[0081] Figure 5 This is a comparison diagram of the simulation experiments of forward, drift, and yaw signals in this embodiment;

[0082] Figure 6 This is a comparison chart of the control input simulation experiment in this embodiment;

[0083] Figure 7 This is a comparison chart of speed simulation experiments in this embodiment;

[0084] Figure 8 This is a diagram showing the convergence effect of the new error after error transformation in this embodiment;

[0085] Figure 9 This is the core block diagram of the adaptive preset time dynamic positioning control method for a semi-submersible platform with input saturation in this embodiment. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0087] This embodiment provides an adaptive preset time dynamic positioning control method for a semi-submersible platform with input saturation, such as... Figure 1 and Figure 9As shown, the specific steps include:

[0088] S1: Obtain a three-degree-of-freedom motion model of a semi-submersible platform with input saturation;

[0089] Specifically, the expression for the three-degree-of-freedom motion model is Equation (1).

[0090]

[0091] In the formula: η=[x,y,ψ] T Let represent the attitude vector of the semi-submersible platform (SSP) in the inertial coordinate system, and the inertial coordinate system and the appendage coordinate system of the SSP are as follows: Figure 3 As shown, (x,y) represents the position of the SSP; ψ represents the heading angle; R(ψ) represents the velocity rotation matrix; ν=[u,v,r] T Let represent the velocity vector of the SSP in the attached coordinate system; u represent the forward velocity of the SSP; v represent the lateral drift velocity; r represent the bow roll angular velocity; M is the inertia matrix; N(ν)ν is the nonlinear derivative term including the added mass, added inertial torque, and hydrodynamics; τ w =[τ wu ,τ wv ,τ wr ] T The vector represents the marine environmental disturbance, containing the disturbance forces and moments in the forward, drift, and yaw degrees of freedom of the SSP; τ represents the ideal control input under unsaturated conditions; τ re This represents the actual control input; it should be noted that the lateral thrust generated by the SSP (semi-submersible platform) power system is limited, and is also affected by the mechanical structure and material reliability, making the amplitude of the control input objectively limited. The reason for considering saturation in the controller design is to make the designed controller more in line with the actual SSP drive structure and facilitate engineering applications. Therefore, the three-degree-of-freedom control input force and torque should meet the constraints of formula (2);

[0092]

[0093] In the formula: τ max ,τ min These represent the upper and lower limits of the SSP side thrust of the semi-submersible platform, respectively.

[0094] S2: Define the desired attitude and obtain the dynamic attitude error based on the three-degree-of-freedom motion model;

[0095] Construct a fixed-time tracking performance function and a fixed-time chimney boundary function;

[0096] The dynamic attitude error is transformed based on the fixed-time chimney boundary function and the fixed-time tracking performance function to obtain the transformed variable error.

[0097] Specifically, such as Figure 2 As shown, before introducing the preset time control law proposed in this embodiment, it is necessary to first introduce two smooth functions μ(t) and

[0098] a). Assume a smooth function μ(t): It satisfies the following characteristics: (1) μ(t) > 0 and (2)lim t→T μ(t)=η T ,η T >0 is an arbitrarily small constant; (3) for μ(t)=η T , where T is a preset time, then μ(t) can be selected as a fixed-time funnel boundary (FTFBs), and the fixed-time funnel boundary function in this embodiment is as shown in equation (3);

[0099] The fixed-time chimney boundary function μ jν The expression is

[0100]

[0101] In the formula: η jν0 ,η jνT ,m j All represent positive adjustable parameters, and j = 1, 2, ν = u, v, r; T jν Indicates a preset time; μ 1ν =[μ 1u ,μ 1v ,μ 1r ] T With μ 2ν =[μ 2u ,μ 2v ,μ 2r ] T These represent the upper and lower boundaries during the error convergence process, respectively.

[0102] b) Assuming a smooth function It satisfies the following properties: (1) (2) and for If T0 is the specified preset time, then If it can be selected as FTTPF, then the fixed-time tracking performance function in this embodiment is as shown in equation (4);

[0103] The fixed-time tracking performance function The expression is

[0104]

[0105] In the formula: k ν ,T 0ν Indicates a positive adjustable parameter; T 0ν It is represented as a specified preset time;

[0106]

[0107] Specifically, the following steps are included:

[0108] S21: Define the desired posture η d =[x d ,y d ,ψ d ] T The dynamic attitude error η is obtained based on the three-degree-of-freedom motion model. e =[xx d yy d ,ψ-ψ d ] T ;

[0109] S22: Construct a fixed-time tracking performance function and a fixed-time chimney boundary function;

[0110] S23: Perform error transformation on the dynamic attitude error based on the fixed-time tracking performance function to obtain the new error variable Υ(t).

[0111]

[0112] In the formula: η e Indicates η e (t) in short form; η e (0) represents the dynamic attitude error η. e The initial value of (t);

[0113] In this embodiment, η e =η-η d For attitude error, η can be adjusted by combining radial basis function neural networks (RBF-NNs). e The transient and steady-state responses are obtained, but the corresponding preset performance depends on specific initial conditions. Meanwhile, the asymmetric performance constraints based on RBF-NNs cannot be resolved. To address these challenges, an intermediate variable transformation formula is introduced.

[0114] S24: Based on the fixed-time chimney boundary function μ jν The asymmetric performance constraint for obtaining the new error variable Υ(t) is as follows:

[0115] -μ 1ν(t)<Υ(t)<μ 2ν (t) (6)

[0116] S25: By introducing an intermediate variable transformation formula, and obtaining the transformation variable error based on the new error variable Υ(t) and asymmetric performance constraints;

[0117] The intermediate variable transformation formula is as follows:

[0118]

[0119] ρ(t)=(μ 1ν -μ 2ν ) / 2, Γ(t)=(μ 1ν +μ 2ν ) / 2 (9)

[0120] In the formula: The output of the intermediate variable transformation formula is represented by ρ(t) and Γ(t). ρ(t) represents the intermediate parameter variables, Γ(t) represents the average difference between the upper and lower boundaries, and Γ(t) represents the average sum between the upper and lower boundaries. By combining equations (7) and (9), equation (6) can be expressed as equation (8) again, thereby solving the problem of error asymmetric performance constraints.

[0121] In addition, to obtain better control performance, the transformation variable error z1 is finally obtained as shown in equation (10) through the following chimney error transformation, wherein the transformation variable error z1 is:

[0122]

[0123] Based on the above analysis, the following section describes the design of the controller. The controller design is divided into two parts: First, a virtual controller is designed based on the three-degree-of-freedom motion mathematical model and the new conversion error z1. Second, the controller and adaptive law are designed based on the virtual controller and dynamic surface technology. Ultimately, this enables the SSP to achieve closed-loop stability of the system within a preset time when performing dynamic positioning tasks, and the singularity problem caused by actuator saturation is also resolved. The details are as follows:

[0124] S3: Based on neural network approximation technology, a virtual controller is constructed according to the three-degree-of-freedom motion model and the error of the transformed variables. The specific steps include:

[0125] S31: Define η d Indicates the desired posture and Then η e The derivative can be written as

[0126] Based on the three-degree-of-freedom motion model and the transformed variable error, the transformed variable error z1 is taken to contain Γ(t) and Obtaining the time derivative of the transformed variable error derivative The dynamic equation is expressed as follows:

[0127]

[0128] In the formula: Φ(t) represents the intermediate parameter quantity, and

[0129] S32: Definition For the error derivative of the transformed variable The uncertainty term in the dynamic equation is approximated online by the nonlinear continuous function F1(η,A1) in the RBF-NNs approximation technique, and its expression is:

[0130]

[0131] In the formula: A1 represents the weight matrix; S1(η) represents the RBF basis function vector with Gaussian function form; S1 represents the abbreviation of S1(η); η represents the attitude vector and serves as the input vector for the nonlinear continuous function F1(η,A1); ε η This represents the approximation error term;

[0132] S33: Construct a virtual controller based on the transformation variable error z1 and step S32, and the expression of the virtual controller is:

[0133]

[0134] In the formula: k η =diag{k η1 k η2 k η3} represent the virtual controller parameters in the three degrees of freedom x, y, and ψ, respectively; a1 represents the positive design parameters; θ1 represents the adaptive parameters and θ1=||A1η|| 2 ; This represents an estimate of θ1;

[0135] S4: Construct an adaptive law based on the virtual controller, and obtain the velocity error vector based on the virtual controller using dynamic surface control technology. This includes the following steps:

[0136] S41: Construct an adaptive law based on the virtual controller, and the adaptive law is...

[0137]

[0138] Where: γ1, γ2, All represent positive adaptive design parameters; ν e This represents the velocity error vector to be solved;

[0139] Where the adaptive parameter θ2=||A2ν|| 2 Specifically, it is obtained by online approximating the nonlinear derivative term N(ν)ν in the three-degree-of-freedom motion model based on the nonlinear continuous function F2(ν,A2) in the RBF-NNs approximation technique, and its expression is:

[0140] N(ν)ν=F2(ν,A2)=S2(ν)A2ν+ε ν (15)

[0141] In the formula: F2(ν,A2) represents a nonlinear continuous function; A2 represents the weight matrix; S2(ν) represents the RBF basis function vector with Gaussian function form; ε ν This represents the approximation error term of the nonlinear derivative term;

[0142] S42: Based on dynamic surface control technology, the velocity error vector ν to be solved is obtained from the virtual controller. e ;

[0143] S421: To avoid α ν The problem of "complexity explosion" in control laws caused by continuous differentiation is eliminated by applying dynamic surface techniques. Specifically, the filter in dynamic surface control technology eliminates the complexity explosion problem caused by continuous differentiation of the virtual controller. The expression of the filter is as follows:

[0144]

[0145] In the formula: t ν =diag{t u ,t v ,t r} is the time constant matrix; β ν This indicates that the output vector is the reference signal of velocity vector ν; β ν (0),α ν (0) represents β respectively. ν With α ν The initial value;

[0146] S422: Based on the output vector β ν Obtain the velocity error vector ν to be solved using the saturation correction signal. e Its expression is

[0147]

[0148] In the formula: Θ 12 ,Θ 22 This represents the saturation correction signal, and Θ 12 =[λ u12 ,λ v12 ,λ r12 ] T,Θ 22 =[λ u22 ,λ v22 ,λ r22 ] T ;λ u12 ,λ v12 and λ r12 These represent the first-order correction signals in the three degrees of freedom; λ u22 ,λ v22 and λ r22 These represent the second-order correction signals in the three degrees of freedom; p1 and p2 represent positive saturation auxiliary parameters, with p1 > 0 and p2 > 0; it is worth noting that the saturation correction signal is related to the input saturation error τ. re (τ)-τ is related to and obtained from equation (18); parameters p1 and p2 are positive saturation auxiliary parameters used to describe the maximum value of the correction signal implanted when saturation occurs; I represents the unit vector [1,1,1]. T To ensure the concise expression of subsequent complex formulas, and to enable... And combining equations (9) and (10), the error derivative of the transformation variable is... The dynamic equations are rewritten as follows:

[0149]

[0150] S5: Design an asymmetric saturation auxiliary system for acquiring saturation correction signals, its expression is:

[0151]

[0152] Where: G - (τ,τ min ),G + (τ,τ max () indicates the amount of intermediate parameters;

[0153] S6: Based on adaptive law and asymmetric saturation auxiliary system, a final controller is constructed according to the velocity error vector. This final controller enables adaptive preset-time dynamic positioning control of a semi-submersible platform with input saturation. The expression of the final controller is:

[0154]

[0155] In the formula: k2=diag{k 21 ,k 22 ,k 23} represent the controller parameters in the three degrees of freedom u, v, and r respectively; σ2 and a2 represent positive design parameters.

[0156] In this embodiment, the correction signal Θ in the asymmetric saturation auxiliary system is noteworthy. 12 With Θ22 The input saturation error Δτ=τ generated in formula (18) re -τ has a correlation; in asymmetric saturated auxiliary systems, G - (τ,τ min )+G + (τ,τ max ) = M -1 (τ re -τ) can be derived and cleverly applied in the design of the controller to counteract the negative effects of driver input saturation, so that when saturation occurs, the system input will smoothly reach the upper limit of saturation without jittering or stopping.

[0157] In this embodiment, to verify the effectiveness and superiority of the present invention in system control, a numerical simulation experiment was conducted in a simulated marine environment, comparing it with the existing algorithm A mentioned in the background art. The results of the present invention's method in handling actuator input saturation and achieving convergence within a preset time were analyzed in detail. The main differences between the present invention's method and the existing algorithm A are shown in Table 1.

[0158] Table 1. Similarities and differences between the method in this embodiment and existing algorithms.

[0159]

[0160] The method and algorithm A in this embodiment were simulated and compared on an industrial computer (main configuration: Intel(R) Core(TM) i5-12500 HQ CPU@2.50GHz, RAM: 8.00GB). Figures 4 to 8 The main comparison results are presented. Figure 4 The results of trajectory comparison when SSPs perform dynamic localization tasks are presented. It is evident that the method in this embodiment produces a smoother trajectory, while the convergence trajectory of Algorithm A is more tortuous. When SSPs reach the vicinity of the desired position, under the same environmental disturbances, the method in this embodiment exhibits higher steady-state accuracy. Figure 5 The comparison curves of the three degrees of freedom x, y, and ψ during SSP motion are given respectively, which show that the convergence process of the kinematic state of the method in this embodiment is smoother and more stable. Figure 6The control input comparison curves of the actuator throughout the entire control task are presented. Specifically, because the method in this embodiment considers the asymmetric amplitude limitation of the actuator, when the control input reaches the upper and lower boundaries, it automatically transitions to the upper and lower amplitudes and no longer changes, then tends to decrease to the lower boundary and then stabilizes. Compared to Algorithm A, this embodiment exhibits smaller oscillation amplitude and frequency after the control input signal converges. Furthermore, the overall control input generated by the method in this embodiment is smaller than that of Algorithm A, which can effectively reduce the actuator's movement and thus reduce system energy consumption. Figure 7 This is a speed comparison between the method in this embodiment and Algorithm A. Because the present invention requires less control input, it has a smaller velocity vector. In this simulation experiment, the preset time is set to T. 0u =300s,T 0v =300s,T 0r =300s, from Figure 8 As can be seen, the new errors after error transformation all achieved stable convergence after reaching the preset time. Therefore, it can be demonstrated that the anti-saturation control and preset time control proposed in this embodiment have achieved the expected results. In future marine engineering practices, adjusting the preset time parameter can enable the SSP to achieve "on-demand stability" when performing dynamic positioning tasks.

[0161] In summary, the adaptive preset time dynamic positioning control method for semi-submersible platforms with input saturation proposed in this embodiment achieves the following two beneficial effects in the field of SSP dynamic positioning motion control:

[0162] 1) Compared with existing robust neural damping techniques, the adaptive neural network controller proposed in this embodiment has a simpler form, effectively reducing the computational load during algorithm implementation. Simultaneously, under the action of the asymmetric saturation auxiliary system, the system singularity problem caused by input saturation is avoided by embedding the saturation correction signal into the velocity error. Since this embodiment incorporates FTFBs technology, the transformed new error has the property of changing from an initial state of 0, thus successfully limiting the error within the boundary and enabling the error to converge successfully within a preset time.

[0163] 2) Numerical simulations verified that the method in this embodiment achieves excellent control performance in SSP dynamic positioning control tasks, especially in achieving control results with preset time convergence even when considering asymmetric saturated input. SSP has broader prospects in marine exploration, marine operations, and marine resource extraction operations. The method in this embodiment enables SSP to develop towards a more intelligent, energy-efficient, and reliable trend.

[0164] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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 method for adaptive preset-time dynamic positioning control of a semi-submersible platform with input saturation, characterized in that, Specifically, the following steps are included: S1: Obtain a three-degree-of-freedom motion model of a semi-submersible platform with input saturation; S2: Define the desired attitude and obtain the dynamic attitude error based on the three-degree-of-freedom motion model; Construct a fixed-time tracking performance function and a fixed-time chimney boundary function; The dynamic attitude error is transformed based on the fixed-time chimney boundary function and the fixed-time tracking performance function to obtain the transformed variable error. Specifically, the following steps are included: S21: Define the desired pose The dynamic attitude error is obtained based on the three-degree-of-freedom motion model. ; S22: Construct the fixed-time tracking performance function and the fixed-time chimney boundary function; The fixed-time chimney boundary function The expression is (3) In the formula: Both represent positive adjustable parameters, and ; This indicates a pre-set time; and These represent the upper and lower boundaries during the error convergence process, respectively. The fixed-time tracking performance function The expression is (4) In the formula: Indicates a positive adjustable parameter; It is represented as a specified preset time; S23: Perform error transformation on the dynamic attitude error based on the fixed-time tracking performance function to obtain new error variables. for (5) In the formula: express The abbreviated form; Indicates dynamic attitude error The initial value; S24: Based on the fixed-time chimney boundary function Obtain new error variables The asymmetric performance constraint is (6) S25: Introduce the intermediate variable transformation formula, and based on the new error variable... Obtain the error of the transformation variable using asymmetric performance constraints; The intermediate variable transformation formula is as follows: (7) (8) (9) In the formula: This represents the output of the formula for transforming intermediate variables; Indicates intermediate parameter variables; The transformed variable error for (10) S3: Based on neural network approximation technology, a virtual controller is constructed according to the three-degree-of-freedom motion model and the error of the transformed variables; S4: Construct an adaptive law based on the virtual controller, and obtain the velocity error vector based on the virtual controller using dynamic surface control technology; S5: Design an asymmetric saturation auxiliary system for acquiring saturation correction signals, its expression is: (18) (19) In the formula: Indicates the amount of intermediate parameters; S6: Based on the adaptive law and asymmetric saturation auxiliary system, the final controller is constructed according to the velocity error vector, so as to realize the adaptive preset time dynamic positioning control of the semi-submersible platform with input saturation according to the final controller.

2. The adaptive preset time dynamic positioning control method for a semi-submersible platform with input saturation according to claim 1, characterized in that, The three-degree-of-freedom motion model of the semi-submersible platform with input saturation described in S1 is expressed by formula (1). (1) (2) In the formula: This represents the attitude vector of the semi-submersible platform (SSP) in the inertial coordinate system. Indicates the location of the SSP; Indicates the heading angle; Represents the velocity rotation matrix; This represents the velocity vector of the SSP within the attached coordinate system; Indicates the forward speed of the SSP; Indicates the drift speed; Indicates the bow roll angular velocity; The inertia matrix; For the nonlinear derivative terms including added mass, added inertial torque, and hydrodynamics; Represents the marine environmental disturbance vector, which includes the disturbance forces and moments in the forward, lateral, and yaw degrees of freedom of the SSP; This represents the ideal control input under conditions without saturation limitations; This represents the actual control input; and the three-degree-of-freedom control input force and torque should satisfy the piecewise input saturation constraint condition in formula (2). These represent the upper and lower limits of the SSP side thrust of a semi-submersible platform, respectively.

3. The adaptive preset time dynamic positioning control method for a semi-submersible platform with input saturation according to claim 2, characterized in that, S3 specifically includes the following steps: S31: Based on the three-degree-of-freedom motion model and the error of the transformed variable, obtain the derivative of the error of the transformed variable. The dynamic equation is expressed as follows: （11） In the formula: Indicates the amount of intermediate parameters, and ; S32: Definition For the error derivative of the transformed variable The uncertainty term of the dynamic equation, based on the nonlinear continuous function in the RBF-NNs approximation technique. The online approximation of this uncertain term is expressed as follows: （12） In the formula: Represents the weight matrix; Represents a vector of RBF basis functions in Gaussian form; express The abbreviated form; Represents the attitude vector and is a nonlinear continuous function. The input vector; This represents the approximation error term; S33: Based on the error of the transformed variable Combined with step S32, a virtual controller is constructed, and the expression of the virtual controller is: (13) In the formula: They represent in Virtual controller parameters in three degrees of freedom; Indicates a positive design parameter; Indicates adaptive parameters and ; Indicates to The estimated value.

4. The adaptive preset time dynamic positioning control method for a semi-submersible platform with input saturation according to claim 3, characterized in that, S4 specifically includes the following steps: S41: Construct an adaptive law based on the virtual controller, and the adaptive law is... (14) In the formula: All of these represent positive adaptive design parameters; This represents the velocity error vector to be solved; Indicates a positive design parameter; Where adaptive parameters Specifically, it refers to the nonlinear continuous function based on the RBF-NNs approximation technique. Online approximation of the nonlinear derivative term in a three-degree-of-freedom motion model Obtain, its expression is (15) In the formula: Represents a nonlinear continuous function; Represents the weight matrix; Represents a vector of RBF basis functions in Gaussian form; This represents the approximation error term of the nonlinear derivative term; S42: Based on dynamic surface control technology, the velocity error vector to be solved is obtained from the virtual controller. ; S421: A filter using dynamic surface control technology eliminates the complexity explosion problem of the control law caused by continuous differentiation of the virtual controller. The expression of the filter is: (16) In the formula: The time constant matrix; This indicates that the output vector is a velocity vector. Reference signal; They represent and The initial value; S422: Based on the output vector Obtain the velocity error vector to be solved using the saturation correction signal. Its expression is (17) In the formula: This represents the saturation correction signal, and ; and These represent the first-order correction signals in the three degrees of freedom, respectively. and These represent the second-order correction signals in the three degrees of freedom, respectively; Represents a unit vector; This represents a positive saturation auxiliary parameter, and .

5. The adaptive preset time dynamic positioning control method for a semi-submersible platform with input saturation according to claim 4, characterized in that, In S6, based on adaptive law and asymmetric saturation auxiliary system, the final controller is constructed according to the velocity error vector, and its expression is: (20) In the formula: They represent in Controller parameters in three degrees of freedom; and Indicates a positive design parameter.

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