Semi-submersible platform pre-set performance dynamic positioning control method considering actuator dynamic fault compensation

Abstract

The application discloses a semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation, comprising the following steps: constructing an ln type preset performance boundary function; obtaining a conversion error function for ensuring that a dynamic error converges in a time-varying dynamic boundary function; constructing an obstacle conversion function according to the conversion error function based on the ln type preset performance boundary function, and constructing a virtual controller according to the obstacle conversion function; obtaining a speed dynamic error derivative containing an uncertain damping term according to the virtual controller; constructing an auxiliary vector for positioning control; constructing a robust neural damping term according to the auxiliary vector and the speed dynamic error, so as to obtain a virtual control law considering actuator dynamic faults; and constructing an actual control law and a parameter adaptive law according to the virtual control law and introducing a thrust configuration matrix, so as to solve the problems that the existing actuator fault model cannot fully reflect the long time, multiple factors and complex and changeable characteristics when the fault occurs, is not convenient for algorithm popularization and application in actual offshore engineering, and cannot ensure accurate control accuracy while considering actuator faults.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ship motion control, and particularly relates to a semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation. BACKGROUND

[0002] During the execution of the dynamic positioning control task, the actuator is one of the core components of the ship motion control system, and its fault may cause the control performance of the ship to decline or even fail, thereby causing the ship to deviate from the course, collide, run aground, or cause damage to the surrounding facilities and environment. Although the existing method solves the problems of system uncertainty, actuator fault, and limited communication resources, when the ship encounters a fault condition, it is usually a long time, multiple factors, and complex and changeable situation (for example, friction, elasticity, hysteresis, and the influence of wind flow elements). In order to fully consider the influence of the actuator dynamic fault on the control performance, a dynamic fault model is introduced to simulate the complex and changeable fault situation. By transferring the actuator fault to the real control input, the influence of the fault on the entire control system when the fault occurs is more obviously magnified. On the other hand, the transient and steady-state preset performance constraints of the dynamic positioning control when the actuator fault occurs have not been realized in the current control algorithm, and the control strategy considering this technology further guarantees the control accuracy of the dynamic positioning operation.

[0003] Based on the above analysis, the existing ship dynamic positioning control algorithm has the following two defects:

[0004] 1) The existing actuator fault model cannot fully reflect the long time, multiple factors, and complex and changeable characteristics when the fault occurs, which is not convenient for the algorithm to be popularized and applied in actual sea engineering.

[0005] 2) Considering the needs of the dynamic positioning ship for the operation condition and operation accuracy, the existing algorithm cannot ensure accurate control accuracy while considering the actuator fault. SUMMARY

[0006] The present application provides a semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation to overcome the above technical problems.

[0007] In order to achieve the above purpose, the technical scheme of the present application is:

[0008] A semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation, specifically comprising the following steps:

[0009] S1: obtaining a semi-submersible platform nonlinear mathematical model based on the maneuvering theory;

[0010] S2: Based on the preset performance control technology, an ln-type preset performance boundary function is designed to drive the positioning control system to achieve the desired performance index according to the constructed time-varying dynamic boundary function.

[0011] S3: Define the platform dynamic error based on the nonlinear mathematical model of the semi-submersible platform;

[0012] The platform's dynamic error is then mapped and transformed to obtain a transformation error function that ensures the dynamic error converges within the time-varying dynamic boundary function.

[0013] S4: Based on the ln-type preset performance boundary function, construct the obstacle transformation function according to the transformation error function, and construct the virtual controller according to the obstacle transformation function;

[0014] S5: First-order filtering will be performed on the virtual controller to obtain the speed dynamic error;

[0015] Based on the nonlinear mathematical model of the semi-submersible platform, the derivative of the velocity dynamic error is obtained by taking the derivative of the velocity dynamic error including the uncertain damping term;

[0016] Furthermore, the RBF-NNs approximation technique is used to approximate the uncertain damping term in the derivative of the velocity dynamic error in order to construct an auxiliary vector for positioning control;

[0017] S6: Based on the auxiliary vector and velocity dynamic error, construct a robust neural damping term for positioning control, and construct a virtual control law considering actuator dynamic faults based on the robust neural damping term;

[0018] S7: Based on the virtual control law and by introducing the thrust configuration matrix, the actual control law and parameter adaptive law are constructed to realize the preset performance dynamic positioning control of the semi-submersible platform that takes into account the dynamic fault compensation of the actuator.

[0019] Furthermore, the expression for the nonlinear mathematical model of the semi-submersible platform based on manipulation theory in S1 is as follows:

[0020]

[0021] τ re =γ(t)τ

[0022] τ=T(β)κ(n)u p

[0023] In the formula: η represents the attitude vector of the semi-submersible platform and η = [x, y, ψ] T x, y represent the horizontal and vertical coordinates of the semi-submersible platform's position; ψ represents the bow angle of the semi-submersible platform; υ represents the velocity vector of the semi-submersible platform, and υ = [u, v, r] Tu, v, r represent the pitch velocity, sway velocity, and yaw rate of the semi-submersible platform, respectively; M represents the inertia matrix combining the mass and added mass of the semi-submersible platform; D lh (v) and D nh (v) represents the linear and nonlinear hydrodynamic damping matrices, respectively; τ re This represents the actual control input force and torque of the semi-submersible platform in three degrees of freedom, and τ re =[τ u ,τ v ,τ r ] T ;τ en This represents the force and torque that include external environmental disturbances, and τ en =[τ enu ,τ env ,τ enr ] T aγ(t) represents the time-varying, uncertain dynamic fault gain function; τ represents the total driving force of the actuator when no fault occurs; T(β) represents the actuator allocation matrix; κ(n) represents the configuration gain coefficient; u p β represents the rotational speed; β represents the azimuth angle in the propeller. Let x, y, and ψ represent the first derivatives, respectively.

[0024] Furthermore, the expression for the ln-type preset performance boundary function constructed in S2 is as follows:

[0025]

[0026] In the formula: Φ represents the upper bound of the non-negative conversion error. η The time-varying dynamic boundary represents the system's dynamic error; A represents the adjustable performance gain parameter; h(t) represents the auxiliary variable; I represents the identity matrix; λ(t) represents the time-varying dynamic boundary function and λ(t) = [λ u ,λ v ,λ r ] T ;λ u ,λ v ,λ r Let represent the time-varying dynamic boundary functions of the semi-submersible platform in three degrees of freedom, and respectively.

[0027]

[0028] In the formula: T k Indicates the set convergence time; c k represents the steady-state value of the preset performance function; m represents the design parameters.

[0029] Furthermore, S3 specifically includes the following steps:

[0030] S31: Set the desired reference attitude signal η for the semi-submersible platform. d And η d =[x d ,y d ,ψ d ] T , where x d ,y d ,ψ d These represent the desired x-coordinate, desired y-coordinate, and desired heading angle, respectively.

[0031] The dynamic position error η of the platform is defined based on the nonlinear mathematical model of the semi-submersible platform. e Its expression is

[0032] η e =η-η d

[0033] S32: Perform error mapping transformation on the platform's dynamic position error to obtain a transformation error function used to ensure that the dynamic error converges within the time-varying dynamic boundary function;

[0034] The expression for the conversion error function is as follows:

[0035]

[0036] In the formula: ξ represents the system dynamic error after mapping transformation and...

[0037] Furthermore, S4 specifically includes the following steps:

[0038] S41: Based on the ln-type preset performance boundary function, a barrier transformation function is constructed according to the transformation error function; and the expression of the barrier transformation function is:

[0039]

[0040] In the formula: l represents the barrier transformation function; λ represents the abbreviated form of λ(t);

[0041] Here, it is assumed that λξ can be constrained to... Within the interval, we can obtain

[0042]

[0043] S42: Take the derivative of the barrier transformation function to obtain its expression:

[0044]

[0045] In the formula: The first derivative of l is represented; δ and ζ represent intermediate variables. Denotes the first derivative of λ; Indicates η e The first derivative;

[0046] S43: To ensure the stability of the derivative of the obstacle transition function, a virtual controller is constructed based on the obstacle transition function. The expression of the virtual controller is:

[0047] α v =R -1 (ψ)(-k η lζ -1 -δζ -1 )

[0048]

[0049] In the formula: α v R(ψ) represents the input of the virtual controller; R(ψ) represents the parameter matrix; k η This represents the positive definite diagonal gain matrix.

[0050] Furthermore, S5 specifically includes the following steps:

[0051] S51: First-order filtering will be performed on the virtual controller to obtain the speed dynamic error;

[0052] And the expression for obtaining the dynamic error of the speed is:

[0053]

[0054] v e =v-β v

[0055] Where: β v This represents the filtered speed control signal; t υ Represent a time-constant diagonal matrix; Indicates β v First derivative; α v (0),β v (0) represents α respectively v ,β v Initial value; υ e Indicates dynamic speed error;

[0056] S52: Based on the nonlinear mathematical model of the semi-submersible platform, the derivative of the velocity dynamic error is obtained, which includes the uncertain damping term;

[0057] And the expression for the derivative of the velocity dynamic error is:

[0058]

[0059] In the formula: Indicates v e The first derivative; M represents the first derivative of v; -1 (-D lh (v)-D nh (v)) represents an uncertain damping term;

[0060] S53: The uncertain damping term in the derivative of the velocity dynamic error is approximated using the RBF-NNs approximation technique, and its expression is as follows:

[0061]

[0062] Where: g nn (υ) represents the RBF-NNs approximation function; Represents the radial basis functions in Gaussian form; Represents the weight matrix; This represents the upper bounded approximation error for approximating the uncertain term; The design is obtained from step S54;

[0063] S54: Introduce the norm matrix based on step S53 And order

[0064] Then we can obtain the equation relationship.

[0065] S55: Based on step S54 and combined with S53, construct an auxiliary vector for positioning control, and the expression of the auxiliary vector is:

[0066]

[0067] In the formula: This represents an auxiliary vector.

[0068] Furthermore, S6 specifically includes the following steps:

[0069] S61: Based on the auxiliary vector and the dynamic error of velocity, an inequality is established to introduce the robust damping term, and its expression is:

[0070]

[0071] In the formula: Represents τ en The upper bound;

[0072] S62: Set intermediate parameters And according to Young's inequality, we can obtain

[0073]

[0074] In the formula: Indicates the auxiliary damping term and k υn This represents the positive diagonal control parameter matrix; λ min Represents the smallest eigenvalue of the matrix;

[0075] S63: Construct a robust neural damping term for positioning control based on step S62;

[0076] And robust nerve damping term The expression is

[0077]

[0078] S64: Define parameter quantities

[0079] Where q represents the number of actuators configured in the semi-submersible platform; This represents the pseudo-inverse operation of T(·);

[0080] According to the parameter g p Obtain the adaptive parameter θ, where θ = g p -1 =[θ1,θ2,...,θ q ] T ;

[0081] S65: To avoid input overshoot of the semi-submersible platform, λ is introduced to adjust the dynamic speed error υ. e To obtain the adjustment error Υ = λv e ;

[0082] Based on the derivative of the adjustment error, an adaptive parameter is set to account for the uncertainty of the fault coefficient. Dynamic fault compensation is performed on it, thereby achieving dynamic fault compensation for the actuator of the semi-submersible platform, and its expression is:

[0083]

[0084] S66: Based on step S65 and combined with the robust neural damping term, construct a virtual control law α that considers actuator dynamic faults. up Its expression is

[0085]

[0086] In the formula: This represents the positive definite control parameter matrix; Indicates to The estimate; k s Indicates the fault correction gain parameter and

[0087] Furthermore, in S7, the actual control law and parameter adaptive law are constructed based on the virtual control law and by introducing the thrust configuration matrix. Their expressions are as follows:

[0088]

[0089] In the formula: u p Indicates the propeller speed; The dot product symbol is represented; p represents the pitch ratio of the propeller. This represents an estimate of the uncertain thrust coefficient matrix κ(n); γ θi ,σ θi , All represent positive gain adaptive design parameters; since it is a summation matrix, T represents the matrix element in the i-th row and j-th degree of freedom of the pseudo-inverse of the thrust configuration matrix; ki (·) represents the matrix element in the k-th row and at the i-th degree of freedom of the thrust configuration matrix; α jp Represents the virtual control law α up The three components of the semi-submersible platform in the pitch, sway, and yaw directions; k e Represents the dynamic error of velocity υ e The three components of the semi-submersible platform in the pitch, sway, and yaw directions; c represents the design parameter and c = [c u ,c v ,c r ] T ;T indicates transpose; express The initial value; This represents the estimate of the adaptive parameter θ; express The initial value; express The first derivative; express The first derivative.

[0090] This invention provides a pre-set performance dynamic positioning control method for a semi-submersible platform that considers dynamic fault compensation of actuators, which has the following two beneficial effects:

[0091] 1) Compared with existing ship actuator failure models, this invention can more comprehensively consider failure factors and the complex and variable characteristics of actuator failure. It integrates adaptive technology to achieve online estimation of uncertain failure coefficients to realize failure compensation. It fully considers the continuous impact of elasticity, friction, delay and environment to construct a virtual control law that considers the dynamic failure of actuators. The controller designed on this basis is more in line with the engineering practice and operation requirements of semi-submersible platforms.

[0092] 2) The preset performance control scheme proposed in this invention addresses the need for finer error control in dynamic positioning of semi-submersible platforms. The designed ln-type preset performance boundary function and obstacle transformation function realize the constrained convergence behavior of the system dynamic error. Considering the safety of the subsea pipeline laid below the semi-submersible platform, the preset performance function of this invention is more in line with the development direction of finer control of dynamic positioning of semi-submersible platforms. Attached Figure Description

[0093] 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 from these drawings without creative effort.

[0094] Figure 1 A flowchart of the semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation according to the present invention;

[0095] Figure 2 This is a diagram of the SSP DP control target framework in this embodiment;

[0096] Figure 3 This is a diagram of the SSP DP control structure based on dynamic faults and preset performance in this embodiment;

[0097] Figure 4 This is a flowchart of the SSP DP control algorithm based on dynamic faults and preset performance in this embodiment;

[0098] Figure 5 This is a comparison curve of the trajectories under the two algorithms in this embodiment;

[0099] Figure 6 This is a comparison chart of the x, y, ψ control input variation curves under the two algorithms in this embodiment;

[0100] Figure 7 This is a comparison chart of the control input change curves under the two algorithms in this embodiment;

[0101] Figure 8 This is a simulation diagram showing the preset performance of the system dynamic error under the method of the present invention in this embodiment;

[0102] Figure 9 This is a graph showing the variation of the estimated values ​​of the seven adaptive parameters under the method of the present invention in this embodiment;

[0103] Figure 10 This is a graph showing the change in the actual control input pitch ratio and the actuator azimuth angle under the method of the present invention in this embodiment. Detailed Implementation

[0104] 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.

[0105] This embodiment provides a pre-set performance dynamic positioning control method for a semi-submersible platform that considers dynamic fault compensation of the actuator, such as... Figures 1 to 4 As shown, the specific steps include:

[0106] S1: Obtain a nonlinear mathematical model of a semi-submersible platform (SSP) based on manipulation theory;

[0107] Specifically, the expression for the nonlinear mathematical model of the semi-submersible platform based on manipulation theory in S1 is as follows:

[0108]

[0109] τ re =γ(t)τ

[0110] τ=T(β)κ(n)u p

[0111] In the formula: η represents the attitude vector of the semi-submersible platform and η = [x, y, ψ] T x, y represent the horizontal and vertical coordinates of the semi-submersible platform's position; ψ represents the bow angle of the semi-submersible platform; υ represents the velocity vector of the semi-submersible platform, and v = [u, v, r]. T u, v, r represent the pitch velocity, sway velocity, and yaw rate of the semi-submersible platform, respectively; M represents the inertia matrix combining the mass and added mass of the semi-submersible platform; D lh (v) and D nh (v) represents the linear and nonlinear hydrodynamic damping matrices, respectively; τ re This represents the actual control input force and torque of the semi-submersible platform in three degrees of freedom, and τ re =[τ u ,τ v ,τ r ] T ;τ en This represents the force and torque that include external environmental disturbances, and τ en =[τ enu ,τ env ,τ enr ] Tγ(t) represents the time-varying, uncertain dynamic fault gain function; τ represents the total driving force of the actuator when no fault occurs; T(β) represents the actuator allocation matrix; κ(n) represents the configuration gain coefficient; u p β represents the rotational speed; β represents the azimuth angle in the propeller. Let x, y, and ψ represent the first derivatives, respectively.

[0112] S2: Based on the preset performance control technology, an ln-type preset performance boundary function is designed to drive the positioning control system to achieve the desired performance index according to the constructed time-varying dynamic boundary function.

[0113] In this embodiment, a preset performance control technique is used to construct a ln-type preset performance boundary function. This performance function is a time-varying dynamic boundary function that is independent of the initial dynamic error of the system and is constructed by utilizing the monotonicity of the ln-type function. This function is used to drive the control system to achieve the desired performance index.

[0114] Specifically, the expression for the constructed ln-type preset performance boundary function is as follows:

[0115]

[0116] In the formula: Φ represents the upper bound of the non-negative conversion error. η The time-varying dynamic boundary represents the system's dynamic error; A represents an adjustable performance gain parameter that automatically adjusts to a suitable value to accommodate the initial dynamic error within the time-varying boundary; h(t) represents an auxiliary variable; I represents the identity matrix; λ(t) represents the time-varying dynamic boundary function and λ(t) = [λ u ,λ v ,λ r ] T ;λ u ,λ v ,λ r Let represent the time-varying dynamic boundary functions of the semi-submersible platform in three degrees of freedom, and respectively.

[0117]

[0118] In the formula: T k Indicates the set convergence time; c k This represents the steady-state value of the preset performance function; m represents the design parameters.

[0119] Among them, the ln-type preset performance boundary function has the following characteristics:

[0120] (1) When t→0, it naturally satisfies Φ η (0)→+∞.

[0121] (2) For t≤Tk , Φ η Monotonically decreasing, ensuring the error boundary converges over time; when t > T k At that time, Φ η If the value stabilizes within a constant range, that value is the predetermined steady-state error range; and T mentioned above... k Let k represent a specific convergence time, where k = u, v, r; after λ(t) reaches its steady-state time, its steady-state value is c. k >0; it is very clear that λ can be observed. k (0) = 1, in t ≤ T k The time is decreasing, when t > T. k When it remains at the steady-state value c k constant.

[0122] S3: Define the platform dynamic error based on the nonlinear mathematical model of the semi-submersible platform;

[0123] The platform's dynamic error is then mapped and transformed to obtain a transformation error function that ensures the dynamic error converges within the time-varying dynamic boundary function.

[0124] Specifically, the following steps are included:

[0125] S31: Set the desired reference attitude signal η for the semi-submersible platform. d And η d =[x d ,y d ,ψ d ] T , where x d ,y d ,ψ d These represent the desired x-coordinate, desired y-coordinate, and desired heading angle, respectively.

[0126] The dynamic position error η of the platform is defined based on the nonlinear mathematical model of the semi-submersible platform. e Its expression is

[0127] η e =η-η d

[0128] S32: Perform error mapping transformation on the platform's dynamic position error to obtain a transformation error function used to ensure that the dynamic error converges within the time-varying dynamic boundary function;

[0129] The expression for the conversion error function is as follows:

[0130]

[0131] In the formula: ξ represents the system dynamic error after mapping transformation and...

[0132] The change of A in this embodiment and η e Relatedly, to avoid the problem of computational explosion in the complex domain, the adaptive rate of A is expressed as follows:

[0133]

[0134] Where: o, ε represent positive design parameters;

[0135] And based on the adaptive rate of A, η e It can be represented in the following form:

[0136]

[0137] S4: Based on the ln-type preset performance boundary function, construct the obstacle transformation function according to the transformation error function, and construct the virtual controller according to the obstacle transformation function;

[0138] Specifically, the following steps are included:

[0139] S41: In order to facilitate the design of the controller and meet the preset performance constraints of the ln-type preset performance boundary function, a barrier transformation function is constructed based on the ln-type preset performance boundary function and the transformation error function.

[0140] And the expression for the barrier transformation function is:

[0141]

[0142] In the formula: l represents the barrier transformation function; λ represents the abbreviated form of λ(t);

[0143] Here, it is assumed that λξ can be constrained to... Within the interval, we can obtain

[0144]

[0145] S42: Take the derivative of the barrier transformation function to obtain its expression:

[0146]

[0147] In the formula: The first derivative of l is represented; δ and ζ represent intermediate variables. Denotes the first derivative of λ; Indicates η e The first derivative;

[0148] S43: In order to ensure the stability of the derivative of the obstacle transition function, a virtual controller is constructed based on the obstacle transition function. That is, by ensuring the stability of the derivative of the obstacle transition function, the virtual controller of this embodiment is designed, which can ensure that the virtual controller is stable and feasible.

[0149] The expression for the virtual controller is:

[0150] α v =R -1 (ψ)(-k η lζ -1 -δζ -1 )

[0151]

[0152] In the formula: α v R(ψ) represents the input of the virtual controller; R(ψ) represents the parameter matrix; k η This represents the positive definite diagonal gain matrix;

[0153] S5: First-order filtering will be performed on the virtual controller to obtain the speed dynamic error;

[0154] The velocity dynamic error is differentiated based on the nonlinear mathematical model of the semi-submersible platform to obtain the velocity dynamic error derivative containing the uncertain damping term; and the uncertain damping term in the velocity dynamic error derivative is approximated by the RBF-NNs approximation technique to construct an auxiliary vector for positioning control.

[0155] Specifically, the following steps are included:

[0156] S51: To avoid [the situation] with α v The process of differentiation leads to an explosion of computational complexity. Therefore, a first-order filter is introduced to perform first-order filtering on the virtual controller to obtain the dynamic speed error.

[0157] And the expression for obtaining the dynamic error of speed is:

[0158]

[0159] v e =v-β v

[0160] Where: β v This represents the filtered speed control signal; t v This represents a time-constant diagonal matrix that ensures smoother transmission of control signals and avoids α. v A sudden and drastic change; Indicates β v First derivative; α v (0),βv (0) represents α respectively v ,β v Initial value; υ e Indicates dynamic speed error;

[0161] This embodiment also includes a filtering error q. v =α v -β v Furthermore, the dynamic change of the filtering error can be expressed as...

[0162]

[0163] In the formula: C(·)=[C u C v C r ] represents a bounded, nonlinear, continuous function vector that depends on the system state and parameters; C u C v C r Let u, v, and r represent the components of C(·) in the three degrees of freedom, respectively.

[0164] S52: Based on the nonlinear mathematical model of the semi-submersible platform, the derivative of the velocity dynamic error is obtained, which includes the uncertain damping term;

[0165] And the expression for the derivative of the velocity dynamic error is:

[0166]

[0167] In the formula: Indicates v e The first derivative; M represents the first derivative of v; -1 (-D lh (v)-D nh (v)) represents an uncertain damping term;

[0168] S53: The uncertain damping term in the derivative of the velocity dynamic error is approximated using the RBF-NNs approximation technique, and its expression is as follows:

[0169]

[0170] Where: g nn (v) represents the RBF-NNs approximation function; Represents the radial basis functions in Gaussian form; Represents the weight matrix; This represents the upper bounded approximation error for approximating the uncertain term; The design is obtained from step S54;

[0171] S54: In this embodiment, to achieve the boundedness of systematic error, a norm matrix is ​​introduced based on step S53. And order

[0172] Then we can obtain the equation relationship.

[0173] S55: Based on step S54 and combined with S53, construct an auxiliary vector for positioning control, and the expression of the auxiliary vector is:

[0174]

[0175] In the formula: Represents an auxiliary vector;

[0176] S6: Based on the auxiliary vector and velocity dynamic error, construct a robust neural damping term for positioning control, and construct a virtual control law considering actuator dynamic faults based on the robust neural damping term;

[0177] Specifically, the following steps are included:

[0178] S61: Based on the auxiliary vector and the dynamic error of velocity, an inequality is established to introduce the robust damping term, and its expression is:

[0179]

[0180] In the formula: Represents τ en The upper bound;

[0181] S62: Set intermediate parameters And according to Young's inequality, we can obtain

[0182]

[0183] In the formula: Indicates the auxiliary damping term and k υn This represents the positive diagonal control parameter matrix; λ min Represents the smallest eigenvalue of the matrix;

[0184] S63: Construct a robust neural damping term for positioning control based on step S62;

[0185] And robust nerve damping term The expression is

[0186]

[0187] S64: Define parameter quantities

[0188] Where q represents the number of actuators configured in the semi-submersible platform; This represents the pseudo-inverse operation of T(·);

[0189] According to the parameter g p Obtain the adaptive parameter θ, where θ = g p -1 =[θ1,θ2,...,θ q ] T ;

[0190] S65: To avoid input overshoot of the semi-submersible platform, λ is introduced to adjust the dynamic speed error υ. e To obtain the adjustment error Υ = λv e ;

[0191] Based on the derivative of the adjustment error, an adaptive parameter is set to account for the uncertainty of the fault coefficient. Dynamic fault compensation is performed on it, thereby achieving dynamic fault compensation for the actuator of the semi-submersible platform, and its expression is:

[0192]

[0193] S66: Based on step S65 and combined with the robust neural damping term, construct a virtual control law α that considers actuator dynamic faults. up Its expression is

[0194]

[0195] In the formula: This represents the positive definite control parameter matrix; Indicates to The estimate; k s Indicates the fault correction gain parameter and

[0196] S7: Based on the virtual control law and by introducing the thrust configuration matrix, the actual control law and parameter adaptive law are constructed to realize the preset performance dynamic positioning control of the semi-submersible platform that takes into account the dynamic fault compensation of the actuator.

[0197] Furthermore, based on the virtual control law, the actual control law and parameter adaptive law are constructed, and their expressions are as follows:

[0198]

[0199] In the formula: u p Indicates the propeller speed; The dot product symbol is represented; p represents the pitch ratio of the propeller. This represents an estimate of the uncertain thrust coefficient matrix κ(n); γ θi ,σ θi , All represent positive gain adaptive design parameters; since it is a summation matrix, T represents the matrix element in the i-th row and j-th degree of freedom of the pseudo-inverse of the thrust configuration matrix; ki (·) represents the matrix element in the k-th row and at the i-th degree of freedom of the thrust configuration matrix; α jp Represents the virtual control law α up The three components of the semi-submersible platform in the pitch, sway, and yaw directions; k e Represents the dynamic error of velocity υ e The three components of the semi-submersible platform in the pitch, sway, and yaw directions; c represents the design parameter and c = [c u ,c v ,c r ] T T represents transpose; express The initial value; This represents the estimate of the adaptive parameter θ; express The initial value; express The first derivative; express The first derivative.

[0200] To verify that this embodiment can generate an effective control signal and transmit the pitch input command to the actuator through the control system when the SSP encounters an actuator failure, so that the SSP reaches the desired state, while ensuring that the output signal generated by the entire control system meets the preset performance requirements, this embodiment uses computer simulation experiments to conduct numerical comparison simulations in a simulated external marine environment. By comparing this embodiment with the existing vector backstepping method (Algorithm A), the effectiveness and superiority of the method in this embodiment are verified. The main differences between the method in this embodiment and Algorithm A are shown in Table 1.

[0201] Table 1. Similarities and differences between the method in this embodiment and Algorithm A

[0202]

[0203] The method of this embodiment and Algorithm A were compared and simulated on an industrial computer (Intel(R) Core(TM) i5-7300 HQ CPU@2.50GHz, RAM: 8.00GB). Figures 5 to 7 The main comparison results are presented. Figure 5 This represents the trajectory comparison results of SSP in DP control tasks under two different algorithms. Figure 5In the two algorithms, although both achieved relatively good positioning trajectories, the algorithm proposed in this invention uses adaptive technology and realizes online estimation and learning of uncertain gain functions, resulting in a smoother positioning trajectory. In contrast, the positioning trajectory of Algorithm A, which deploys a dissipative observer, exhibits greater jitter. Figure 6 The curves depicting the changes in position and heading angle across the three degrees of freedom of the SSP throughout the entire control process are described. It is evident that the proposed algorithm exhibits a faster convergence speed and smoother convergence effect. In comparison, the method in this embodiment demonstrates satisfactory results. Figure 7 The diagram shows a comparison of the control torque components of all actuators in the SSP across the three degrees of freedom. It can be seen that the method of this invention has a smaller control torque in the initial state of the control process. However, during the gradual convergence and stabilization process, Algorithm A exhibits stronger oscillations. In contrast, the method of this invention is superior in terms of energy efficiency. Furthermore, the preset performance of the output signal of the entire control system is also discussed. Figure 8 This demonstrates that the system's dynamic error is fully contained within the proposed pre-defined time-varying dynamic boundary [-Φ]. η ,Φ η Within this range, including after the system state has stabilized, no step-out behavior occurred. Furthermore, the preset performance behavior of the dynamic error was successfully confined within the time-varying dynamic boundary in the initial state. This is due to the fact that the preset performance control method proposed in this algorithm does not rely on the constraints of the initial conditions, because the adjustment gain parameter A in the ln-type performance function proposed in this invention solves this problem. From Figure 9 The data shows the changes in the six adaptive parameters constructed from the uncertain gain coefficients of the six omnidirectional propellers in the SSP. Figure 10 This is the curve showing the actual control input pitch ratio and actuator azimuth angle under the method of this invention. It is worth noting that the 200s-300s period is precisely the stage where dynamic faults occur, thus causing oscillations in both the pitch ratio and azimuth angle. However, after the dynamic fault ends, they still quickly converge to a stable state.

[0204] Based on existing technologies, this embodiment proposes an SSP preset performance dynamic positioning control method that considers actuator dynamic faults, through design and numerical comparison simulation of an SSP dynamic positioning controller with actuator dynamic faults. It has two main characteristics:

[0205] (1) It can fully and more comprehensively consider the fault factors and conform to the dynamic fault model of marine engineering practice. It can more realistically reflect the control performance of SSP actuator when a fault occurs. By introducing the thrust configuration matrix to construct the actual control law and parameter adaptive law, the real control input is transferred to the pitch ratio command in the omnidirectional propeller, which can more clearly reflect the real change of pitch ratio.

[0206] (2) A ln-type preset performance boundary function is constructed, and the initial dynamic error is tuned to converge within the preset boundary by introducing an adaptive adjustment parameter A. In addition, online estimation and learning are performed on two uncertain gain functions to compensate for unknown fault coefficients and thrust distribution coefficients.

[0207] 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 they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for 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 pre-set performance dynamic positioning control method for a semi-submersible platform considering actuator dynamic fault compensation, characterized in that, Specifically, the following steps are included: S1: Obtain a nonlinear mathematical model of a semi-submersible platform based on manipulation theory; S2: Based on the preset performance control technology, an ln-type preset performance boundary function is designed to drive the positioning control system to achieve the desired performance index according to the constructed time-varying dynamic boundary function. S3: Define the platform dynamic error based on the nonlinear mathematical model of the semi-submersible platform; The platform's dynamic error is then mapped and transformed to obtain a transformation error function that ensures the dynamic error converges within the time-varying dynamic boundary function. S4: Based on the ln-type preset performance boundary function, construct the obstacle transformation function according to the transformation error function, and construct the virtual controller according to the obstacle transformation function; S5: First-order filtering will be performed on the virtual controller to obtain the speed dynamic error; Based on the nonlinear mathematical model of the semi-submersible platform, the derivative of the velocity dynamic error is obtained by taking the derivative of the velocity dynamic error including the uncertain damping term; Furthermore, the RBF-NNs approximation technique is used to approximate the uncertain damping term in the derivative of the velocity dynamic error in order to construct an auxiliary vector for positioning control; S6: Based on the auxiliary vector and velocity dynamic error, construct a robust neural damping term for positioning control, and construct a virtual control law considering actuator dynamic faults based on the robust neural damping term; S7: Based on the virtual control law and by introducing the thrust configuration matrix, the actual control law and parameter adaptive law are constructed to realize the preset performance dynamic positioning control of the semi-submersible platform that takes into account the dynamic fault compensation of the actuator.

2. The semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation according to claim 1, characterized in that, The expression for the nonlinear mathematical model of the semi-submersible platform based on manipulation theory in S1 is as follows: t re =γ(t)τ τ=T(β)κ(n)u p In the formula: η represents the attitude vector of the semi-submersible platform and η = [x, y, ψ] T x, y represent the horizontal and vertical coordinates of the semi-submersible platform's position; ψ represents the bow angle of the semi-submersible platform; υ represents the velocity vector of the semi-submersible platform, and υ = [u, v, r] T u, v, r represent the pitch velocity, sway velocity, and yaw rate of the semi-submersible platform, respectively; M represents the inertia matrix combining the mass and added mass of the semi-submersible platform; D lh (υ) and D nh (υ) represents the linear and nonlinear hydrodynamic damping matrices, respectively; τ re This represents the actual control input force and torque of the semi-submersible platform in three degrees of freedom, and τ re =τ[ u ,τ v ,τ r ] T ;τ en This represents the force and torque that include external environmental disturbances, and τ en =[τ enu ,τ env ,τ enr ] T γ(t) represents the time-varying, uncertain dynamic fault gain function; τ represents the total driving force of the actuator when no fault occurs; T(β) represents the actuator allocation matrix; κ(n) represents the configuration gain coefficient; u p β represents the rotational speed; β represents the azimuth angle in the propeller. Let x, y, and ψ represent the first derivatives, respectively.

3. The semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation according to claim 2, characterized in that, The expression for the ln-type preset performance boundary function constructed in S2 is: In the formula: Φ represents the upper bound of the non-negative conversion error. η The time-varying dynamic boundary represents the system's dynamic error; A represents the adjustable performance gain parameter; h(t) represents the auxiliary variable; I represents the identity matrix; λ(t) represents the time-varying dynamic boundary function and λ(t) = [λ u ,λ v ,λ r ] T ; λ u ,λ v ,λ r Let represent the time-varying dynamic boundary functions of the semi-submersible platform in three degrees of freedom, and respectively. In the formula: T k Indicates the set convergence time; c k represents the steady-state value of the preset performance function; m represents the design parameters.

4. The semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation according to claim 3, characterized in that, S3 specifically includes the following steps: S31: Set the desired reference attitude signal η for the semi-submersible platform. d And η d =[x d ,y d ,ψ d ] T , where x d ,y d ,ψ d These represent the desired x-coordinate, desired y-coordinate, and desired heading angle, respectively. The dynamic position error η of the platform is defined based on the nonlinear mathematical model of the semi-submersible platform. e Its expression is or e =th-th d S32: Perform error mapping transformation on the platform's dynamic position error to obtain a transformation error function used to ensure that the dynamic error converges within the time-varying dynamic boundary function; The expression for the conversion error function is as follows: In the formula: ξ represents the system dynamic error after mapping transformation and...

5. A semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation according to claim 4, characterized in that, S4 specifically includes the following steps: S41: Based on the ln-type preset performance boundary function, construct the barrier transformation function according to the transformation error function; And the expression for the barrier transformation function is: In the formula: l represents the barrier transformation function; λ represents the abbreviated form of λ(t); Here, it is assumed that λξ can be constrained to... Within the interval, we can obtain S42: Take the derivative of the barrier transformation function to obtain its expression: In the formula: The first derivative of l is represented; δ and ζ represent intermediate variables. Denotes the first derivative of λ; Indicates η e The first derivative; S43: To ensure the stability of the derivative of the obstacle transition function, a virtual controller is constructed based on the obstacle transition function. The expression of the virtual controller is: a υ =R -1 (ψ)(-k) η lz -1 -dz -1 ) In the formula: α υ R(ψ) represents the input of the virtual controller; R(ψ) represents the parameter matrix; k η This represents the positive definite diagonal gain matrix.

6. The semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation according to claim 5, characterized in that, S5 specifically includes the following steps: S51: First-order filtering will be performed on the virtual controller to obtain the speed dynamic error; And the expression for obtaining the dynamic error of speed is: u e =u-b υ Where: β υ This represents the filtered speed control signal; t υ Represent a time-constant diagonal matrix; Indicates β υ First derivative; α υ (0),β υ (0) represents α respectively υ ,β v Initial value; υ e Indicates dynamic speed error; S52: Based on the nonlinear mathematical model of the semi-submersible platform, the derivative of the velocity dynamic error is obtained, which includes the uncertain damping term; And the expression for the derivative of the velocity dynamic error is: In the formula: Indicates υ e The first derivative; M represents the first derivative of υ; -1 (-D lh (υ)-D nh (υ)) represents an uncertain damping term; S53: The uncertain damping term in the derivative of the velocity dynamic error is approximated using the RBF-NNs approximation technique, and its expression is as follows: Where: g nn (ν) represents the RBF-NNs approximation function; Represents the radial basis functions in Gaussian form; Represents the weight matrix; This represents the upper bounded approximation error for approximating the uncertain term; The design is obtained from step S54; S54: Introduce the norm matrix based on step S53 And order Then we can obtain the equation relationship. S55: Based on step S54 and combined with S53, construct an auxiliary vector for positioning control, and the expression of the auxiliary vector is: In the formula: This represents an auxiliary vector.

7. A semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation according to claim 6, characterized in that, S6 specifically includes the following steps: S61: Based on the auxiliary vector and the dynamic error of velocity, an inequality is established to introduce the robust damping term, and its expression is: In the formula: Represents τ en The upper bound; S62: Set intermediate parameters And according to Young's inequality, we can obtain In the formula: Indicates the auxiliary damping term and k υn This represents the positive diagonal control parameter matrix; λ min Represents the smallest eigenvalue of the matrix; S63: Construct a robust neural damping term for positioning control based on step S62; And robust nerve damping term The expression is S64: Define parameter quantities Where q represents the number of actuators configured in the semi-submersible platform; This represents the pseudo-inverse operation of T(·); According to the parameter g p Obtain the adaptive parameter θ, where θ = g p -1 =[θ1,θ2,...,θ q ] T ; S65: To avoid input overshoot of the semi-submersible platform, λ is introduced to adjust the dynamic speed error υ. e To obtain the adjustment error γ = λυ e ; An adaptive parameter θ is selected based on the derivative of the adjustment error to account for the uncertainty of the fault coefficient, thereby enabling dynamic fault compensation for the semi-submersible platform actuator. Its expression is: S66: Based on step S65 and combined with the robust neural damping term, construct a virtual control law α that considers actuator dynamic faults. up Its expression is In the formula: This represents the positive definite control parameter matrix; This represents an estimate of θ; k s Indicates the fault correction gain parameter and 8. A semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation according to claim 7, characterized in that, In S7, the actual control law and parameter adaptive law are constructed based on the virtual control law and by introducing the thrust configuration matrix. Their expressions are as follows: In the formula: u p Indicates the propeller speed; The dot product symbol is represented; p represents the pitch ratio of the propeller. This represents an estimate of the uncertain thrust coefficient matrix κ(n); γ θi ,σ θi ,Γ θ ,σ θ All represent positive gain adaptive design parameters; since it is a summation matrix, T represents the matrix element in the i-th row and j-th degree of freedom of the pseudo-inverse of the thrust configuration matrix; ki (·) represents the matrix element in the k-th row and at the i-th degree of freedom of the thrust configuration matrix; α jp Represents the virtual control law α up The three components of the semi-submersible platform in the pitch, sway, and yaw directions; k e Represents the dynamic error of velocity υ e The three components of the semi-submersible platform in the pitch, sway, and yaw directions; c represents the design parameter and c = [c u ,c v ,c r ] T T represents transpose; express The initial value; This represents the estimate of the adaptive parameter θ; express The initial value; express The first derivative; express The first derivative.

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