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

Abstract

The invention discloses a semi-submersible platform preset performance dynamic positioning control method considering actuator dynamic fault compensation. The method comprises the following steps: constructing an ln type preset performance boundary function; acquiring a conversion error function for ensuring that the dynamic error is converged in the time-varying dynamic boundary function; based on an ln-type preset performance boundary function, an obstacle conversion function is constructed according to the conversion error function, and a virtual controller is constructed according to the obstacle conversion function; acquiring a speed dynamic error derivative containing an uncertain damping item according to the virtual controller; constructing an auxiliary vector for positioning control; constructing a robust neural damping item according to the auxiliary vector and the speed dynamic error so as to obtain a virtual control law considering the dynamic fault of the actuator; according to the virtual control law, a thrust configuration matrix is introduced to construct an actual control law and a parameter adaptive law, so that the problems that an existing actuator fault model cannot fully reflect long-time, multi-factor, complex and changeable characteristics when a fault occurs, and the algorithm is inconvenient to popularize and apply in actual offshore engineering are solved; and accurate control precision cannot be ensured while the fault of the actuator is considered.

Description

Technical Field

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

[0002] During the process of performing dynamic positioning control tasks, the actuator is one of the core components of the ship motion control system. Its failure may lead to a decline or even failure of the ship control performance, resulting in the ship deviating from its course, colliding, running aground, or causing damage to surrounding facilities and the environment. Although existing methods have solved problems such as system uncertainty, actuator faults, and limited communication resources, when a ship encounters a fault situation, it is usually a long-term, multi-factor, and complex and changeable situation (such as the influence of friction, elasticity, hysteresis, wind and current elements). In order to fully consider the impact of actuator dynamic faults on control performance, a dynamic fault model is introduced to simulate complex and changeable fault situations. By transferring the actuator fault to the real control input, the impact of the fault on the entire control system during the fault occurrence is more significantly amplified. On the other hand, the transient and steady-state preset performance constraints of dynamic positioning control during actuator fault occurrence have not been realized in the current control algorithms. The control strategy considering this technology further guarantees the control accuracy of dynamic positioning operations.

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

[0004] 1) The existing actuator fault model cannot fully reflect the long-term, multi-factor, and complex and changeable characteristics during fault occurrence, which is not conducive to the promotion and application of the algorithm in actual marine engineering.

[0005] 2) Considering the requirements of dynamic positioning ships for operating conditions and operating accuracy, the existing algorithms cannot ensure accurate control accuracy while considering actuator faults. Summary of the Invention

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

[0007] To achieve the above object, the technical solution of the present invention is:

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

[0009] S1: Obtain a non-linear mathematical model of the semi-submersible platform based on the manipulation theory;

[0010] S2: Based on the preset performance control technology, design the ln-type preset performance boundary function for driving the positioning control system to reach the desired performance index according to the constructed time-varying dynamic boundary function;

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

[0012] And perform error mapping transformation on the platform dynamic error to obtain the transformed error function for ensuring that the dynamic error converges within the time-varying dynamic boundary function;

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

[0014] S5: Perform first-order filtering on the virtual controller to obtain the velocity dynamic error;

[0015] Derive the velocity dynamic error based on the nonlinear mathematical model of the semi-submersible platform to obtain the derivative of the velocity dynamic error containing the uncertain damping term;

[0016] And use the RBF-NNs approximation technology to approximate the uncertain damping term in the derivative of the velocity dynamic error to construct the auxiliary vector for positioning control;

[0017] S6: Construct the robust neural damping term for positioning control according to the auxiliary vector and the velocity dynamic error, and construct the virtual control law considering the dynamic fault of the actuator according to the robust neural damping term;

[0018] S7: Construct the actual control law and the parameter adaptive law according to the virtual control law and introduce the thrust configuration matrix to achieve the preset performance dynamic positioning control of the semi-submersible platform considering the dynamic fault compensation of the actuator.

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

[0020]

[0021] τ re = γ(t)τ

[0022] τ = T(β)κ(n)u p

[0023] Where: η represents the attitude vector of the semi-submersible platform and η = [x, y, ψ] T ; x, y represent the abscissa and ordinate of the position of the semi-submersible platform; ψ represents the heading angle of the semi-submersible platform; υ represents the velocity vector of the semi-submersible platform and υ = [u, v, r] T; u, v, and r represent the surge velocity, sway velocity, and yaw angular velocity of the semi-submersible platform, respectively; M represents the inertia matrix combining the mass of the semi-submersible platform and the added mass; D lh (v) and D nh (v) represent the linear and nonlinear hydrodynamic damping matrices, respectively; τ re represents the true control input forces and moments of the semi-submersible platform in three degrees of freedom, and τ re = [τ u , τ v , τ r T ; τ en represents the forces and moments including external environmental disturbances, and τ en = [τ enu , τ env , τ enr T ; aγ(t) represents the set uncertain dynamic fault gain function that changes with time; 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 represents the rotational speed; β represents the azimuth angle in the azimuth thruster; represent the first derivatives of x, y, and ψ, respectively.

[0024] Furthermore, the expression of the ln-type preset performance boundary function constructed in S2 is

[0025]

[0026] In the formula: represents the non-negative upper bound of the conversion error; Φ η represents the time-varying dynamic boundary of the system 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 represent the time-varying dynamic boundary functions of the semi-submersible platform in three degrees of freedom, respectively, and

[0027]

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

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

[0030] S31: Set the desired reference attitude signal η of the semi-submersible platform d and η d = [x d , y d , ψ d T , where x d , y d , ψ d represent the desired abscissa, the desired ordinate, and the desired heading angle, respectively;

[0031] Define the platform dynamic position error η according to the non-linear mathematical model of the semi-submersible platform e , and its expression is

[0032] η e = η - η d

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

[0034] The expression of the transformation error function is

[0035]

[0036] In the formula: ξ represents the error after the system dynamic error is mapped and transformed, and

[0037] Furthermore, the specific steps of S4 are as follows:

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

[0039]

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

[0041] where, assuming that λξ can be limited within the interval range, then we can obtain

[0042]

[0043] S42: Take the derivative of the obstacle transformation function to obtain the derivative of the obstacle transformation function, and its expression is

[0044]

[0045] In the formula: ​Denote the first derivative of l; δ and ζ denote intermediate variables; Denote the first derivative of λ; Denote η e of the first derivative;

[0046] S43: To ensure the stability of the derivative of the obstacle conversion function, a virtual controller is constructed according to the obstacle conversion function, and the expression of the virtual controller is

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

[0048]

[0049] where: α v denotes the input of the virtual controller; R(ψ) denotes the parameter matrix; k η denotes a positive definite diagonal gain matrix.

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

[0051] S51: Perform first-order filtering on the virtual controller to obtain the velocity dynamic error;

[0052] And the expression for obtaining the velocity dynamic error is

[0053]

[0054] v e = v - β v

[0055] where: β v denotes the filtered velocity control signal; t υ denotes a time constant diagonal matrix; denotes the first derivative of β v ; α v (0), β v (0) respectively denote the initial values of α v , β v ; υ e denotes the velocity dynamic error;

[0056] S52: Take the derivative of the velocity dynamic error based on the nonlinear mathematical model of the semi-submersible platform to obtain the derivative of the velocity dynamic error containing uncertain damping terms;

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

[0058]

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

[0060] S53: Use the RBF-NNs approximation technique to approximate the uncertain damping term in the derivative of the velocity dynamic error, and its expression is

[0061]

[0062] In the formula: g nn (υ) represents the RBF-NNs approximation function; represents the radial basis function in Gaussian form; represents the weight matrix; represents the bounded approximation error for approximating the uncertain term; is designed by the steps obtained in step S54;

[0063] S54: Based on step S53, introduce the norm matrix and let

[0064] Then the equation relationship can be obtained

[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: represents the auxiliary vector.

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

[0069] S61: According to the auxiliary vector and the velocity dynamic error, establish an inequality for introducing the robust damping term, and its expression is

[0070]

[0071] In the formula: represents τ en ;

[0072] S62: Let the intermediate parameter and according to the Young's inequality, it can be obtained

[0073]

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

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

[0076] And the robust neural damping term The expression of is

[0077]

[0078] S64: Define the parameter quantity

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

[0080] According to the parameter quantity g p Obtain the adaptive parameter θ, and θ = g p -1 = [θ 1 , θ 2 ,..., θ q T ;

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

[0082] According to the derivative of the adjustment error, set the adaptive parameter for the selection of the fault coefficient uncertainty to perform dynamic fault compensation for it, and further realize the dynamic fault compensation of the actuators of the semi-submersible platform. Its expression is

[0083]

[0084] S66: Based on step S65, combine the robust neural damping term to construct a virtual control law α considering actuator dynamic faults up , and its expression is

[0085]

[0086] In the formula: represents a positive definite control parameter matrix; represents the estimation of ; k s represents the fault correction gain parameter and​

[0087] Furthermore, in S7, an actual control law and a parameter adaptation law are constructed according to the virtual control law and by introducing a thrust allocation matrix, and their expressions are

[0088]

[0089] where: u p represents the propeller rotational speed; represents the dot product symbol; p represents the pitch ratio of the propeller; represents the estimation of the uncertain thrust coefficient matrix κ(n); γ θi , σ θi , both represent positive gain adaptive design parameters; Σ is the summation matrix, represents the matrix element of the i-th row and the j-th degree of freedom of the pseudo-inverse of the thrust allocation matrix; T ki (·) represents the matrix element of the k-th row and the i-th degree of freedom of the thrust allocation matrix; α jp represents the virtual control law α up in the three components in the surge direction, sway direction, and yaw direction of the semi-submersible platform; k e represents the velocity dynamic error υ e in the three components in the surge direction, sway direction, and yaw direction of the semi-submersible platform; c represents a design parameter and c = [c u , c v , c r T ; T represents the transpose; represents the initial value of; represents the estimation of the adaptive parameter θ; represents the initial value of; represents the first derivative of; represents the first derivative of.

[0090] The present invention provides a preset performance dynamic positioning control method for a semi-submersible platform considering actuator dynamic fault compensation, which has the following two beneficial effects:

[0091] 1) Compared with the existing ship actuator fault model, the present invention can more comprehensively consider the fault factors and the complex and changeable characteristics of the actuator when a fault occurs, fuse the adaptive technology to estimate the uncertain fault coefficient online to achieve fault compensation, fully consider the elastic, frictional, delay and continuous influence of the environment, so as to construct a virtual control law considering actuator dynamic faults, and the designed controller based on this is more in line with the engineering practice and operation requirements of the semi-submersible platform.​

[0092] 2) The preset performance control scheme proposed by the present invention solves the demand for refined error in the dynamic positioning control of semi-submersible platforms. The designed ln-type preset performance boundary function and obstacle conversion function achieve the constrained convergence behavior of the system's dynamic error. Considering the safety of the submarine pipeline laid under the semi-submersible platform, the preset performance function of the present invention is more in line with the development direction of refined control of the dynamic positioning of semi-submersible platforms. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

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

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

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

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

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

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

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

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

[0102] Figure 9 It is a curve change diagram of seven adaptive parameter estimates under the method of the present invention in this embodiment;

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

[0104] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0105] This embodiment provides a preset performance dynamic positioning control method for a semi-submersible platform considering actuator dynamic fault compensation, as Figures 1 to 4 shown, and specifically includes the following steps:

[0106] S1: Obtain the non-linear mathematical model of the semi-submersible platform (SSP) based on the maneuvering theory;

[0107] Specifically, the expression of the non-linear mathematical model of the semi-submersible platform based on the maneuvering theory in S1 is

[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 abscissa and ordinate of the position of the semi-submersible platform; ψ represents the heading 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 respectively represent the surge velocity, sway velocity, and yaw angular velocity of the semi-submersible platform; M represents the inertia matrix combining the mass of the semi-submersible platform and the added mass; D lh (v) and D nh (v) respectively represent the linear and non-linear hydrodynamic damping matrices; τ re represents the true control input forces and moments of the semi-submersible platform in three degrees of freedom and τ re = [τ u , τ v , τ r T ; τ en represents the forces and moments including external environmental disturbances and τ en = [τ enu , τ​env , τ enr T ; γ(t) represents the set uncertain dynamic fault gain function that varies with time; 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 represents the rotational speed; β represents the azimuth angle in the azimuth propeller; respectively represent the first derivatives of x, y, and ψ;

[0112] S2: Based on the preset performance control technology, design the ln-type preset performance boundary function for driving the positioning control system to reach the desired performance index according to the constructed time-varying dynamic boundary function;

[0113] In this embodiment, the preset performance control technology is used to construct the ln-type preset performance boundary function, and this performance function is a time-varying dynamic boundary function independent of the initial dynamic error of the system constructed by using the monotonicity of the ln-type function, so as to drive the control system to reach the desired performance index;

[0114] Specifically, the expression of the constructed ln-type preset performance boundary function is

[0115]

[0116] In the formula: represents the non-negative upper bound of the conversion error; Φ η represents the time-varying dynamic boundary of the system dynamic error; A represents an adjustable performance gain parameter that can be automatically adjusted to a suitable value to adapt 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 respectively represent the time-varying dynamic boundary functions of the semi-submersible platform in three degrees of freedom and

[0117]

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

[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 ≤ T k , Φ η monotonically decreases to ensure that the error bound converges over time; when t > T k , Φ η stabilizes within a constant value, which is the predetermined steady-state error range; and T in the above represents k a specific convergence time, where k = u, v, r; after λ(t) reaches the steady-state time, its steady-state value is c k > 0; it can be clearly observed that λ k (0) = 1, which is decreasing when t ≤ T k and remains at the steady-state value c k when t > T k unchanged.

[0122] S3: Define the platform dynamic error according to the semi-submersible platform non-linear mathematical model;

[0123] and perform an error mapping transformation on the platform dynamic error to obtain a transformed error function for ensuring that the dynamic error converges within a time-varying dynamic boundary function;

[0124] Specifically, it includes the following steps:

[0125] S31: Set the desired reference attitude signal η d of the semi-submersible platform and η d = [x d , y d , ψ d T , where x d , y d , ψ d represent the desired abscissa, desired ordinate, and desired heading angle respectively;

[0126] Define the platform dynamic position error η e according to the semi-submersible platform non-linear mathematical model, and its expression is

[0127] η e = η - η d

[0128] S32: Perform an error mapping transformation on the platform dynamic position error to obtain a transformed error function for ensuring that the dynamic error converges within a time-varying dynamic boundary function;

[0129] The expression of the transformed error function is

[0130]

[0131] In the formula: ξ represents the error after the system dynamic error is mapped and transformed and​

[0132] In this embodiment, the change of A is related to η e To avoid the problem of computational explosion in the complex domain, the adaptation rate of A is expressed as follows:

[0133]

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

[0135] And according to the adaptation rate of A, η e is expressed in the following form:

[0136]

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

[0138] Specifically, it includes the following steps:

[0139] S41: To facilitate the design of the controller and meet the preset performance constraint requirements of the ln-type preset performance boundary function, based on the ln-type preset performance boundary function, construct a barrier transformation function according to the conversion error function;

[0140] And the expression of 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] where, assuming that λξ can be limited to within the interval range, then

[0144]

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

[0146]

[0147] In the formula: represents the first derivative of l; δ, ζ represent intermediate variables; represents the first derivative of λ; represents η e of the first derivative;

[0148] S43: To ensure the stability of the derivative of the barrier conversion function, a virtual controller is constructed based on the barrier conversion function. That is, on the premise of ensuring the stability of the derivative of the barrier conversion function, the virtual controller of this embodiment is designed to ensure that the virtual controller is stable and feasible;

[0149] The expression of the virtual controller is

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

[0151]

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

[0153] S5: The virtual controller will be subjected to first-order filtering to obtain the velocity dynamic error;

[0154] Based on the nonlinear mathematical model of the semi-submersible platform, the derivative of the velocity dynamic error is obtained to obtain the derivative of the velocity dynamic error containing the uncertain damping term; and the RBF-NNs approximation technology is used to approximate the uncertain damping term in the derivative of the velocity dynamic error to construct an auxiliary vector for positioning control;

[0155] Specifically, it includes the following steps:

[0156] S51: To avoid the problem of computational complexity explosion during the process of taking the derivative of α v , a first-order filter is introduced, and the virtual controller will be subjected to first-order filtering to obtain the velocity dynamic error;

[0157] And the expression for obtaining the velocity dynamic error is

[0158]

[0159] v e =v-β v

[0160] In the formula: β v represents the filtered velocity control signal; t v represents a time constant diagonal matrix, which can ensure smoother transmission of the control signal and avoid sudden large changes in α v ; represents the first derivative of β v ; α v (0), βv (0) respectively represent the initial values of α v , β v ; υ e represents the velocity dynamic error;

[0161] wherein this embodiment further includes a filtering error q v = α v - β v , and 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 vector of bounded nonlinear continuous functions dependent on the system state and parameters; C u , C v , C r respectively represent the components of C(·) in the three degrees of freedom u, v, r;

[0164] S52: Derive the velocity dynamic error based on the nonlinear mathematical model of the semi-submersible platform to obtain the derivative of the velocity dynamic error containing an uncertain damping term;

[0165] and the expression of the derivative of the velocity dynamic error is

[0166]

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

[0168] S53: Use the RBF-NNs approximation technique to approximate the uncertain damping term in the derivative of the velocity dynamic error, and its expression is

[0169]

[0170] In the formula: g nn (v) represents the RBF-NNs approximation function; represents the radial basis function in Gaussian form; represents the weight matrix; represents the approximation error with an upper bound for approximating the uncertain term; is designed by what is obtained in step S54;

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

[0172] Then the equation relationship can be obtained

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

[0174]

[0175] In the formula: represents the auxiliary vector;

[0176] S6: According to the auxiliary vector and the velocity dynamic error, a robust neural damping term for positioning control is constructed, and a virtual control law considering the dynamic fault of the actuator is constructed according to the robust neural damping term;

[0177] Specifically, it includes the following steps:

[0178] S61: According to the auxiliary vector and the velocity dynamic error, an inequality for introducing the robust damping term is established, and its expression is

[0179]

[0180] In the formula: represents the upper bound of τ en ;

[0181] S62: Let the intermediate parameter And according to the Young's inequality, it can be obtained

[0182]

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

[0184] S63: Based on step S62, a robust neural damping term for positioning control is constructed;

[0185] And the robust neural damping term The expression of is

[0186]

[0187] S64: Define the parameter quantity

[0188] Among them, q represents the number of actuators configured for the semi-submersible platform; represents the pseudo-inverse operation of T(·);

[0189] According to the parameter quantity g p obtain the adaptive parameter θ, and θ = g p -1 = [θ 1 , θ 2 ,..., θ q T ;

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

[0191] According to the derivative of the adjustment error, set the adaptive parameter for the uncertain selection of the fault coefficient to perform dynamic fault compensation on it, and then realize the dynamic fault compensation of the actuators of the semi-submersible platform. Its expression is

[0192]

[0193] S66: Based on step S65 and combined with the robust neural damping term, construct the virtual control law α considering the dynamic fault of the actuator up , and its expression is

[0194]

[0195] In the formula: represents a positive definite control parameter matrix; represents the estimation of ; k s represents the fault correction gain parameter and

[0196] S7: According to the virtual control law and introducing the thrust configuration matrix, construct the actual control law and the parameter adaptive law to realize the preset performance dynamic positioning control of the semi-submersible platform considering the dynamic fault compensation of the actuator;

[0197] And according to the virtual control law, construct the actual control law and the parameter adaptive law, and its expression is

[0198]

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

[0200] In order to verify that this embodiment can generate effective control signals when the SSP encounters actuator failures and transmit the pitch input command to the actuator through the control system to make the SSP reach the desired state, while ensuring that the output signals generated by the entire control system meet the preset performance requirements. This embodiment uses computer simulation experiments to conduct numerical comparison simulations under simulated external ocean environments. By comparing this embodiment with the existing vector backstepping method (Algorithm A) respectively, the effectiveness and superiority of the method of this embodiment are verified. Among them, the main differences between the method of this embodiment and Algorithm A are shown in Table 1.

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

[0202]

[0203] The method of this embodiment and Algorithm A are compared and simulated on an industrial computer (Inter(R) Core(TM) i5-7300 HQ CPU@2.50GHz, RAM: 8.00GB), Figures 5 to 7 showing the main comparison results. Figure 5 represents the trajectory comparison results of the DP control task of the SSP under the action of the two algorithms. In Figure 5 ​Among them, although both algorithms have achieved relatively good positioning trajectories, since the algorithm proposed in the present invention applies adaptive technology and realizes online estimation and learning of the uncertain gain function, the positioning trajectory shown is smoother. On the contrary, the positioning trajectory under Algorithm A with a dissipative observer shows relatively large jitter. Figure 6 Describes the change curves of the position and heading angle on three degrees of freedom of the SSP during the entire control process. It can be clearly observed that the proposed algorithm has a faster convergence speed and a smooth convergence effect. In comparison, the method in this embodiment shows a satisfactory effect. Figure 7 Shows a comparison diagram of the control torque components of all actuators of the SSP on three degrees of freedom. It can be seen that the method of the present invention has a smaller control torque at the initial state of the control process. During the process of gradually converging and stabilizing, Algorithm A shows a more intense oscillation phenomenon. In comparison, the method of the present invention is more superior in terms of energy efficiency savings. In addition, for the preset performance of the output signal of the entire control system, Figure 8 Shows that the system dynamic error is completely included in the proposed preset performance time-varying dynamic boundary [-Φ η , Φ η , including that no step-out-of-boundary behavior occurs even in the stage after the system state stabilizes. In addition, the preset performance behavior of the dynamic error is successfully restricted within the time-varying dynamic boundary at the initial state. This is because the preset performance control method proposed by this algorithm does not depend on the limitation of the initial conditions. This is because the adjustment gain parameter A in the ln-type performance function proposed by the method of the present invention solves this problem. From Figure 9 It can be seen the variation of the six adaptive parameters constructed by the uncertain gain coefficients of the six omnidirectional propellers in the SSP. Figure 10 Is the change curve of the actual control input pitch ratio and the actuator azimuth angle under the method of the present invention. It should be noted that the time period from 200s to 300s is exactly the stage when the dynamic fault occurs. Therefore, both the pitch ratio and the azimuth angle have oscillations. However, after the dynamic fault ends, they still quickly converge to the stable state.

[0204] Combined with the existing technology, based on the design of the SSP dynamic positioning controller considering actuator dynamic faults and numerical comparison simulations, this embodiment proposes a method for preset performance dynamic positioning control of SSP considering actuator dynamic faults, which mainly has two characteristics:

[0205] (1) It can fully and more comprehensively consider failure factors and conform to the dynamic failure model of ocean engineering practice. It can more realistically reflect the control performance of the SSP actuator during the occurrence of a failure. By introducing a thrust configuration matrix to construct the actual control law and parameter adaptation 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 the pitch ratio.

[0206] (2) Construct an ln-type preset performance boundary function, and tune the initial dynamic error to converge within the preset boundary by introducing an adaptive adjustment parameter A. In addition, online estimation and learning are carried out on two uncertain gain functions to achieve compensation for unknown failure 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, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic positioning control method for a semi-submersible platform with preset performance considering actuator dynamic fault compensation, characterized in that: The specific steps include: S1: Obtain a nonlinear mathematical model of a semi-submersible platform based on manipulation theory; S2: Based on the preset performance control technology, a 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; and performing error mapping conversion on the platform dynamic error to obtain a conversion error function for ensuring that the dynamic error converges within the time-varying dynamic boundary function; S4: Based on the ln-type preset performance boundary function, a barrier conversion function is constructed according to the conversion error function, and a virtual controller is constructed according to the barrier conversion function; S5: The virtual controller will be subjected to first-order filtering to obtain the speed dynamic error; Based on the nonlinear mathematical model of the semi-submersible platform, the velocity dynamic error is derived to obtain the velocity dynamic error derivative including the uncertain damping term; The RBF-NNs approximation technique is used to approximate the uncertain damping term in the velocity dynamic error derivative to construct an auxiliary vector for positioning control. S6: Based on the auxiliary vector and velocity dynamic error, a robust neural damping term for positioning control is constructed, and a virtual control law considering the dynamic fault of the actuator is constructed based on the robust neural damping term; S7: Based on the virtual control law and introducing the thrust configuration matrix, the actual control law and parameter adaptation law are constructed to achieve the dynamic positioning control of the semi-submersible platform with preset performance considering the dynamic fault compensation of the actuator.

2. A method for dynamic positioning control of a semi-submersible platform with preset performance considering actuator dynamic fault compensation according to claim 1, characterized in that: The expression of the nonlinear mathematical model of the semi-submersible platform based on the manipulation theory in S1 is: t re =γ(t)τ τ=T(β)κ(n)u p Where: 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 position of the semi-submersible platform; ψ represents the heading 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 longitudinal velocity, transverse velocity and bow angular velocity of the semi-submersible platform respectively; M represents the inertia matrix combining the mass of the semi-submersible platform and the additional mass; D lh (υ) and D nh (υ) represents the linear and nonlinear hydrodynamic damping matrices respectively; τ re represents the real 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 represents the force and torque including the external environment interference and τ en =[τ enu ,τ env ,τ enr ] T ; γ(t) represents the uncertain dynamic fault gain function that changes with time; 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 represents the rotation speed; β represents the azimuth angle in the azimuth propeller; Represent the first-order derivatives of x, y, and ψ respectively.

3. A method for dynamic positioning control of a semi-submersible platform with preset performance considering actuator dynamic fault compensation according to claim 2, characterized in that: The expression of the ln-type preset performance boundary function constructed in S2 is: Where: represents the non-negative upper bound of the conversion error; Φ η represents the time-varying dynamic boundary of the system dynamic error; A represents an adjustable performance gain parameter; h(t) represents an auxiliary variable; I represents an identity matrix; λ(t) represents a time-varying dynamic boundary function and λ(t)=[λ u ,λ v ,λ r ] T ; λ u ,λ v ,λ r They represent the time-varying dynamic boundary functions of the semi-submersible platform in three degrees of freedom and Where: T k Indicates the set convergence time; c k represents the steady-state value of the preset performance function; m represents the design parameter.

4. A method for dynamic positioning control of a semi-submersible platform with preset performance considering actuator dynamic fault compensation according to claim 3, characterized in that: The S3 specifically includes the following steps: S31: Setting the expected reference attitude signal η of the semi-submersible platform d And η d =[x d ,y d ,ψ d ] T , where x d ,y d ,ψ d represent the expected abscissa, expected ordinate and expected heading angle respectively; Define the platform dynamic position error η according to the nonlinear mathematical model of the semi-submersible platform e , whose expression is or e =th-th d S32: performing error mapping conversion on the platform dynamic position error to obtain a conversion error function for ensuring that the dynamic error converges within the time-varying dynamic boundary function; The expression of the conversion error function is: Where: ξ represents the error of the system dynamic error after mapping transformation and 5. A method for dynamic positioning control of a semi-submersible platform with preset performance considering actuator dynamic fault compensation according to claim 4, characterized in that: The S4 specifically comprises the following steps: S41: Based on the ln-type preset performance boundary function, a barrier conversion function is constructed according to the conversion error function; And the expression of the barrier conversion function is Where: l represents the barrier conversion function; λ represents the abbreviated form of λ(t); Here, it is assumed that λξ can be limited to Within the range, we can get S42: Deriving the barrier transfer function to obtain the derivative of the barrier transfer function, the expression of which is: Where: represents the first-order derivative of l; δ,ζ represent intermediate variables; represents the first derivative of λ; Represents η e The first derivative of S43: In order to ensure the stability of the derivative of the obstacle transfer function, a virtual controller is constructed according to the obstacle transfer function. The expression of the virtual controller is: a υ =R -1 (ψ)(-k) η lz -1 -dz -1 ) Where: α υ represents the input of the virtual controller; R(ψ) represents the parameter matrix; k η represents a positive definite diagonal gain matrix.

6. A method for dynamic positioning control of a semi-submersible platform with preset performance considering actuator dynamic fault compensation according to claim 5, characterized in that: The S5 specifically includes the following steps: S51: Perform first-order filtering on the virtual controller to obtain speed dynamic error; And the expression for obtaining the velocity dynamic error is: u e =u-b υ Where: β υ Represents the speed control signal after filtering; t υ represents a time constant diagonal matrix; Represents β υ The first derivative of υ (0),β υ (0) respectively represent α υ ,β v The initial value of e Indicates the speed dynamic error; S52: Deriving the velocity dynamic error based on the nonlinear mathematical model of the semi-submersible platform to obtain the velocity dynamic error derivative including the uncertain damping term; And the expression of velocity dynamic error derivative is Where: Indicates e The first derivative of represents the first derivative of υ; M -1 (-D lh (υ)-D nh (υ)) represents the uncertain damping term; S53: The uncertain damping term in the velocity dynamic error derivative is approximated using RBF-NNs approximation technology, and its expression is: Where: g nn (ν) represents the RBF-NNs approximation function; Radial basis function representing Gaussian form; represents the weight matrix; represents the upper bounded approximation error of the approximation of the uncertain term; The design is obtained by step S54; S54: Introducing the norm matrix based on step S53 And order Then we can get the equation relationship S55: Based on step S54 and S53, an auxiliary vector for positioning control is constructed, and the expression of the auxiliary vector is: Where: represents an auxiliary vector.

7. A method for dynamic positioning control of a semi-submersible platform with preset performance considering actuator dynamic fault compensation according to claim 6, characterized in that: The S6 specifically comprises the following steps: S61: Based on the auxiliary vector and velocity dynamic error, an inequality for introducing robust damping terms is established, and its expression is: Where: Represents τ en The upper bound of S62: Let the intermediate parameters According to Young's inequality, we can get Where: represents the auxiliary damping term and k υn represents a positive diagonal control parameter matrix; λ min Represents the smallest eigenvalue of a matrix; S63: constructing a robust neural damping term for positioning control based on step S62; And the robust neural damping term The expression is S64: Define parameter quantities Wherein, q represents the number of actuators configured on the semi-submersible platform; represents the pseudo-inverse operation of T(·); According to the parameter g p Get the adaptive parameter θ, and θ = g p -1 =[θ1,θ2,...,θ q ] T ; S65: In order to avoid input overshoot of the semi-submersible platform, λ is introduced to adjust the speed dynamic error υ e , to obtain the adjustment error γ = λυ e ; According to the derivative of the adjustment error, the adaptive parameter θ selected for the uncertainty of the fault coefficient is set to perform dynamic fault compensation on it, thereby realizing dynamic fault compensation for the actuator of the semi-submersible platform. Its expression is: S66: Based on step S65 and the robust neural damping term, a virtual control law α is constructed considering the dynamic fault of the actuator. up , whose expression is Where: represents a positive definite control parameter matrix; represents the estimate of θ; k s represents the fault correction gain parameter and 8. A method for dynamic positioning control of a semi-submersible platform with preset performance considering actuator dynamic fault compensation according to claim 7, characterized in that: In S7, the actual control law and parameter adaptation law are constructed based on the virtual control law and the thrust configuration matrix, and its expression is: Where: u p Indicates propeller speed; represents the dot product symbol; p represents the pitch ratio of the propeller; represents the estimation of the uncertain thrust coefficient matrix κ(n); γ θi ,σ θi ,Γ θ ,σ θ Both represent positive gain adaptation design parameters; between is the summation matrix, represents the ith row of the pseudo-inverse of the thrust configuration matrix and the matrix element at the jth degree of freedom; T ki (·) represents the kth row of the thrust configuration matrix and the matrix element under the i-th degree of freedom; α jp Denotes the virtual control law α up The three components of the semi-submersible platform in the longitudinal, transverse and bow directions; k e Represents the speed dynamic error υ e The three components of the semi-submersible platform in the longitudinal, transverse and bow directions; c represents the design parameter and c = [c u ,c v ,c r ] T ; T represents transpose; express The initial value of represents the estimate of the adaptive parameter θ; express The initial value of express The first derivative of express The first derivative of .

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