Dynamic positioning active disturbance rejection control method based on adaptive extended Kalman filtering algorithm

Abstract

The invention discloses a dynamic positioning active-disturbance-rejection control method based on an adaptive extended Kalman filtering algorithm, and relates to the field of ship dynamic positioning control. The invention aims to solve the problems that an existing ship dynamic positioning active-disturbance-rejection control method cannot meet the control stability requirement while ensuring the response speed, the positioning speed is low, and the service life of an executing mechanism is short. The method comprises the following steps: obtaining a ship motion model by using a dynamic positioning ship low-frequency motion model and a dynamic positioning ship high-frequency motion model in a state space form; designing a non-linear state error feedback control law, and obtaining a thrust value applied by the propeller by using the non-linear state error feedback control law; discretizing the ship motion model to obtain a discretized ship motion model; and based on an adaptive extended Kalman filtering method, designing a dynamic positioning active-disturbance-rejection controller by using the discretized ship motion model and a thrust value applied by a propeller. The method is used for ship dynamic positioning active-disturbance-rejection control.

Description

Technical Field

[0001] The invention relates to the field of ship dynamic positioning control, and in particular to a dynamic positioning self-disturbance rejection control method based on an adaptive extended Kalman filter algorithm. Background Art

[0002] With the continuous development of marine engineering, human beings are no longer limited to land resources, but are gradually turning their attention to rich marine resources. The complexity of offshore operations is increasing, the environmental interference they face is more complex and changeable, and the requirements for ship positioning capabilities are also increasing. Dynamic positioning uses the ship's own propulsion device to generate thrust to resist the interference of the marine environment, thereby achieving fixed-point hovering on the sea surface. However, when operating at sea, the dynamic positioning ship will be affected by the complex marine environment, making it impossible for the ship to accurately position to the desired position, causing the dynamic positioning controller to continuously change the output control force, resulting in serious wear of the actuator and greatly reducing the service life of the actuator. Therefore, it is very important for the self-disturbance control of dynamic positioning.

[0003] At present, the ship dynamic positioning automatic disturbance rejection control is mainly implemented by the method of adjusting PID parameters by algorithm and combining tracking differentiator with state observer. However, the parameter adjustment of the ship dynamic positioning automatic disturbance rejection control method based on PID control method is complex, which makes it difficult to balance the response speed and stability. Therefore, it is impossible to meet the control stability requirements while ensuring the response speed, which in turn makes it impossible to meet the control stability requirements while ensuring the positioning speed. The ship dynamic positioning automatic disturbance rejection control method based on the combination of tracking differentiator and state observer does not consider the influence of high-frequency interference in the marine environment, which will still cause serious wear of the actuator, resulting in a short life of the actuator. At the same time, this method does not consider the influence of high-frequency interference in the marine environment, resulting in the problem of slow positioning speed. Summary of the invention

[0004] The purpose of the present invention is to solve the problems that the existing ship dynamic positioning self-disturbance rejection control method still cannot meet the control stability requirements while ensuring the positioning speed and will cause the life of the actuator to be short, and a dynamic positioning self-disturbance rejection control method based on an adaptive extended Kalman filter algorithm is proposed.

[0005] A dynamic positioning self-disturbance rejection control method based on an adaptive extended Kalman filter algorithm is specifically as follows:

[0006] Step 1: Establish a low-frequency motion model of a dynamic positioning vessel;

[0007] Step 2: Establish a high-frequency motion model of a dynamic positioning vessel, and convert the high-frequency motion model of a dynamic positioning vessel into a state space form;

[0008] Step 3: using the low-frequency motion model of the dynamic positioning ship obtained in step 1 and the high-frequency motion model of the dynamic positioning ship in the state space form obtained in step 2, a ship motion model is obtained;

[0009] Step 4: design a nonlinear state error feedback control law, and use the nonlinear state error feedback control law to obtain the thrust value applied by the propeller;

[0010] Step 5: discretize the ship motion model obtained in step 3 to obtain a discretized ship motion model;

[0011] Step 6: Based on the adaptive extended Kalman filter method, the dynamic positioning anti-disturbance control controller is designed using the discretized ship motion model obtained in step 5 and the thrust value applied by the propeller obtained in step 4.

[0012] Furthermore, the establishment of the low-frequency motion model of the dynamic positioning vessel in step 1 is specifically as follows:

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] in, x l is the horizontal coordinate of the low-frequency motion of the ship, y l is the ordinate of the low-frequency motion of the ship, ψ l is the angle of the ship's low-frequency motion, V is the velocity vector of the combination of the longitudinal sway velocity, transverse sway velocity and bow angular velocity of the ship's low-frequency motion, u is the longitudinal sway velocity of the ship's low-frequency motion, v is the transverse sway velocity of the ship's low-frequency motion, r is the bow angular velocity of the ship's low-frequency motion, τ is the thrust vector applied by the propeller, τ1 is the thrust applied by the propeller in the longitudinal direction, τ2 is the thrust applied by the propeller in the transverse direction, and τ3 is the thrust applied by the propeller in the yaw direction. b is the environmental disturbance force vector, b1(t) is the environmental disturbance force in the longitudinal direction of the ship's low-frequency motion, b2(t) is the environmental disturbance force in the transverse direction of the ship's low-frequency motion, b3(t) is the environmental disturbance force in the bow direction of the ship's low-frequency motion, t is time, R(η) and R(ψ) are rotation matrices, M, C(V) and D(V) are intermediate matrices, m is the ship's mass, Xu ,Y v ,Y r ,N v ,N r , is the hydrodynamic coefficient, x G is the center of gravity of the ship, I z is the ship's moment of inertia.

[0020] Furthermore, the rotation matrix R(ψ l ) satisfies the following formula:

[0021]

[0022] R T (ψ l )S(r)R(ψ l )=R(ψ l )S(r)R T (ψ l )=S(r)

[0023]

[0024] R T (ψ l )R(ψ l )=I

[0025] ||R(ψ l )||=1

[0026] Among them, S(r) is the intermediate matrix and I is the identity matrix.

[0027] Furthermore, the step 2 of establishing a high-frequency motion model of a dynamic positioning vessel and converting the high-frequency motion model of a dynamic positioning vessel into a state space form is specifically as follows:

[0028] Step 21: Establish a high-frequency motion model of a dynamic positioning vessel, specifically:

[0029]

[0030] Among them, s is the Laplace operator, K ωi is the coefficient of wave intensity in direction i, ζ i is the relative damping coefficient in the i direction, ω 0i is the dominant frequency of the wave in the i direction in the PM wave energy spectrum, i=1, 2, 3 represent the surge direction, sway direction, and bow roll direction respectively;

[0031] Step 22: Convert the high-frequency motion model of the dynamic positioning vessel into a state space form, specifically:

[0032]

[0033]

[0034]

[0035] C h =[0 3×3 I 3×3 ]

[0036]

[0037] A 22 =-diag{2ζ1ω 01 2ζ2ω 02 2ζ3ω 03}

[0038] ∑=diag[K w1 K w2 K w3 ]

[0039] K wi =2ξ i ω 0i σ i

[0040] Among them, η h =[x h ,y h ,ψ h ],η h is the vector of the ship's high-frequency motion, consisting of the ship's position and heading angle, x h is the horizontal coordinate of the ship during high-frequency motion, y h is the ordinate of the ship during high-frequency motion, ψ h is the heading angle of the ship during high-frequency motion, ξ h =[x h ,y h ,ψ h ,ξ x ,ξ y ,ξ ψ ] T ,ξ h is the state vector of the high-frequency motion of the ship, ξ x is the longitudinal swell linear velocity of the ship during high-frequency motion, ξ y is the sway velocity of the ship during high-frequency motion, ξ ψ is the bow angular velocity during high-frequency motion of the ship, ω h =[ω h1 ,ω h2 ,ω h3 ] T ,ω his a zero-mean Gaussian white noise vector, ω h1 ,ω h2 ,ω h3 are zero-mean Gaussian white noises representing the surge, sway, and pitch directions, respectively. h , h , C h is the coefficient matrix, A 21 , A 22 ,∑ is the intermediate matrix, K wi is the intermediate variable, I 3×3 is a 3×3 identity matrix, diag[] is a diagonal matrix, ξ1=ξ x , ξ2=ξ y , ξ3=ξ ψ , σ i is a constant for the wave strength in the i direction, 0 3×3 is a 3×3 matrix of zeros.

[0041] Furthermore, the ship motion model is obtained by using the low-frequency motion model of the dynamic positioning ship obtained in step 1 and the high-frequency motion model of the dynamic positioning ship in the state space form obtained in step 2 in step 3, specifically:

[0042]

[0043] Where f(x) is the state variable function, B is the thruster configuration control matrix, x is the state variable, E is the noise coefficient matrix, ω and ω' are two zero-mean Gaussian white noise matrices, H is the observation coefficient matrix, and y is the system output.

[0044] Furthermore, the design of the nonlinear state error feedback control law in step 4 uses the nonlinear state error feedback control law to obtain the thrust value applied by the propeller, specifically:

[0045] Step 41: Obtain the system state equation and discretize the system state equation to obtain the discretized system state equation, which is specifically:

[0046] First, obtain the system state equation:

[0047]

[0048] Among them, x1 is the vector composed of the ship's position and angle, x2 is the vector composed of the ship's linear velocity and angular velocity, and x3 is the disturbance acceleration vector. is the derivative of x1, x2, x3, η'(t) is the marine environment disturbance function;

[0049] Then, the system state equation is discretized to obtain the discretized system state equation:

[0050]

[0051]

[0052] Among them, e1 is the vector composed of the ship position error and angle error, z1 is the vector composed of the ship position and angle observation values, z2 is the vector composed of the ship linear velocity and angular velocity observation values, z3 is the disturbance acceleration vector, is the derivative of z1, z2, z3, β 01 >0,β 02 >0,β 03 >0,β 01 , β 02 , β 03 is the adjustable gain of the observer, a1 and a2 are the shape parameters of the fal function, a takes a1 or a2, and δ is the gain interval coefficient;

[0053] Step 42: Obtain the system state feedback equation using the discretized system state equation;

[0054] Step 43: Use the system state feedback equation obtained in step 42 to obtain the value of the thrust vector applied by the propeller.

[0055] Furthermore, the system state feedback equation is obtained by using the discretized system state equation in step 42, specifically:

[0056] make:

[0057]

[0058] Among them, e2 is the vector composed of linear velocity error and angular velocity error, and e3 is the disturbance acceleration error vector;

[0059] According to the discretized system state equation, the error vectors e1, e2, and e3 are expressed as follows:

[0060]

[0061] Assuming that variables x1 and x2 are known, for any V, the following equation has a solution:

[0062] f(x1,x2,τ)=V

[0063] Assume τ = g(x1, x2, V), then the system state feedback is as follows:

[0064]

[0065] The above formula is finally rewritten as:

[0066]

[0067] Among them, v1 is a preset vector composed of the ship position and angle preset according to experience, k1 and k2 are preset coefficients, is the derivative of v1.

[0068] Furthermore, the value of the thrust vector applied by the propeller is obtained by using the system state feedback equation obtained in step 42 in step 43, specifically:

[0069] First, obtain the thrust vector applied by the propeller:

[0070]

[0071] τ0=k1fal(e1,α1,δ)+k2fal(e2,α2,δ)

[0072] Where c is the compensation intensity factor, z3(t) is the disturbance acceleration observation value at time t;

[0073] Then, a fixed-time dilated state observer is designed, specifically:

[0074]

[0075] w=R(ψ)V

[0076]

[0077]

[0078] in, is an estimate of η, yes The derivative of , w is the auxiliary velocity vector, is the estimated value of w, χ is the set of unknown perturbations, is the estimated value of χ, H n <Υ, μ1, μ2, μ3, ε1, ε2, ε3, Υ are constants, H n is a bounded constant, α i ∈(0,1),β i >1, is a constant, l1, l2 are both infinitesimal, α i , β i is an intermediate variable, i=1,2,3;

[0079] The gain range of the fixed-time extended state observer FESO satisfies the following Hurwitz matrix:

[0080]

[0081]

[0082] Finally, the thrust vector applied to the propeller is discretized based on the fixed time dilated state observer to obtain the final thrust vector applied by the propeller, which is:

[0083]

[0084] τ0(k)=k1fal(e1,α1,δ)+k2fal(e2,α2,δ)

[0085] e2=x2(k)-z2(k)

[0086] e1=x1(k)-z1(k)

[0087] Wherein, k is the discretized time t, τ(k) is the thrust applied by the propeller at time k, z3(k) is the observed value of the disturbance acceleration at time k, τ0(k) is the theoretical value of the thrust applied by the propeller at time k, x1(k) is the vector of the ship’s position and angle at time k, z2(k) is the vector of the ship’s linear velocity and angular velocity observations at time k, z1(k) is the vector of the ship’s position and angle observations at time k, and x2(k) is the vector of the ship’s linear velocity and angular velocity at time k.

[0088] Furthermore, in step 5, the ship motion model obtained in step 3 is discretized to obtain the discretized ship motion model, which is specifically:

[0089]

[0090] Δ=A -1 (Φ-I)B

[0091] Γ=A -1 (Φ-I)E

[0092] R=R T >0

[0093] Φ=exp(Ah)

[0094] Where x(k) is the system state variable at time k, x(k-1) is the system state variable at time k-1, Φ, Δ, Γ, and H are coefficient matrices, τ(k-1) is the thrust applied by the propeller at time k-1, ω(k-1) is the zero-mean Gaussian white noise with a covariance matrix of Q at time k-1, ω'(k-1) is the zero-mean Gaussian white noise with a covariance matrix of R at time k-1, y(k) is the system output at time k, R and Q are the covariance matrices of ω'(k-1) and ω(k-1) respectively, A is the coefficient matrix of the state variable function f(x), h is the sampling time, and I is the identity matrix.

[0095] Furthermore, the step 6 is based on the adaptive extended Kalman filter method, and uses the discretized ship motion model obtained in step 5 and the thrust value applied by the propeller obtained in step 4 to design the dynamic positioning anti-disturbance control controller, specifically:

[0096] Step 6.1: Initialize the estimated value of the system state variable Initial value of covariance estimate

[0097] Step 6.2: Use the discretized ship motion model to obtain the predicted value of the system state variable at time k:

[0098]

[0099] in, is the estimated value of the system state variable at time k-1, τ(k-1) is the thrust applied by the propeller at time k-1, is the predicted value of the system state variable at time k;

[0100] Step 6.3. Obtain the error covariance prediction value:

[0101]

[0102] in, is the predicted value of error covariance at time k, is the error covariance estimate at time k-1;

[0103] Step 64: Introduce the forgetting factor ff to obtain the updated adjustment parameter d(k):

[0104]

[0105] Among them, d(k) is the adjustment parameter at time k, ff k+1 It is ff raised to the power of k+1, where ff is the forgetting factor;

[0106] Step 65: Use the predicted value of the system state variable at time k obtained in step 62 Get the predicted value of system output at time k:

[0107]

[0108] in, is the predicted value of the system output at time k;

[0109] Step 66: Use y(k) obtained in step 65 to obtain the system output error:

[0110]

[0111] Among them, y(k) is the actual value of the system output at time k, is the predicted value of the system output at time k, and Z(k) is the system output error at time k;

[0112] Step 67: Update the observation noise covariance matrix R(k):

[0113] R(k)=(1-d(k))R(k-1)

[0114] +d(k)([IH(k)K(k-1)]w'(k)w' T (k)[IH(k)K(k-1)] T

[0115] +H(k)P(k-1)H T (k))

[0116] Where R(k-1) is the observation noise covariance matrix at time k-1, H(k) is the coefficient matrix at time k, w'(k) is the Gaussian white noise at time k, K(k-1) is the Kalman filter gain coefficient at time k-1, and P(k-1) is the filter estimation mean square error matrix at time k-1;

[0117] Step 68: Use the error covariance prediction value obtained in step 63 Calculate the Kalman filter gain coefficient K(k):

[0118]

[0119] Among them, K(k) is the Kalman filter gain coefficient at time k, and R(k) is the observation noise covariance matrix at time k;

[0120] Step 69: Use K(k) obtained in step 68 and Z(k) obtained in step 66 to obtain the estimated value of the system state variable

[0121]

[0122] in, is the estimated value of the system state variable at time k;

[0123] Step 60: Use K(k) obtained in step 68 and R(k) obtained in step 67 to obtain the error covariance estimate.

[0124]

[0125] in, is the error covariance estimate at time k;

[0126] Step 61: Use error covariance to predict values Composition filter estimation mean square error matrix Let k=k+1, and return to step 62.

[0127] The beneficial effects of the present invention are:

[0128] The present invention performs dynamic positioning anti-disturbance control based on an adaptive extended Kalman filter algorithm, which is more suitable for systems with nonlinearity and uncertainty. The present invention introduces a forgetting factor and adaptively adjusts the observation noise covariance matrix on the basis of the extended Kalman filter algorithm, improves the existing dynamic positioning anti-disturbance control method, effectively weakens the influence of the initial value on the filtering effect of the filter, and improves the positioning accuracy and positioning speed. The parameter adjustment of the present invention is simple, and it can meet the control stability requirements while improving the response speed. The present invention uses an adaptive extended Kalman filter algorithm to filter the first-order wave force interference of the marine environment, solves the problem of increased wear of the actuator due to the high-frequency reciprocating motion of the dynamic positioning ship under the influence of the first-order wave force of the marine environment, reduces the loss of the actuator, and improves the life of the actuator. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] Figure 1 This is a schematic diagram of the coordinate system of a dynamic positioning vessel;

[0130] Figure 2 This is the schematic diagram of the Kalman filter algorithm;

[0131] Figure 3 This is the structural block diagram of the active disturbance rejection controller based on the adaptive extended Kalman filter algorithm. DETAILED DESCRIPTION

[0132] Specific implementation method 1: This implementation method is a dynamic positioning anti-disturbance control method based on an adaptive extended Kalman filter algorithm. The specific process is as follows:

[0133] Step 1: Establish a low-frequency motion model of a dynamic positioning vessel:

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] in, x l is the horizontal coordinate of the low-frequency motion of the ship, y lis the ordinate of the low-frequency motion of the ship, ψ l is the angle of the ship's low-frequency motion, is the velocity vector of the combination of the longitudinal sway line velocity, the transverse sway line velocity and the bow angular velocity of the ship's low-frequency motion, u is the longitudinal sway line velocity of the ship's low-frequency motion, v is the transverse sway line velocity of the ship's low-frequency motion, r is the bow angular velocity of the ship's low-frequency motion, is the thrust vector applied by the propeller, τ1 is the thrust applied by the propeller in the longitudinal direction, τ2 is the thrust applied by the propeller in the transverse direction, τ3 is the thrust applied by the propeller in the yaw direction, is the environmental disturbance force vector, b1(t) is the environmental disturbance force in the longitudinal direction of the ship's low-frequency motion, b2(t) is the environmental disturbance force in the transverse direction of the ship's low-frequency motion, b3(t) is the environmental disturbance force in the bowing direction of the ship's low-frequency motion, t is time, R(η), R(ψ) are rotation matrices, M, C(V), D(V) are intermediate matrices, m is the ship's mass, X u ,Y v ,Y r ,N v ,N r , is the hydrodynamic coefficient ( is the additional mass of the ship in the directions of surge, sway and pitch, X u ,Y v ,Y r ,N v ,N r is the linear damping of the ship in the surge, sway and pitch directions), x G is the center of gravity of the ship, I z is the ship's moment of inertia; the schematic diagram of the dynamic positioning ship's coordinate system is as follows Figure 1 shown.

[0140] The rotation matrix R(ψ l ) meets the following conditions:

[0141]

[0142] R T (ψ l )S(r)R(ψ l )=R(ψ l )S(r)R T (ψ l )=S(r)

[0143]

[0144] R T (ψ l )R(ψ l )=I

[0145] ||R(ψ l )||=1

[0146] Among them, S(r) is the intermediate matrix and I is the identity matrix;

[0147] Step 2: By adding a second-order harmonic oscillator with damping terms to the ship position and heading angle to simulate the high-frequency motion of the ship, a high-frequency motion model of the dynamic positioning ship is established and converted into a state space form, specifically:

[0148] The high-frequency motion model equation of a dynamic positioning vessel is:

[0149]

[0150] Among them, s is the Laplace operator, K ωi (i=1,2,3) is the coefficient of wave strength in direction i, ζ i (i=1,2,3) is the relative damping coefficient in the i direction, ω 0i (i=1,2,3) represents the dominant frequency of the waves in the i direction in the PM wave energy spectrum, i is 1, 2, 3 represents the surge direction, sway direction, and bow roll direction respectively;

[0151] Convert formula (3) into state space form as follows:

[0152]

[0153]

[0154]

[0155] C h =[0 3×3 I 3×3 ]

[0156]

[0157] A 22 =-diag{2ζ1ω 01 2ζ2ω 02 2ζ3ω 03}

[0158] ∑=diag[K w1 K w2 K w3 ]

[0159] K wi =2ξ i ω 0i σ i

[0160] Among them, η h=[x h ,y h ,ψ h ] is the vector of the ship’s high-frequency motion, consisting of the ship’s position and heading angle, ξ h =[x h ,y h ,ψ h ,ξ x ,ξ y ,ξ ψ ] T is the state vector of the ship’s high-frequency motion, x h is the horizontal coordinate of the ship during high-frequency motion, y h is the ordinate of the ship during high-frequency motion, ψ h is the heading angle of the ship during high-frequency motion, ξ x is the longitudinal swell linear velocity of the ship during high-frequency motion, ξ y is the sway velocity of the ship during high-frequency motion, ξ ψ is the bow angular velocity during high-frequency motion of the ship, ω h =[ω h1 ,ω h2 ,ω h3 ] T is a zero-mean Gaussian white noise vector, ω h1 ,ω h2 ,ω h3 are zero-mean Gaussian white noises representing the surge, sway, and pitch directions, respectively. h , h , C h is the coefficient matrix, A 21 , A 22 ,∑ is the intermediate matrix, K wi is the intermediate variable, I 3×3 is a 3×3 identity matrix, diag[] is a diagonal matrix, ξ1=ξ x , ξ2=ξ y , ξ3=ξ ψ , σ i is a constant for the wave strength in the i direction, 0 3×3 is a 3×3 zero matrix;

[0161] Low-frequency motion is mainly caused by ocean currents, second-order wave forces and wind forces, and manifests itself as changes in the ship's position and heading. High-frequency motion is mainly caused by first-order wave forces, and manifests itself as periodic reciprocating motion in the equilibrium position.

[0162] Step 3: Using the low-frequency motion model of the dynamic positioning ship obtained in step 1 and the high-frequency motion model of the dynamic positioning ship in the state space form obtained in step 2, the ship motion model is obtained as follows:

[0163] The low-frequency motion model of the dynamic positioning ship and the high-frequency motion model of the dynamic positioning ship in state space form are rewritten as:

[0164]

[0165] Where f(x) is the state variable function, B is the thruster configuration control matrix, x is the state variable, E is the noise coefficient matrix, ω and ω' are two zero-mean Gaussian white noise matrices, H is the observation coefficient matrix, and y is the system output.

[0166] Step 4: Design a nonlinear state error feedback control law and use the nonlinear state error feedback control law to obtain the value of the thrust τ(k) applied by the propeller at time k:

[0167] Step 41: Obtain the system state equation and discretize the system state equation to obtain the discretized system state equation:

[0168] For the following second-order nonlinear system:

[0169]

[0170] Among them, x1 is the vector composed of the ship's position and angle, x2 is the vector composed of the ship's linear velocity and angular velocity, is the derivative of x1 and x2;

[0171] The system state equation is obtained using the observed state and the second-order nonlinear system:

[0172]

[0173] Among them, x3 is the disturbance acceleration vector, η'(t) is the ocean environment disturbance function, which is an uncertain bounded function;

[0174] Discretize the system state equation to obtain the discretized system state equation:

[0175]

[0176]

[0177] Among them, e1 is the vector composed of the ship position error and angle error, z1 is the vector composed of the ship position and angle observation values, z2 is the vector composed of the ship linear velocity and angular velocity observation values, z3 is the disturbance acceleration vector, is the derivative of z1, z2, z3, β 01 >0,β 02 >0,β 03 >0,β 01 , β 02 , β 03is the adjustable gain of the observer, a1 and a2 are the shape parameters of the fal function, a is a1 or a2, δ is the gain interval coefficient, which is a positive integer that can change the size of the linear change interval of the function gain, and is generally very small;

[0178] Step 42: Use the discretized system state equation to obtain system state feedback:

[0179] make:

[0180]

[0181] Among them, e2 is the vector composed of linear velocity error and angular velocity error, and e3 is the disturbance acceleration error vector;

[0182] The error expression obtained according to the discretized system state equation is as follows:

[0183]

[0184] Assume that variables x1 and x2 are known quantities. If for any V, the following equation has a solution:

[0185] f(x1,x2,τ)=V

[0186] Assume τ = g(x1, x2, V), then the system state feedback is as follows:

[0187]

[0188] The above formula is finally rewritten as:

[0189]

[0190] Among them, v1 is a preset vector composed of the ship position and angle preset according to experience, k1 and k2 are preset coefficients, is the derivative of v1;

[0191] Step 43: Use the system state feedback obtained in step 42 to obtain the value of the thrust vector τ applied by the propeller:

[0192] Replace e1 and e2 with the fal(e1,α1,δ) function to obtain the output control quantity τ0:

[0193] τ0=k1fal(e1,α1,δ)+k2fal(e2,α2,δ)

[0194] Among them, k1, k2, α1, α2, and δ can all be adjusted to enable the controller to quickly track the desired value;

[0195] The thrust vector applied by the propeller is obtained by canceling the observed disturbance:

[0196]

[0197] Where c is the compensation intensity factor, z3(t) is the disturbance acceleration observation value at time t;

[0198] The design formula of the fixed-time dilated state observer is:

[0199]

[0200] w=R(ψ)V

[0201]

[0202]

[0203] in, is an estimate of η, yes The derivative of , w is the auxiliary velocity vector, is the estimated value of w, χ is the set of unknown perturbations, is the estimated value of χ, H n <Υ, μ1, μ2, μ3, ε1, ε2, ε3, Υ are constants, H n is a bounded constant, α i ∈(0,1),β i >1, is a constant, l1, l2 are both infinitesimal, α i , β i is an intermediate variable, i=1,2,3;

[0204] The gain range of the fixed-time extended state observer FESO must satisfy the following Hurwitz matrix:

[0205]

[0206]

[0207] Based on the fixed time dilation state observer, the thrust vector applied to the propeller is discretized to obtain the final thrust vector applied by the propeller:

[0208]

[0209] in,

[0210] τ0(k)=k1fal(e1,α1,δ)+k2fal(e2,α2,δ)

[0211] e2=x2(k)-z2(k)

[0212] e1=x1(k)-z1(k)

[0213] Wherein, k is the discretized time t, τ(k) is the thrust applied by the propeller at time k, z3(k) is the observed value of the disturbance acceleration at time k, τ0(k) is the theoretical value of the thrust applied by the propeller at time k, x1(k) is the vector of the ship’s position and angle at time k, z2(k) is the vector of the ship’s linear velocity and angular velocity observations at time k, z1(k) is the vector of the ship’s position and angle observations at time k, and x2(k) is the vector of the ship’s linear velocity and angular velocity at time k.

[0214] When time approaches a certain T value, the observed values ​​of e1, e2, and e3 approach the 0 vector, and the system converges.

[0215] Step 5: Discretize the ship motion model obtained in step 3 to obtain the discretized ship motion model:

[0216]

[0217] Δ=A -1 (Φ-I)B

[0218] Γ=A -1 (Φ-I)E

[0219] R=R T >0

[0220] Φ=exp(Ah)

[0221] Where x(k) is the system state variable at time k, x(k-1) is the system state variable at time k-1, Φ, Δ, Γ, H are coefficient matrices, τ(k-1) is the thrust applied by the propeller at time k-1, and ω(k-1) is the covariance matrix at time k-1, which is Q=Q T >0, ω'(k-1) is the covariance matrix of k-1 time R=R T >0, y(k) is the system output at time k, R and Q are the covariance matrices of ω'(k-1) and ω(k-1) respectively, A is the coefficient matrix of the state variable function f(x), h is the sampling time, and I is the identity matrix.

[0222] Step 6: Figure 2-Figure 3 As shown in FIG, based on the adaptive extended Kalman filter method, the dynamic positioning active disturbance rejection controller is designed using the discretized ship motion model obtained in step five and the thrust applied by the propeller obtained in step four, and the dynamic positioning active disturbance rejection control is realized using the dynamic positioning active disturbance rejection controller, specifically:

[0223] Step 6.1: Initialize the estimated value of the system state variable Initial value of covariance estimate

[0224] Step 6.2: Use the discretized ship motion model to obtain the predicted value of the system state variable at time k, i.e., the prior estimate:

[0225]

[0226] in, is the estimated value of the system state variable at time k-1, τ(k-1) is the thrust applied by the propeller at time k-1, is the predicted value of the system state variable at time k;

[0227] Step 6.3. Obtain the error covariance prediction value:

[0228]

[0229] in, is the predicted value of error covariance at time k, is the error covariance estimate at time k-1;

[0230] Step 64: Introduce the forgetting factor ff to obtain the updated adjustment parameter d(k):

[0231]

[0232] Among them, d(k) is the adjustment parameter at time k, ff k+1 It is ff raised to the power of k+1, where ff is the forgetting factor;

[0233] Step 65: Use the predicted value of the system state variable at time k obtained in step 62 Get the predicted value of the system output (measured value) at time k:

[0234]

[0235] in, is the predicted value of the system output at time k;

[0236] Step 66: Use the data obtained in step 65 Get the system output error:

[0237]

[0238] Among them, y(k) is the actual value of the system output at time k, is the predicted value of the system output at time k, and Z(k) is the system output error at time k;

[0239] Step 67: Update the observation noise covariance matrix R(k):

[0240] R(k)=(1-d(k))R(k-1)

[0241] +d(k)([IH(k)K(k-1)]w'(k)w' T (k)[IH(k)K(k-1)] T

[0242] +H(k)P(k-1)H T (k))

[0243] Where R(k-1) is the observation noise covariance matrix at time k-1, H(k) is the coefficient matrix at time k, w'(k) is the Gaussian white noise at time k, K(k-1) is the Kalman filter gain coefficient at time k-1, and P(k-1) is the filter estimation mean square error matrix at time k-1;

[0244] Step 68: Use the error covariance prediction value obtained in step 63 Calculate the Kalman filter gain coefficient K(k):

[0245]

[0246] Among them, K(k) is the Kalman filter gain coefficient at time k, and R(k) is the observation noise covariance matrix at time k;

[0247] Step 69: Use K(k) obtained in step 68 and Z(k) obtained in step 66 to obtain the estimated value of the system state variable

[0248]

[0249] in, is the estimated value of the system state variable at time k;

[0250] Step 60: Use K(k) obtained in step 68 and R(k) obtained in step 67 to obtain the error covariance estimate.

[0251]

[0252] in, is the error covariance estimate at time k;

[0253] Step 61: Use error covariance to predict values Composition filter estimation mean square error matrix Let k=k+1, and return to step 62.

[0254] The present invention adopts an adaptive extended Kalman filter algorithm to design a dynamic positioning anti-disturbance controller, adopts an adaptive Kalman filter algorithm to process noise, introduces a forgetting factor and an adaptive observation noise covariance matrix R to improve the algorithm based on the Kalman algorithm, weakens the influence of the initial value on the filtering effect, and more effectively filters out high-frequency interference in the ship's position and attitude information, so as to improve the accuracy and performance of dynamic positioning and reduce the wear of the actuator. The effect to be achieved by the present invention is to enable the dynamic positioning ship to reach the desired position quickly and accurately, and reduce the loss of the actuator caused by high-frequency movement under the influence of the complex ocean environment. The nonlinear state feedback anti-disturbance controller is used to solve the problem of rapid positioning of ship dynamic positioning, and introduces an adaptive extended Kalman filter to reduce the loss of the actuator, so as to achieve better dynamic positioning control.

Claims

1. A dynamic positioning anti-disturbance control method based on an adaptive extended Kalman filter algorithm, characterized in that The specific process of the method is: Step 1: Establish a low-frequency motion model of a dynamic positioning vessel; Step 2: Establish a high-frequency motion model of a dynamic positioning vessel, and convert the high-frequency motion model of a dynamic positioning vessel into a state space form; Step 3: using the low-frequency motion model of the dynamic positioning ship obtained in step 1 and the high-frequency motion model of the dynamic positioning ship in the state space form obtained in step 2, a ship motion model is obtained; Step 4: design a nonlinear state error feedback control law, and use the nonlinear state error feedback control law to obtain the thrust value applied by the propeller; Step 5: discretize the ship motion model obtained in step 3 to obtain a discretized ship motion model; Step 6: Based on the adaptive extended Kalman filter method, the dynamic positioning anti-disturbance control controller is designed using the discretized ship motion model obtained in step 5 and the thrust value applied by the propeller obtained in step 4.

2. The method for dynamic positioning auto-disturbance rejection control based on the adaptive extended Kalman filter algorithm according to claim 1, characterized in that: The step 1 of establishing the low-frequency motion model of the dynamic positioning vessel is specifically as follows: in, x l is the horizontal coordinate of the low-frequency motion of the ship, y l is the ordinate of the low-frequency motion of the ship, ψ l is the angle of the ship's low-frequency motion, V is the velocity vector of the combination of the longitudinal sway velocity, transverse sway velocity and bow angular velocity of the ship's low-frequency motion, u is the longitudinal sway velocity of the ship's low-frequency motion, v is the transverse sway velocity of the ship's low-frequency motion, r is the bow angular velocity of the ship's low-frequency motion, τ is the thrust vector applied by the propeller, τ1 is the thrust applied by the propeller in the longitudinal direction, τ2 is the thrust applied by the propeller in the transverse direction, and τ3 is the thrust applied by the propeller in the yaw direction. b is the environmental disturbance force vector, b1(t) is the environmental disturbance force in the longitudinal direction of the ship's low-frequency motion, b2(t) is the environmental disturbance force in the transverse direction of the ship's low-frequency motion, b3(t) is the environmental disturbance force in the bow direction of the ship's low-frequency motion, t is time, R(η) and R(ψ) are rotation matrices, M, C(V) and D(V) are intermediate matrices, m is the ship's mass, X u ,Y v ,Y r ,N v ,N r , is the hydrodynamic coefficient, x G is the center of gravity of the ship, I z is the ship's moment of inertia.

3. The method for dynamic positioning anti-disturbance control based on adaptive extended Kalman filter algorithm according to claim 2, characterized in that: The rotation matrix R(ψ l ) satisfies the following formula: R T (ψ l )S(r)R(ψ l )=R(ψ l )S(r)R T (ψ l )=S(r) R T (ψ l )R(ψ l )=I ||R(ψ l )||=1 Among them, S(r) is the intermediate matrix and I is the identity matrix.

4. The method for dynamic positioning anti-disturbance control based on adaptive extended Kalman filter algorithm according to claim 3 is characterized in that: The step 2 of establishing a high-frequency motion model of a dynamic positioning vessel and converting the high-frequency motion model of a dynamic positioning vessel into a state space form is specifically as follows: Step 21: Establish a high-frequency motion model of a dynamic positioning vessel, specifically: Among them, s is the Laplace operator, K ωi is the coefficient of wave intensity in direction i, ζ i is the relative damping coefficient in the i direction, ω 0i is the dominant frequency of the wave in the i direction in the PM wave energy spectrum, i=1, 2, 3 represent the surge direction, sway direction, and bow roll direction respectively; Step 22: Convert the high-frequency motion model of the dynamic positioning vessel into a state space form, specifically: C h =[0 3×3 I 3×3 ] A 22 =-diag{2ζ1ω 01 2z2w 02 2z3h 03 } Σ=diag[K w1 K w2 K w3 ] K wi =2ξ i oh 0i s i Among them, η h =[x h ,y h ,ψ h ],η h is the vector of the ship's high-frequency motion, consisting of the ship's position and heading angle, x h is the horizontal coordinate of the ship during high-frequency motion, y h is the ordinate of the ship during high-frequency motion, ψ h is the heading angle of the ship during high-frequency motion, ξ h =[x h ,y h ,ψ h ,ξ x ,ξ y ,ξ ψ ] T ,ξ h is the state vector of the high-frequency motion of the ship, ξ x is the longitudinal swell linear velocity of the ship during high-frequency motion, ξ y is the sway velocity of the ship during high-frequency motion, ξ ψ is the bow angular velocity during high-frequency motion of the ship, ω h =[ω h1 ,ω h2 ,ω h3 ] T ,ω h is a zero-mean Gaussian white noise vector, ω h1 ,ω h2 ,ω h3 are zero-mean Gaussian white noises representing the surge, sway, and pitch directions, respectively. h , h , C h is the coefficient matrix, A 21 , A 22 ,Σ is the intermediate matrix, K wi is the intermediate variable, I 3×3 is a 3×3 identity matrix, diag[] is a diagonal matrix, ξ1=ξ x , ξ2=ξ y , ξ3=ξ ψ , σ i is a constant for the wave strength in the i direction, 0 3×3 is a 3×3 matrix of zeros.

5. The method for dynamic positioning auto-disturbance rejection control based on adaptive extended Kalman filter algorithm according to claim 4, characterized in that: The ship motion model is obtained by using the low-frequency motion model of the dynamic positioning ship obtained in step 1 and the high-frequency motion model of the dynamic positioning ship in the state space form obtained in step 2 in step 3, specifically: Where f(x) is the state variable function, B is the thruster configuration control matrix, x is the state variable, E is the noise coefficient matrix, ω and ω' are two zero-mean Gaussian white noise matrices, H is the observation coefficient matrix, and y is the system output.

6. The method for dynamic positioning auto-disturbance rejection control based on adaptive extended Kalman filter algorithm according to claim 5, characterized in that: The design of the nonlinear state error feedback control law in step 4 uses the nonlinear state error feedback control law to obtain the thrust value applied by the propeller, specifically: Step 41: Obtain the system state equation and discretize the system state equation to obtain the discretized system state equation, which is specifically: First, obtain the system state equation: Among them, x1 is the vector composed of the ship's position and angle, x2 is the vector composed of the ship's linear velocity and angular velocity, and x3 is the disturbance acceleration vector. is the derivative of x1, x2, x3, η'(t) is the marine environment disturbance function; Then, the system state equation is discretized to obtain the discretized system state equation: Among them, e1 is the vector composed of the ship position error and angle error, z1 is the vector composed of the ship position and angle observation values, z2 is the vector composed of the ship linear velocity and angular velocity observation values, z3 is the disturbance acceleration vector, is the derivative of z1, z2, z3, β 01 >0,β 02 >0,β 03 >0,β 01 , β 02 , β 03 is the adjustable gain of the observer, a1 and a2 are the shape parameters of the fal function, a takes a1 or a2, and δ is the gain interval coefficient; Step 42: Obtain the system state feedback equation using the discretized system state equation; Step 43: Use the system state feedback equation obtained in step 42 to obtain the value of the thrust vector applied by the propeller.

7. The method for dynamic positioning auto-disturbance rejection control based on adaptive extended Kalman filter algorithm according to claim 6, characterized in that: The system state feedback equation is obtained by using the discretized system state equation in step 42, specifically: make: Among them, e2 is the vector composed of linear velocity error and angular velocity error, and e3 is the disturbance acceleration error vector; According to the discretized system state equation, the error vectors e1, e2, and e3 are expressed as follows: Assuming that variables x1 and x2 are known, for any V, the following equation has a solution: f(x1,x2,τ)=V Assume τ = g(x1, x2, V), then the system state feedback is as follows: The above formula is finally rewritten as: Among them, v1 is a preset vector composed of the ship position and angle preset according to experience, k1 and k2 are preset coefficients, is the derivative of v1.

8. The method for dynamic positioning anti-disturbance control based on adaptive extended Kalman filter algorithm according to claim 7, characterized in that: The value of the thrust vector applied by the propeller is obtained by using the system state feedback equation obtained in step 42 in step 43, specifically: First, obtain the thrust vector applied by the propeller: τ0=k1fal(e1,α1,δ)+k2fal(e2,α2,δ) Where c is the compensation intensity factor, z3(t) is the disturbance acceleration observation value at time t; Then, a fixed-time dilated state observer is designed, specifically: w=R(ψ)V in, is an estimate of η, yes The derivative of , w is the auxiliary velocity vector, is the estimated value of w, χ is the set of unknown perturbations, is the estimated value of χ, H n <γ, μ1, μ2, μ3, ε1, ε2, ε3, γ are constants, H n is a bounded constant, α i ∈(0,1),β i >1, is a constant, l1, l2 are both infinitesimal, α i , β i is an intermediate variable, i=1,2,3; The gain range of the fixed-time extended state observer FESO satisfies the following Hurwitz matrix: Finally, the thrust vector applied to the propeller is discretized based on the fixed time dilated state observer to obtain the final thrust vector applied by the propeller, which is: τ0(k)=k1fal(e1,α1,δ)+k2fal(e2,α2,δ) e2=x2(k)-z2(k) e1=x1(k)-z1(k) Wherein, k is the discretized time t, τ(k) is the thrust applied by the propeller at time k, z3(k) is the observed value of the disturbance acceleration at time k, τ0(k) is the theoretical value of the thrust applied by the propeller at time k, x1(k) is the vector of the ship’s position and angle at time k, z2(k) is the vector of the ship’s linear velocity and angular velocity observations at time k, z1(k) is the vector of the ship’s position and angle observations at time k, and x2(k) is the vector of the ship’s linear velocity and angular velocity at time k.

9. The method for dynamic positioning anti-disturbance control based on adaptive extended Kalman filter algorithm according to claim 8, characterized in that: The step 5 is to discretize the ship motion model obtained in step 3 to obtain the discretized ship motion model, specifically: Δ=A -1 (Φ-I)B C=A -1 (Φ-I)E R=R T >0 Φ=exp(Ah) Where x(k) is the system state variable at time k, x(k-1) is the system state variable at time k-1, Φ, Δ, Γ, and H are coefficient matrices, τ(k-1) is the thrust applied by the propeller at time k-1, ω(k-1) is the zero-mean Gaussian white noise with a covariance matrix of Q at time k-1, ω'(k-1) is the zero-mean Gaussian white noise with a covariance matrix of R at time k-1, y(k) is the system output at time k, R and Q are the covariance matrices of ω'(k-1) and ω(k-1) respectively, A is the coefficient matrix of the state variable function f(x), h is the sampling time, and I is the identity matrix.

10. The method for dynamic positioning auto-disturbance rejection control based on adaptive extended Kalman filter algorithm according to claim 9, characterized in that: The step 6 is based on the adaptive extended Kalman filter method, and uses the discretized ship motion model obtained in step 5 and the thrust value applied by the propeller obtained in step 4 to design the dynamic positioning anti-disturbance control controller, specifically: Step 6.1 Initialize the estimated value of the system state variable Initial value of covariance estimate Step 6.2: Use the discretized ship motion model to obtain the predicted value of the system state variable at time k: in, is the estimated value of the system state variable at time k-1, τ(k-1) is the thrust applied by the propeller at time k-1, is the predicted value of the system state variable at time k; Step 6.

3. Obtain the error covariance prediction value: in, is the predicted value of error covariance at time k, is the error covariance estimate at time k-1; Step 64: Introduce the forgetting factor ff to obtain the updated adjustment parameter d(k): Among them, d(k) is the adjustment parameter at time k, ff k+1 It is ff raised to the power of k+1, where ff is the forgetting factor; Step 65: Use the predicted value of the system state variable at time k obtained in step 62 Get the predicted value of system output at time k: in, is the predicted value of the system output at time k; Step 66: Use the data obtained in step 65 Get the system output error: Among them, y(k) is the actual value of the system output at time k, is the predicted value of the system output at time k, and Z(k) is the system output error at time k; Step 67: Update the observation noise covariance matrix R(k): R(k)=(1-d(k))R(k-1)+d(k)([I-H(k)K(k-1)]w'(k)w' T (k)[I-H(k)K(k-1)] T +H(k)P(k-1)H T (k)) Where R(k-1) is the observation noise covariance matrix at time k-1, H(k) is the coefficient matrix at time k, w'(k) is the Gaussian white noise at time k, K(k-1) is the Kalman filter gain coefficient at time k-1, and P(k-1) is the filter estimation mean square error matrix at time k-1; Step 68: Use the error covariance prediction value obtained in step 63 Calculate the Kalman filter gain coefficient K(k): Among them, K(k) is the Kalman filter gain coefficient at time k, and R(k) is the observation noise covariance matrix at time k; Step 69: Use K(k) obtained in step 68 and Z(k) obtained in step 66 to obtain the estimated value of the system state variable in, is the estimated value of the system state variable at time k; Step 60: Use K(k) obtained in step 68 and R(k) obtained in step 67 to obtain the error covariance estimate. in, is the error covariance estimate at time k; Step 61: Use error covariance to predict values Composition filter estimation mean square error matrix Let k=k+1, and return to step 62.

Images