Filtering backstepping ship movement control system based on self-adaption fuzzy estimator

[0024] The present invention will be described in detail below:

[0025] figure 1 The overall structure of the filter backstepping ship motion control system based on the adaptive fuzzy estimator of the present invention is given. figure 1 The meanings of the numbers in the figures are as follows: 1—environmental interference; 2—control system; 3—filter backstepping controller; 4—guidance system; 5—adaptive fuzzy estimator; 6—differential homeomorphism converter; 7— Data processing system; 8—filtering system; 9—data fusion system; 10—speed sensor; 11—position sensor; 12—sensor system; 13—ship.

[0026] Combine figure 1 The filter backstepping ship motion control system based on the adaptive fuzzy estimator of the present invention includes a control system 2, a guidance system 4, a differential homeomorphism converter 6, a data processing system 7, and a sensor system 12. The pose sensor 11 in the sensor system 12 collects the actual pose of the ship, and the ship motion speed information collected by the speed sensor 10 is packaged and passed to the data processing system 7. These data are processed by the data fusion system 9 and the filtering system 8 to obtain Ship pose information and speed information applied to the control system 2; the processed data is transferred to the differential homeomorphic converter 6, and new state variables are obtained through state transformation for backstepping design; these new variables are transferred The filtering backstepping controller 3 and the adaptive fuzzy estimator 5 of the control system 2 are provided for the control system to perform corresponding calculations; the adaptive fuzzy estimator 5 receives the data of the guidance system 4 and the differential homeomorphic converter 6 at the same time, The unknown nonlinear function required by the controller is estimated, including the estimation of low-frequency interference; the filter backstepping controller also receives the expected information and its derivative provided by the guidance system 4, and the new The state variable information and the estimated output of the unknown nonlinear function provided by the adaptive fuzzy estimator 5 are obtained through a series of calculations to obtain the corresponding control command information, and adjust the ship’s longitudinal thrust, lateral thrust and turning moment to achieve The accurate control.

[0027] 1) The guidance system 4 is based on the set expected value η d As well as the initial position of the ship, a smooth path is automatically generated. According to the path, the desired position x of the ship at each time can be obtained d ,y d And expected heading ψ d And its derivative with The ship can reach the designated position through the process of uniform acceleration, uniform speed and uniform deceleration. For convenience, you can write η r =[x d ,y d ,ψ d ] Τ , η · r = v r = [ u d , v d , r d ] T .

[0028] 2) The sensor system 12 includes a pose sensor 11 and a speed sensor 10, which respectively collect the actual position and actual heading angle of the ship, as well as speed information. The posture information and speed information of the ship are transmitted to the data processing system 7, and the posture information of the ship that can be applied to the control system 2 is obtained after processing by the data fusion system 9 and the filtering system η=[x,y,ψ] Τ And velocity information ν=[u,v,r]; the processed data is passed to the differential homeomorphic transformer 6 for state transformation, and the coordinate transformation x 1 =η,x 2 =J(η)ν to get the new variable x 1 ,x 2 , Which constitutes a new model equivalent to the original system. In order to meet the needs of the new model, the new expected pose and speed are denoted as x 1d =η r ,

[0029] The original system model is:

[0030] η · = J ( η ) v

[0031] M v · = - C ( v ) v - D ( v ) v + J T ( η ) b + τ

[0032] τ · = A ‾ τ + B ‾ τ e

[0033] Where: η is the ship’s position and heading vector, ν is the ship’s velocity vector, b is the low-frequency interference force, J(η) is the conversion matrix between the hull coordinate system and the geodetic coordinate system, Μ is the system inertia matrix, C (ν) is the Coriolis centripetal force matrix, D(ν) is the damping matrix, τ is the control vector, τ e Is the control instruction vector, with Is the coefficient matrix related to the implementing agency.

[0034] After the differential homeomorphism transformation, the equivalent system obtained is:

[0035] x · 1 = x 2

[0036] x · 2 = M η - 1 ( x 1 ) ( u + Jω ) - M η - 1 ( x 1 ) C η ( x 1 , x 2 ) x 2 - M η - 1 ( x 1 ) D η ( x 1 , x 2 ) x 2 + M η - 1 ( x 1 ) b

[0037] u · = Au + B τ e

[0038] Where: D η (x 1 ,x 2 )=J -Τ (η)D(ν)J -1 (η),

[0039] C η ( x 1 , x 2 ) = J - T ( η ) [ C ( v ) - M J - 1 ( η ) J · ( η ) ] J - 1 ( η ) ,

[0040] Μ η (x 1 )=J -Τ (η)MJ -1 (η)

[0041] u=J -Τ (η)τ

[0042] A = J - T ( η ) A ‾ J T ( η ) + J · - T ( η ) J T ( η )

[0043] B = J - T ( η ) B ‾

[0044] 3) According to the equivalent model obtained above, design the following filter back step controller:

[0045] z 1 = x ~ 1 = x 1 - x 1 c

[0046] z 2 = x ~ 2 = x 2 - x 2 c

[0047] z 3 = x ~ 3 = u - x 3 c

[0048] Where x ic (i=1,2,3) is the output of the second-order filter, used to approximate each virtual control variable, its derivative Also output by the second-order filter.

[0049] The expectation of each virtual control quantity at this time is:

[0050] α 1 = - k 1 z 1 + x · 1 c

[0051] α 2 = M η ( - k 2 z 2 + x · 2 c - f ( x 1 , x 2 ) - v 1 )

[0052] α 3 = B - 1 ( - k 3 z 3 + x · 3 c - Au - M η - T v 2 )

[0053] Where f(x 1 ,x 2 )=-Μ η -1 (η)((C η (ν,η)+D η (ν,η))x 2 +b+Jω]; k i (i=1,2,3) is the control gain matrix (positive definite diagonal matrix); v i (i=1,2,3) is the compensation vector of each tracking error, and is defined as

[0054] v i =z i -ζ i

[0055] Where the vector ζ i defined as

[0056] ζ · i = - k i ζ i + g i ( x ( i + 1 ) c - α i ) + g i ζ i + 1 , ( i = 1,2 )

[0057] Where g 1 =1, g 2 =M η -1 , G 2 =B, and ζ i The initial value of is zero (ζ i (0)=0, i=1,2), ζ 3 =0, the control law is:

[0058] τ e =α 3

[0059] X needed in the controller design process ic with It is defined as follows:

[0060] 1) When i=1, x 1 c = x 1 d = α ‾ 0 , x · 1 c = x · 1 d = α ‾ · 0 ;

[0061] 2) When i=2,3, x ic with It is output by the filter.

[0062] Note: Is the set target x 1d , Is the set tracking speed

[0063] Each filter can be defined as follows:

[0064] φ · i 1 φ · i 2 = 0 I - ω ni 2 I - 2 ζ i ω ni I φ i 1 φ i 2 + 0 ω ni 2 I α ( i - 1 ) c

[0065] x ic x · ic = φ i 1 φ i 2

[0066] In the formula, I is the third-order unit matrix. It can be seen that when α (i-1)c When bounded, x ic with It is bounded and continuous.

[0067] 4) The above designs are all carried out when the model parameters are known, but usually the model parameters are unknown or partly unknown. At this time, it is very difficult to design a model-based controller. The unknown nonlinear function required by the controller is estimated by introducing an adaptive fuzzy system to solve the problem of unknown model parameters.

[0068] Assuming that there are N rules in the fuzzy rule base, the ith rule has the following form:

[0069] R i :IF x 1 isμ 1 i and… and x n isμ n i ,then y is B i (i=1,2,...,N)

[0070] Where μ n i X n (n=1,2,...,N) membership function.

[0071] Then, the output of the fuzzy system can be expressed as:

[0072] y = X i = 1 N θ i Π j = 1 n μ j i ( x i ) X i = 1 N Π j = 1 n μ j i ( x i ) = ξ T ( x ) θ

[0073] Where ξ(x)=[ξ 1 (x), …, ξ N (x)] Τ , Is the fuzzy estimation parameter vector, and has

[0074] ξ i ( x ) = Π j = 1 n μ j i ( x i ) X i = 1 N Π j = 1 n μ j i ( x i ) .

[0075] In order to approximate the unknown nonlinear function f required in the controller, an adaptive fuzzy system can be used to approximate each element of f one by one, namely

[0076]

[0077] The approximation function of the nonlinear function f Can be defined as:

[0078]

[0079] Among them, ξ Τ (x)=diag{ξ 1 Τ ,ξ 2 Τ ,ξ 3 Τ },θ=[θ 1 ,θ 2 ,θ 3 ] Τ.

[0080] Define the optimal estimation vector as θ * , And for a given arbitrarily small positive value ε(ε> 0) Meet the conditions:

[0081]

[0082] among them

[0083] make Select the adaptive rate:

[0084] θ · i = r i ( v 2 i ξ i T ( x ) ) T - 2 k i θ i , ( i = 1,2,3 )

[0085] Where r i 0, k i 0 is the design parameter, v 2i Is v 2 The i-th element of.

[0086] make And define:

[0087] γ=diag{r 1 I N ,r 2 I N ,r 3 I N },κ=diag{k 1 I N ,k 2 I N ,k 3 I N }

[0088] Where I n It is the unit matrix of order n. Then the adaptation rate is written in vector form as:

[0089] θ · = γ ( v 2 T ξ T ( x ) ) T - 2 κθ .

[0090] Therefore, the control system 2 can be based on the formula τ e =α 3 Calculate the control instructions to control the position and heading of the ship.

[0091] The present invention uses a non-linear mathematical model of a certain surface ship for simulation experiments, and the ship model parameters of the simulation experiment are:

[0092] M = 9.1948 · 10 7 0 0 0 9.1948 · 10 7 1.2607 · 10 9 0 1.2607 · 10 9 1.0724 · 10 11

[0093] D l = 1.5073 · 10 6 0 0 0 8.1687 · 10 6 - 1.3180 · 10 8 0 - 1.3180 · 10 8 1.2568 · 10 11

[0094] D n (ν)=-diag{X |u|u |u|,Y |v|v |v|,N |r|r |r|}

[0095] Among them: D(ν)=D l +D n (ν)

[0096] X |u|u =-2.9766·10 4 ,

[0097] Y |v|v =-8.0922·10 4 ,

[0098] N |r|r =-1.2228·10 12.

[0099] In the simulation, add the following interference and uncertain parameters:

[0100] b=[0.25×10 5 sin(0.1t),0.25×10 5 sin(0.1t),0.25×10 6 sin(0.1t)] Τ

[0101] M η =(1+0.3sin(0.8t))M η *

[0102] C η =(1+0.3sin(0.8t))C η *

[0103] D η =(1+0.3sin(0.8t))D η *

[0104] The parameters marked with "*" are the nominal model parameters.

[0105] The initial position coordinates (0m, 0m, 0deg), the initial speed is (0m/s, 0m/s, 0deg/s), and the desired position is (2m, 1m, 5deg). See attached simulation results Figure 3-5.

[0106] After analyzing the simulation curve and data, it can be seen that under the action of the filter backstepping ship motion controller based on the adaptive fuzzy estimator proposed in the present invention, the ship can overcome the influence of the uncertainty of model parameters, and in the presence of external interference In the case of rapid tracking of the desired position provided by the upper guidance system, and maintain a given heading, the desired control effect can be achieved under the action of a relatively smooth control force. It shows that the designed adaptive fuzzy estimator can better estimate the unknown nonlinear function and interference of the ship model, and the filter in the filter backstepping method can approximate the virtual control variable and its derivative very well, avoiding the conventional inversion. The derivation process of the virtual control quantity in the footwork simplifies the controller design process. The simulation results show that the control law of the present invention has global asymptotic tracking characteristics, and has better robustness to model parameter uncertainty and unmodeled dynamics.