CN105807610A - Self-adaptive weight matrix weighing pseudo-inverse thrust distribution and saturation handling method - Google Patents

Abstract

The invention relates to a self-adaptive weight matrix weighing pseudo-inverse thrust distribution and saturation handling method. The method includes establishing a thrust distribution mathematic model in a fixed angle distribution mode; solving a non-constrained optimization problem; establishing a weight self-adaption rule and adjusting the weight matrix in real time to solve a problem of thrust saturation of a thruster; and iterating repeatedly until the thrust of the thruster meets inequality constraints. According to the invention, inhibiting and enhancing effects on the thrust by elements in the weight matrix are utilized fully and the weighing pseudo-inverse weight self-adaption rule is established, so that the saturated thrust does not need interception and quitting distribution treatment is avoided. by adopting the method provided by the invention, high calculation speed of the pseudo-inverse is utilized effectively and a problem of thrust saturation of the thrust existing when the simple weighting pseudo-inverse method is used for solving the thrust distribution problem is solved.

Description

Adaptive weight matrix weights puppet reverse thrust towards Ship Dynamic Positioning Systems Based is distributed and saturated processing method

Technical field

The present invention relates to a kind of dynamic positioning of vessels thrust distribution method, particularly relate to the thrust distribution of a kind of weighted pseudo-inverse adopting adaptive weight matrix and saturated processing method.

Background technology

Along with day by day exhausted and people's great demand to the energy of land traditional energy coal, oil, the development and exploration of ocean is goed deep into by the mankind gradually.Marine structure in profundal zone operation, for instance the positioning operation precision of platform supply vessel, drilling ship, drilling platforms etc. is more and more high.Dynamic positioning technology rapidly be attention in this context, becomes one of key technology of carrying out ocean development exploration.The marine structure being provided with dynamic positioning system adopts the positioning means such as satellite, GPS to obtain the position of current marine structure, controller calculates required power and moment according to its drift gauge with setting position, produced required power and moment again by impeller system, be finally reached the requirement of positioning operation.

Thrust distribution is one of important component part of dynamic positioning system, it needs quickly to be controlled by upper level in real time, and system-computed obtains makes a concerted effort and resultant moment is assigned on each propeller in an optimal manner, also needing to consider angle of rake physical restriction and realize energy consumption optimum, therefore thrust assignment problem is actually an optimization problem.Pseudoinverse technique is simple with its principle, real-time good and is widely used in solving the constrained control assignment problem of aircraft, satellite, boats and ships etc..

Thrust distribution must account for angle of rake physical restriction and angle of rake thrust size, thrust variation rate and angle variable rate restriction.If control system sends excessive thrust command to propeller, propulsion system is unable to reach required thrust size actually, and this will cause that power that propulsion system produces and moment are not equal to the power required by control system and moment, ultimately results in positioning operation failure.For this problem, Chinese scholars proposes the methods such as kernel, cascade generalized inverse and weighted pseudo-inverse.Zero Space Method and Its is adopted to exist when processing propeller saturation problem without processing the problem increased with propeller quantity with algorithm complex and increase severely when solving；Cascade generalized inverse is taked saturated to block, the mode of configuring matrix reconstruct carries out saturated process, but the method can not be all provide feasible solution up to output, and occurs distributing unsuccessfully phenomenon when distributing one group and changing comparatively intense environment load.Angle of rake suppression, potentiation are carried out saturated process according to the large and small of weights element by weighted pseudo-inverse method, simple and easy to do, it is not necessary to configuring matrix reconstructs, and real-time is good.

Summary of the invention

Present invention aim to overcome that problem saturated at the propeller thrust solving the existence of thrust assignment problem in prior art, and then propose a kind of adaptive weight matrix weights puppet reverse thrust distribution towards Ship Dynamic Positioning Systems Based and saturated processing method.

Realizing the object of the invention and the technical scheme is that a kind of adaptive weight matrix weights puppet reverse thrust towards Ship Dynamic Positioning Systems Based is distributed and saturated processing method, the method comprises the following steps:

S100, the thrust set up under fixed angle allocation model distribution mathematical model；

S200, solve the solution of Unconstrained Optimization Problem；

S300, set up Weight number adaptively rule, adjust in real time weight matrix and reach to solve the problem that propeller thrust is saturated；

S400, iterate until angle of rake thrust meets inequality constraints.

Further, in S100, distribute founding mathematical models for the thrust under fixed angle allocation model, thrust assignment problem be converted into optimization problem, with energy consumption for object function, obtain such as drag:

MinJ=u^TWu(1.1)

$\begin{array}{c}s.tB*u=\mathrm{\τ}\\ max(T_{\min },T_0-\mathrm{\Δ}T)\≤u\≤min(T_{max},T_0+\mathrm{\Δ}T)\end{array}---\left(1.2\right)$

Wherein, J object function；W is weight matrix, and initial value is set to unit matrix, online updating in the control cycle behind；U is angle of rake thrust to be solved；T₀For the upper one propeller thrust size controlling the cycle；T_min、T_maxRespectively the angle of rake thrust that can send is minimum, maximum thrust；Δ T is propeller thrust maximum knots modification of thrust within a control cycle；τ is required gross thrust and moment；

B is arranged, by propeller, the configuring matrix determined, it i-th is classified as:

$B_i=\left[\begin{array}{c}cos\left({\mathrm{\α}}_i\right)\\ sin\left({\mathrm{\α}}_i\right)\\ -l_{iy}cos\left({\mathrm{\α}}_i\right)+l_{ix}sin\left({\mathrm{\α}}_i\right)\end{array}\right]---\left(1.3\right)$

Wherein, α_iFor angle of rake direction；(l_xil_yi) for propeller with the installation site coordinate under ship coordinate system.

Further, in step S200, adopting augmented vector approach that the RegionAlgorithm for Equality Constrained Optimization in step S100 is converted into Unconstrained Optimization Problem when only considering equality constraint, the simple pseudoinverse solution that can obtain problem according to KKT condition is:

U=W^-1B^T(BW^-1B^T)^-1(1.4)

Further, in step S300, reach to solve the problem that propeller thrust is saturated by adjusting weight matrix in real time, particularly as follows:

Formula (1.4) is made following indentily transformation:

U=[I+ (I-B^T(BB^T)^-1B)W]B^T(BB^T)^-1τ(1.5)

Introduce Ω=diag (B^T(BB^T)^-1τ), above formula can be write as following expression:

U=B^T(BB^T)^-1τ+(I-B^T(BB^T)^-1B)ΩW(1.6)

In formula, W=[w₁₁w₂₂…w_nn]^T, for the column vector that the diagonal element of weight matrix forms；

Definition u_cBeing the direct pseudoinverse solution obtained by formula (1.4), u is the propeller thrust after saturated process, deviation e_uDefined by following formula:

e_u=u_c-u(1.7)

Deviation e can be obtained by formula (1.6) and (1.7)_uExpression formula be:

e_u=[I-B^T(BB^T)^-1B]ΔWΦ(1.8)

In formula, Δ W=[W₁₁-W₁₁ ^*W₂₂-W₂₂ ^*…W_nn-W_nn ^*]^T；

It is set as follows weight matrix adaptive law:

Δ W=Proj_W>0{-γΩ^T(I-B^T(BB^T)^-1B)e_u}(1.9)

In formula, Proj_W>0Just, γ is normal number to the diagonal element perseverance of { } expression guarantee weight matrix；

Weight matrix real-time update step is as follows:

(1) calculating angle of rake thrust size according to weighted pseudo-inverse method, if there is thrust saturation problem, propeller thrust being blocked in the thrust upper limit or lower limit；

(2) calculate thrust and block the deviation e of front and back_u, calculate new weight matrix according to the adaptive law of following formula:

Δ W=Proj_W>0{-γΩ^T(I-B^T(BB^T)^-1B)e_u}(1.10)

New weight matrix is:

W'=W+diag (Δ W) (1.11)

Further, in step S400, according to right value update rule in (1.9), the adjustment weight matrix that iterates is until angle of rake thrust meets inequality constraints.

Compared with distributing saturated treatment technology with existing thrust, the present invention makes full use of element in weight matrix and, to angle of rake suppression, potentiation, establishes the Weight number adaptively rule of weighted pseudo-inverse, do not need again saturated thrust to be blocked, exited allocation process.Saturated conditions according to propeller thrust, updates weights according to weight matrix adaptive law given herein above, until making angle of rake thrust fall into zone of reasonableness.Adopt this way to be not only effectively utilized pseudoinverse technique to calculate fireballing advantage but also solve simple weighted pseudoinverse and solving the problem that propeller thrust that thrust assignment problem exists is saturated.

Accompanying drawing explanation

Fig. 1 is the angle of rake layout schematic diagram of ship model used by the present embodiment.

Fig. 2 is the present invention to be distributed and saturated process flow figure towards the adaptive weight matrix weights puppet reverse thrust of Ship Dynamic Positioning Systems Based.

Power and moment that Fig. 3 is adopt the present invention to carry out power to be allocated that emulation experiment obtains and moment and the actual generation of propeller contrast schematic diagram, in figure, a () contrasts schematic diagram for surging, (b) contrasts schematic diagram for swaying, and (c) is for turning bow contrast schematic diagram.

Fig. 4 is power and the moment aberration curve comparison diagram of the actual generation of power to be allocated and moment and propeller, and in figure, (a) is surging deviation comparison diagram, and (b) is swaying deviation comparison diagram, and (c) is for turning bow deviation comparison diagram.

Fig. 5 is the thrust variation curve chart adopting the present invention to carry out emulating the afterbody propeller 1 obtained.

Fig. 6 is the thrust variation curve chart adopting the present invention to carry out emulating the afterbody propeller 2 obtained.

Fig. 7 is the thrust variation curve chart adopting the present invention to carry out emulating the bow side propeller 1 obtained.

Fig. 8 is the thrust variation curve chart adopting the present invention to carry out emulating the bow side propeller 2 obtained.

Detailed description of the invention

For the technological means making the present invention realize, creation characteristic, reach the purpose effectiveness with the problem of solution it can be readily appreciated that further illustrate in conjunction with Examples below.

The present embodiment adopts the propeller of model ship to arrange schematic diagram as it is shown in figure 1, the present invention is illustrated with this ship model for calculating object, each propeller parameter such as following table of this ship model:

Fig. 2 is the present invention to be distributed and saturated process flow figure towards the adaptive weight matrix weights puppet reverse thrust of Ship Dynamic Positioning Systems Based.

The weighted pseudo-inverse thrust distribution method adopting adaptive weight matrix needs to control last layer gross thrust that system-computed obtains and Torque distribution to each propeller, solves each angle of rake thrust size.

Step S100 is first carried out, and thrust assignment problem is converted into optimization problem and obtains by founding mathematical models:

MinJ=u^TWu

S.tB*u=τ

max(T_min,T₀-ΔT)≤u≤min(T_max,T₀+ΔT)

Wherein, W is weight matrix, and initial value is set to unit matrix and W=daig ([1111]), and in the control cycle behind, real-time online updates；The thrust that the propeller that u is to be solved sends；T₀For the propeller thrust size in the upper control cycle, for instance be taken as [115-1.5] within a certain control cycle；T_min、T_maxRespectively the angle of rake thrust that can send is minimum, maximum thrust, is set to T according to angle of rake physical restriction_min=[00-14.5-14.5], T_max=[49.549.514.514.5]；Δ T is propeller thrust maximum knots modification of thrust within a control cycle, is set to Δ T=[101033] according to angle of rake physical conditions, and thus can obtain the feasible zone of thrust in current control period is [002-4.5]≤u≤[111181.5]；τ be required by the gross thrust that sends and moment, such as τ=[5.47086.4708-1.0584]；

B is arranged, by propeller, the configuring matrix determined, it i-th is classified as:

$B_i=\left[\begin{array}{c}cos\left({\mathrm{\α}}_i\right)\\ sin\left({\mathrm{\α}}_i\right)\\ -l_{iy}cos\left({\mathrm{\α}}_i\right)+l_{ix}sin\left({\mathrm{\α}}_i\right)\end{array}\right]$

Wherein α_iFor angle of rake direction；(l_xil_yi) for propeller with the installation site coordinate under ship coordinate system；For afterbody all-direction propeller angle, this ship model is taken as 90 °, 0 ° respectively under a certain fixed angle allocation model, and can obtain configuring matrix is:

$B=\left[\begin{array}{cccc}0& 1& 0& 0\\ 1& 0& 1& 1\\ -1.68& -0.75& 1.245& 1.365\end{array}\right]$

Step S200, adopts augmented vector approach that the optimization problem in step S100 is converted into the form of Unconstrained Optimization Problem when only accounting for equality constraint, utilizes the solution that pseudoinverse technique can obtain problem to be:

U=W^-1B^T(BW^-1B^T)^-1=[2.86195.47081.82571.7832]

The solution of above formula is unsatisfactory for the constraint of propeller thrust size, reaches to solve the problem that propeller thrust is saturated by adjusting weight matrix in real time；

Step S300, restrains according to following flow processing propeller saturation problem according to the adaptive weight matrix that the present invention adopts:

(1) propeller thrust is blocked in the thrust upper limit or lower limit, obtain u=[2.86195.470821.5]；

(2) calculate thrust and block the deviation e of front and back_u=[00-0.17430.2832], calculates the increment of weights according to following formula:

Δ W=Proj_W>0{-γΩ^T(I-B^T(BB^T)^-1B)e_u}=[-0.261600-3.9730]

In formula, Proj_W>0Just, γ takes normal number 10 to the diagonal element perseverance of { } expression guarantee weight matrix.New weight matrix is:

W'=W+diag (Δ W)=diag ([1.26161.00001.00004.9730])

(3) new weights substitute into Ship Dynamic Positioning Systems Based thrust distribution mathematical model recalculate propeller thrust and calculate and obtain propeller thrust and be:

U=W'^-1B^T(BW'^-1B^T)^-1=[2.81375.47083.04820.6088]

After the adaptive weight of present invention employing carries out weight matrix online updating, angle of rake thrust falls in zone of reasonableness.

The algorithm of invention is emulated by MATLAB environment, power and the M curve of the power and M curve and the actual generation of propeller that control system needs as seen from Figure 3 agree with better, and the aberration curve in Fig. 4 also indicates that the thrust distribution method that the present invention proposes is effective with saturated treating method；Fig. 5-Fig. 8 is each angle of rake thrust, and as can be seen from the figure each angle of rake thrust is all in feasible region.

More than show the ultimate principle of the present invention, principal character and advantage.The relevant technical staff of the industry should be understood that; the present invention is not limited by above-mentioned example; above-mentioned example and the application principle being only to illustrate the present invention described in this description; outside without departing from the ultimate principle of the present invention and purport; the present invention also has the various form of expression and change, improvement, and these forms of expression, changes and improvements are all within rights protection of the presently claimed invention.

Claims (5)

1. the adaptive weight matrix weights puppet reverse thrust towards Ship Dynamic Positioning Systems Based is distributed and saturated processing method, it is characterised in that comprise the following steps:

S100, the thrust set up under fixed angle allocation model distribution mathematical model；

S200, solve the solution of Unconstrained Optimization Problem；

S300, set up Weight number adaptively rule, adjust in real time weight matrix and reach to solve the problem that propeller thrust is saturated；

S400, iterate until angle of rake thrust meets inequality constraints.

2. the adaptive weight matrix weights puppet reverse thrust towards Ship Dynamic Positioning Systems Based according to claim 1 is distributed and saturated processing method, it is characterized in that: in S100, founding mathematical models is distributed for the thrust under fixed angle allocation model, thrust assignment problem is converted into optimization problem, with energy consumption for object function, obtain such as drag:

MinJ=u^TWu(1.1)

Wherein, J object function；W is weight matrix, and initial value is set to unit matrix, online updating in the control cycle behind；U is angle of rake thrust to be solved；T₀For the upper one propeller thrust size controlling the cycle；T_min、T_maxRespectively the angle of rake thrust that can send is minimum, maximum thrust；Δ T is propeller thrust maximum knots modification of thrust within a control cycle；τ is required gross thrust and moment；

B is arranged, by propeller, the configuring matrix determined, it i-th is classified as:

Wherein, α_iFor angle of rake direction；(l_xil_yi) for propeller with the installation site coordinate under ship coordinate system.

3. the weighted pseudo-inverse thrust of adaptive weight matrix according to claim 1 is distributed and saturated processing method, it is characterized in that: in step S200, adopt augmented vector approach that the RegionAlgorithm for Equality Constrained Optimization in step S100 is converted into Unconstrained Optimization Problem when only considering equality constraint, the simple pseudoinverse solution that can obtain problem according to KKT condition is:

U=W^-1B^T(BW^-1B^T)^-1(1.4)。

4. the weighted pseudo-inverse thrust of adaptive weight matrix according to claim 1 is distributed and saturated processing method, it is characterised in that: in step S300, reach to solve the problem that propeller thrust is saturated by adjusting weight matrix in real time, particularly as follows:

Formula (1.4) is made following indentily transformation:

U=[I+ (I-B^T(BB^T)^-1B)W]B^T(BB^T)^-1τ(1.5)

Introduce Ω=diag (B^T(BB^T)^-1τ), above formula can be write as following expression:

U=B^T(BB^T)^-1τ+(I-B^T(BB^T)^-1B)ΩW(1.6)

In formula, W=[w₁₁w₂₂...w_nn]^T, for the column vector that the diagonal element of weight matrix forms；

Definition u_cBeing the direct pseudoinverse solution obtained by formula (1.4), u is the propeller thrust after saturated process, deviation e_uDefined by following formula:

e_u=u_c-u(1.7)

Deviation e can be obtained by formula (1.6) and (1.7)_uExpression formula be:

e_u=[I-B^T(BB^T)^-1B]ΔWΦ(1.8)

In formula, Δ W=[W₁₁-W₁₁ ^*W₂₂-W₂₂ ^*…W_nn-W_nn ^*]^T；

It is set as follows weight matrix adaptive law:

Δ W=Proj_W>0{-γΩ^T(I-B^T(BB^T)^-1B)e_u}(1.9)

In formula, Proj_W>0Just, γ is normal number to the diagonal element perseverance of { } expression guarantee weight matrix；

Weight matrix real-time update step is as follows:

(1) calculating angle of rake thrust size according to weighted pseudo-inverse method, if there is thrust saturation problem, propeller thrust being blocked in the thrust upper limit or lower limit；

(2) calculate thrust and block the deviation e of front and back_u, calculate new weight matrix according to the adaptive law of following formula:

Δ W=Proj_W>0{-γΩ^T(I-B^T(BB^T)^-1B)e_u}(1.10)

New weight matrix is:

W'=W+diag (Δ W) (1.11).

5. the weighted pseudo-inverse thrust of adaptive weight matrix according to claim 1 is distributed and saturated processing method, it is characterized in that: in step S400, according to right value update rule in (1.9), the adjustment weight matrix that iterates is until angle of rake thrust meets inequality constraints.