CN103529842B - A kind of ship's fix control method based on asymptotic guiding - Google Patents

Abstract

The invention belongs to dynamic positioning boats and ships control field, be specifically related to a kind of ship's fix control method based on asymptotic guiding.The present invention includes: (1) determine the target bow of boats and ships to and target location；(2) calculate real-time desired locations and bow to；(3) according to current northern position, east position and bow to, longitudinal force that position, target north, position, east, bow need to the instantaneous velocity of, boats and ships vertical and horizontal and the longitudinal force, cross force and the Calculating Torque during Rotary that produce along number revolution rate and environmental disturbances, cross force, turn moment required during bow and north orientation, the position deviation of east orientation and bow to deviation.The present invention is based on the control method of asymptotic guiding and control design case location.Moment and thrust variation that the method obtains are mild, it is ensured that in angle of rake quota limit, so that boats and ships smoothly arrive target location, do not have vibration, and positioning precision is higher.

Description

A kind of ship's fix control method based on asymptotic guiding

Technical field

The invention belongs to dynamic positioning boats and ships control field, be specifically related to a kind of ship's fix control method based on asymptotic guiding.

Background technology

Along with marine cause is from shallow sea continually developing to deep-sea, safety during to shipping work is had higher requirement.And dynamic positioning technology becomes the boats and ships support system at deep ocean work, it is primarily characterized in that the dynamic positioning boats and ships propulsion plant mainly by boats and ships self so that it is corresponding location and tracking function can be automatically obtained.

Dynamic positioning boats and ships are in actual job, it is often necessary to boats and ships need to specify position to realize fixed point location at certain, and be maintained at the bow specified to.It addition, the mode of operations such as the tracking of boats and ships, position rotating, target following are required for being realized as auxiliary by the high-precision fixed point location of boats and ships.Therefore, fixed point location is the basic model of Ship Dynamic Positioning Systems Based, is also the most important pattern of controller part of whole dynamic positioning system.A kind of high accuracy of research, high performance fixed point location control method is the successful most basic premise of Ship Dynamic Positioning Systems Based, is also the most basic guarantee of dynamic positioning boats and ships operation on the sea.

There are many technique study about ship control both at home and abroad at present, such achievement in research is concentrated mainly on control method design ship's fix or the tracking controller of application of advanced, and in actual applications, the thrust size of boats and ships depends on the propeller performance that boats and ships are installed, the thrust provided is past is limited, the inertia of boats and ships is big especially, so requiring during fixed point location that the thrust that propeller provides is wanted suitably, otherwise, vibration is got up by boats and ships, being difficult to control, these are the most dangerous in engineer applied.So the control method of application requires higher in Practical Project.Considering big inertia and the strong nonlinearity feature of boats and ships, the present invention is by designing asymptotic guiding module, and devises a kind of high-precision fixed point location control method in conjunction with Nonlinear backstepping method.

Summary of the invention

It is an object of the invention to provide a kind of high-precision ship's fix control method based on asymptotic guiding.

The object of the present invention is achieved like this:

(1) determine the target bow of boats and ships to and target location；

(2) calculate real-time desired locations and bow to:

1), when turning bow, target bow is calculated to ψ_dWith current bow to ψ_nDifference obtain the relative bow of boats and ships to, ψ_g1=ψ₁, relative bow is to during more than 0, then boats and ships turn to forward, and relative bow is to during less than 0, then boats and ships are to counter steering；Boats and ships to forward turn to time, it is desirable to bow is to for ψ_gn=ψ_g(n-1)+K_turnTs, ψ_gnFor the expectation bow that obtains in the n-th moment to, K_turnFor the revolution rate that host computer sets, Ts is the sampling time of control system, if ψ_gn-ψ_d≤ 0, ψ_gn=ψ_d, otherwise re-read target bow to current bow to being calculated；When boats and ships are to counter steering, it is desirable to bow is to for ψ_gn=ψ_g(n-1)-K_turnTs, ψ_gn-ψ_d>=0, ψ_gn=ψ_d, otherwise re-read target bow to current bow to being calculated；

2), when moving to target location, boats and ships current location in the n-th moment in two dimensional surface is P=[n_n,e_n]^T, the desired locations that the n-th moment obtained is P_gn=[n_gn,e_gn]^T, the target location of boats and ships is P_d=[n_d,e_d]^T, [n_g1,e_g1]^T=[n₁,e₁]^T, [n_gn,e_gn]^T=[n_n,e_n]^T, Ship ' target location and current location are at the angle of east northeast coordinate systemIt is 1 by mark position, the relative distance of Ship ' current location and target location,Calculating speed used during desired locations is v_g=k*r_dn-0.1, k=0.015, direction is the boats and ships line directions along current location and target location, and calculating is carved the relative distance of desired locations and target location for the moment, it may be assumed that

$r_{gd}=\sqrt{{(e_{g(n-1)}-e_d)}^2+{(n_{g(n-1)}-n_d)}^2}$

E in formula_g(n-1) for the position, expectation east that a upper moment obtains, n_g(n-1) for position, expectation north that a upper moment obtains；

r_gdDuring more than 1m, then the desired locations in this moment is:

$\left[\begin{array}{c}{n}_{gn}\\ e_{gn}\end{array}\right]=\left[\begin{array}{c}{n}_g(n-1)+v_s*Ts*cos\left(\mathrm{\θ}\right)\\ e_g(n-1)+v_s*Ts*sin\left(\mathrm{\θ}\right)\end{array}\right]$

r_gdLess than or equal to 1m, then the desired locations in this moment is: [n_gn,e_gn]^T=[n_d,e_d]^T, it is 2 by mark position simultaneously,

If longitudinal direction or lateral velocity are more than 0.5m/s, being 3 by mark position, desired locations now is the position of the current time of boats and ships, it may be assumed that [n_gn,e_gn]^T=[n_n,e_n]^T。

When the relative distance of boats and ships current location and target location is 2 more than 3m and flag bit, flag bit being set to 4 again, desired locations now is target location, i.e. [n_g,e_g]^T=[n_d,e_d]^T, after obtaining new desired locations, flag bit is set to 1 again,；

(3) according to current northern position, east position and bow to, longitudinal force that position, target north, position, east, bow need to the instantaneous velocity of, boats and ships vertical and horizontal and the longitudinal force, cross force and the Calculating Torque during Rotary that produce along number revolution rate and environmental disturbances, cross force, turn moment required during bow and north orientation, the position deviation of east orientation and bow to deviation:

1) target location of boats and ships and target bow are to for η_d=[n_d,e_d,ψ_d]^TTime, this vector is permanent vector, and the Three Degree Of Freedom model of boats and ships is: $\begin{array}{c}\stackrel{\·}{\mathrm{\η}}=R\left(\mathrm{\ψ}\right)v\\ M\stackrel{\·}{v}+C\left(v\right)v+D\left(v\right)v=\mathrm{\τ}+{\mathrm{\τ}}_e\end{array},$

$R\left(\mathrm{\ψ}\right)=\left[\begin{array}{ccc}cos\left(\mathrm{\ψ}\right)& -sin\left(\mathrm{\ψ}\right)& 0\\ sin\left(\mathrm{\ψ}\right)& \cos \left(\mathrm{\ψ}\right)& 0\\ 0& 0& 1\end{array}\right];$

The position tracking error of boats and ships is:

Derivation: $\stackrel{\·}{\widetilde{\mathrm{\η}}}=\stackrel{\·}{\mathrm{\η}}-{\stackrel{\·}{\mathrm{\η}}}_d=R\left(\mathrm{\ψ}\right)v,$

Virtual reference velocity under earth coordinates isΛ ∈ R in formula^3×3For the diagonal matrix of positive definite,

Virtual reference velocity under hull coordinate system is

The tracking error of speed is: $s=\stackrel{\·}{\mathrm{\η}}-{\stackrel{\·}{\mathrm{\η}}}_r=R\left(\mathrm{\ψ}\right)v+\mathrm{\Λ}\widetilde{\mathrm{\η}},$

Boats and ships Three Degree Of Freedom model deformation obtains: $M*\left(\mathrm{\η}\right)\stackrel{\·\·}{\mathrm{\η}}+C*(\mathrm{\η},v)\stackrel{\·}{\mathrm{\η}}+D*(\mathrm{\η},v)\stackrel{\·}{\mathrm{\η}}=\mathrm{\τ}+{\mathrm{\τ}}_e$

M* (η)=R (ψ) MR^-1(ψ),

$C*(\mathrm{\η},v)=R\left(\mathrm{\ψ}\right)\[C\left(v\right)-{\mathrm{MR}}^{-1}\left(\mathrm{\ψ}\right)\stackrel{\·}{R}\left(\mathrm{\ψ}\right)\]R^{-1}\left(\mathrm{\ψ}\right),$

D* (η, v)=R (ψ) D (v) R^-1(ψ),

$\begin{array}{c}M*\left(\mathrm{\η}\right)\stackrel{\·}{s}\\ =-C*(\mathrm{\η},v)s-D*(\mathrm{\η},v)s+R\left(\mathrm{\ψ}\right)(\mathrm{\τ}+{\mathrm{\τ}}_e)-M*\left(\mathrm{\η}\right){\stackrel{\·\·}{\mathrm{\η}}}_r-C*(\mathrm{\η},v){\stackrel{\·}{\mathrm{\η}}}_r-D*(\mathrm{\η},v){\stackrel{\·}{\mathrm{\η}}}_r\\ =-C*(\mathrm{\η},v)s-D*(\mathrm{\η},v)s+R\left(\mathrm{\ψ}\right)(\mathrm{\τ}+{\mathrm{\τ}}_e-M{\stackrel{\·}{v}}_r-C(v)v_r+D(v\left)v_r\right)\end{array}$

Position tracking error is:

First Liapunov function

K in formula_P∈R^3×3Diagonal matrix for positive definite.

To V₁Carry out derivation: ${\stackrel{\·}{V}}_1={\widetilde{\mathrm{\η}}}^T{K}_P\stackrel{\·}{\widetilde{\mathrm{\η}}}={\widetilde{\mathrm{\η}}}^T{K}_P(s-\mathrm{\Λ}\widetilde{\mathrm{\η}})=-{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}+s^T{K}_P\widetilde{\mathrm{\η}}$

Second Liapunov function

${\stackrel{\·}{V}}_2=s^{T}M*\left(\mathrm{\η}\right)\stackrel{\·}{s}+\frac{1}{2}{s}^T\stackrel{\·}{M}*\left(\mathrm{\η}\right)s+{\stackrel{\·}{V}}_1$

To V₂Carry out derivation: $\begin{array}{c}=-s^T\[C*(\mathrm{\η},v)+D*(\mathrm{\η},v)\]s+\frac{1}{2}{s}^T\stackrel{\·}{M}*\left(\mathrm{\η}\right)s\\ +s^T\[R\left(\mathrm{\ψ}\right)(\mathrm{\τ}+{\mathrm{\τ}}_e-M{\stackrel{\·}{v}}_r-C(v)v_r+D(v\left)v_r\right)\]\\ -{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}+s^T{K}_P\widetilde{\mathrm{\η}}\end{array}$

$s^T\[\stackrel{\·}{M}*\left(\mathrm{\η}\right)-2C*(\mathrm{\η},v)\]s=0,$

$\begin{array}{c}{\stackrel{\·}{V}}_2=-s^{T}D*(\mathrm{\η},v)s-{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}\\ =s^T\[R\left(\mathrm{\ψ}\right)(\mathrm{\τ}+{\mathrm{\τ}}_e-M{\stackrel{\·}{v}}_r-C(v)v_r+D(v)v_r+R^{-1}(\mathrm{\ψ}\left)K_P\widetilde{\mathrm{\η}}\right)\]\end{array}$

Selection controls input:

$\mathrm{\τ}=M{\stackrel{\·}{v}}_r+C\left(v\right)v_r+D\left(v\right)v_r-R^{-1}\left(\mathrm{\ψ}\right)K_P\widetilde{\mathrm{\η}}-R^{-1}\left(\mathrm{\ψ}\right)K_D{s}_n-{\mathrm{\τ}}_e$

${\stackrel{\·}{V}}_2=-s^T(D*(\mathrm{\η},v)+K_D)s-{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}$

Due to V₂Positive definite,Negative definite, so equilibrium point

Thus driving boats and ships gradually to target location and target bow to close, and boats and ships are made to be maintained at target location and target bow to, it is achieved hi-Fix；

2) current location of the boats and ships of each sampling instant of boats and ships and bow are to for η_n=[n_n,e_n,ψ_n]^TTime, the expectation bow of the desired locations obtained by step (2) is to for η_gn=[n_gn,e_gn,ψ_gn]^T,

The position tracking error in the n-th moment under earth coordinates: ${\widetilde{\mathrm{\η}}}_n={\mathrm{\η}}_n-{\mathrm{\η}}_{gn}=\left[\begin{array}{c}{n}_n-n_{gn}\\ e_n-e_{gn}\\ {\mathrm{\ψ}}_n-{\mathrm{\ψ}}_{gn}\end{array}\right]$

Virtual reference velocity under earth coordinates is:Then the virtual reference velocity under hull coordinate system is；

The tracking error of speed is: $s_n=R\left({\mathrm{\ψ}}_n\right)v_n+\mathrm{\Λ}{\widetilde{\mathrm{\η}}}_n,$

The control power input that boats and ships need is:

${\mathrm{\τ}}_n=M(v_{r(n-1)}-v_{r(n-1)})+{\mathrm{Cv}}_{rn}+{\mathrm{Dv}}_{rn}-R^{-1}\left({\mathrm{\ψ}}_n\right)K_P{\widetilde{\mathrm{\η}}}_n-R^{-1}\left({\mathrm{\ψ}}_n\right)K_D{s}_n-{\mathrm{\τ}}_e$

τ_eFor the active force to boats and ships of marine environment, according to controlling input, by propeller driven ship to target location；

M is boats and ships inertial matrix, C (v) is boats and ships Coriolis centripetal force matrix, D (v) is boats and ships damping matrix, Ψ be boats and ships under earth coordinates bow to angle, τ is longitudinal force under boats and ships coordinate system, cross force and flywheel moment three-dimensional state vector, η is that boats and ships north orientation position, east orientation position and bow under earth coordinates are vectorial to angle three-dimensional state, η_rFor the boats and ships virtual reference position vector under earth coordinates, v is boats and ships longitudinal velocity, lateral velocity and the angle of revolution speed three-dimensional state vector under hull coordinate, v_nIt is the boats and ships longitudinal velocity in the n-th moment, lateral velocity and the angle of revolution speed three-dimensional state vector under hull coordinate, v_rFor the virtual reference velocity vector under boats and ships coordinate system, v_rnBeing the virtual reference velocity vector under the boats and ships coordinate system in the n-th moment, s is the tracking error under geodetic coordinates to virtual reference speed, s_nIt is the tracking error to virtual reference speed under the geodetic coordinates in the n-th moment, K_DFor the diagonal matrix of positive definite, Ψ₁For the current bow of boats and ships to, n_nFor the position, current north of boats and ships, e_nFor the position, current east of boats and ships, n_gnFor the position, expectation north of boats and ships, e_gnFor the position, expectation east of boats and ships, n_dFor the position, target north of boats and ships, e_dFor the position, target east of boats and ships, v_sFor considering under geodetic coordinates the speed of the tracking error to virtual reference speed, η_dFor the target bow of boats and ships to, v_r(n-1)Virtual reference velocity under hull coordinate system.

The beneficial effects of the present invention is:

The present invention is based on the control method of asymptotic guiding and control design case location.Moment and thrust variation that the method obtains are mild, it is ensured that in angle of rake quota limit, so that boats and ships smoothly arrive target location, do not have vibration, and positioning precision is higher.

Accompanying drawing explanation

The flow chart of Fig. 1 boats and ships fixed point location program；

Fig. 2 boats and ships turn the flow chart of asymptotic steering routine during bow；

The flow chart of the asymptotic steering routine that Fig. 3 boats and ships move to target location；

Fig. 4 boats and ships error change curve when fixing point positions；

Fig. 5 resets the plane motion response curve of ship's fix during anchor point；

Bow when Fig. 6 resets ship's fix during anchor point is to change curve；

Fig. 7 resets error change curve during ship's fix during anchor point.

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention is described in more detail:

The fixed point location control method of boats and ships is divided into two modules to design: first design the asymptotic guiding module of boats and ships, make its provide the expectation bow of time-varying to and desired locations, redesign corresponding Nonlinear control law, make boats and ships forward to target bow to, making boats and ships move to target location, the fixed point location finally realizing boats and ships controls simultaneously.Its concrete implementation step is as follows:

(1) first according to task it needs to be determined that the target bow of boats and ships fixed point location to and target location.

(2) according to target bow to asymptotic guiding module when turning bow with the revolution rate design boats and ships that can be manually set, thus obtaining desired bow to sequence.

(3) design, according to the target location of boats and ships and current location, the asymptotic guiding module that boats and ships move to target location, thus obtaining desired position sequence.

(4) the expectation bow obtained according to the asymptotic guiding module that above designs to and desired locations, apply the control law of non-linear Backstepping design fixed point location, obtain boats and ships motion and the longitudinally, laterally thrust required for turning bow and turn bow moment, impeller system is issued in instruction, thus drive boats and ships arrive target bow to and target location, and be maintained at target bow to and target location.

It is specifically described as:

(1) first according to actual job determine the target bow of boats and ships to and target location.

(2) design asymptotic guiding module according to target bow to target location, this module is divided asymptotic guiding when turning bow and moves to asymptotic guiding two parts of target location.

1. according to target bow to the asymptotic guidance method designed with revolution rate when boats and ships turn bow, thus obtaining desired bow to sequence.The realization of asymptotic guidance method when turning bow, it is necessary first to judge boats and ships when turning bow be forward turn bow to or reversely turn bow to, then according to the asymptotic guidance method turning bow, the expectation bow in this moment of Ship ' to.Calculate expectation bow to time the revolution rate used can the person of being operated by set at host computer, it is also possible in asymptotic guidance system, application process realizes.

2. design, according to the target location of boats and ships and current location, the asymptotic guidance method that boats and ships move to target location, thus obtaining desired position sequence.The realization of asymptotic guidance method when position is moved has taken into full account the current location of boats and ships and the relative position relation of target location, devise the different guidance method under diverse location relation, including from target location farther out, boats and ships speed in either direction under hull coordinate system is bigger, close to target location, with arrive after source location due to the marine environment impacts such as wind, wave, stream, these several situations of remotely located point again.

(3) according to the asymptotic guiding module above designed, what the asymptotic guidance method moved when namely boats and ships turn bow and to target location obtained expectation bow is to value and desired locations, the control law of ship's fix is determined in application Nonlinear backstepping method design, obtain boats and ships and turn the moment of bow needs and the vertical and horizontal thrust that boats and ships motion is required, thus gradually forwarded to by propeller driven ship target bow to, and it is close to target location, and be maintained at target bow to and target location, finally realize boats and ships fixed point location control.

Illustrate below in conjunction with accompanying drawing:

The present invention mainly realizes boats and ships and positions in target location, and namely the position of boats and ships to be maintained at target location, simultaneously the bow of boats and ships to be also maintained at target bow to.The control method of location includes the asymptotic guiding module that moves when boats and ships turn bow and to target location and the desired locations obtained according to asymptotic guiding module and bow to the Nonlinear control law module of design.The flow chart of fixed point location program is as shown in Figure 1.The present invention comprises following step:

(1) first determine the target bow of boats and ships to and target location.Control panel is pressed the button of station-keeping mode, namely boats and ships realize determining simultaneously bow to, fixed horizontal and fixed indulge.Target bow can the person of being operated by set at host computer to target location, when speed of the ship in metres per second is relatively low, it is also possible to using position when putting into station-keeping mode first and bow to as target location and target bow to.

(2) call asymptotic guiding module, calculate real-time desired locations and bow to.Asymptotic guiding when wherein this module is divided into boats and ships to turn bow and the asymptotic guiding two parts moved to target location.

Asymptotic guidance method when 1. turning bow by current bow to, target bow to, current revolution rate as input, be output as boats and ships and turn expectation bow real-time during bow to sequence.The program flow diagram of the method is as shown in Figure 2.Asymptotic guidance system method when turning bow realizes in the following several ways: if target bow is to ψ_dRepresenting, the expectation bow obtained in the n-th moment in method is to ψ_gnRepresenting, the current bow that boats and ships obtained from sensor in the n-th moment is to for ψ_n, boats and ships put into first determines bow to control method, boats and ships expectation bow this moment to for the current bow of boats and ships to, i.e. ψ_g1=ψ₁.Calculate target bow to current bow to difference obtain the relative bow of boats and ships to, if bow is to during more than 0 relatively, then boats and ships turn to forward, if bow is to during less than 0 relatively, then boats and ships are to counter steering.

If the revolution rate that host computer sets is as K_turn, then boats and ships to forward turn to time, expectation bow now is to for ψ_gn=ψ_g(n-1)+K_turnTs, ψ in formula_g(n-1)For upper one the moment calculate expectation bow to, Ts is the sampling time of control system.Calculate expectation bow to target bow to difference, if this difference is less than 0 or when the absolute value of this difference is only small, boats and ships at the expectation bow in the n-th moment to for ψ_gn=ψ_d。

When boats and ships are to counter steering, expectation bow now is to for ψ_gn=ψ_g(n-1)-K_turnTs, ψ in formula_g(n-1)With Ts with above-mentioned definition.Calculate expectation bow to target bow to difference, if this difference is more than 0 or when the absolute value of this difference is only small, boats and ships at the expectation bow in the n-th moment to for ψ_gn=ψ_d。

2. the asymptotic guidance method moved to target location is by the north orientation of boats and ships and the current location of east orientation and target location, and the current and target bow of boats and ships is to as input, being output as position, expectation north real-time when boats and ships move and expectation east position sequence.The program flow diagram of the method is as shown in Figure 3.The realization of the asymptotic guidance method moved to target location is mainly by four flag bits of definition, and adopts diverse ways to obtain the desired locations of each sampling instant according to these four flag bits, thus realizing the asymptotic guiding of boats and ships.If definition boats and ships current location in the n-th moment in two dimensional surface is expressed as P=[n_n,e_n]^T, the desired locations that the n-th moment obtained is P_gn=[n_gn,e_gn]^T, the target location of boats and ships is expressed as: P_d=[n_d,e_d]^T.When putting into station-keeping mode first, it should using the current location desired locations as this moment, it may be assumed that [n_g1,e_g1]^T=[n₁,e₁]^TIf during the speed that boats and ships move, when namely flag bit is 3, desired locations now is also the position of the current time of boats and ships, i.e. [n_gn,e_gn]^T=[n_n,e_n]^T, Ship ' target location and current location are at the angle of east northeast coordinate system, namelyIt is now 1 by mark position, is next directly entered the cycle calculations of asymptotic guidance system.

The relative distance of Ship ' current location and target location, it may be assumed thatCalculating speed used during desired locations is v_g=k*r_dn-0.1, k=0.015, this speed obtained generally to be limited in 0.1m/s～0.3m/s, and its direction is the boats and ships line directions along current location and target location.Calculating is carved the relative distance of desired locations and target location for the moment, it may be assumed that

$r_{gd}=\sqrt{{(e_{g(n-1)}-e_d)}^2+{(n_{g(n-1)}-n_d)}^2}$

E in formula_g(n-1) for the position, expectation east that a upper moment obtains, n_g(n-1) for position, expectation north that a upper moment obtains.

If carving the relative distance of desired locations and target location upper a period of time namely: r_gdMore than 1m, then the desired locations in this moment should adopt following methods to obtain.

$\left[\begin{array}{c}{n}_{gn}\\ e_{gn}\end{array}\right]=\left[\begin{array}{c}{n}_g(n-1)+v_s*Ts*cos\left(\mathrm{\θ}\right)\\ e_g(n-1)+v_s*Ts*sin\left(\mathrm{\θ}\right)\end{array}\right]$

If carving the relative distance of desired locations and target location upper a period of time namely: r_gdLess than or equal to 1m, then the desired locations in this moment is: [n_gn,e_gn]^T=[n_d,e_d]^T, it is 2 by mark position simultaneously.

Judge the real-time speed of boats and ships when having calculated desired locations, if longitudinal direction or lateral velocity are more than 0.5m/s, then the speed of boats and ships motion, is 3 by mark position.Desired locations now is the position of the current time of boats and ships, it may be assumed that [n_gn,e_gn]^T=[n_n,e_n]^T。

Interference boats and ships if as environment deviate target location, when namely the relative distance of boats and ships current location and target location is more than 3m and when flag bit is 2, flag bit are set to 4 again.Desired locations now is target location, i.e. [n_g,e_g]^T=[n_d,e_d]^T.After obtaining new desired locations, flag bit is set to 1 again, is again introduced into circulation next time of asymptotic guiding.

(3) the Nonlinear control law method of fixed point location by current northern position, east position and bow to, position, target north, east position, bow to, the instantaneous velocity of boats and ships vertical and horizontal and the longitudinal force, cross force and the moment that produce along number revolution rates and environmental disturbances as input, the longitudinal force that is output as needing, cross force, turn moment required during bow and north orientation, the position deviation of east orientation and bow to deviation.

Representing in order to convenient, the form of the variable vector used in control law represents.Assume that the target location of boats and ships and target bow are to for η_d=[n_d,e_d,ψ_d]^T, this vector is permanent vector.The Three Degree Of Freedom mathematical model of boats and ships is:

$\stackrel{\·}{\mathrm{\η}}=R\left(\mathrm{\ψ}\right)v$

$M\stackrel{\·}{v}+C\left(v\right)v+D\left(v\right)v=\mathrm{\τ}+{\mathrm{\τ}}_e$

In formula $R\left(\mathrm{\ψ}\right)=\left[\begin{array}{ccc}cos\left(\mathrm{\ψ}\right)& -sin\left(\mathrm{\ψ}\right)& 0\\ sin\left(\mathrm{\ψ}\right)& \cos \left(\mathrm{\ψ}\right)& 0\\ 0& 0& 1\end{array}\right].$

The position tracking error of definition boats and ships is:

It is carried out derivation can obtain: $\stackrel{\·}{\widetilde{\mathrm{\η}}}=\stackrel{\·}{\mathrm{\η}}-{\stackrel{\·}{\mathrm{\η}}}_d=R\left(\mathrm{\ψ}\right)v$

The definition virtual reference velocity under earth coordinates isΛ ∈ R in formula^3×3Diagonal matrix for positive definite.

Virtual reference velocity under hull coordinate system is

The tracking error of definition speed is: $s=\stackrel{\·}{\mathrm{\η}}-{\stackrel{\·}{\mathrm{\η}}}_r=R\left(\mathrm{\ψ}\right)v+\mathrm{\Λ}\widetilde{\mathrm{\η}}$

Ship model is carried out deformation can obtain: $M*\left(\mathrm{\η}\right)\stackrel{\·\·}{\mathrm{\η}}+C*(\mathrm{\η},v)\stackrel{\·}{\mathrm{\η}}+D*(\mathrm{\η},v)\stackrel{\·}{\mathrm{\η}}=\mathrm{\τ}+{\mathrm{\τ}}_e$

M* (η)=R (ψ) MR^-1(ψ),

$C*(\mathrm{\η},v)=R\left(\mathrm{\ψ}\right)\[C\left(v\right)-{\mathrm{MR}}^{-1}\left(\mathrm{\ψ}\right)\stackrel{\·}{R}\left(\mathrm{\ψ}\right)\]R^{-1}\left(\mathrm{\ψ}\right)$

D* (η, v)=R (ψ) D (v) R^-1(ψ)

So can obtain:

$\begin{array}{c}M*\left(\mathrm{\η}\right)\stackrel{\·}{s}\\ =-C*(\mathrm{\η},v)s-D*(\mathrm{\η},v)s+R\left(\mathrm{\ψ}\right)(\mathrm{\τ}+{\mathrm{\τ}}_e)-M*\left(\mathrm{\η}\right){\stackrel{\·\·}{\mathrm{\η}}}_r-C*(\mathrm{\η},v){\stackrel{\·}{\mathrm{\η}}}_r-D*(\mathrm{\η},v){\stackrel{\·}{\mathrm{\η}}}_r\\ =-C*(\mathrm{\η},v)s-D*(\mathrm{\η},v)s+R\left(\mathrm{\ψ}\right)(\mathrm{\τ}+{\mathrm{\τ}}_e-M{\stackrel{\·}{v}}_r-C(v)v_r+D(v\left)v_r\right)\end{array}$

Position tracking error can also be written as:

Define first Liapunov function

K in formula_P∈R^3×3Diagonal matrix for positive definite.

To V₁Carry out derivation can obtain: ${\stackrel{\·}{V}}_1={\widetilde{\mathrm{\η}}}^T{K}_P\stackrel{\·}{\widetilde{\mathrm{\η}}}={\widetilde{\mathrm{\η}}}^T{K}_P(s-\mathrm{\Λ}\widetilde{\mathrm{\η}})=-{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}+s^T{K}_P\widetilde{\mathrm{\η}}$

Define second Liapunov function

${\stackrel{\·}{V}}_2=s^{T}M*\left(\mathrm{\η}\right)\stackrel{\·}{s}+\frac{1}{2}{s}^T\stackrel{\·}{M}*\left(\mathrm{\η}\right)s+{\stackrel{\·}{V}}_1$

To V₂Carry out derivation can obtain: $\begin{array}{c}=-s^T\[C*(\mathrm{\η},v)+D*(\mathrm{\η},v)\]s+\frac{1}{2}{s}^T\stackrel{\·}{M}*\left(\mathrm{\η}\right)s\\ +s^T\[R\left(\mathrm{\ψ}\right)(\mathrm{\τ}+{\mathrm{\τ}}_e-M{\stackrel{\·}{v}}_r-C(v)v_r+D(v\left)v_r\right)\]\\ -{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}+s^T{K}_P\widetilde{\mathrm{\η}}\end{array}$

Due to $s^T\[\stackrel{\·}{M}*\left(\mathrm{\η}\right)-2C*(\mathrm{\η},v)\]s=0,$ So can obtain:

$\begin{array}{c}{\stackrel{\·}{V}}_2=-s^{T}D*(\mathrm{\η},v)s-{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}\\ =s^T\[R\left(\mathrm{\ψ}\right)(\mathrm{\τ}+{\mathrm{\τ}}_e-M{\stackrel{\·}{v}}_r-C(v)v_r+D(v)v_r+R^{-1}(\mathrm{\ψ}\left)K_P\widetilde{\mathrm{\η}}\right)\]\end{array}$

Selection controls input:

$\mathrm{\τ}=M{\stackrel{\·}{v}}_r+C\left(v\right)v_r+D\left(v\right)v_r-R^{-1}\left(\mathrm{\ψ}\right)K_P\widetilde{\mathrm{\η}}-R^{-1}\left(\mathrm{\ψ}\right)K_D{s}_n-{\mathrm{\τ}}_e$

Therefore: ${\stackrel{\·}{V}}_2=-s^T(D*(\mathrm{\η},v)+K_D)s-{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}$

Due to V₂Positive definite,Negative definite, so we can obtain equilibrium pointIt it is Global Exponential Stability.

Expectation bow that asymptotic guidance method during bow obtains is turned to the desired locations obtained with the asymptotic guidance method moved to target location according to boats and ships, call the control law of ship's fix based on Nonlinear backstepping method, longitudinally, laterally thrust required for obtaining boats and ships real time kinematics and the moment turning bow, thus driving boats and ships gradually to target location and target bow to close, and make boats and ships be maintained at target location and target bow to, finally realize hi-Fix.

Assume that the current location of the boats and ships of each sampling instant of boats and ships and bow are to for η_n=[n_n,e_n,ψ_n]^T, the expectation bow of the desired locations obtained by asymptotic guidance system is to for η_gn=[n_gn,e_gn,ψ_gn]^T。

The position tracking error in the n-th moment under definition earth coordinates: ${\widetilde{\mathrm{\η}}}_n={\mathrm{\η}}_n-{\mathrm{\η}}_{gn}=\left[\begin{array}{c}{n}_n-n_{gn}\\ e_n-e_{gn}\\ {\mathrm{\ψ}}_n-{\mathrm{\ψ}}_{gn}\end{array}\right]$

The definition virtual reference velocity under earth coordinates is:Then the virtual reference velocity under hull coordinate system is； $v_{rn}=-R^{-1}\left({\mathrm{\ψ}}_n\right)\mathrm{\Λ}{\widetilde{\mathrm{\η}}}_n.$

The tracking error of definition speed is:

The control power selecting boats and ships needs inputs and is:

${\mathrm{\τ}}_n=M(v_{r(n-1)}-v_{r(n-1)})+{\mathrm{Cv}}_{rn}+{\mathrm{Dv}}_{rn}-R^{-1}\left({\mathrm{\ψ}}_n\right)K_P{\widetilde{\mathrm{\η}}}_n-R^{-1}\left({\mathrm{\ψ}}_n\right)K_D{s}_n-{\mathrm{\τ}}_e$

τ in formula_eThe active force to boats and ships for the marine environment that rule of thumb formula is calculated.According to controlling input, boats and ships can be driven to target location by propeller.

Realize the situation of location for boats and ships in certain fixing target location, be verified by following instance.Set the initial position of certain dynamic positioning vessel and bow to for [n₀e₀ψ₀]=[0m0m0 °], it is assumed that sea situation now is: wind speed is 20 joints, and direction of the wind comes from is fore direction.The speed of ocean current is 1 joint, and the direction of stream is starboard 30 °.If it is 20 joints that sea situation becomes wind speed when 300s, direction of the wind comes from is ship starboard 45 °.The speed of ocean current is 1.5 joints, and the direction of stream is starboard 30 °；When 700s, sea situation becomes wind speed is 20 joints, and direction of the wind comes from is ship starboard 90 °.The speed of ocean current is 1.5 joints, and the direction of stream is starboard 30 °.Require under the sea situation of this change boats and ships can also be maintained at current position and current bow to.According to the control method above designed, the simulated program of establishment fixed point location, the effectiveness of checking the method.The error change curve that boats and ships position in fixing target location is as shown in Figure 4.

When resetting for the target location of boats and ships, it is verified by following instance.Set the initial position of certain dynamic positioning vessel and bow to for [n₀e₀ψ₀]=[0m0m0 °], target location and bow to for:

[n_de_dψ_d]=[10m10m40 °].Assuming that sea situation at that time be wind speed is 20 joints, direction of the wind comes from is starboard 50 ° simultaneously.The speed of ocean current is 1.5 joints, and the direction of stream is starboard 30 °.When resetting target location, the plane motion response of ship's fix is as it is shown in figure 5, the bow of ship's fix is to changing as shown in Figure 6, and the error change curve of ship's fix is as shown in Figure 7.

Two above example describes the localization method of the present invention well can realize high-precision location under common sea situation；And the method is simple, reliable, it is possible to ensure the safety work of dynamic positioning boats and ships, there is significantly high engineer applied and be worth.

Claims (1)

1. the ship's fix control method based on asymptotic guiding, it is characterised in that:

(1) determine the target bow of boats and ships to and target location；

(2) calculate real-time desired locations and bow to:

1), when turning bow, target bow is calculated to ψ_dWith current bow to ψ_nDifference obtain the relative bow of boats and ships to, ψ_g1=ψ₁, relative bow is to during more than 0, then boats and ships turn to forward, and relative bow is to during less than 0, then boats and ships are to counter steering；Boats and ships to forward turn to time, it is desirable to bow is to for ψ_gn=ψ_g(n-1)+K_turnTs, ψ_gnFor the expectation bow that obtains in the n-th moment to, K_turnFor the revolution rate that host computer sets, Ts is the sampling time of control system, if ψ_gn-ψ_d≤ 0, then ψ_gn=ψ_d, otherwise re-read target bow to current bow to being calculated；When boats and ships are to counter steering, it is desirable to bow is to for ψ_gn=ψ_g(n-1)-K_turnTs, if ψ_gn-ψ_d>=0, then ψ_gn=ψ_d, otherwise re-read target bow to current bow to being calculated；

2), when moving to target location, boats and ships current location in the n-th moment in two dimensional surface is P=[n_n,e_n]^T, the desired locations that the n-th moment obtained is P_gn=[n_gn,e_gn]^T, the target location of boats and ships is P_d=[n_d,e_d]^T, [n_g1,e_g1]^T=[n₁,e₁]^T, Ship ' target location and current location are at the angle of east northeast coordinate systemIt is 1 by mark position, the relative distance of Ship ' current location and target location,Calculating speed used during desired locations is v_g=k*r_dn-0.1, k=0.015, direction is the boats and ships line directions along current location and target location, and calculating is carved the relative distance of desired locations and target location for the moment, it may be assumed that

$r_{gd}=\sqrt{{(e_{g(n-1)}-e_d)}^2+{(n_{g(n-1)}-n_d)}^2}$

E in formula_g(n-1)For the position, expectation east that a upper moment obtains, n_g(n-1)For the position, expectation north that a upper moment obtains；

r_gdDuring more than 1m, then the desired locations in this moment is:

$\left[\begin{array}{c}{n}_{gn}\\ e_{gn}\end{array}\right]=\left[\begin{array}{c}{n}_{g(n-1)}+v_s*Ts*cos\left(\mathrm{\θ}\right)\\ e_{g(n-1)}+v_s*Ts*sin\left(\mathrm{\θ}\right)\end{array}\right]$

r_gdLess than or equal to 1m, then the desired locations in this moment is: [n_gn,e_gn]^T=[n_d,e_d]^T, it is 2 by mark position simultaneously,

If longitudinal direction or lateral velocity are more than 0.5m/s, being 3 by mark position, desired locations now is the position of the current time of boats and ships, it may be assumed that [n_gn,e_gn]^T=[n_n,e_n]^T；

When the relative distance of boats and ships current location and target location is 2 more than 3m and flag bit, flag bit being set to 4 again, desired locations now is target location, i.e. [n_g,e_g]^T=[n_d,e_d]^T, after obtaining new desired locations, flag bit is set to 1 again；

(3) according to current northern position, east position and bow to, longitudinal force that longitudinal force, cross force and the Calculating Torque during Rotary that position, target north, position, east, bow produce to, the instantaneous velocity of boats and ships vertical and horizontal and instantaneous revolution rate and environmental disturbances needs, cross force, turn moment required during bow and north orientation, the position deviation of east orientation and bow to deviation:

1) target location of boats and ships and target bow are to for η_d=[n_d,e_d,ψ_d]^TTime, the target location of boats and ships and target bow are to for permanent vector, and the Three Degree Of Freedom model of boats and ships is: $\begin{array}{c}\stackrel{\·}{\mathrm{\η}}=R\left(\mathrm{\ψ}\right)v\\ M\stackrel{\·}{v}+C\left(v\right)v+D\left(v\right)v=\mathrm{\τ}+{\mathrm{\τ}}_e\end{array},$

$R\left(\mathrm{\ψ}\right)=\left[\begin{array}{ccc}cos\left(\mathrm{\ψ}\right)& -sin\left(\mathrm{\ψ}\right)& 0\\ sin\left(\mathrm{\ψ}\right)& \cos \left(\mathrm{\ψ}\right)& 0\\ 0& 0& 1\end{array}\right];$

The position tracking error of boats and ships is:

Derivation: $\stackrel{\·}{\widetilde{\mathrm{\η}}}=\stackrel{\·}{\mathrm{\η}}-{\stackrel{\·}{\mathrm{\η}}}_d=R\left(\mathrm{\ψ}\right)v,$

Virtual reference velocity under earth coordinates isΛ ∈ R in formula^3×3For the diagonal matrix of positive definite,

Virtual reference velocity under hull coordinate system is

The tracking error of speed is: $s=\stackrel{\·}{\mathrm{\η}}-{\stackrel{\·}{\mathrm{\η}}}_r=R\left(\mathrm{\ψ}\right)v+\mathrm{\Λ}\widetilde{\mathrm{\η}},$

Boats and ships Three Degree Of Freedom model deformation obtains: $M*\left(\mathrm{\η}\right)\stackrel{\·\·}{\mathrm{\η}}+C*(\mathrm{\η},v)\stackrel{\·}{\mathrm{\η}}+D*(\mathrm{\η},v)\stackrel{\·}{\mathrm{\η}}=\mathrm{\τ}+{\mathrm{\τ}}_e$

M* (η)=R (ψ) MR^-1(ψ),

$C*(\mathrm{\η},v)=R\left(\mathrm{\ψ}\right)\[C\left(v\right)-{\mathrm{MR}}^{-1}\left(\mathrm{\ψ}\right)\stackrel{\·}{R}\left(\mathrm{\ψ}\right)\]R^{-1}\left(\mathrm{\ψ}\right),$

D* (η, v)=R (ψ) D (v) R^-1(ψ),

$\begin{array}{c}M*\left(\mathrm{\η}\right)\stackrel{\·}{s}\\ =-C*\left(\mathrm{\η},v\right)s-D*\left(\mathrm{\η},v\right)s+R\left(\mathrm{\ψ}\right)\left(\mathrm{\τ}+{\mathrm{\τ}}_e\right)-M*\left(\mathrm{\η}\right){\stackrel{\·\·}{\mathrm{\η}}}_r-C*\left(\mathrm{\η},v\right){\stackrel{\·}{\mathrm{\η}}}_r-D*\left(\mathrm{\η},v\right){\stackrel{\·}{\mathrm{\η}}}_r\\ =-C*\left(\mathrm{\η},v\right)s-D*\left(\mathrm{\η},v\right)s+R\left(\mathrm{\ψ}\right)\left(\mathrm{\τ}+{\mathrm{\τ}}_e-M{\stackrel{\·}{v}}_r-C\left(v\right)v_r+D\left(v\right)v_r\right)\end{array}$

Position tracking error is:

First Liapunov function

K in formula_P∈R^3×3Diagonal matrix for positive definite；

To V₁Carry out derivation: ${\stackrel{\·}{V}}_1={\widetilde{\mathrm{\η}}}^T{K}_P\stackrel{\·}{\widetilde{\mathrm{\η}}}={\widetilde{\mathrm{\η}}}^T{K}_P(s-\mathrm{\Λ}\widetilde{\mathrm{\η}})=-{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}+s^T{K}_P\widetilde{\mathrm{\η}}$

Second Liapunov function $V_2=\frac{1}{2}{s}^{T}M*\left(\mathrm{\η}\right)s+V_1$

To V₂Carry out derivation: $\begin{array}{c}{\stackrel{\·}{V}}_2=s^{T}M*\left(\mathrm{\η}\right)\stackrel{\·}{s}+\frac{1}{2}{s}^T\stackrel{\·}{M}*\left(\mathrm{\η}\right)s+{\stackrel{\·}{V}}_1\\ =-s^T\[C*\left(\mathrm{\η},v\right)+D*\left(\mathrm{\η},v\right)\]s+\frac{1}{2}{s}^T\stackrel{\·}{M}*\left(\mathrm{\η}\right)s\\ +s^T\[R\left(\mathrm{\ψ}\right)\left(\mathrm{\τ}+{\mathrm{\τ}}_e-M{\stackrel{\·}{v}}_r-C\left(v\right)v_r+D\left(v\right)v_r\right)\]\\ -{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}+s^T{K}_P\widetilde{\mathrm{\η}}\end{array}$

$s^T\[\stackrel{\·}{M}*\left(\mathrm{\η}\right)-2C*(\mathrm{\η},v)\]s=0,$

$\begin{array}{c}{\stackrel{\·}{V}}_2=-s^{T}D*(\mathrm{\η},v)s-{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}\\ +s^T\[R\left(\mathrm{\ψ}\right)(\mathrm{\τ}+{\mathrm{\τ}}_e-M{\stackrel{\·}{v}}_r-C(v)v_r+D(v)v_r+R^{-1}(\mathrm{\ψ}\left)K_P\widetilde{\mathrm{\η}}\right)\]\end{array}$

Selection controls input:

$\mathrm{\τ}=M{\stackrel{\·}{v}}_r+C\left(v\right)v_r+D\left(v\right)v_r-R^{-1}\left(\mathrm{\ψ}\right)K_P\widetilde{\mathrm{\η}}-R^{-1}\left(\mathrm{\ψ}\right)K_D{s}_n-{\mathrm{\τ}}_e$

${\stackrel{\·}{V}}_2=-s^T(D*(\mathrm{\η},v)+K_D)s-{\widetilde{\mathrm{\η}}}^T{K}_P\mathrm{\Λ}\widetilde{\mathrm{\η}}$

Due to V₂Positive definite,Negative definite, so equilibrium point

Thus driving boats and ships gradually to target location and target bow to close, and boats and ships are made to be maintained at target location and target bow to, it is achieved hi-Fix；

2) current location of the boats and ships of each sampling instant of boats and ships and current bow are to for η_n=[n_n,e_n,ψ_n]^TTime, the desired locations obtained by step (2) and expectation bow are to for η_gn=[n_gn,e_gn,ψ_gn]^T,

The position tracking error in the n-th moment under earth coordinates: ${\widetilde{\mathrm{\η}}}_n={\mathrm{\η}}_n-{\mathrm{\η}}_{gn}=\left[\begin{array}{c}{n}_n-n_{gn}\\ e_n-e_{gn}\\ {\mathrm{\ψ}}_n-{\mathrm{\ψ}}_{gn}\end{array}\right]$

Virtual reference velocity under earth coordinates is:Then the virtual reference velocity under hull coordinate system is: $v_{rn}=-R^{-1}\left({\mathrm{\ψ}}_n\right)\mathrm{\Λ}{\widetilde{\mathrm{\η}}}_n,$

The tracking error of speed is: $s_n=R\left({\mathrm{\ψ}}_n\right)v_n+\mathrm{\Λ}{\widetilde{\mathrm{\η}}}_n,$

The control power input that boats and ships need is:

${\mathrm{\τ}}_n=M(v_{rn}-v_{r(n-1)})+{\mathrm{Cv}}_{rn}+{\mathrm{Dv}}_{rn}-R^{-1}\left({\mathrm{\ψ}}_n\right)K_P{\widetilde{\mathrm{\η}}}_n-R^{-1}\left({\mathrm{\ψ}}_n\right)K_D{s}_n-{\mathrm{\τ}}_e$

τ_eFor the active force to boats and ships of marine environment, according to controlling input, by propeller driven ship to target location；

M is boats and ships inertial matrix, C (v) is boats and ships Coriolis centripetal force matrix, D (v) is boats and ships damping matrix, Ψ be boats and ships under earth coordinates bow to angle, τ is longitudinal force under boats and ships coordinate system, cross force and flywheel moment three-dimensional state vector, η is that boats and ships north orientation position, east orientation position and bow under earth coordinates are vectorial to angle three-dimensional state, η_rFor the boats and ships virtual reference position vector under earth coordinates, v is boats and ships longitudinal velocity, lateral velocity and the angle of revolution speed three-dimensional state vector under hull coordinate, v_nIt is the boats and ships longitudinal velocity in the n-th moment, lateral velocity and the angle of revolution speed three-dimensional state vector under hull coordinate, v_rFor the virtual reference velocity vector under boats and ships coordinate system, v_rnBeing the virtual reference velocity vector under the boats and ships coordinate system in the n-th moment, s is the tracking error under geodetic coordinates to virtual reference speed, s_nIt is the tracking error to virtual reference speed under the geodetic coordinates in the n-th moment, K_DFor the diagonal matrix of positive definite, Ψ₁For the current bow of boats and ships to, n_nFor the position, current north of boats and ships, e_nFor the position, current east of boats and ships, n_gnFor the position, expectation north of boats and ships, e_gnFor the position, expectation east of boats and ships, n_dFor the position, target north of boats and ships, e_dFor the position, target east of boats and ships, v_sFor considering under geodetic coordinates the speed of the tracking error to virtual reference speed, η_dFor the target bow of boats and ships to, v_r(n-1)Virtual reference velocity under hull coordinate system.