CN102910265A - Rudder and fin combination stabilization method based on dual-control H to infinite design - Google Patents

Abstract

The invention provides a rudder and fin combination stabilization method based on a dual-control H to infinite design, which comprises the steps that a roll angle signal is acquired and initial control parameter values are set; a stabilization fin loop control output u1(t) is calculated by adopting the roll angle signal as an input; a sensitivity weight function and a control sensitivity weight function are determined, and a stabilization rudder loop control output u2(t) is calculated by adopting the roll angle signal as the input; an open-loop Nyquist characteristic of a system is drawn according to a rudder and fin combination stabilization object model and a synthetized rudder and fin control action; then whether the open-loop Nyquist characteristic meets an index requirement is judged; and if the open-loop Nyquist characteristic does not meet the index requirement, the control parameter values are readjusted till the open-loop Nyquist characteristic meets the index requirement. The rudder and fin combination stabilization method takes full advantages of actions of a rudder and a stabilization fin; with the adoption of the zero phase shift design on a rudder loop and a stabilization fin loop, stabilization effects synthetized by the rudder and the stabilization fin are superimposed; and the dual-control on the system is realized, so that the stabilization capability of a ship is improved greatly.

Description

A kind of rudder and fin based on dual H∞ control design subtracts the method for shaking

Technical field

What the present invention relates to is a kind of ship control method, specifically ship stabilization method.

Background technology

When boats and ships ride the sea, owing to being subject to the effect of the ambient interference such as stormy waves, can produce various swaying, this all can have a negative impact to the safety of boats and ships, equipment, goods and crewman on the ship, and is wherein serious with the rolling impact.Rudder and fin subtracts that to shake be to utilize existing rudder and steering control system on the ship, join together to control with stabilizer, wherein stabilizer plays the main effect of shaking that subtracts, and autopilot is when going as course, play the auxiliary effect of shaking that subtracts, this rudder and fin control, can play strong compensating action to stabilizer, can under the prerequisite of control accuracy that goes as course, greatly improve the ability of shaking that subtracts of system, when improving whole stabilizing efficiency, can also reduce action and the noise of stabilizer, thereby make the navigability of boats and ships, safety and member's traveling comfort is improved accordingly.At present, the research of rudder and fin control is the Hot Contents of ship stabilization area research always.

At present for the control of rudder and fin sway stabilisation system, certain research is arranged both at home and abroad, but find that not yet the dual control of application carries out rudder and fin and subtract document and the patent achievement that shakes design.

External main literature has: 1996, the article that Sharff etc. deliver at " Control Eng.Practice " " Final Experimental Results of Full Scale Fin/Rudder Roll Stabilisation Sea Trials " has designed the PID controller of rudder/fin combined stabilization with classical way, but it does not consider between yawing and the rolling, the interaction between stabilizer loop and the rudder loop, and given PID controller can not guarantee that system can both reach the higher rate of shaking that subtracts in the main frequency band that wave disturbs.1997, the article that Roberts etc. deliver at " IEE Proceedings of Control Theory Applications " " Robust control methodology applied to the design of a combined steering/stabilizer system for warships " is used H ∞ control theory and has been designed the rudder-fin joint control device, and contrast with classical PID controller design result, but coupling between the loop and the optimization of Comprehensive Control effect have been ignored in the controller design process.1999, the article that Sgobbo etc. deliver at " Marine Technology " " Rudder/Fin Roll Stabilization of the USCG WMEC 901 Class Vessel " utilizes the existing rudder of the WMEC901 of U.S. Coast Guard level warship/fin transmission device, adopt the LQR method to design the controller of rudder/fin combined stabilization, by comparing with independent stabilizer, point out that rudder/fin united controller can improve stabilizing efficiency in the control accuracy that goes as course.The given controller of the document is too simple, and does not also carry out certain optimization and regulate aspect the performances weighting functions selection, and anti-rolling efficiency is lower.2004, the article that Tanguy etc. deliver at " Proceedings of the 2004 American Control Conference " " Fin Rudder Roll Stabilisation of Ships:a Gain Scheduling Control Methodology " is demarcated control method with gain and has been designed the closed loop control system of rudder/fin combined stabilization, but does not consider that rolling control is on the impact in course.

Domestic main literature has: 2005, the article that Zhang Bing etc. deliver at " Chinese navigation " " research of rudder/fin combined stabilization Fuzzy Variable-Structure Control " has provided the equation of state of rudder/fin combined stabilization control system, and has designed the change structure controller of rudder/fin combined stabilization.2002, the article that Yu Ping etc. deliver at " Journal of System Simulation " " the Nonlinear Rudder fin combined control system emulation based on H ∞ design method is ground " based on H ∞ feedback of status, carried out the design of rudder/fin combined control system.2006, the article that Zhang Xianku etc. deliver at " Communication and Transportation Engineering journal " " rudder and fin subtracts the robust control system that shakes " designed the control system of rudder/fin combined stabilization with the MIMO Closed Loop Gain Shaping Algorithm.The designed controller of document is not mostly analyzed the Different Dynamic characteristic in stabilizer loop and rudder stabilization loop, can only guarantee the stack of control action, can not guarantee the optimization of optimization and the performance of comprehensive stabilizing efficiency, also not consider the how effect of maximized performance stabilizer and rudder.

Summary of the invention

The object of the present invention is to provide the Nyquist curve in rudder and two loops of fin to accomplish all that on the natural frequency of ship a kind of rudder and fin based on dual H∞ control design of zero phase-shift subtracts the method for shaking.

The object of the present invention is achieved like this:

A kind of rudder and fin based on dual H∞ control design of the present invention subtracts the method for shaking, and it is characterized in that:

(1) gathers the roll angle signal

Set the ship rolling resonance frequency omega _nAnd control parameter initial value, comprise roll angle feedback factor k ₁, angular velocity in roll feedback factor k ₂, roll angle acceleration/accel feedback factor k ₃, sensitivity weight function W ₁Gain factor k ₄, damping ratio ξ, control sensitivity weight function W ₂Gain factor k ₅, corner frequency ω ₁, ω ₂, ω ₃

(2) with

Be input, the adjustable parameter control algorithm of using based on zero phase-shift calculates stabilizer loop control output u ₁(t):

Calculate control output u according to following formula ₁(t):

In the following formula

The expression angular velocity in roll,

Expression roll angle acceleration/accel;

To u ₁(t) carry out Laplace transform, obtain subtracting the transfer function K that shakes the device controller _f(s):

$K_f\left(s\right)=\frac{U_1\left(s\right)}{\mathrm{\φ}\left(s\right)}=k_1+\frac{k_2}{{\mathrm{\ω}}_n}s+\frac{k_3}{{\mathrm{\ω}}_n^2}{s}^2,$

φ in the following formula (s) is roll angle

Laplace transform, U ₁(s) be output u ₁(t) Laplace transform;

(3) with

Be input, determine sensitivity weight function and control sensitivity weight function according to the designing requirement of zero phase-shift, then use H ∞ control algorithm and calculate rudder stabilization loop control output u ₂(t):

Adopt H ∞ Mixed Sensitivity S/KS problem solving rudder stabilization controller, determine the weight function in the H ∞ design, namely determine sensitivity weight function W ₁With control sensitivity weight function W ₂:

Sensitivity weight function W ₁(s) be taken as:

$W_1\left(s\right)=\frac{k_4{\mathrm{\ω}}_n^{2}s}{s^2+2\mathrm{\ξ}{\mathrm{\ω}}_{n}s+{\mathrm{\ω}}_n^2},$

Control sensitivity weight function W ₂Be taken as:

$W_2\left(s\right)=\frac{k_5(s+{\mathrm{\ω}}_1)(s+{\mathrm{\ω}}_2)}{s(s+{\mathrm{\ω}}_3)},$

According to weight function structure and initial control parameter value, find the solution H ∞ optimization problem, obtain the H ∞ controller K of rudder stabilization _rAnd then the Laplace transform U that obtains exporting (s), ₂(s) be:

U ₂(s)＝K _r(s)·φ(s)，

To U ₂(s) carry out inverse Laplace transform, obtain u ₂(t);

(4) according to the open loop Nyquist characteristic of rudder, fin control output drawing system, then judge whether to satisfy index request, if do not satisfy, readjust and respectively control parameter value and return step (2), until satisfy index request:

Setting up rudder and fin and subtract and shake object model, will be u with fin angle α ₁(t) and rudder angle δ to be u2 (t) be input, roll angle

For the rudder/fin combined stabilization object model of output represents with transfer function G (s):

G(s)＝[G _f(s) G _r(s)]，

Then with control action u ₁(t) and u ₂(t) superimposed, order

$u\left(t\right)=\left[\begin{array}{c}{u}_1\left(t\right)\\ u_2\left(t\right)\end{array}\right],$

Then its Laplace transform U (s) is,

$U\left(s\right)=\left[\begin{array}{c}{U}_1\left(s\right)\\ U_2\left(s\right)\end{array}\right]=K\left(s\right)\mathrm{\φ}\left(s\right)=\left[\begin{array}{c}{K}_f\left(s\right)\\ K_r\left(s\right)\end{array}\right]\mathrm{\φ}\left(s\right)$

Obtain the open loop transfer function L (s) of system=K (s) G (s) according to K (s) and G (s), draw open loop Nyquist figure, judge whether to satisfy simultaneously following index request:

A, robustness require: greater than 0.5, angular frequency all is distributed in the right side of the imaginary axis to open loop Nyquist figure greater than 0.1 open-loop gain from-1 distance; B, zero phase-shift require: the ω on the Nyquist figure line _nPoint drops on the positive real axis, and maximum in the open-loop gain of this Frequency point system; C, subtract and shake performance requriements: maximum open-loop gain value 〉=13;

Last judged result according to indices is required is regulated control parameter k ₁, k ₂, k ₃, ξ, k ₄, k ₅, ω ₁, ω ₂And ω ₃Value, until satisfy index request.

The present invention can also comprise:

1, described control parameter initial value is set as respectively: ω _n=1, k ₁=2, k ₂=6/ ω _n, k ₃=2/ ω _n ², k ₄=1, ξ=0.3, k ₅=1, ω ₁=0.1, ω ₂=2, ω ₃=500.

Advantage of the present invention is:

(1) takes full advantage of the effect of rudder and stabilizer, make the two synthetic stabilizing efficiency superimposed by the zero phase-shift design to rudder and stabilizer loop, realized the dual control to system, thereby greatly strengthened the ability of shaking that subtracts of boats and ships.

(2) introducing of rudder stabilization control action has been played strong compensating action to stabilizer, has reduced the action of stabilizer when improving whole stabilizing efficiency.

(3) patent structure of the present invention is simple, is easy to realize, can the fine needs that satisfy practical engineering application.

Description of drawings

Fig. 1 is diagram of circuit of the present invention;

Fig. 2 is that rudder stabilization of the present invention loop H ∞ control algorithm is realized block diagram;

Fig. 3 is the open loop Nyquist curve of system.

The specific embodiment

For example the present invention is described in more detail below in conjunction with accompanying drawing:

In conjunction with Fig. 1～3, the present invention includes following step:

Step 1: gather the roll angle signal

And setting ship rolling resonance frequency omega _nAnd control parameter initial value;

Set the ship rolling resonance frequency omega _n=1;

Set roll angle feedback factor k in the Ship-Fin-Stabilizer Control algorithm ₁=2, angular velocity in roll feedback factor k ₂=6/ ω _n, roll angle acceleration/accel feedback factor k ₃=2/ ω _n ²

Set rudder stabilization H ∞ control algorithm medium sensitivity weight function W ₁Gain factor k ₄=1, damping ratio ξ=0.3, control sensitivity weight function W ₂Gain factor k ₅=1, corner frequency ω ₁=0.1, ω ₂=2, ω ₃=500.

Step 2: with

Be input, the adjustable parameter control algorithm of using based on zero phase-shift calculates stabilizer loop control output u ₁(t);

At first calculate control output u according to following formula ₁(t):

In the following formula

The expression angular velocity in roll,

Expression roll angle acceleration/accel.

Output u to formula (1) ₁(t) carry out Laplace transform, obtain subtracting the transfer function K that shakes the device controller _f(s),

$K_f\left(s\right)=\frac{U_1\left(s\right)}{\mathrm{\φ}\left(s\right)}=k_1+\frac{k_2}{{\mathrm{\ω}}_n}s+\frac{k_3}{{\mathrm{\ω}}_n^2}{s}^2---\left(2\right)$

φ in the following formula (s) is roll angle

Laplace transform, U ₁(s) be output u ₁(t) Laplace transform.

Control parameter k in the formula (1) (2) ₁, k ₂, k ₃To in the 4th step, regulate according to concrete boats and ships image parameter.Specifically with the rolling resonance frequency omega of boats and ships _nAs projected working point (because its dominant frequency when representing rolling), make the ω on the Nyquist figure line of system _nPoint drops on the positive real axis, and near this Frequency point, the open-loop gain of system is maximum, to guarantee that stabilizer has best stabilizing efficiency under the prerequisite that satisfies the zero phase-shift designing requirement.

Step 3: with

Be input, determine sensitivity weight function and control sensitivity weight function according to the designing requirement of zero phase-shift, then use H ∞ control algorithm and calculate rudder stabilization loop control output u ₂(t);

In order to guarantee zero phase-shift, adopt H ∞ Mixed Sensitivity S/KS problem solving rudder stabilization controller.In conjunction with Fig. 2, at first to determine the weight function in the H ∞ design, namely determine sensitivity weight function W ₁With control sensitivity weight function W ₂

According to the designing requirement of zero phase-shift, sensitivity weight function W ₁(s) be taken as

$W_1\left(s\right)=\frac{k_4{\mathrm{\ω}}_n^{2}s}{s^2+2\mathrm{\ξ}{\mathrm{\ω}}_{n}s+{\mathrm{\ω}}_n^2}---\left(3\right)$

At W ₂In establish an integral element, make the rudder stabilization controller have derivative characteristic, thereby make the rudder stabilization loop not affect course, W ₂The high band characteristic be used for the high band gain of restriction controller, finally control sensitivity weight function W ₂Be taken as

$W_2\left(s\right)=\frac{k_5(s+{\mathrm{\ω}}_1)(s+{\mathrm{\ω}}_2)}{s(s+{\mathrm{\ω}}_3)}---\left(4\right)$

Then according to weight function structure and initial control parameter value, find the solution H ∞ optimization problem, obtain the H ∞ controller K of rudder stabilization _rAnd then the Laplace transform U that obtains exporting (s), ₂(s) be,

U ₂(s)＝K _r(s)·φ(s) (5)

Pass through U at last ₂(s) carry out inverse Laplace transform, obtain u ₂(t).

Step 4: subtract according to rudder and fin and to shake object model and synthetic rudder, the open loop Nyquist characteristic of fin control action drawing system, then judge whether to satisfy index request, if do not satisfy, readjust and respectively control parameter value and return step 2, until satisfy index request.

Detailed process is as follows:

Set up rudder and fin and subtract and shake object model, will be with fin angle α (the output u that second step provides ₁(t) be the fin angle) and rudder angle δ (the output u that the 3rd step provided ₂(t) be rudder angle) for inputting rolling

For the rudder/fin combined stabilization object model of output represents with transfer function G (s),

G(s)＝[G _f(s)G _r(s)] (6)

Then with control action u ₁(t) and u ₂(t) superimposed, order

$u\left(t\right)=\left[\begin{array}{c}{u}_1\left(t\right)\\ u_2\left(t\right)\end{array}\right]---\left(7\right)$

Then its Laplace transform U (s) is,

$U\left(s\right)=\left[\begin{array}{c}{U}_1\left(s\right)\\ U_2\left(s\right)\end{array}\right]=K\left(s\right)\mathrm{\φ}\left(s\right)=\left[\begin{array}{c}{K}_f\left(s\right)\\ K_r\left(s\right)\end{array}\right]\mathrm{\φ}\left(s\right)---\left(8\right)$

Ask the open loop transfer function L (s) of system=K (s) G (s) according to K (s) and G (s), draw open loop Nyquist figure, judge whether to satisfy following index request: (1) robustness requires: open loop Nyquist figure is away from-1 point, and principal particulars all is distributed in the right side of the imaginary axis; (2) zero phase-shift requires: the ω on the Nyquist figure line _nPoint drops on the positive real axis, and maximum in the open-loop gain of this Frequency point system; (3) subtract and shake performance requriements: maximum open-loop gain value 〉=13, so that the wave of dominant frequency at resonant frequency point disturbed, subtracting the rate of shaking will reach about 90%.

Last judged result according to indices is required is regulated control parameter k ₁, k ₂, k ₃, ξ, k ₄, k ₅, ω ₁, ω ₂And ω ₃Value, until satisfy index request.

Certain captain L=142m, beam B=19.06m, Mean Draft T=6.15m, rolling resonance frequency omega _n=0.8rad/s.

Final control parameter is k1=0.5, k2=1.5, k3=0.5, ξ=0.1, k4=3, k5=8, ω ₁=0.3, ω ₂=2.4 and ω ₃=1000.Fig. 3 is the Nyquist characteristic of system, and verification is satisfied the robustness requirement as can be known, and zero phase-shift requires and subtract to shake performance requriements.

Claims (2)

1. the rudder and fin based on dual H∞ control design subtracts the method for shaking, and it is characterized in that:

(1) gathers the roll angle signal

Set the ship rolling resonance frequency omega _nAnd control parameter initial value, comprise roll angle feedback factor k ₁, angular velocity in roll feedback factor k ₂, roll angle acceleration/accel feedback factor k ₃, sensitivity weight function W ₁Gain factor k ₄, damping ratio ξ, control sensitivity weight function W ₂Gain factor k ₅, corner frequency ω ₁, ω ₂, ω ₃

(2) with

Be input, the adjustable parameter control algorithm of using based on zero phase-shift calculates stabilizer loop control output u ₁(t):

Calculate control output u according to following formula ₁(t):

In the following formula

The expression angular velocity in roll, Expression roll angle acceleration/accel;

To u ₁(t) carry out Laplace transform, obtain subtracting the transfer function K that shakes the device controller _f(s):

$K_f\left(s\right)=\frac{U_1\left(s\right)}{\mathrm{\φ}\left(s\right)}=k_1+\frac{k_2}{{\mathrm{\ω}}_n}s+\frac{k_3}{{\mathrm{\ω}}_n^2}{s}^2,$

φ in the following formula (s) is roll angle Laplace transform, U ₁(s) be output u ₁(t) Laplace transform;

(3) with

Be input, determine sensitivity weight function and control sensitivity weight function according to the designing requirement of zero phase-shift, then use H ∞ control algorithm and calculate rudder stabilization loop control output u ₂(t):

Adopt H ∞ Mixed Sensitivity S/KS problem solving rudder stabilization controller, determine the weight function in the H ∞ design, namely determine sensitivity weight function W ₁With control sensitivity weight function W ₂:

Sensitivity weight function W ₁(s) be taken as:

$W_1\left(s\right)=\frac{k_4{\mathrm{\ω}}_n^{2}s}{s^2+2\mathrm{\ξ}{\mathrm{\ω}}_{n}s+{\mathrm{\ω}}_n^2},$

Control sensitivity weight function W ₂Be taken as:

$W_2\left(s\right)=\frac{k_5(s+{\mathrm{\ω}}_1)(s+{\mathrm{\ω}}_2)}{s(s+{\mathrm{\ω}}_3)},$

According to weight function structure and initial control parameter value, find the solution H ∞ optimization problem, obtain the H ∞ controller K of rudder stabilization _rAnd then the Laplace transform U that obtains exporting (s), ₂(s) be:

U ₂(s)＝K _r(s)·φ(s)，

To U ₂(s) carry out inverse Laplace transform, obtain u ₂(t);

(4) according to the open loop Nyquist characteristic of rudder, fin control output drawing system, then judge whether to satisfy index request, if do not satisfy, readjust and respectively control parameter value and return step (2), until satisfy index request:

Setting up rudder and fin and subtract and shake object model, will be u with fin angle α ₁(t) and rudder angle δ to be u2 (t) be input, roll angle

For the rudder/fin combined stabilization object model of output represents with transfer function G (s):

G(s)＝[G _f(s) G _r(s)]，

Then with control action u ₁(t) and u ₂(t) superimposed, order

$u\left(t\right)=\left[\begin{array}{c}{u}_1\left(t\right)\\ u_2\left(t\right)\end{array}\right],$

Then its Laplace transform U (s) is,

$U\left(s\right)=\left[\begin{array}{c}{U}_1\left(s\right)\\ U_2\left(s\right)\end{array}\right]=K\left(s\right)\mathrm{\φ}\left(s\right)=\left[\begin{array}{c}{K}_f\left(s\right)\\ K_r\left(s\right)\end{array}\right]\mathrm{\φ}\left(s\right)$

Obtain the open loop transfer function L (s) of system=K (s) G (s) according to K (s) and G (s), draw open loop Nyquist figure, judge whether to satisfy simultaneously following index request:

A, robustness require: greater than 0.5, angular frequency all is distributed in the right side of the imaginary axis to open loop Nyquist figure greater than 0.1 open-loop gain from-1 distance; B, zero phase-shift require: the ω on the Nyquist figure line _nPoint drops on the positive real axis, and maximum in the open-loop gain of this Frequency point system; C, subtract and shake performance requriements: maximum open-loop gain value 〉=13;

Last judged result according to indices is required is regulated control parameter k ₁, k ₂, k ₃, ξ, k ₄, k ₅, ω ₁, ω ₂And ω ₃Value, until satisfy index request.

2. a kind of rudder and fin based on dual H∞ control design according to claim 1 subtracts the method for shaking, and it is characterized in that: described control parameter initial value is set as respectively: ω _n=1, k ₁=2, k ₂=6/ ω _n, k ₃=2/ ω _n ², k ₄=1, ξ=0.3, k ₅=1, ω ₁=0.1, ω ₂=2, ω ₃=500.

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