CN103935480B - A kind of rudder stabilization method based on analytic modell analytical model Predictive control design - Google Patents

Abstract

The invention belongs to Marine engineering, control science and control engineering field, relating to a kind of rudder stabilization method based on analytic modell analytical model Predictive control design.The present invention includes: obtain each term coefficient of control object；Gather roll angle signal；Obtain angular velocity in roll signal；Setting controller initial parameter values.The present invention takes full advantage of the boundedness of indeterminate, in conjunction with analytic modell analytical model PREDICTIVE CONTROL, efficiently solves the Parameter uncertainties sex chromosome mosaicism of rudder stabilization control system, and the method provided is compared additive method, is improved on anti-rolling efficiency.Present configuration is simple, it is easy to accomplish, the needs of practical engineering application can be met very well.

Description

A kind of rudder stabilization method based on analytic modell analytical model Predictive control design

Technical field

The invention belongs to Marine engineering, control science and control engineering field, relating to a kind of based on analytic modell analytical model Predictive control design Rudder stabilization method.

Background technology

Owing to ship rolling motion damping is the least so that boats and ships can produce violent rolling in stormy waves, excessive rolling can be to ship Oceangoing ship navigation performance and security bring the biggest impact, for ensureing that boats and ships are in complicated sea situation safe navigation, rudder roll damping technology conduct A kind of Novel control thought, the most at home and abroad has been a great concern, and carries out the design of stabilizer with rudder, Simple and convenient, cheap, therefore, rudder stabilization technology is an important subject in ship motion controller field.

At present for the control of rudder roll damping system, there is certain research both at home and abroad, but not yet find analytic application model prediction Control to carry out document and the patent achievement of rudder stabilization design.

Owing to being nonlinear on boats and ships motion essence, knowable to boats and ships movement environment and displacement feature, its accurate mathematics Model is difficult to obtain, and causes model parameter to have uncertainty, thus, rudder rollstabilization controller should be based on non-linear control Theory processed designs, and must have the robustness to model parameter perturbation.Rudder rollstabilization controls to require at nonlinear model Having the rolling motion suppression under Parameter uncertainties premise caused wave, rudder roll damping shakes controller design and must is fulfilled for model The robustness of Parameter Perturbation.But traditional PI D, LQG control algolithm, it is impossible to effectively process model nonlinear and parameter uncertainty Problem.Analytic modell analytical model PREDICTIVE CONTROL proposes for nonlinear model, have be prone to modeling, response rapidly, control performance relatively Good, strong robustness and the feature such as logical construction is simple, but analytic modell analytical model PREDICTIVE CONTROL in most instances, only solves to determine at present Property nominal system control problem, for this for nonlinear system model Parameter uncertainties sex chromosome mosaicism, propose one and improve and resolve mould Type forecast Control Algorithm.First, redefined into indeterminate nominal system model, based on analytic modell analytical model PREDICTIVE CONTROL Theoretical carry out theory deduction to redefining nominal model, obtain the control law containing indeterminate.Due to control law bounded, take Its boundary value, eliminates the indeterminate in controller from theory deduction, effectively solves the parameter uncertainty in model Problem.

Rudder rollstabilization control system is only capable of measuring boats and ships roll angle, must introduce state during analytic application model predictive control method Observer is to obtain the rollrate information that controller needs.Compare other observers, the stability of High-gain observer and essence Degree has theoretical guarantee, calculates easy parameter few, and parameter is once selected, it is not necessary to adjust.Due in High-gain observer design process Partial function need to meet Local Lipschitz condition, and such rudder roll damping controls finally to provide it and meets design High-gain observer Required condition, proves herein to provide its detailed proof needing to meet condition, provides foundation for its application.The program is without state Can survey, directly obtain observation by state observer, solve angular velocity in roll and can not survey problem.

Summary of the invention

It is an object of the invention to provide can the ship based on analytic modell analytical model Predictive control design of the effective Parameter Perturbation of inhibition Oceangoing ship rudder stabilization method.

The object of the present invention is achieved like this:

Rudder stabilization method based on analytic modell analytical model Predictive control design includes:

(1) each term coefficient of control object is obtained, including a₁, a₂, a₃, a₄, b and corresponding by the speed of a ship or plane and transverse metacentric height The boundary value m of the indeterminate that change causes_i(i=1,2,3,4), b₁, control object is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=(a_1+\mathrm{\Δ}{a}_1)x_2+(a_2+\mathrm{\Δ}{a}_2)\left|x_2\right|x_2+(a_3+\mathrm{\Δ}{a}_3)x_1+(a_4+\mathrm{\Δ}{a}_4)x_1^3+(b+\mathrm{\Δb})u+w\end{array}\right.,$

$a_1=-\frac{K_p}{I_{\mathrm{xx}}+J_{\mathrm{xx}}},a_2=-\frac{K_{\mathrm{pp}}}{I_{\mathrm{xx}}+J_{\mathrm{xx}}},a_3=-\frac{W\·\mathrm{GM}}{I_{\mathrm{xx}}+J_{\mathrm{xx}}},a_4=\frac{W\·\mathrm{GM}}{I_{\mathrm{xx}}+J_{\mathrm{xx}}},$

$b=-I_{\mathrm{\δz}}{U}^2{Y}_{\mathrm{\δyy}}/(I_{\mathrm{xx}}+J_{\mathrm{xx}}),I_{\mathrm{xx}}+J_{\mathrm{xx}}=\frac{W}{g}{\left[(0.3085+0.0227B/d-0.0043L/100)B\right]}^2,$

K_pp=3k_b(I_xx+J_xx)/4, k_a、k_bFor attenuation coefficient with ship type, and row The water yield is relevant, and W is displacement, and GM is that transverse stability is high, and B is the beam, and d is draft, and L is captain, and g is gravity Acceleration；

(2) roll angle signal is gathered

(3) angular velocity in roll signal is obtainedTake High-gain observer gain p^-1(θ)C₀ ^T=[2 θ, θ²]^T, setup parameter θ value； High-gain observer state is:

$\left\{\begin{array}{c}\stackrel{\stackrel{\·}{\‾}}{x}=\left[\begin{array}{cc}0& 1\\ a_3+\mathrm{\Δ}{a}_3& a_1+\mathrm{\Δ}{a}_1\end{array}\right]\stackrel{\‾}{x}+\left[\begin{array}{c}0\\ 1\end{array}\right](b+\mathrm{\Δb})u+(a_2+\mathrm{\Δ}{a}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_4+\mathrm{\Δ}{a}_4){\stackrel{\‾}{x}}_1^3-p^{-1}\left(\mathrm{\θ}\right)C^T(\stackrel{\‾}{y}-y)\\ \stackrel{\‾}{y}=\left[\begin{array}{c}1\\ 0\end{array}\right]\stackrel{\‾}{x}\end{array}\right.$

Wherein, "-" represents observation,For nonlinear terms, p^-1(θ)C₀ ^T=[2 θ, θ²]^T, having observer system is:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\·}{\‾}}{x}}_1={\stackrel{\‾}{x}}_2-2\mathrm{\θ\ϵ}\\ {\stackrel{\stackrel{\·}{\‾}}{x}}_2=(a_1+\mathrm{\Δ}{a}_1){\stackrel{\‾}{x}}_2+(a_2+\mathrm{\Δ}{a}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_3+\mathrm{\Δ}{a}_3){\stackrel{\‾}{x}}_1(a_4+\mathrm{\Δ}{a}_4){\stackrel{\‾}{x}}_1^3+(b+\mathrm{\Δb})u_r\left(\stackrel{\‾}{x}\right)-{\mathrm{\θ}}^2\mathrm{\ϵ}\\ \mathrm{\ϵ}=\stackrel{\‾}{y}-y\end{array}\right.;$

(4) setting controller initial parameter values k₁, k₂, to expect roll angleRoll angleAnd angular velocity in rollFor input letter Number, calculate the control output u in rudder stabilization loop₁,

$u_1\left(\stackrel{\‾}{x}\right)=-\frac{1}{b\±b_1}(k_0{\stackrel{\‾}{x}}_1+k_1{\stackrel{\‾}{x}}_2+(a_1\±m_1){\stackrel{\‾}{x}}_2+(a_2\±m_2)|{\stackrel{\‾}{x}}_2|{\stackrel{\‾}{x}}_2+(a_3\±m_3){\stackrel{\‾}{x}}_1+(a_4\±m_4){\stackrel{\‾}{x}}_1^3),$ Obtain Rudder rollstabilization control system based on analytic modell analytical model Predictive control design is:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\·}{\‾}}{x}}_1={\stackrel{\‾}{x}}_2-2\mathrm{\θ\ϵ}\\ {\stackrel{\stackrel{\·}{\‾}}{x}}_2=(a_1+\mathrm{\Δ}{a}_1){\stackrel{\‾}{x}}_2+(a_2+\mathrm{\Δ}{a}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_3+\mathrm{\Δ}{a}_3){\stackrel{\‾}{x}}_1+(a_4+\mathrm{\Δ}{a}_4){\stackrel{\‾}{x}}_1^3+(b+\mathrm{\Δb})u_r\left(\stackrel{\‾}{x}\right)+w-{\mathrm{\θ}}^2\mathrm{\ϵ}\\ u_1\left(\stackrel{\‾}{x}\right)=-\frac{1}{b\±b_1}(k_0{\stackrel{\‾}{x}}_1+k_1{\stackrel{\‾}{x}}_2+(a_1\±m_1){\stackrel{\‾}{x}}_2+(a_2\±m_2)|{\stackrel{\‾}{x}}_2|{\stackrel{\‾}{x}}_2+(a_3\±m_3){\stackrel{\‾}{x}}_1+(a_4\±m_4){\stackrel{\‾}{x}}_1^3)\\ \mathrm{\ϵ}=\stackrel{\‾}{y}-y\end{array}\right.,$

Wherein:For the observation of x,

Predictive controller initial value design, it was predicted that cycle T₁=60s, controls order l=4, observer parameter θ=3, and controller is joined Number k₀=0.05, k₁=0.375.

The beneficial effects of the present invention is:

(1) take full advantage of the boundedness of indeterminate, in conjunction with analytic modell analytical model PREDICTIVE CONTROL, efficiently solve rudder stabilization control system Parameter uncertainties sex chromosome mosaicism.

(2) method provided by the present invention compares additive method, is improved on anti-rolling efficiency.

(3) patent structure of the present invention is simple, it is easy to accomplish, the needs of practical engineering application can be met very well.

Accompanying drawing explanation

The workflow diagram of a kind of rudder stabilization method based on analytic modell analytical model Predictive control design of Fig. 1,

The composition frame chart of Fig. 2 actual boats and ships rudder roll damping control system based on analytic modell analytical model Predictive control design,

Rolling motion and rudder angle Output simulation figure under Fig. 3 proposed analytic modell analytical model PREDICTIVE CONTROL.

Detailed description of the invention

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

A kind of rudder stabilization method based on analytic modell analytical model Predictive control design of the present invention, including:

(1) each term coefficient of control object is obtained, including a₁, a₂, a₃, a₄, b and the boundary value of corresponding indeterminate m_i(i=1,2,3,4), b₁。

The mathematic(al) representation of control object:

WhereinFor the moment of inertia of rolling,For roll-damping moment,For rolling righting moment,For roll angle,For Angular velocity in roll,For roll angle acceleration, K_R=-I_δzU²Y_δyyδ, K_DFor wave disturbance moment. $I_{\mathrm{xx}}+J_{\mathrm{xx}}=\frac{W}{g}{\left[(0.3085+0.0227B/d-0.0043L/100)B\right]}^2,K_p=2k_a\sqrt{W\·\mathrm{GM}\·(I_{\mathrm{xx}}+J_{\mathrm{xx}})}/\mathrm{\π},$ K_pp=3k_b(I_xx+J_xx)/4, k_a、k_bFor attenuation coefficient with ship type, and displacement is relevant.W is displacement, and GM is horizontal steady Property high, B is the beam, and d is draft, and L is captain, and g is acceleration of gravity,For the flooding angle of boats and ships, U is boat Speed, δ rudder angle.

Formula (1) is expressed as state space form

$\left\{\begin{array}{c}\stackrel{\·}{x}=f\left(x\right)+g\left(x\right)u+w\\ y=h\left(x\right)\end{array}\right.---\left(2\right)$

Wherein, $f\left(x\right)=\left[\begin{array}{c}{x}_2\\ a_1{x}_2+a_2\left|x_2\right|x_2+a_3{x}_1+a_4{x}_1^3\end{array}\right],$ G (x)=b, h (x)=x₁, w is sea Wave disturbance, a₁, a₂, a₃, a₄For the known coefficient calculated.

Wherein, $a_1=-\frac{K_p}{I_{\mathrm{xx}}+J_{\mathrm{xx}}},a_2=-\frac{K_{\mathrm{pp}}}{I_{\mathrm{xx}}+J_{\mathrm{xx}}},a_3=-\frac{W\·\mathrm{GM}}{I_{\mathrm{xx}}+J_{\mathrm{xx}}},a_4=\frac{W\·\mathrm{GM}}{I_{\mathrm{xx}}+J_{\mathrm{xx}}},$

B=-I_δzU²Y_δyy/(I_xx+J_xx)。

And owing to speed and initial metacentric height change cause the variable quantity of coefficient be: Δ a₁, Δ a₂, Δ a₃, Δ a₄, Δ b, these The change of amount typically can not accurately be obtained, but can be designated as: m with its maximum value of pre-estimation_iAnd b (i=1,2,3,4)₁。

To illuminated (2), then show that the uncertain nonlinear system of rudder rollstabilization is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=(a_1+\mathrm{\Δ}{a}_1)x_2+(a_2+\mathrm{\Δ}{a}_2)\left|x_2\right|x_2+(a_3+\mathrm{\Δ}{a}_3)x_1+(a_4+\mathrm{\Δ}{a}_4)x_1^3+(b+\mathrm{\Δb})u+w\\ y=h\left(x\right)\end{array}\right.---\left(3\right)$

Being certain cargo ship herein, the parameters of this ship is given by table 1.

The each parameter of table 1 ship model

The initial speed of a ship or plane is 10m/s, and a height of 0.776m of initial horizontal stability can be calculated each term coefficient of model, it is assumed that ship's speed by table 1 Changing between (0.5U, 1.5U), and initial metacentric height is also between (0.5GM, 1.5GM) during change, we can be with pre-estimation model system The maximum value of number variable quantity is shown in Table 2.

Table 2 rudder stabilization equation of motion coefficient and index variation amount

(2) roll angle signal is gatheredRoll angle signal is gathered by compass.

(3) angular velocity in roll signal is obtainedTake High-gain observer gain p^-1(θ)C₀ ^T=[2 θ, θ²]^T, setup parameter θ value. Take High-gain observer state equation as follows:

$\left\{\begin{array}{c}\stackrel{\stackrel{\·}{\‾}}{x}=A\stackrel{\‾}{x}+\mathrm{Bb}\left(\stackrel{\‾}{x}\right)u+\mathrm{\φ}\left(\stackrel{\‾}{x}\right)-p^{-1}\left(\mathrm{\θ}\right)C^T(\stackrel{\‾}{y}-y)\\ \stackrel{\‾}{y}=C\stackrel{\‾}{x}\end{array}\right.---\left(4\right)$

Wherein, "-" represents observation,For nonlinear terms, p (θ) is defined as non trivial solution:

0=-θ p (θ)-(A^Tp(θ)+p(θ)A)+C^TC (5)

By the state equation that formula (3) is write as shape such as formula (4) it is:

$\left\{\begin{array}{c}\stackrel{\stackrel{\·}{\‾}}{x}=\left[\begin{array}{cc}0& 1\\ a_3+\mathrm{\Δ}{a}_3& a_1+\mathrm{\Δ}{a}_1\end{array}\right]\stackrel{\‾}{x}+\left[\begin{array}{c}0\\ 1\end{array}\right](b+\mathrm{\Δb})u+(a_2+\mathrm{\Δ}{a}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_4+\mathrm{\Δ}{a}_4){\stackrel{\‾}{x}}_1^3-p^{-1}\left(\mathrm{\θ}\right)C^T(\stackrel{\‾}{y}-y)\\ \stackrel{\‾}{y}=\left[\begin{array}{c}1\\ 0\end{array}\right]\stackrel{\‾}{x}\end{array}\right.---\left(6\right)$

Wherein, p^-1(θ)C₀ ^T=[C_n ¹θ,C_n ²θ²,…,C_n ⁿθⁿ]^T。

Due to p herein^-1(θ)C₀ ^T=[2 θ, θ²]^T, formula (6) is expressed as:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\·}{\‾}}{x}}_1={\stackrel{\‾}{x}}_2-2\mathrm{\θ\ϵ}\\ {\stackrel{\stackrel{\·}{\‾}}{x}}_2=(a_1+\mathrm{\Δ}{a}_1){\stackrel{\‾}{x}}_2+(a_2+\mathrm{\Δ}{a}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_3+\mathrm{\Δ}{a}_3){\stackrel{\‾}{x}}_1(a_4+\mathrm{\Δ}{a}_4){\stackrel{\‾}{x}}_1^3+(b+\mathrm{\Δb})u_r\left(\stackrel{\‾}{x}\right)-{\mathrm{\θ}}^2\mathrm{\ϵ}\\ \mathrm{\ϵ}=\stackrel{\‾}{y}-y\end{array}\right.---\left(7\right)$

Angular velocity in roll signal can be obtained by formula (7)Information.

(4) setting controller initial parameter values k₁, k₂, withAndFor input signal, analytic application Model Predictive Control Control algolithm thought, does not consider in model in the presence of indeterminate, the control output u in calculating rudder stabilization loop:

$u=-\frac{1}{b}(k_0{\stackrel{\‾}{x}}_1+k_1{\stackrel{\‾}{x}}_2+a_1{\stackrel{\‾}{x}}_2+a_2|{\stackrel{\‾}{x}}_2|{\stackrel{\‾}{x}}_2+a_3{\stackrel{\‾}{x}}_1+a_4{\stackrel{\‾}{x}}_1^3)---\left(8\right)$

Due to existence and the bounded of indeterminate, the analytic modell analytical model predictive control algorithm that application improves the most further, process the most true Obtain after determining item controlling output u₁:

$u_1\left(\stackrel{\‾}{x}\right)=-\frac{1}{b\±b_1}(k_0{\stackrel{\‾}{x}}_1+k_1{\stackrel{\‾}{x}}_2+(a_1\±m_1){\stackrel{\‾}{x}}_2+(a_2\±m_2)|{\stackrel{\‾}{x}}_2|{\stackrel{\‾}{x}}_2+(a_3\±m_3){\stackrel{\‾}{x}}_1+(a_4\±m_4){\stackrel{\‾}{x}}_1^3)---\left(9\right)$

Rudder rollstabilization control system based on analytic modell analytical model Predictive control design can be obtained by formula (3), (7), (9) be:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\·}{\‾}}{x}}_1={\stackrel{\‾}{x}}_2-2\mathrm{\θ\ϵ}\\ {\stackrel{\stackrel{\·}{\‾}}{x}}_2=(a_1+\mathrm{\Δ}{a}_1){\stackrel{\‾}{x}}_2+(a_2+\mathrm{\Δ}{a}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_3+\mathrm{\Δ}{a}_3){\stackrel{\‾}{x}}_1+(a_4+\mathrm{\Δ}{a}_4){\stackrel{\‾}{x}}_1^3+(b+\mathrm{\Δb})u_r\left(\stackrel{\‾}{x}\right)+w-{\mathrm{\θ}}^2\mathrm{\ϵ}\\ u_1\left(\stackrel{\‾}{x}\right)=-\frac{1}{b\±b_1}(k_0{\stackrel{\‾}{x}}_1+k_1{\stackrel{\‾}{x}}_2+(a_1\±m_1){\stackrel{\‾}{x}}_2+(a_2\±m_2)|{\stackrel{\‾}{x}}_2|{\stackrel{\‾}{x}}_2+(a_3\±m_3){\stackrel{\‾}{x}}_1+(a_4\±m_4){\stackrel{\‾}{x}}_1^3)\\ \mathrm{\ϵ}=\stackrel{\‾}{y}-y\end{array}\right.---\left(10\right)$

Wherein, it is consistent that ± symbol chooses corresponding previous item symbol.

The design of Nonlinear Analytical Model Predictive Control controller realizes eliminating the indeterminate in controller from theory deduction, complete Become rudder rollstabilization to improve the design of Nonlinear Analytical model predictive controller, be specially

A) the analytic modell analytical model PREDICTIVE CONTROL rule containing indeterminate.

Formula (2) with indeterminate is converted to:

$\left\{\begin{array}{c}\stackrel{\·}{x}=f^{*}\left(x\right)+g^{*}\left(x\right)u\\ y=h\left(x\right)\end{array}\right.---\left(11\right)$

Wherein, f^*(x)=f (x)+Δ f (x), g^*(x)=g (x)+Δ g (x).Without loss of generality, it is assumed that the equalization point x of system (11)^o, There is f^*(x^o)=0, g^*(x^o) ≠ 0, h (x^o)=0, formula (11) is called the nominal model under redefining.

The performance function of the rolling time horizon of system (11) is:

$J=\frac{1}{2}{\∫}_0^{T_1}{(\hat{y}(t+\mathrm{\τ})-{\hat{y}}_d(t+\mathrm{\τ}))}^T(\hat{y}(t+\mathrm{\τ})-{\hat{y}}_d(t+\mathrm{\τ}))\mathrm{d\τ}---\left(12\right)$

Wherein,WithIt is respectively output and reference signal at [t, t+T₁] predicted value, τ ∈ [0, T₁], T₁For in advance The survey cycle.

System (11) is described as in the PREDICTIVE CONTROL problem of t:

$\left\{\begin{array}{c}\stackrel{\·}{x}=f^{*}\left(\hat{x}(t+\mathrm{\τ})\right)+g^{*}\left(\hat{x}(t+\mathrm{\τ})\right)\hat{u}(t+\mathrm{\τ})\\ y=h\left(\hat{x}(t+\mathrm{\τ})\right)\end{array}\right.---\left(13\right)$

State variableInitial value give be:

$\hat{x}\left(t\right)=x\left(t\right)---\left(14\right)$

Actual control lawInitial value, it may be assumed that

$u\left(t\right)=\hat{u}(t+\mathrm{\τ}),\mathrm{\τ}=0---\left(15\right)$

Obtain based on analytic modell analytical model PREDICTIVE CONTROL thought:

${L_{f^{*}}}^{\mathrm{\ρ}}h\left(x\right)+L_{g^{*}}{L_{f^{*}}}^{\mathrm{\ρ}-1}h\left(x\right)\hat{u}{\left(t\right)}^{*}-{y_d}^{\left[\mathrm{\ρ}\right]}+K{M}_{\mathrm{\ρ}}=0---\left(16\right)$

Wherein, K=[k₀,k₁,…,k_ρ-1] represent matrix Γ_ll ^-1Γ_ρl ^TThe first row element, by predetermined period T₁, control order l and Degree of correlation ρ determines,For optimal control law.

${\mathrm{\Γ}}_{(i,j)}=\frac{T_1^{i+j-1}}{(i-1)!(j-1)!(i+j-1)},i,j=1,...,\mathrm{\ρ}+l+1---\left(19\right)$

By formula (16), the optimal control law of the analytic modell analytical model PREDICTIVE CONTROL with indeterminate can be obtained:

$u\left(t\right)={\hat{u}}^{*}\left(t\right)=-{\left(L_{g^{*}}{L}_{f^{*}}^{\mathrm{\ρ}-1}h\left(x\right)\right)}^{-1}\·\{\underset{i=0}{\overset{\mathrm{\ρ}-1}{\mathrm{\Σ}}}{k}_i(L_{f^{*}}^{i}h\left(x\right)-y_d^{\left[i\right]}\left(t\right))+L_{f^{*}}^{\mathrm{\ρ}}h\left(x\right)-y_d^{\left[\mathrm{\ρ}\right]}\left(t\right)\}---\left(20\right)$

B) indeterminate in control law is eliminated.

From formula (11):

$\begin{array}{c}\left|\right|f^{*}\left(x\right)\left|\right|=\left|\right|f\left(x\right)+\mathrm{\Δf}\left(x\right)\\ \≤\left|\right|f\left(x\right)\left|\right|+\underset{i=0}{\overset{p}{\mathrm{\Σ}}}{m}_i{\left|\right|x\left|\right|}^i\end{array}---\left(21\right)$

Then know f^*(x) bounded, and remember

$\begin{array}{c}\left|\right|g^{*}\left(x\right)\left|\right|=\left|\right|g\left(x\right)+\mathrm{\Δg}\left(x\right)\left|\right|\\ \≤\left|\right|g\left(x\right)\left|\right|+b_1\end{array}---\left(22\right)$

Then know g^*(x) bounded.Have again:

$\begin{array}{c}\left|\right|L_{f^{*}}^{k}h\left(x\right)\left|\right|=\left|\right|L_f^{k}h\left(x\right)+L_{\mathrm{\Δf}}^{k}h\left(x\right)\\ \≤\left|\right|L_f^{k}h\left(x\right)\left|\right|+\left|\right|L_{f_d}^{k}h\left(x\right)\left|\right|\end{array}---\left(23\right)$

$\begin{array}{c}\left|\right|L_{g^{*}}{L}_{f^{*}}^{k}h\left(x\right)\left|\right|=\left|\right|L_g{L}_f^{k}h\left(x\right)+L_{\mathrm{\Δg}}{L}_f^{k}h\left(x\right)+L_g{L}_{\mathrm{\Δf}}^{k}h\left(x\right)+L_{\mathrm{\Δg}}{L}_{\mathrm{\Δf}}^{k}h\left(x\right)\left|\right|\\ \≤\left|\right|L_g{L}_f^{k}h\left(x\right)\left|\right|+b_1\left|\right|\frac{\∂\left(L_f^{k}h\left(x\right)\right)}{\∂x}\left|\right|+\left|\right|L_g{L}_{f_d}^{k}h\left(x\right)\left|\right|+b_1\left|\right|\frac{\∂\left(L_{f_d}^{k}h\left(x\right)\right)}{\∂x}\left|\right|\end{array}---\left(24\right)$

From formula (23), (24)WithAll bounded,Boundary value:

$L_{f^{*}}^{k}h\left(x\right)=L_f^{k}h\left(x\right)+L_{\±f_d}^{k}h\left(x\right)---\left(25\right)$

Wherein, formula (25) place ± symbol chooses identical with f (x) respective items.

$L_{g^{*}}{L}_{f^{*}}^{k}h\left(x\right)$ Boundary value:

$L_{g^{*}}{L}_{f^{*}}^{k}h\left(x\right)=L_g{L}_f^{k}h\left(x\right)\±b_1\frac{\∂\left(L_f^{k}h\left(x\right)\right)}{\∂x}+L_g{L}_{\±f_d}^{k}h\left(x\right)\±b_1\frac{\∂\left(L_{\±f_d}^{k}h\left(x\right)\right)}{\∂x}---\left(26\right)$

Wherein, formula (26) b₁Before Xiang ± symbol is identical with g (x), containing f_dSymbol before Xiang is identical with f (x) respective items.

To sum up, it is known that u (t) bounded, u is taken₁For its boundary value, obtain the rudder roll damping analytic modell analytical model predictive controller improved:

$u_1=-\frac{1}{b\±b_1}(k_0{x}_1+k_1{x}_2+(a_1\±m_1)x_2+(a_2\±m_2)|x_2|x_2+(a_3\±m_3)x_1+(a_4\±m_4)x_1^3)---\left(27\right)$

Wherein, it is consistent that ± symbol chooses corresponding previous item symbol.

In conjunction with the analytic modell analytical model Predictive control law of High-gain observer and improvement, rudder rollstabilization control system is:

$\left\{\begin{array}{c}{\stackrel{\stackrel{\·}{\‾}}{x}}_1={\stackrel{\‾}{x}}_2-2\mathrm{\θ\ϵ}\\ {\stackrel{\stackrel{\·}{\‾}}{x}}_2=(a_1+\mathrm{\Δ}{a}_1){\stackrel{\‾}{x}}_2+(a_2+\mathrm{\Δ}{a}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_3+\mathrm{\Δ}{a}_3){\stackrel{\‾}{x}}_1+(a_4+\mathrm{\Δ}{a}_4){\stackrel{\‾}{x}}_1^3+(b+\mathrm{\Δb})u_r\left(\stackrel{\‾}{x}\right)+w-{\mathrm{\θ}}^2\mathrm{\ϵ}\\ u_1\left(\stackrel{\‾}{x}\right)=-\frac{1}{b\±b_1}(k_0{\stackrel{\‾}{x}}_1+k_1{\stackrel{\‾}{x}}_2+(a_1\±m_1){\stackrel{\‾}{x}}_2+(a_2\±m_2)|{\stackrel{\‾}{x}}_2|{\stackrel{\‾}{x}}_2+(a_3\±m_3){\stackrel{\‾}{x}}_1+(a_4\±m_4){\stackrel{\‾}{x}}_1^3)\\ \mathrm{\ϵ}=\stackrel{\‾}{y}-y\end{array}\right.---\left(28\right)$

Wherein, u_rFor controller output actual rudder angle after steering wheel actuator.

This controller can the Parameter Perturbation of effective inhibition.The one that the present invention proposes is based on analytic modell analytical model Predictive control design Rudder stabilization method clear thinking, step is complete, be prone to Project Realization.Meanwhile, according to according to Louth-Hall dimension thatch criterion reason Opinion understands, Louth-Hall dimension thatch criterion the k meeting span determined_iCan ensure that closed-loop system is stable.

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

Step one: calculate each term coefficient of control object.Including a₁, a₂, a₃, a₄, b and corresponding by the speed of a ship or plane and horizontal steady The boundary value m of the indeterminate that property height change causes_i(i=1,2,3,4), b₁.Control object is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=(a_1+\mathrm{\Δ}{a}_1)x_2+(a_2+\mathrm{\Δ}{a}_2)\left|x_2\right|x_2+(a_3+\mathrm{\Δ}{a}_3)x_1+(a_4+\mathrm{\Δ}{a}_4)x_1^3+(b+\mathrm{\Δb})u+w\end{array}\right.$

Step 2: gathered roll angle signal by compass

Step 3: obtain angular velocity in roll signal by High-gain observer

Step 4: to expect that roll angle, roll angle and angular velocity in roll, as input signal, are input to by the pre-observing and controlling of analytic modell analytical model Controller designed by algorithm processed, it is thus achieved that control rudder angle, then be input in steering wheel actuator by this rudder angle, exports actual rudder angle, Actual rudder angle is input in control object obtain roll angle information again, judges whether to meet control by the gained roll angle value of information Effect requirements, regulates controller parameter k₁, k₂, until the control good results of output.

The present invention is to be accepted expectation roll angle information, high-gain observation by the analytic modell analytical model predictive controller of rudder rollstabilization system The system output roll angle information that device information and compass obtain, through computing output order rudder angle, steering wheel actuator refers to according to rudder angle Order output actual rudder angle records and inputs to high increasing to hull, the roll angle that boats and ships suppression produces, the roll angle of output via compass Benefit observer and controller, be thusly-formed closed-loop control system, as shown in Figure 2.

Accordingly, herein as a example by certain ship, predetermined period T is chosen₁=60s, controls order l=4, observer parameter θ=3, control Device parameter k processed₀=0.05, k₁=0.375, there iing adopted wave height to be 3m, wave encounter angle is 90 °, and wave period is under the sea situation of 8s, Provide before and after analytic modell analytical model PREDICTIVE CONTROL rolling motion and rudder angle Output simulation figure as shown in Figure 3.

Claims (2)

1. a rudder stabilization method based on analytic modell analytical model Predictive control design, it is characterised in that:

(1) each term coefficient of control object is obtained, including a₁, a₂, a₃, a₄, b and corresponding by the speed of a ship or plane and transverse metacentric height The boundary value m of the indeterminate that change causes_i(i=1,2,3,4), b₁, control object is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=(a_1+{\mathrm{\Δa}}_1)x_2+(a_2+{\mathrm{\Δa}}_2)\left|x_2\right|x_2+(a_3+{\mathrm{\Δa}}_3)x_1+(a_4+{\mathrm{\Δa}}_4)x_1^3+(b+\mathrm{\Δ}b)u+w\end{array}\right.,$

$a_1=-\frac{K_p}{I_{xx}+J_{xx}},a_2=-\frac{K_{pp}}{I_{xx}+J_{xx}},a_3=-\frac{W\·GM}{I_{xx}+J_{xx}},a_4=\frac{W\·GM}{I_{xx}+J_{xx}},$

B=-I_δzU²Y_δyy/(I_xx+J_xx),

K_pp=3k_b(I_xx+J_xx)/4, k_a、k_bFor attenuation coefficient with ship type and draining Measuring relevant, W is displacement, and GM is that transverse stability is high, and B is the beam, and d is draft, and L is captain, and g is that gravity accelerates Degree, w is wave disturbance, and u is the control output calculating rudder stabilization loop, and U is the speed of a ship or plane, u_rExport through steering wheel for controller Actual rudder angle after actuator；

(2) roll angle signal is gathered

(3) angular velocity in roll signal is obtainedTake High-gain observer gain p^-1(θ)C^T=[2 θ, θ²]^T, setup parameter θ value；

High-gain observer state is:

$\left\{\begin{array}{c}\stackrel{\·}{\stackrel{\‾}{x}}=\left[\begin{array}{cc}0& 1\\ a_3+{\mathrm{\Δa}}_3& a_1+{\mathrm{\Δa}}_1\end{array}\right]\stackrel{\‾}{x}+\left[\begin{array}{c}0\\ 1\end{array}\right](b+\mathrm{\Δ}b)u+(a_2+\mathrm{\Δ}{a}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_4+\mathrm{\Δ}{a}_4){\stackrel{\‾}{x}}_1^3-p^{-1}\left(\mathrm{\θ}\right)C^T(\stackrel{\‾}{y}-y)\\ \stackrel{\‾}{y}=\left[\begin{array}{c}1\\ 0\end{array}\right]\stackrel{\‾}{x}\end{array}\right.$

Wherein, "-" represents observation, and having observer system is:

$\left\{\begin{array}{c}{\stackrel{\·}{\stackrel{\‾}{x}}}_1={\stackrel{\‾}{x}}_2-2\mathrm{\θ}\mathrm{\ϵ}\\ {\stackrel{\·}{\stackrel{\‾}{x}}}_2=(a_1+{\mathrm{\Δa}}_1){\stackrel{\‾}{x}}_2+(a_2+{\mathrm{\Δa}}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_3+{\mathrm{\Δa}}_3){\stackrel{\‾}{x}}_1+(a_4+{\mathrm{\Δa}}_4){\stackrel{\‾}{x}}_1^3+(b+\mathrm{\Δ}b)u_r\left(\stackrel{\‾}{x}\right)-{\mathrm{\θ}}^2\mathrm{\ϵ}\\ \mathrm{\ϵ}=\stackrel{\‾}{y}-y\end{array}\right.;$

(4) setting controller initial parameter values k₀, k₁, to expect roll angleRoll angleAnd angular velocity in rollFor input letter Number, calculate the control output u in rudder stabilization loop₁,

Obtain Rudder rollstabilization control system based on analytic modell analytical model Predictive control design is:

$\left\{\begin{array}{c}{\stackrel{\·}{\stackrel{\‾}{x}}}_1={\stackrel{\‾}{x}}_2-2\mathrm{\θ}\mathrm{\ϵ}\\ {\stackrel{\·}{\stackrel{\‾}{x}}}_2=(a_1+{\mathrm{\Δa}}_1){\stackrel{\‾}{x}}_2+(a_2+{\mathrm{\Δa}}_2)\left|{\stackrel{\‾}{x}}_2\right|{\stackrel{\‾}{x}}_2+(a_3+{\mathrm{\Δa}}_3){\stackrel{\‾}{x}}_1+(a_4+{\mathrm{\Δa}}_4){\stackrel{\‾}{x}}_1^3+(b+\mathrm{\Δ}b)u_r\left(\stackrel{\‾}{x}\right)+w-{\mathrm{\θ}}^2\mathrm{\ϵ}\\ u_1\left(\stackrel{\‾}{x}\right)=-\frac{1}{b\±b_1}(k_0{\stackrel{\‾}{x}}_1+k_1{\stackrel{\‾}{x}}_2+(a_1\±m_1){\stackrel{\‾}{x}}_2+(a_2\±m_2\left)\right|{\stackrel{\‾}{x}}_2|{\stackrel{\‾}{x}}_2+(a_3\±m_3){\stackrel{\‾}{x}}_1+(a_4\±m_4\left){\stackrel{\‾}{x}}_1^3\right)\\ \mathrm{\ϵ}=\stackrel{\‾}{y}-y\end{array}\right.,$

Wherein:For the observation of x,

A kind of rudder stabilization method based on analytic modell analytical model Predictive control design the most according to claim 1, its feature exists In: described predictive controller initial value design, it was predicted that cycle T₁=60s, controls order l=4, observer parameter θ=3, control Device parameter k processed₀=0.05, k₁=0.375.