CN104527944A - Integrated stabilization chaotic system based PID (Proportion Integration Differentiation) controller optimization control method - Google Patents

Abstract

The invention provides an integrated stabilization chaotic system based PID (Proportion Integration Differentiation) controller optimization control method. The analysis is performed on an integrated stabilization system dynamic model equation to obtain a chaotic system so as to solve the problem of ship stabilization. The chaotic behavior of the system under the certain conditions is verified by a phase diagram and Lyapunov exponent spectrum analysis method, controlled parameters are selected, and the chaotic behavior of the system can be effectively controlled by a nonlinear feedback control method. According to the integrated stabilization chaotic system based PID controller optimization control method, the chaotic dynamics behavior of the system is improved and the original dynamic characteristics of the system are reserved; a chaotic search algorithm is combined with an ant colony algorithm to implement the optimization of the PID control parameters and accordingly the global optimization capability of the ant colony algorithm is high, meanwhile the system convergence speed is improved, and accordingly the control system performance is significantly improved; the value of application to a controller device is high, wherein the ship rolling motion is effectively designed through the controller device.

Description

A kind of PID controller optimal control method based on integrated value method chaos system

Technical field

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

Background technology

Along with the theoretical develop rapidly of ship rolling motion, Chinese scholars utilizes nonlinear theory and method to start occurring in ship stabilization process that large amount of complex non-linear phenomena is researched and analysed.The ship rolling motion analysis that develops into of chaology and chaos controlling theory provides new approaches.

C.Novara-L.Fagiano proposes to utilize Direct Feedback Control Design nonlinear system, overcome to be changed by nonlinear parameter and bring difficulty to design, Li Tianwei utilizes rectangular pulse to carry out perturbation control to ship course kinematic model and obtains good control effects, open favour employing numerical analysis method and point out that construction parameter change has an impact to wing nonlinear system chaotic motion, realize chaotic characteristic for utilizing change structure parameter and effectively control to provide reference frame.

Ma Lei and Zhang Xianku of the Dalian Maritime University is in Ship Mechanics SUM (the 17th volume the 7th phase, in July, 2013, p741-747.) " ship parameter excitation rolling motion and Ship-Fin-Stabilizer Control research thereof based on chaos analysis " has been delivered above, article uses Liapunov exponent (Lyapunov) and Welch method to carry out chaos analysis to ship parameter excitation rolling motion, find when frequency of parametric close to 2 times to boats and ships natural rolling frequency time, there is chaos phenomenon in ship parameter excitation rolling motion, boats and ships occur that large-amplitude roll even has danger of toppling.Then utilize Backstepping method and Closed Loop Gain Shaping Algorithm to design the boats and ships large-amplitude roll of the counteracting parametric excitation of Ship-Fin-Stabilizer Control device and the generation of extraneous sea wave disturbance, make boats and ships finally break away from chaos, be in stable safe condition.Due to this Ship-Fin-Stabilizer Control device only under the high speed of a ship or plane stabilizing efficiency better.But under the low speed of a ship or plane, Control System of Ship Fin cisco unity malfunction, can affect Actual Control Effect of Strong.

Summary of the invention

The object of the present invention is to provide a kind of PID controller optimal control method based on integrated value method chaos system that can significantly improve control system performance.

The object of the present invention is achieved like this:

The present invention is a kind of subtracts the PID controller optimal control method of shaking chaos system based on ship craft integrated, it is characterized in that:

(1) set up integrated value method system model, input using wave slope of wave surface as integrated value method system:

Boats and ships equip stabilizer and passive anti-rolling tank simultaneously, and stabilizer produces righting moment time, integrated value method system model is:

$\left\{\begin{array}{c}(I_1+J_t+C)\stackrel{\·\·}{\mathrm{\φ}}+({2N}_{\mathrm{\φ}}+B)\stackrel{\·}{\mathrm{\φ}}+(D{h}^{\′}+A)\mathrm{\φ}-{\mathrm{\ρ}}_t{S}_0{b}^2\stackrel{\·\·}{z}-2{\mathrm{\ρ}}_{t}g{S}_0\mathrm{Rz}=K_{\mathrm{\ω}}\\ {2\mathrm{\ρ}}_t{S}_0{\mathrm{\λ}}_t\stackrel{\·\·}{z}+{2N}_t\stackrel{\·}{z}+2{\mathrm{\ρ}}_{t}g{S}_{0}z-{\mathrm{\ρ}}_t{S}_0{b}^2\stackrel{\·\·}{\mathrm{\φ}}-2{\mathrm{\ρ}}_{t}g{S}_0\mathrm{R\φ}=0\end{array}\right.$

$A=l_f{\mathrm{\ρ}}_t{V}^2{A}_F\frac{\∂\mathrm{Cy}}{\∂\mathrm{\α}}{K}_h{K}_I,B=l_f{\mathrm{\ρ}}_t{V}^2{A}_F\frac{\∂\mathrm{Cy}}{\∂\mathrm{\α}}{K}_h{K}_P,C=l_f{\mathrm{\ρ}}_t{V}^2{A}_F\frac{\∂\mathrm{Cy}}{\∂\mathrm{\α}}{K}_h{K}_D,$ L _ffor going up the acting force arm of hydrodynamic pressure center to boats and ships center of gravity from stabilizer, ρ _tfor sea water density, V is the speed of a ship or plane, A _ffor the area of conter of stabilizer, for lift coefficient slope, φ is roll angle, for angular velocity in roll, for roll angle acceleration/accel, K _hfor speed of a ship or plane adjustment factor, K _i, K _p, K _dfor pid parameter, be respectively $K_I=\frac{\mathrm{DhF}}{l_f{\mathrm{\ρ}}_t{A}_F\frac{\∂\mathrm{Cy}}{\∂\mathrm{\α}}{V}^2},K_D=\frac{I_{1}F}{l_f{\mathrm{\ρ}}_t{A}_F\frac{\∂\mathrm{Cy}}{\∂\mathrm{\α}}{V}^2},$ H is that first metancenter is high, f is constant, K _ω=Dh α _ecos ω t is distrubing moment, I ₁for inertia and the additional inertial sum of the longitudinal axis with respect to boats and ships center of gravity, for liquid in cabin is to the maskant moment of inertia of axis of roll, S amasss along the partial cross section of the normal direction of water tank axis, and r is the distance micro-quality of barycenter to axis of roll of micro-quality dm, for boats and ships damping coefficient, D is displacement, h ' for metancenter after adding water tank high, ρ _tfor sea water density, S ₀for wing tank free surface area, for water tank axis is to the static pressure moment of axis of roll, γ is the angle between r and d, and dl is the length of liquid micro-volume along water tank axis, and l is U-shaped water tank axial length, and z is elevation of water surface in wing tank, for water column equivalent length in cabin, N _tfor water tank damping coefficient, R indulges the horizontal throw of middle planing surface to boats and ships in wing tank, and g is acceleration due to gravity;

(2) integrated value method system model is converted into integrated value method Chaotic Systems, and utilizes phasor and Lyapunov exponential spectrum analysis method checking integrated value method system model to have chaotic characteristic:

The expression formula of integrated value method system model is carried out nondimensionalization obtain:

$\left\{\begin{array}{c}\stackrel{\·\·}{\mathrm{\φ}}+{2v}_{\mathrm{\φ}}\stackrel{\·}{\mathrm{\φ}}+{\mathrm{\ω}}_{\mathrm{\φ}}^2\mathrm{\φ}-\mathrm{\β}\stackrel{\·\·}{z}-a_{t}z=K_{\mathrm{\ω}}\\ \stackrel{\·\·}{z}+{2v}_t\stackrel{\·}{z}+{\mathrm{\ω}}_t^{2}z-b_t\stackrel{\·\·}{\mathrm{\φ}}-R{\mathrm{\ω}}_t^2\mathrm{\φ}=0\end{array}\right.$

In formula: $T_{\mathrm{\φ}}=\frac{2\mathrm{\π}}{{\mathrm{\ω}}_{\mathrm{\φ}}},{2v}_t=\frac{{2N}_t}{{2\mathrm{\ρ}}_t{S}_0{\mathrm{\λ}}_t},b_t=\frac{b^2}{{2\mathrm{\λ}}_t},{2v}_{\mathrm{\φ}}=\frac{{2N}_{\mathrm{\φ}}+B}{(I_1+J_t+C)},{\mathrm{\ω}}_t^2=\frac{g}{{\mathrm{\λ}}_t},{\mathrm{\α}}_t=\frac{{2\mathrm{\ρ}}_{t}g{S}_{0}R}{(I_1+J_t+C)},$ $\mathrm{\β}=\frac{{\mathrm{\ρ}}_t{S}_0{b}^2}{(I_1+J_t+C)},{\mathrm{\ω}}_{\mathrm{\φ}}^2=\frac{D{h}^{\′}+A}{(I_1+J_t+C)};$

Make x ₁=φ, x ₃=z, dimensionless equation is converted into integrated value method Chaotic Systems equation:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=\frac{K_{\mathrm{\ω}}+(a_t-{\mathrm{\β\ω}}_t^2)x_3+({\mathrm{\βR\ω}}_t^2-{\mathrm{\ω}}_{\mathrm{\φ}}^2)x_1-{2\mathrm{\βv}}_t{x}_4-{2v}_{\mathrm{\φ}}{x}_2}{1-{\mathrm{\βb}}_t}\\ {\stackrel{\·}{x}}_3=x_4\\ {\stackrel{\·}{x}}_4=\frac{b_t{K}_{\mathrm{\ω}}+(a_t{b}_t-{\mathrm{\ω}}_t^2)x_3+({\mathrm{R\ω}}_t^2-{\mathrm{\ω}}_{\mathrm{\φ}}^2{b}_t)x_1-{2v}_t{x}_4-{2v}_{\mathrm{\φ}}{b}_t{x}_2}{1-{\mathrm{\βb}}_t}\end{array}\right.$

(3) chaos controlling is carried out to integrated value method Chaotic Systems:

Utilize Piecewise Quadratic Functions x|x| as the producer producing chaos, the fork K parameter of selective system Liapunov exponent all corresponding to anon-normal is done this and is ship craft integratedly subtracted the nonlinear feedback controller of shaking chaos system, and be applied to ship craft integrated subtract to shake in chaos system carry out feedback operation, ship craft integrated subtracting is made to shake chaos system searching unstable periodic orbits, realize effective control of chaos system simultaneously, chaos controlling is carried out to the integrated value method Chaotic Systems in step (2), parameter is identical with integrated value method Chaotic Systems equation, now chaos controlling equation is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=\frac{K_{\mathrm{\ω}}+(a_t-{\mathrm{\β\ω}}_t^2)x_3+({\mathrm{\βR\ω}}_t^2-{\mathrm{\ω}}_{\mathrm{\φ}}^2)x_1-{2\mathrm{\βv}}_t{x}_4-{2v}_{\mathrm{\φ}}{x}_2}{1-{\mathrm{\βb}}_t}+{\mathrm{Kx}}_2\left|x_2\right|\\ {\stackrel{\·}{x}}_3=x_4\\ {\stackrel{\·}{x}}_4=\frac{b_t{K}_{\mathrm{\ω}}+(a_t{b}_t-{\mathrm{\ω}}_t^2)x_3+({\mathrm{R\ω}}_t^2-{\mathrm{\ω}}_{\mathrm{\φ}}^2{b}_t)x_1-{2v}_t{x}_4-{2v}_{\mathrm{\φ}}{b}_t{x}_2}{1-{\mathrm{\βb}}_t}\end{array}\right.$

In formula: K is the fork parameter of Chaotic Systems;

(4) method adopting chaos algorithm to combine with ant group algorithm, to pid parameter K _p, K _iand K _dcarry out adjusting and optimizing:

First ant group algorithm is utilized tentatively to determine the size of optimal solution in-scope; Then use chaotic optimization algorithm to carry out Chaos Search around global optimum ant, be better than the solution of current optimum ant if find, then replace current global optimum ant with it, calculate the path of updated optimum ant, just obtain optimal value;

(5) Optimum Synthesis subtracts the roll angle φ shaking chaos system and export:

By the optimum PID parameter K that step (4) obtains _p, K _iand K _doptimum Synthesis subtracts the roll angle φ shaking chaos system and export, thus make integrated value method chaos system anti-rolling efficiency reach more than 75%, otherwise repeated execution of steps (4) and (5), Chaos Ant Colony Optimization is utilized to carry out pid parameter optimization, until anti-rolling efficiency reaches more than 75%, wherein, anti-rolling efficiency R computing formula is:

$R=\frac{\stackrel{\‾}{\mathrm{\φ}}-\stackrel{\‾}{{\mathrm{\φ}}_0}}{\stackrel{\‾}{{\mathrm{\φ}}_0}}$

In formula: roll angle aviation value during for not installing stabilizer; for roll angle aviation value during installation stabilizer.

The present invention can also comprise:

1, chaos algorithm is utilized to combine with ant group algorithm as follows to the searching process of PID controller parameter:

(1) pid control parameter optimization problem is converted into Chaos Ant Colony Optimization optimization problem:

First the controling parameters K of controller _p, K _i, K _dbe convertible into the problem of combination optimizing, controling parameters value be considered as 5 position effective digitals, parameter (K to be sought _p, K _i, K _d) the composition Serial No. of 15 is designated as { c _i, i=1,2 ... 15}, each c _ivalue y _j{ j=1,2 ... 9}, therefore every subsequence can at { (c _i, y _j) | i=1,2 ... 15, j=1,2 ... represent in 9} compositing area, namely this sequence is exactly a paths of human oasis exploited;

(2) foundation of objective function

Adopt and improve ITAE performance figure as objective function:

$\mathrm{ITAE}=\left\{\begin{array}{cc}{\&Integral;}_0^{t_i}|y\left(t\right)-y_{*p}\left(t\right)|\mathrm{dt}& y\left(t\right)\&GreaterEqual;y_{*p}\left(t\right)\\ {\&Integral;}_0^{t_i}|y\left(t\right)-y_{*p}\left(t\right)|\mathrm{dt}& y\left(t\right)<y_{*p}\left(t\right)\end{array}\right.$

Wherein, P is regulatory factor, generally gets P and is greater than 1, suitably can adjust according to practical problems;

(3) structure in path

When ant is from (c _i-1, y _j) crawl into the next one (c _i, y _j) node selects according to random ratio probability, when all ants arrive (15, y _j) namely realize once circulating, in the process, suppose that ant neighborhood of nodes time used of creeping is equal, with path independence, then ant is from (c _i-1, y _j) crawl into the next one (c _i, y _j) node is by the probability of formula following formula as selecting paths:

$P_k(c_i,y_j,t)=\frac{{\mathrm{\&tau;}}^a(c_i,y_j,t){\mathrm{\&eta;}}^B(c_i,y_j,t)}{\underset{j=0}{\overset{9}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}^a(c_i,y_j,t){\mathrm{\&eta;}}^B(c_i,y_j,t)}$

In formula: P _k(c _i, y _j, t) represent that t ant is from (c _i-1, y _j) crawl into the next one (c _i, y _j) some rate, τ (c _i, y _j, t) be t (c _i, y _j) quantity of information on node, η (c _i, y _j, t) be t (c _i, y _j) visbility on node;

(4) renewal of pheromones, determine optimum ant:

When whole ant is from initial point, after 15 unit time, every ant all climbs to terminal, calculates the path of each ant, finds current optimal solution, is optimum ant;

(5) utilize chaos algorithm to carry out Chaos Search to around global optimum ant, obtain optimal solution:

Chaos algorithm is utilized to carry out Chaos Search to around global optimum ant, the solution of current optimum ant is better than if find, then replace current global optimum ant with it, calculate updated optimum ant, just optimal value is obtained, be better than the solution of current optimum ant if do not find, then the solution of current ant is optimal value.

Advantage of the present invention is: the present invention uses chaology to carry out chaotic behavior analysis to integrated value method system (stabilizer and antirolling tank) kinetics equation, and adopt nonlinear feedback control methods to realize chaos controlling to system, not only make chaotic systems dynamic behavior be improved, go back the original dynamics of retention system.Simultaneously and utilize Chaos Ant Colony Optimization to realize pid control parameter optimizing, shown by contrast, this algorithm not only expands search coverage, also improves search efficiency and search precision.The controller performance of the controller after optimizing is significantly improved.

Accompanying drawing explanation

Fig. 1 is ship stabilization principle of optimality block scheme of the present invention;

Fig. 2 is control method diagram of circuit of the present invention;

Fig. 3 is Liapunov exponent (Lyapunov) dynamic change figure;

The three-dimensional chaos phasor d of the three-dimensional chaos phasor b of Fig. 4 a to be the three-dimensional chaos phasor a of system, Fig. 4 b be system, Fig. 4 c to be the three-dimensional chaos phasor c of system, Fig. 4 d be system;

Fig. 5 is that Liapunov exponent (Lyapunov) is with K change curve;

The phasor d of the phasor b of Fig. 6 a to be the phasor a of nonlinear feedback control system, Fig. 6 b be nonlinear feedback control system, Fig. 6 c to be the phasor c of nonlinear feedback control system, Fig. 6 d be nonlinear feedback control system;

Fig. 7 is the step response schematic diagram of two kinds of Different Optimization strategy PID systems.

Detailed description of the invention

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

Composition graphs 1 ~ 7, the present invention includes following steps:

(1) set up integrated value method system model, wave slope of wave surface is inputted as system.

(2) integrated value method system model is converted into integrated value method Chaotic Systems, and utilizes phasor and Lyapunov exponential spectrum analysis method checking integrated value method system model to carry out chaotic characteristic.

(3) utilize segmentation Quadratic Function Optimization x|x| as the producer producing chaos, the fork K parameter of selective system Liapunov exponent all corresponding to anon-normal is done this and is ship craft integratedly subtracted the nonlinear feedback controller of shaking chaos system, carries out chaos controlling to integrated value method chaos system.

(4) method adopting chaotic optimization algorithm to combine with ant group algorithm, to pid parameter K _p, K _iand K _dcarry out adjusting and optimizing.

(5) by optimum PID parameter K that step 4 obtains _p, K _iand K _doptimum Synthesis subtracts the roll angle φ shaking chaos system and export, thus makes integrated value method chaos system anti-rolling efficiency reach more than 75%, otherwise repeated execution of steps (4), Chaos Ant Colony Optimization is utilized to carry out pid parameter optimization, until anti-rolling efficiency reaches more than 75%.

Specifically, the present invention includes following step.

Step one: set up integrated value method system model, inputs using wave slope of wave surface as integrated value method system.

When boats and ships equip stabilizer and passive anti-rolling tank simultaneously, stabilizer produces righting moment time, integrated value method system model is such as formula shown in (1):

$\left\{\begin{array}{c}(I_1+J_t+C)\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}+({2N}_{\mathrm{\&phi;}}+B)\stackrel{\&CenterDot;}{\mathrm{\&phi;}}+(D{h}^{\&prime;}+A)\mathrm{\&phi;}-{\mathrm{\&rho;}}_t{S}_0{b}^2\stackrel{\&CenterDot;\&CenterDot;}{z}-2{\mathrm{\&rho;}}_{t}g{S}_0\mathrm{Rz}=K_{\mathrm{\&omega;}}\\ {2\mathrm{\&rho;}}_t{S}_0{\mathrm{\&lambda;}}_t\stackrel{\&CenterDot;\&CenterDot;}{z}+{2N}_t\stackrel{\&CenterDot;}{z}+2{\mathrm{\&rho;}}_{t}g{S}_{0}z-{\mathrm{\&rho;}}_t{S}_0{b}^2\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}-2{\mathrm{\&rho;}}_{t}g{S}_0\mathrm{R\&phi;}=0\end{array}\right.---\left(1\right)$

Wherein, $A=l_f{\mathrm{\&rho;}}_t{V}^2{A}_F\frac{\&PartialD;\mathrm{Cy}}{\&PartialD;\mathrm{\&alpha;}}{K}_h{K}_I,B=l_f{\mathrm{\&rho;}}_t{V}^2{A}_F\frac{\&PartialD;\mathrm{Cy}}{\&PartialD;\mathrm{\&alpha;}}{K}_h{K}_P,$ l _ffor going up the acting force arm of hydrodynamic pressure center to boats and ships center of gravity from stabilizer; ρ _tfor sea water density; V is the speed of a ship or plane; A _ffor the area of conter of stabilizer; for lift coefficient slope; φ is roll angle; for angular velocity in roll; for roll angle acceleration/accel; K _hfor speed of a ship or plane adjustment factor; K _i, K _p, K _dfor pid parameter, they are respectively $K_D=\frac{I_{1}F}{l_f{\mathrm{\&rho;}}_t{A}_F\frac{\&PartialD;\mathrm{Cy}}{\&PartialD;\mathrm{\&alpha;}}{V}^2},$ H is that first metancenter is high; f is constant; K _ω=Dh α _ecos ω t is distrubing moment; I ₁for inertia and the additional inertial sum of the longitudinal axis with respect to boats and ships center of gravity; for liquid in cabin is to the maskant moment of inertia of axis of roll; S is long-pending along the partial cross section of the normal direction of water tank axis; R is the distance micro-quality of barycenter to axis of roll of micro-quality dm; for boats and ships damping coefficient; D is displacement; H ' for metancenter after adding water tank high; ρ _tfor sea water density; S ₀for wing tank free surface area; for water tank axis is to the static pressure moment of axis of roll; γ is the angle between r and d; Dl is the length of liquid micro-volume along water tank axis; L is U-shaped water tank axial length; Z is elevation of water surface in wing tank; for water column equivalent length in cabin; N _tfor water tank damping coefficient; R indulges the horizontal throw of middle planing surface to boats and ships in wing tank; G is acceleration due to gravity.

Step 2: integrated value method system model is converted into integrated value method Chaotic Systems, and utilize phasor and Lyapunov exponential spectrum analysis method checking integrated value method system model to have chaotic characteristic.

(1) formula is carried out nondimensionalization obtain:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}+{2v}_{\mathrm{\&phi;}}\stackrel{\&CenterDot;}{\mathrm{\&phi;}}+{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2\mathrm{\&phi;}-\mathrm{\&beta;}\stackrel{\&CenterDot;\&CenterDot;}{z}-a_{t}z=K_{\mathrm{\&omega;}}\\ \stackrel{\&CenterDot;\&CenterDot;}{z}+{2v}_t\stackrel{\&CenterDot;}{z}+{\mathrm{\&omega;}}_t^{2}z-b_t\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}-R{\mathrm{\&omega;}}_t^2\mathrm{\&phi;}=0\end{array}\right.---\left(2\right)$

In formula: $T_{\mathrm{\&phi;}}=\frac{2\mathrm{\&pi;}}{{\mathrm{\&omega;}}_{\mathrm{\&phi;}}};{2v}_t=\frac{{2N}_t}{{2\mathrm{\&rho;}}_t{S}_0{\mathrm{\&lambda;}}_t};b_t=\frac{b^2}{{2\mathrm{\&lambda;}}_t};{2v}_{\mathrm{\&phi;}}=\frac{{2N}_{\mathrm{\&phi;}}+B}{(I_1+J_t+C)};{\mathrm{\&omega;}}_t^2=\frac{g}{{\mathrm{\&lambda;}}_t};{\mathrm{\&alpha;}}_t=\frac{{2\mathrm{\&rho;}}_{t}g{S}_{0}R}{(I_1+J_t+C)};$ $\mathrm{\&beta;}=\frac{{\mathrm{\&rho;}}_t{S}_0{b}^2}{(I_1+J_t+C)};{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2=\frac{D{h}^{\&prime;}+A}{(I_1+J_t+C)}.$

Make x ₁=φ, x ₃=z, equation (2) is converted into integrated value method Chaotic Systems equation:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=\frac{K_{\mathrm{\&omega;}}+(a_t-{\mathrm{\&beta;\&omega;}}_t^2)x_3+({\mathrm{\&beta;R\&omega;}}_t^2-{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2)x_1-{2\mathrm{\&beta;v}}_t{x}_4-{2v}_{\mathrm{\&phi;}}{x}_2}{1-{\mathrm{\&beta;b}}_t}\\ {\stackrel{\&CenterDot;}{x}}_3=x_4\\ {\stackrel{\&CenterDot;}{x}}_4=\frac{b_t{K}_{\mathrm{\&omega;}}+(a_t{b}_t-{\mathrm{\&omega;}}_t^2)x_3+({\mathrm{R\&omega;}}_t^2-{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2{b}_t)x_1-{2v}_t{x}_4-{2v}_{\mathrm{\&phi;}}{b}_t{x}_2}{1-{\mathrm{\&beta;b}}_t}\end{array}\right.---\left(3\right)$

Step 3: chaos controlling is carried out to integrated value method Chaotic Systems

Utilize Piecewise Quadratic Functions x|x| as the producer producing chaos, the fork K parameter of selective system Liapunov exponent all corresponding to anon-normal is done this and is ship craft integratedly subtracted the nonlinear feedback controller of shaking chaos system, and be applied to ship craft integrated subtract to shake in chaos system carry out feedback operation, make ship craft integrated subtracting shake chaos system searching unstable periodic orbits, realize effective control of chaos system simultaneously.Carry out chaos controlling to the integrated value method Chaotic Systems in step 2, parameter is identical with (3) formula.Now the chaos controlling equation of system is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=\frac{K_{\mathrm{\&omega;}}+(a_t-{\mathrm{\&beta;\&omega;}}_t^2)x_3+({\mathrm{\&beta;R\&omega;}}_t^2-{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2)x_1-{2\mathrm{\&beta;v}}_t{x}_4-{2v}_{\mathrm{\&phi;}}{x}_2}{1-{\mathrm{\&beta;b}}_t}+{\mathrm{Kx}}_2\left|x_2\right|\\ {\stackrel{\&CenterDot;}{x}}_3=x_4\\ {\stackrel{\&CenterDot;}{x}}_4=\frac{b_t{K}_{\mathrm{\&omega;}}+(a_t{b}_t-{\mathrm{\&omega;}}_t^2)x_3+({\mathrm{R\&omega;}}_t^2-{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2{b}_t)x_1-{2v}_t{x}_4-{2v}_{\mathrm{\&phi;}}{b}_t{x}_2}{1-{\mathrm{\&beta;b}}_t}\end{array}\right.---\left(4\right)$

In formula: K is the fork parameter of Chaotic Systems.

Fig. 5 is the Liapunov exponent of controlled system under parameter K (Lyapunov) figure.As shown in Figure 5, when K ∈ [-2,4], Liapunov exponent (Lyapunov) all anon-normal of system, system is in period state always.Fig. 6 gives the three-dimensional phase diagram of system under fork parameter K=2 value.Can to obtain from Fig. 6: now system is in period state, but not chaotic motion, therefore to select Liapunov exponent (Lyapunov) be all when bearing, system is in stabilized conditions, and now the K value of correspondence can the chaotic behavior of effective control system.

Step 4: adopt the method that chaos algorithm combines with ant group algorithm, to pid parameter K _p, K _iand K _dcarry out adjusting and optimizing.

First ant group algorithm is utilized tentatively to determine the size of optimal solution in-scope; Then use chaotic optimization algorithm to carry out Chaos Search around global optimum ant, be better than the solution of current optimum ant if find, then replace current global optimum ant with it, calculate the path of updated optimum ant, just obtain optimal value.

Fig. 1 is that Chaos Ant Colony Optimization is applied to integrated value method chaos system PID controller principle of optimality block scheme.

Utilize the searching process of Chaos Ant Colony Optimization PID controller parameter as follows:

(1) pid control parameter optimization problem is converted into Chaos Ant Colony Optimization optimization problem

First the controling parameters K of controller _p, K _i, K _dbe convertible into the problem of combination optimizing, meeting under control accuracy requirement, controling parameters value can be considered as 5 position effective digitals, so parameter (K to be sought _p, K _i, K _d) the composition Serial No. of 15 is designated as { c _i, i=1,2 ... 15}, each c _ivalue y _j{ j=1,2 ... 9}, therefore every subsequence can at { (c _i, y _j) | i=1,2 ... 15, j=1,2 ... represent in 9} compositing area, namely this sequence is exactly a paths of human oasis exploited.

(2) foundation of objective function

For ensureing that controller has good performance, suitable objective function must be selected, main performance index comprises stability, rapidity and accuracy, also consider that control object is subtract to shake the system overshoot that Fu has a certain amount of transient process simultaneously, therefore, adopt improvement ITAE performance figure as objective function.

$\mathrm{ITAE}=\left\{\begin{array}{cc}{\&Integral;}_0^{t_i}|y\left(t\right)-y_{*p}\left(t\right)|\mathrm{dt}& y\left(t\right)\&GreaterEqual;y_{*p}\left(t\right)\\ {\&Integral;}_0^{t_i}|y\left(t\right)-y_{*p}\left(t\right)|\mathrm{dt}& y\left(t\right)<y_{*p}\left(t\right)\end{array}\right.---\left(5\right)$

Wherein, P is regulatory factor, generally gets P and is greater than 1, suitably can adjust according to practical problems.

(3) structure in path

The structure in path is the key link in ant group algorithm research, when ant is from (c _i-1, y _j) crawl into the next one (c _i, y _j) node selects according to random ratio probability, when all ants arrive (15, y _j) namely realize once circulating.In the process, the neighborhood of nodes time used of supposing to creep in this process of ant is equal, with path independence.Then ant is from (c _i-1, y _j) crawl into the next one (c _i, y _j) node is by the probability of formula (6) as selecting paths.

$P_k(c_i,y_j,t)=\frac{{\mathrm{\&tau;}}^a(c_i,y_j,t){\mathrm{\&eta;}}^B(c_i,y_j,t)}{\underset{j=0}{\overset{9}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}^a(c_i,y_j,t){\mathrm{\&eta;}}^B(c_i,y_j,t)}---\left(6\right)$

In formula: P _k(c _i, y _j, t) represent that t ant is from (c _i-1, y _j) crawl into the next one (c _i, y _j) some rate; τ (c _i, y _j, t) be t (c _i, y _j) quantity of information on node; η (c _i, y _j, t) be t (c _i, y _j) visbility on node.

(4) renewal of pheromones, determines optimum ant.

When whole ant is from initial point, after 15 unit time, every ant all climbs to terminal, calculates the path of each ant, finds current optimal solution, is optimum ant.

(5) utilize chaos algorithm to carry out Chaos Search to around global optimum ant, obtain optimal solution.

Chaos algorithm is utilized to carry out Chaos Search to around global optimum ant.Be better than the solution of current optimum ant if find, then replace current global optimum ant with it, calculate updated optimum ant, just obtain optimal value.

Step 5: Optimum Synthesis subtracts the roll angle φ shaking chaos system and export

The optimum PID parameter K obtained by step 4 _p, K _iand K _doptimum Synthesis subtracts the roll angle φ shaking chaos system and export, thus make integrated value method chaos system anti-rolling efficiency reach more than 75%, otherwise repeated execution of steps (4) and (5), Chaos Ant Colony Optimization is utilized to carry out pid parameter optimization, until anti-rolling efficiency reaches more than 75%.Wherein, anti-rolling efficiency R computing formula is:

$R=\frac{\stackrel{\&OverBar;}{\mathrm{\&phi;}}-\stackrel{\&OverBar;}{{\mathrm{\&phi;}}_0}}{\stackrel{\&OverBar;}{{\mathrm{\&phi;}}_0}}---\left(7\right)$

In formula: roll angle aviation value during for not installing stabilizer; for roll angle aviation value during installation stabilizer.Step 6: Case Simulation

With reference to certain dummy ship, it is controlled function that the chaos system when the parameter K=2 that diverges is is converted into transfer function, and the sampling period is 1ms, when incoming signal is step signal.Chaos ant colony optimization algorithm scheme selection is as follows: iterations N=50, and ant sum m=30, information factor of evaporation ρ=0.85, pheromones strengthens coefficient Q=1, and ant creeper speed v=0.3, after 50 iteration, seeks optimal control parameter K _p=16.563, K _i=2.013, K _d=0.237.Table 1 gives the comparative result of the pid parameter optimized algorithm based on Chaos Ant Colony Optimization with the pid parameter optimized algorithm based on genetic algorithm.

Table 1 Chaos Ant Colony Optimization compares with the pid parameter optimized algorithm based on genetic algorithm

As shown in Table 1: selecting seek in optimal solution quality based on Chaos Ant Colony Optimization pid control parameter optimizing algorithm under Reasonable Parameters condition or in execution efficiency, be all better than the pid parameter optimized algorithm based on genetic algorithm.Fig. 7 is that the PID after the Optimal Parameters adopting genetic algorithm to obtain and the Optimal Parameters adopting ant group algorithm to obtain are adjusted controls step response.

For verification algorithm subtracts the validity of shaking Chaotic system control to ship craft integrated, adopt respectively and under different sea condition, obtain pid control parameter optimal value as table 2, shown in table 3 based on chaos ant colony optimization algorithm and genetic Optimization Algorithm.

Table 2 is based on the pid control parameter optimal value of Chaos Ant Colony Optimization

Table 3 is based on the pid control parameter optimal value of genetic algorithm

Can be obtained by table 2,3, the PID controller anti-rolling efficiency based on Chaos Ant Colony Optimization under different sea condition all can reach more than 75%, and no matter Searching efficiency or anti-rolling efficiency aspect are obviously better than the PID controller control effects based on genetic algorithm.

The Case Simulation checking of step 2 Chaotic Systems

As system parameter K _ω=20000, a _t=0.0131, β=0.0049, r=3.6210, 2v _t=0.1874,2v _φ=0.0596, b _twhen=0.9414, utilize wolf method for numerical simulation try to achieve system in time change tread Liapunov exponent (Lyapunov) spectrogram as shown in Figure 3, it reflects the dynamic characteristics of Kind of Nonlinear Dynamical System with Parameters variation intuitively.As shown in Figure 3, system has 4 Liapunov exponents, and system is in chaos state under this group Parameter Conditions.Analyze from equilibrium point and stability aspect; For obtaining the equilibrium point of system, when system parameter analysis is: a _t=0.0131, β=0.0049, r=3.6210, 2 v _t=0.1874,2 v _φ=0.0596, b _t=0.9414, order obtain the Jacobian matrix at unique equilibrium point (0,0,0, the 0) place of system

$J=\left[\begin{array}{cccc}0& 1& 0& 0\\ 1.6953& -0.0599& 0.0097& 0.00092\\ 0& 0& 0& 1\\ 1.8955& -0.564& -0.6954& -3.883\end{array}\right]$

Its eigenvalue equation is: λ ⁴+ 3.823 λ ³-1.2326 λ ²-6.61902 λ-1.1971=0,4 characteristic roots are respectively λ ₁=-3.6956, λ ₂=1.3329, λ ₃=-1.2688, λ ₄=-0.1915.Know that this system balancing point is unstable saddle point by differential equation theory, describe this system theoretically and there is hyperchaos state, the three-dimensional chaos attractor phasor of this system as shown in Figure 4.

Claims (2)

1. subtract a PID controller optimal control method of shaking chaos system based on ship craft integrated, it is characterized in that:

(1) set up integrated value method system model, input using wave slope of wave surface as integrated value method system:

Boats and ships equip stabilizer and passive anti-rolling tank simultaneously, and stabilizer produces righting moment time, integrated value method system model is:

$\left\{\begin{array}{c}(I_1+J_t+C)\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}+(2N_{\mathrm{\&phi;}}+B)\stackrel{\&CenterDot;}{\mathrm{\&phi;}}+(D{h}^{\&prime;}+A)\mathrm{\&phi;}-{\mathrm{\&rho;}}_t{S}_0{b}^2\stackrel{\&CenterDot;\&CenterDot;}{z}-2{\mathrm{\&rho;}}_{t}g{S}_0\mathrm{Rz}=K_{\mathrm{\&omega;}}\\ 2{\mathrm{\&rho;}}_t{S}_0{\mathrm{\&lambda;}}_t\stackrel{\&CenterDot;\&CenterDot;}{z}+2N_t\stackrel{\&CenterDot;}{z}+2{\mathrm{\&rho;}}_{t}g{S}_{0}z-{\mathrm{\&rho;}}_t{S}_0{b}^2\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}-2{\mathrm{\&rho;}}_{t}g{S}_0\mathrm{R\&phi;}=0\end{array}\right.$

$A=l_f{\mathrm{\&rho;}}_t{V}^2{A}_F\frac{\&PartialD;\mathrm{Cy}}{\&PartialD;\mathrm{\&alpha;}}{K}_h{K}_I,$ $B=l_f{\mathrm{\&rho;}}_t{V}^2{A}_F\frac{\&PartialD;\mathrm{Cy}}{\&PartialD;\mathrm{\&alpha;}}{K}_h{K}_P,$ $C=l_f{\mathrm{\&rho;}}_t{V}^2{A}_F\frac{\&PartialD;\mathrm{Cy}}{\&PartialD;\mathrm{\&alpha;}}{K}_h{K}_D,l_f$ For going up the acting force arm of hydrodynamic pressure center to boats and ships center of gravity from stabilizer, ρ _tfor sea water density, V is the speed of a ship or plane, A _ffor the area of conter of stabilizer, for lift coefficient slope, φ is roll angle, for angular velocity in roll, for roll angle acceleration/accel, K _hfor speed of a ship or plane adjustment factor, K _i, K _p, K _dfor pid parameter, be respectively $K_I=\frac{\mathrm{DhF}}{l_f{\mathrm{\&rho;}}_t{A}_F\frac{\&PartialD;\mathrm{Cy}}{\&PartialD;\mathrm{\&alpha;}}{V}^2},$ $K_D=\frac{I_{1}F}{l_f{\mathrm{\&rho;}}_t{A}_f\frac{\&PartialD;\mathrm{Cy}}{\&PartialD;\mathrm{\&alpha;}}{V}^2},$ H is that first metancenter is high, f is constant, K _ω=Dh α _ecos ω t is distrubing moment, I ₁for inertia and the additional inertial sum of the longitudinal axis with respect to boats and ships center of gravity, for liquid in cabin is to the maskant moment of inertia of axis of roll, S amasss along the partial cross section of the normal direction of water tank axis, and r is the distance micro-quality of barycenter to axis of roll of micro-quality dm, for boats and ships damping coefficient, D is displacement, h ' for metancenter after adding water tank high, ρ _tfor sea water density, S ₀for wing tank free surface area, for water tank axis is to the static pressure moment of axis of roll, γ is the angle between r and d, and dl is the length of liquid micro-volume along water tank axis, and l is U-shaped water tank axial length, and z is elevation of water surface in wing tank, for water column equivalent length in cabin, N _tfor water tank damping coefficient, R indulges the horizontal throw of middle planing surface to boats and ships in wing tank, and g is acceleration due to gravity;

(2) integrated value method system model is converted into integrated value method Chaotic Systems, and utilizes phasor and Lyapunov exponential spectrum analysis method checking integrated value method system model to have chaotic characteristic:

The expression formula of integrated value method system model is carried out nondimensionalization obtain:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}+2v_{\mathrm{\&phi;}}\stackrel{\&CenterDot;}{\mathrm{\&phi;}}+{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2\mathrm{\&phi;}-\mathrm{\&beta;}\stackrel{\&CenterDot;\&CenterDot;}{z}-a_{t}z=K_{\mathrm{\&omega;}}\\ \stackrel{\&CenterDot;\&CenterDot;}{z}+2v_t\stackrel{\&CenterDot;}{z}+{\mathrm{\&omega;}}_t^{2}z-b_t\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&phi;}}-R{\mathrm{\&omega;}}_t^2\mathrm{\&phi;}=0\end{array}\right.$

In formula: $T_{\mathrm{\&phi;}}=\frac{2\mathrm{\&pi;}}{{\mathrm{\&omega;}}_{\mathrm{\&phi;}}},2v_t=\frac{2N_t}{2{\mathrm{\&rho;}}_t{S}_0{\mathrm{\&lambda;}}_t},b_t=\frac{b^2}{2{\mathrm{\&lambda;}}_t},2v_{\mathrm{\&phi;}}=\frac{2N_{\mathrm{\&phi;}}+B}{(I_1+J_t+C)},{\mathrm{\&omega;}}_t^2=\frac{g}{{\mathrm{\&lambda;}}_t},{\mathrm{\&alpha;}}_t=\frac{2{\mathrm{\&rho;}}_{t}g{S}_{0}R}{(I_1+J_t+C)},$ $\mathrm{\&beta;}=\frac{{\mathrm{\&rho;}}_t{S}_0{b}^2}{(I_1+J_t+C)},{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2=\frac{D{h}^{\&prime;}+A}{(I_1+J_t+C)};$

Make x ₁=φ, x ₃=z, dimensionless equation is converted into integrated value method Chaotic Systems equation:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=\frac{K_{\mathrm{\&omega;}}+(a_t-\mathrm{\&beta;}{\mathrm{\&omega;}}_t^2)x_3+(\mathrm{\&beta;R}{\mathrm{\&omega;}}_t^2-{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2)x_1-2\mathrm{\&beta;}{v}_t{x}_4-2v_{\mathrm{\&phi;}}{x}_2}{1-\mathrm{\&beta;}{b}_t}\\ {\stackrel{\&CenterDot;}{x}}_3=x_4\\ {\stackrel{\&CenterDot;}{x}}_4=\frac{b_t{K}_{\mathrm{\&omega;}}+(a_t{b}_t-{\mathrm{\&omega;}}_t^2)x_3+(R{\mathrm{\&omega;}}_t^2-{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2{b}_t)x_1-2v_t{x}_4-2v_{\mathrm{\&phi;}}{b}_t{x}_2}{1-\mathrm{\&beta;}{b}_t}\end{array}\right.$

(3) chaos controlling is carried out to integrated value method Chaotic Systems:

Utilize Piecewise Quadratic Functions x|x| as the producer producing chaos, the fork K parameter of selective system Liapunov exponent all corresponding to anon-normal is done this and is ship craft integratedly subtracted the nonlinear feedback controller of shaking chaos system, and be applied to ship craft integrated subtract to shake in chaos system carry out feedback operation, ship craft integrated subtracting is made to shake chaos system searching unstable periodic orbits, realize effective control of chaos system simultaneously, chaos controlling is carried out to the integrated value method Chaotic Systems in step (2), parameter is identical with integrated value method Chaotic Systems equation, now chaos controlling equation is:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=\frac{K_{\mathrm{\&omega;}}+(a_t-\mathrm{\&beta;}{\mathrm{\&omega;}}_t^2)x_3+(\mathrm{\&beta;R}{\mathrm{\&omega;}}_t^2-{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2)x_1-2\mathrm{\&beta;}{v}_t{x}_4-2v_{\mathrm{\&phi;}}{x}_2}{1-\mathrm{\&beta;}{b}_t}+K{x}_2\left|x_2\right|\\ {\stackrel{\&CenterDot;}{x}}_3=x_4\\ {\stackrel{\&CenterDot;}{x}}_4=\frac{b_t{K}_{\mathrm{\&omega;}}+(a_t{b}_t-{\mathrm{\&omega;}}_t^2)x_3+(R{\mathrm{\&omega;}}_t^2-{\mathrm{\&omega;}}_{\mathrm{\&phi;}}^2{b}_t)x_1-2v_t{x}_4-2v_{\mathrm{\&phi;}}{b}_t{x}_2}{1-\mathrm{\&beta;}{b}_t}\end{array}\right.$

In formula: K is the fork parameter of Chaotic Systems;

(4) method adopting chaos algorithm to combine with ant group algorithm, to pid parameter K _p, K _iand K _dcarry out adjusting and optimizing:

First ant group algorithm is utilized tentatively to determine the size of optimal solution in-scope; Then use chaotic optimization algorithm to carry out Chaos Search around global optimum ant, be better than the solution of current optimum ant if find, then replace current global optimum ant with it, calculate the path of updated optimum ant, just obtain optimal value;

(5) Optimum Synthesis subtracts the roll angle φ shaking chaos system and export:

By the optimum PID parameter K that step (4) obtains _p, K _iand K _doptimum Synthesis subtracts the roll angle φ shaking chaos system and export, thus make integrated value method chaos system anti-rolling efficiency reach more than 75%, otherwise repeated execution of steps (4) and (5), Chaos Ant Colony Optimization is utilized to carry out pid parameter optimization, until anti-rolling efficiency reaches more than 75%, wherein, anti-rolling efficiency R computing formula is:

$R=\frac{\stackrel{\&OverBar;}{\mathrm{\&phi;}}-\stackrel{\&OverBar;}{{\mathrm{\&phi;}}_0}}{\stackrel{\&OverBar;}{{\mathrm{\&phi;}}_0}}$

In formula: roll angle aviation value during for not installing stabilizer; for roll angle aviation value during installation stabilizer.

2. according to claim 1ly a kind ofly subtract the PID controller optimal control method of shaking chaos system based on ship craft integrated, it is characterized in that:

Chaos algorithm is utilized to combine with ant group algorithm as follows to the searching process of PID controller parameter:

(1) pid control parameter optimization problem is converted into Chaos Ant Colony Optimization optimization problem:

First the controling parameters K of controller _p, K _i, K _dbe convertible into the problem of combination optimizing, controling parameters value be considered as 5 position effective digitals, parameter (K to be sought _p, K _i, K _d) the composition Serial No. of 15 is designated as { c _i, i=1,2 ... 15}, each c _ivalue y _j{ j=1,2 ... 9}, therefore every subsequence can at { (c _i, y _j) | i=1,2 ... 15, j=1,2 ... represent in 9} compositing area, namely this sequence is exactly a paths of human oasis exploited;

(2) foundation of objective function

Adopt and improve ITAE performance figure as objective function:

$\mathrm{ITAE}=\left\{\begin{array}{cc}{\&Integral;}_0^{t_i}|y\left(t\right)-y_{*p}\left(t\right)|\mathrm{dt}& y\left(t\right)\&GreaterEqual;y_{*p}\left(t\right)\\ {\&Integral;}_0^{t_i}|y\left(t\right)-y_{*p}\left(t\right)|\mathrm{dt}& y\left(t\right)<y_{*p}\left(t\right)\end{array}\right.$

Wherein, P is regulatory factor, generally gets P and is greater than 1, suitably can adjust according to practical problems;

(3) structure in path

When ant is from (c _i-1, y _j) crawl into the next one (c _i, y _j) node selects according to random ratio probability, when all ants arrive (15, y _j) namely realize once circulating, in the process, suppose that ant neighborhood of nodes time used of creeping is equal, with path independence, then ant is from (c _i-1, y _j) crawl into the next one (c _i, y _j) node is by the probability of formula following formula as selecting paths:

$P_k(c_i,y_j,t)=\frac{{\mathrm{\&tau;}}^a(c_i,y_j,t){\mathrm{\&eta;}}^B(c_i,y_j,t)}{\underset{j=0}{\overset{9}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}^a(c_i,y_j,t){\mathrm{\&eta;}}^B(c_i,y_j,t)}$

In formula: P _k(c _i, y _j, t) represent that t ant is from (c _i-1, y _j) crawl into the next one (c _i, y _j) some rate, τ (c _i, y _j, t) be t (c _i, y _j) quantity of information on node, η (c _i, y _j, t) be t (c _i, y _j) visbility on node;

(4) renewal of pheromones, determine optimum ant:

When whole ant is from initial point, after 15 unit time, every ant all climbs to terminal, calculates the path of each ant, finds current optimal solution, is optimum ant;

(5) utilize chaos algorithm to carry out Chaos Search to around global optimum ant, obtain optimal solution:

Chaos algorithm is utilized to carry out Chaos Search to around global optimum ant, the solution of current optimum ant is better than if find, then replace current global optimum ant with it, calculate updated optimum ant, just optimal value is obtained, be better than the solution of current optimum ant if do not find, then the solution of current ant is optimal value.