CN106444794A - Sliding-mode control method for parameter-free driving-insufficient UUV (Unmanned Underwater Vehicle) vertical plane route tracking - Google Patents

Abstract

The invention provides a sliding-mode control method for parameter-free driving-insufficient UUV (Unmanned Underwater Vehicle) vertical plane route tracking. The sliding-mode control method comprises the following steps: I, performing initialization; II, acquiring a current state of a UUV; III, establishing an error equation of the horizontal plane of the driving-free UUV so as to obtain position deviation values xe and ze and course deviation value theta e; IV, according to a sliding-mode control method, respectively designing traveling speed sliding-mode self-adaptive control rules, position sliding-mode control rules and trimming angle sliding-mode self-adaptive control rules, controlling propelling force Xprop, an excepted traveling speed U and a torque Mprop, wherein eu is 0, xe is 0 and theta e is 0; V, designing fuzzy control rules for a boundary layer, setting k to be equal to k+1, turning to step II, and updating control rules and self-adaptive rules of a next time. By adopting the sliding-mode control method, a controller for stabilizing a system can be designed only according to a vertical surface kinetic model, self-adaptive rules can be designed for water kinetic parameters with uncertainties, furthermore a control system can be relieved from dependency on parameters, the system has robustness, and the influence of the uncertainties on the sliding-mode control approaching process can be reduced.

Description

A kind of printenv drive lacking UUV vertical path trace sliding-mode control

Technical field

The present invention relates to a kind of UUV path tracking control method, specifically a kind of UUV is in vertical to the phase Hope the tracking and controlling method in path.

Background technology

The path following control of UAV navigation (Unmanned Underwater Vehicle, UUV), is to realize The important technical basis of UUV various uses.Problem present in further investigation UUV path trace, to UUV control theory and engineering Application all has great importance.

At present, in terms of drive lacking UUV path following control, a kind of thinking comparing main flow is based on Serret- Frenet coordinate system and set up kinematic error equation, real in conjunction with error equation, kinetics equation and various control method Now control.Wherein, common control algolithm includes Backstepping, Model Predictive Control, Sliding mode variable structure control etc..Backstepping for Calm complicated strong nonlinearity, high degree of coupling system have obvious advantage.However, to uncertain and external disturbance relatively The resistivity of difference, multiple derivation and the derivative that produces expands and haves such problems as singular value, govern this method Application.Model Predictive Control has the ability that Model Parameter error is rolled with real time correction, has good robustness.But This kind of algorithm is mainly used in linear system, for the nonlinear system that similar UUV is so complicated, however it remains non-linear place Reason, challenge the problems such as real-time is lifted.And Sliding mode variable structure control is the control calculation of a kind of strong robustness, strong antijamming capability Method, its buffeting problem can also switch over the methods such as control, design parameter adaptive law by using suitable function and give Weaken.

Also seldom, great majority concentrate on horizontal plane for path trace research on vertical direction for the drive lacking UUV now Path trace.Drive lacking UUV motion on the vertical plane is only controlled to depth mostly.GV Lakhekar and VD Saundarmal was published in 2013 on " IEEE International Conference on Fuzzy Systems " Article " Novel adaptive fuzzy sliding mode controller for depth control of In underwater vehicles ", the severity control for UUV proposes a kind of linear adaptive fuzzy sliding mode controller.

Content of the invention

It is an object of the invention to provide one kind can improve speed of a ship or plane tracking accuracy, reduce the printenv drive lacking of amount of calculation UUV vertical path trace sliding-mode control.

The object of the present invention is achieved like this：

Step one, initialization：

The auto-adaptive parameter of the uncertain parameter for UUVAssign initial value, and determine its ideal velocity for path tracking procedure u_d, define update times t=0, i=1～8；

Step 2, the current state of acquisition UUV：

Current time state is obtained by the sensor of UUV itself：U, w are respectively longitudinal direction and vertical velocity, and r is Angle of Trim Speed, x, z are respectively longitudinal coordinate under fixed coordinate system { I } for the UUV center of gravity and vertical coordinate, and θ is Angle of Trim, determines longitudinally Velocity error e_u=u-u_d；

Step 3, be based on Serret-Frenet coordinate system, set up drive lacking UUV level error equation, obtain UUV weight Lengthwise position deviation x under coordinate { I } for the heart_eWith vertical deviation z_eAnd course deviation value θ_e；

Step 4, utilize sliding-mode control, in the case of unknown parameters, separately design speed of a ship or plane Sliding Mode Adaptive Control Rule, position sliding formwork control ratio and Angle of Trim Sliding Mode Adaptive Control rule, by thrust X_prop, expectation the speed of a ship or planeAnd torque M_propControl, make e_u→0,x_e→0,θ_e→0；

Step 5, the boundary layer thickness k for sliding mode controller_i, i=1～3, separately design Fuzzy Control Law；

Make t=t+1, jump back to step 2, carry out control law and the renewal of adaptive law next time, realize vertical to UUV Face path trace precise control.

Present invention is primarily directed to the vertical path following control of the drive lacking UUV in uncertain parameter.The present invention can be real Now only relying on the design of vertical kinetic model makes system quelling controller, is with the design of probabilistic hydrodynamic parameter Adaptive law, and then make control system break away from the dependence to parameter, system obtains robustness, improves uncertainty to sliding formwork control The impact of approach procedure is it is adaptable to various drive lacking UUV.

The present invention utilizes a kind of thought of decoupling, devises the drive lacking UUV path following control based on adaptive sliding mode System.First, the present invention derived with ocean current interference drive lacking UUV vertical kinetic model and vertical plane position, The error model of attitude.Secondly, the present invention proposes a kind of new sliding formwork tendency rate it was demonstrated that the feasibility of this tendency rate, And utilize this tendency rate, devise vertical drive lacking UUV path following control device.Furthermore, using Lyapunov stability reason By, it is that the uncertain parameter in the tracking of the UUV speed of a ship or plane and Angle of Trim tracing control rate devises adaptive law, so that UUV path Tracking system has broken away from the dependence to parameter, and then makes UUV obtain the robustness to uncertain parameter.Finally, based on border Thickness degree follows the tracks of the larger feature of impact to the UUV speed of a ship or plane, using the boundary layer thickness emulating Experience Design T-S fuzzy control certainly Adapt to rule, in order to improve speed of a ship or plane tracking accuracy, and decrease amount of calculation.

Brief description

Fig. 1 is the vertical modeling figure of UUV；

Fig. 2 is drive lacking UUV vertical path trace coordinate system；

Fig. 3 is the control flow chart of the present invention；

Fig. 4 is that drive lacking UUV vertical plane position follows the tracks of analogous diagram.

Specific embodiment

Illustrate below in conjunction with the accompanying drawings and the present invention is described in more detail.

Specific embodiment one：A kind of printenv drive lacking UUV vertical path trace sliding-mode control, including as follows Step：

It is an object of the invention to provide one kind can improve speed of a ship or plane tracking accuracy, reduce the printenv drive lacking of amount of calculation UUV vertical path trace sliding-mode control.

The object of the present invention is achieved like this：

Step one, initialization：

The auto-adaptive parameter of the uncertain parameter for UUVAssign initial value, and determine its ideal velocity for path tracking procedure u_d, define update times t=0, i=1～8；

Step 2, the current state of acquisition UUV：

Current time state is obtained by the sensor of UUV itself：U, w are respectively longitudinal direction and vertical velocity, and r is Angle of Trim Speed, x, z are respectively longitudinal coordinate under fixed coordinate system { I } for the UUV center of gravity and vertical coordinate, and θ is Angle of Trim, determines longitudinally Velocity error e_u=u-u_d；

Step 3, be based on Serret-Frenet coordinate system, set up drive lacking UUV level error equation, obtain UUV weight Lengthwise position deviation x under coordinate { I } for the heart_eWith vertical deviation z_eAnd course deviation value θ_e；

Step 4, utilize sliding-mode control, in the case of unknown parameters, separately design speed of a ship or plane Sliding Mode Adaptive Control Rule, position sliding formwork control ratio and Angle of Trim Sliding Mode Adaptive Control rule, by thrust X_prop, expectation the speed of a ship or planeAnd torque M_propControl, make e_u→0,x_e→0,θ_e→0；

Step 5, the boundary layer thickness k for sliding mode controller_i, i=1～3, separately design Fuzzy Control Law；

Make t=t+1, jump back to step 2, carry out control law and the renewal of adaptive law next time, realize vertical to UUV Face path trace precise control.

Specific embodiment two：

On the basis of specific embodiment one, being sat based on Serret-Frenet described in step 3 in present embodiment Mark system, sets up drive lacking UUV level error equation, obtains position deviation x_e,z_eAnd course deviation value θ_eDetailed process such as Under：

For motion in vertical for the UUV it is only necessary to set up Three Degree Of Freedom model, the variable that needs consider is：Position The amount of putting x, z, Angle of Trim θ, and longitudinal velocity u, lateral velocity w, and Angle of Trim angular velocity q.Can get UUV diving plane Learning equation is：

, just at the initial point of { B }, gravity is equal with buoyancy, and UUV structure is symmetrical, and thinks upper and lower for the center of gravity making UUV Near symmetrical, through a series of abbreviations, can obtain UUV vertical kinetics equation as follows：

In above formula,d₁=-X_u-X_u|u||u|,d₂=-Z_w-Z_w|w||w|,d₃ =-M_q-M_q|q|| q |,Represent UUV centre of buoyancy to center of gravity distance in the vertical projection of UUV, W represents the gravity of UUV, wherein X₍₎,Z₍₎,M₍₎For hydrodynamic force coefficient, X_prop=C_nThe propeller thrust for UUV for n | the n |, C_nIt is by testing the coefficient recording, n For propeller rotating speed, N_propTurn bow moment for UUV.

The UUV of diving plane cannot consider the interference that horizontal ocean current produces, and the ocean current flow velocity under { I } can represent For：

V_I=[u_I,0,w_I]^T(3)

Ocean current flow velocity so under { B } can be expressed as：

Wherein：

To formula (4) two ends derivation and arranged：

Can solve：

The horizontal plane kinetic model then carrying ocean current interference can be expressed as：

Furthermore, give an expected path under { I } coordinate system：

In formula, the arc length of μ --- -- expected path, x_d,z_dCoordinate under { I } for --- --- the vertical expected path.

Because coordinate figure under { I } for the distance of the initial point O of coordinate system { B } to the initial point D (i.e. the desired point of UUV) of { SF } It is exactly the site error of UUV, therefore, based on UUV with respect to the length velocity relation of desired point D, be not difficult to set up following length velocity relation Formula：

In above formula, k_vThe curvature of --- -- vertical expected path

x_e,z_e--- -- in vertical UUV site error

Front two formulas of (1) formula are substituted in (10) formula, and thinksSo vertical UUV path The error equation followed the tracks of can be written as：

Wherein, θ_e=θ+α-θ_dRepresent trim angle error.

Specific embodiment three：Profit on the basis of specific embodiment one or two, described in present embodiment step 4 With sliding-mode control, in the case of unknown parameters, separately design speed of a ship or plane Sliding Mode Adaptive Control rule, position sliding formwork control ratio And Angle of Trim Sliding Mode Adaptive Control rule, by thrust X_propIt is desirable to the speed of a ship or planeAnd torque M_propControl, make e_u→0,x_e →0,θ_e→ 0 detailed process is as follows：

Using a kind of new sliding formwork tendency rate

Wherein, s represents sliding-mode surface function, k>0 is handoff gain, and ε ＞ 0 is exponential approach term coefficient, and 0 ＜ α ＜ 1 is design Parameter.In formula (12), when state point from sliding-mode surface farther out when, exponential approach item plays a major role so that state point quickly becomes It is bordering on sliding-mode surface；When state point reaches near sliding-mode surface ,-k | s |^αSgns item plays a major role, and reduces switching increasing by suitable Benefit gets a promotion making Control platform.

In conjunction with new tendency rate (12), first for the sliding formwork of UUV design speed tracing subsystem and position tracking subsystem Control law.Choose sliding-mode surface function s that the speed of a ship or plane is followed the tracks of_1ver=u-u_d, sliding-mode surface function s that position is followed the tracks of_2ver=x_e- 0, in conjunction with The first formula in kinetic model (8) with ocean current interference, and the first formula of error model (11) formula, can readily set Count out：

For bow to angle tracking control subsystem, choose sliding-mode surface functionC ＞ 0 formula design parameter, in conjunction with (8) the 3rd formula in and the 3rd formula of (11) formula, bow phase angle tracing control rule is as follows：

k₁＞ 0, k₂＞ 0 and k₃＞ 0 is handoff gain, ε₁＞ 0, ε₂＞ 0 and ε₃＞ 0 is the coefficient of exponential approach item, 0 ＜ α₁ ＜ 1,0 ＜ α₂＜ 1 and 0 ＜ α₃＜ 1 is design parameter.

Empirical tests, three tracing control rules of design all can be stablized.Not true in view of there is parameter in UUV mathematical model The qualitatively impact impact of interference (ocean current added in model), for based on the speed of a ship or plane designed by one, second mathematical model, vertical For the tracing control subsystem of inclination angle, its sliding formwork approach procedure also can be affected by uncertain noises.For this reason, it is necessary to be phase The uncertain parameter design adaptive law closing.

It is first the uncertain parameter design adaptive law in Angle of Trim control law below.Rewrite the power with ocean current interference Learn the 3rd formula in model (8)：

Wherein：

Then control law (14) can be rewritten as：

If the uncertain parameter b (15) and in (17)₁,b₂,b₃And b₄Estimated value be respectivelyWithSimultaneously DefinitionWithThen can obtain：

To bow phase angle sliding-mode surface functionDerivation, hasIn conjunction with (18)：

Choose Lyapunov function：

To (20) two ends derivation, and (19) are substituted into：

According to formula (21) final step, choose indeterminateAdaptive law as follows：

Wherein, constant ρ₁＞ 0, ρ₂＞ 0, ρ₃＞ 0, ρ₄＞ 0.(22) formula is substituted in (21), can obtainEqual sign is only in s_3verObtain when=0, therefore UUV trim angle tracking error is Lyapunov meaning Stable, then s_3verIt is bounded, control input M_propInevitable bounded, is the uncertain parameter design in Angle of Trim control law Adaptive law is stable.

According to the mentality of designing of Angle of Trim, easily draw the uncertain parameter adaptive law of UUV speed of a ship or plane tracing control.Choose (8) in formula, the first formula is as follows：

Wherein：

So indeterminateAdaptive law can be expressed as：

Equally, the speed of a ship or plane tracing subsystem in diving plane for the provable UUV and position tracking subsystem are stable.

Thus can obtain, the UUV vertical path trace adaptive sliding-mode observer system designed by the present invention can be expressed as：

Specific embodiment four：On the basis of a kind of any of the above described specific embodiment, present embodiment step 5 institute The detailed process of the boundary-layer design Fuzzy Control Law to sliding mode controller stated is as follows：

Firstly, it is necessary to Sigmoid function is replaced the sign function in the first formula in (26) formula：

Wherein,λ₁Represent boundary layer thickness parameter.

It is based on experience to design former piece and the consequent of T-S fuzzy control, and then improve UUV speed of a ship or plane tracking accuracy.

By experience, parameter lambda in boundary layer thickness φ and formula (27)₁Relation can be written as：φ=1/ λ₁.Therefore, relatively Little boundary layer thickness φ will correspond to larger λ₁Value, on the contrary less λ will be corresponded to₁Value.Boundary layer thickness φ and the speed of a ship or plane are followed the tracks of steady State error u_essRelation can be expressed as：

φ=k_ess|u_ess| (28)

Wherein, proportionality coefficient k_ess＞ 0.UUV speed of a ship or plane tracking error u_eCan converge to quickly in the presence of control law (27) u_ess, it can be considered that (28) formula is：

φ≈k_ess|u_e| (29)

Due to the relation shown in (29), can be by UUV speed of a ship or plane tracking error | u_e| as the input of fuzzy controller, border Thickness degree φ is as output.The expertise set up for T-S fuzzy model may be summarized to be：When | u_e| when larger, φ is selected Larger, to reduce buffeting；When | u_e| when less, by φ select larger, to improve tracking accuracy.

It is usually no more than 4 sections (about 2m/s) in view of the UUV work speed of a ship or plane used by the present invention, then | u_e| domain be [0,2], the static error that the speed of a ship or plane is followed the tracks of about stable in (speed of a ship or plane (saving) × 0.1) m/s, therefore, using static error as The criteria for classifying of fuzzy set, can be by | u_e| domain divide Z (zero), S (little), the big fuzzy set of B (big) three, as Fig. 1.

l₁,l₂Selection should meet completeness require.Based on relational expression (29), the consequent of T-S fuzzy rule can be set up, So fuzzy rule can be written as：

Wherein, Δ_i, i=1,2,3 represents fuzzy set Z, S, B respectively.Proportionality coefficient k_iess, i=1,2,3 is to be navigated by UUV Fast numerical simulation experience is determining.The parameter identification process of former piece and consequent is eliminated, amount of calculation is few in above-mentioned design process, Real-time is good.

Carry out emulation experiment with reference to checking embodiment, experimental result is as shown in Figure 4：

Path selection y=15sin (0.15x) is as expected path, the initializaing variable of UUVAuto-adaptive parameter initial value b₁=b₂=b₃=b₄=b₅=b₆=b₇=b₈=0；Fig. 4 exhibition Show that drive lacking UUV is in vertical path trace effect under adaptive sliding-mode observer (ASMC) controls.

It is demonstrated experimentally that adaptive sliding mode fuzzy controller proposed by the present invention has more preferable control performance.Answer actual With in, the concrete hydrodynamic parameter of drive lacking UUV need not be obtained, by adaptive method, realize precise path follow the tracks of.With When, control requirement can be met further by adjusting control parameter.

Claims (4)

1. a kind of printenv drive lacking UUV vertical path trace sliding-mode control, is characterized in that：

Step one, initialization：

The auto-adaptive parameter of the uncertain parameter for UUVAssign initial value, and determine its ideal velocity u for path tracking procedure_d, fixed Adopted update times t=0, i=1～8；

Step 2, the current state of acquisition UUV：

Current time state is obtained by the sensor of UUV itself：U, w are respectively longitudinal direction and vertical velocity, and r is Angle of Trim speed Degree, x, z are respectively longitudinal coordinate under fixed coordinate system { I } for the UUV center of gravity and vertical coordinate, and θ is Angle of Trim, determine longitudinally speed Degree error e_u=u-u_d；

Step 3, be based on Serret-Frenet coordinate system, set up drive lacking UUV level error equation, obtain UUV center of gravity and exist Lengthwise position deviation x under coordinate { I }_e, vertical deviation z_eAnd course deviation value θ_e；

Step 4, utilize sliding-mode control, in the case of unknown parameters, separately design speed of a ship or plane Sliding Mode Adaptive Control rule, Position sliding formwork control ratio and Angle of Trim Sliding Mode Adaptive Control rule, by thrust X_prop, expectation the speed of a ship or planeAnd torque M_prop's Control, make e_u→0,x_e→0,θ_e→0；

Step 5, the boundary layer thickness k for sliding mode controller_i, i=1～3, separately design Fuzzy Control Law；

Make k=k+1, jump back to step 2, carry out control law and the renewal of adaptive law next time, realize to UUV vertical road Precise control is followed the tracks of in footpath.

2. printenv drive lacking UUV vertical path trace sliding-mode control according to claim 1, is characterized in that walking Rapid three specifically include：

For motion in vertical for the UUV it is only necessary to set up Three Degree Of Freedom model, UUV diving plane equation is：

$\left\{\begin{array}{c}\stackrel{\·}{x}=ucos\mathrm{\θ}+wsin\mathrm{\θ}\\ \stackrel{\·}{z}=-usin\mathrm{\θ}+w\cos \mathrm{\θ}\\ \stackrel{\·}{\mathrm{\θ}}=q\end{array}\right.---\left(1\right)$

, at the initial point of { B }, gravity is equal with buoyancy for the center of gravity making UUV, and UUV structure is symmetrical, and thinks upper lower aprons pair Claim, abbreviation UUV vertical kinetics equation is：

$\left\{\begin{array}{c}\stackrel{\·}{u}=-\frac{m_2}{m_1}wq-\frac{d_1}{m_1}u+\frac{1}{m_1}{X}_{prop}\\ \stackrel{\·}{w}=\frac{m_1}{m_2}uq-\frac{d_2}{m_2}w\\ \stackrel{\·}{q}=\frac{m_1-m_2}{m_3}uw-\frac{d_3}{m_3}q-\frac{\stackrel{\‾}{BG}W}{m_3}+\frac{1}{m_3}{M}_{prop}\end{array}\right.---\left(2\right)$

In above formula,d₁=-X_u-X_u|u||u|,d₂=-Z_w-Z_w|w||w|,d₃=- M_q-M_q|q|| q |,Represent UUV centre of buoyancy to center of gravity distance in the vertical projection of UUV, W represents the gravity of UUV, wherein X₍₎, Z₍₎,M₍₎For hydrodynamic force coefficient, X_prop=C_nThe propeller thrust for UUV for n | the n |, C_nIt is by testing the coefficient recording, n is to push away Enter device rotating speed, N_propTurn bow moment for UUV；

Ocean current flow velocity under { I } is expressed as：

V_I=[u_I,0,w_I]^T(3)

Ocean current flow velocity under { B } is expressed as：

$\left[\begin{array}{c}{u}_c\\ w_c\end{array}\right]={S_{ver}}^{-1}\left[\begin{array}{c}{u}_I\\ w_I\end{array}\right]---\left(4\right)$

Wherein：

${S_{ver}}^{-1}={S_{ver}}^T=\left[\begin{array}{c}cos\mathrm{\θ}-sin\mathrm{\θ}\\ sin\mathrm{\θ}cos\mathrm{\θ}\end{array}\right]---\left(6\right)$

$\left[\begin{array}{c}{\stackrel{\·}{u}}_c\\ {\stackrel{\·}{w}}_c\end{array}\right]=-{S_{ver}}^{-1}{\stackrel{\·}{S}}_{ver}\left[\begin{array}{c}{u}_c\\ w_c\end{array}\right]---\left(7\right)$

${\[{\stackrel{\·}{u}}_c,{\stackrel{\·}{w}}_c\]}^T={\[-{\mathrm{qw}}_c,{\mathrm{qu}}_c\]}^T---\left(8\right)$

The horizontal plane kinetic model then carrying ocean current interference is expressed as：

$\left\{\begin{array}{c}\stackrel{\·}{u}=-\frac{m_2}{m_1}wq+\frac{m_1-m_2}{m_1}{\stackrel{\·}{u}}_c-\frac{d_1}{m_1}(u-u_c)+\frac{1}{m_1}{X}_{prop}\\ \stackrel{\·}{w}=\frac{m_1}{m_2}uq+\frac{m_1-m_2}{m_2}{\stackrel{\·}{w}}_c-\frac{d_2}{m_2}(w-w_c)\\ \stackrel{\·}{q}=\frac{m_1-m_2}{m_3}(u-u_c)(w-w_c)-\frac{d_3}{m_3}q-\frac{\stackrel{\‾}{BG}Wsin\mathrm{\θ}}{m_3}+\frac{1}{m_3}{M}_{prop}\end{array}\right.---\left(9\right)$

A given expected path under { I } coordinate system：

$\left\{\begin{array}{c}{x}_d=x_d\left(\mathrm{\μ}\right)\\ z_d=z_d\left(\mathrm{\μ}\right)\end{array}\right.---\left(10\right)$

In formula, the arc length of μ --- -- expected path, x_d,z_dCoordinate under { I } for --- --- the vertical expected path；

$\left[\begin{array}{c}{\stackrel{\·}{x}}_e\\ {\stackrel{\·}{z}}_e\end{array}\right]=\left[\begin{array}{cc}{\mathrm{cos\θ}}_d& -{\mathrm{sin\θ}}_d\\ {\mathrm{sin\θ}}_d& {\mathrm{cos\θ}}_d\end{array}\right]\left[\begin{array}{c}\stackrel{\·}{x}\\ \stackrel{\·}{z}\end{array}\right]-\left[\begin{array}{c}\stackrel{\·}{\mathrm{\μ}}\\ 0\end{array}\right]-\left[\begin{array}{c}{k}_v\stackrel{\·}{\mathrm{\μ}}{x}_e\\ k_v\stackrel{\·}{\mathrm{\μ}}{z}_e\end{array}\right]---\left(11\right)$

k_vThe curvature of --- -- vertical expected path

x_e,z_e--- -- in vertical UUV site error

The error equation of vertical UUV path trace is：

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_e=-\stackrel{\·}{\mathrm{\μ}}(1+k_v{z}_e)+u{\mathrm{cos\θ}}_e\\ {\stackrel{\·}{z}}_e=k_v\stackrel{\·}{\mathrm{\μ}}{x}_e+u{\mathrm{sin\θ}}_e\\ {\stackrel{\·}{\mathrm{\θ}}}_e=q+\stackrel{\·}{\mathrm{\α}}-k_v\stackrel{\·}{\mathrm{\μ}}\end{array}\right.---\left(12\right)$

Wherein, θ_e=θ+α-θ_dRepresent trim angle error.

3. printenv drive lacking UUV vertical path trace sliding-mode control according to claim 2, is characterized in that walking Rapid four detailed process includes：

Sliding formwork tendency rate is：

$\stackrel{\·}{s}=-k|s{|}^{\mathrm{\α}}\mathrm{sgn}s-\mathrm{\ϵ}s---\left(13\right)$

Wherein, s represents sliding-mode surface function, k>0 is handoff gain, and ε ＞ 0 is exponential approach term coefficient, and 0 ＜ α ＜ 1 is design ginseng Number；

It is the sliding formwork control ratio of UUV design speed tracing subsystem and position tracking subsystem first, choose the cunning that the speed of a ship or plane is followed the tracks of Mode surface function s_1ver=u-u_d, sliding-mode surface function s that position is followed the tracks of_2ver=x_e- 0, then：

$\begin{array}{c}{X}_{prop}=-m_1\[k_1|s_{1ver}{|}^{{\mathrm{\α}}_1}\mathrm{sgn}\left(s_{1ver}\right)+{\mathrm{\ϵ}}_1{s}_{1ver}\]+m_{2}wq-\left(m_1-m_2\right){\stackrel{\·}{u}}_c+d_1\left(u-u_c\right)\\ \stackrel{\·}{\mathrm{\μ}}=u{\mathrm{cos\θ}}_e+{\mathrm{\ϵ}}_2{s}_{2ver}+k_2|s_{2ver}{|}^{{\mathrm{\α}}_2}\mathrm{sgn}\left(s_{2ver}\right)\end{array}---\left(14\right)$

For bow to angle tracking control subsystem, choose sliding-mode surface functionThen bow phase angle tracing control rule Rule is as follows：

$\begin{array}{c}{M}_{prop}=-m_3.\[\left(c{\stackrel{\·}{\mathrm{\θ}}}_e+{\mathrm{\ϵ}}_3{s}_{3ver}+k_3|s_{3ver}{|}^{{\mathrm{\α}}_3}\mathrm{sgn}\left(s_{3ver}\right)\right)+\stackrel{\·\·}{\mathrm{\α}}-{\stackrel{\·\·}{\mathrm{\θ}}}_d\]\\ -\left(m_2-m_1\right)\left(u-u_c\right)\left(w-w_c\right)+d_{3}q+\stackrel{\‾}{BG}W\sin \mathrm{\θ}\end{array}---\left(15\right)$

k₁＞ 0, k₂＞ 0 and k₃＞ 0 is handoff gain, ε₁＞ 0, ε₂＞ 0 and ε₃＞ 0 is the coefficient of exponential approach item,

0 ＜ α₁＜ 1,0 ＜ α₂＜ 1 and 0 ＜ α₃＜ 1 is design parameter；

In (14) with (15) formula, there is substantial amounts of uncertain parameter, design adaptive law for these uncertain parameter, in hydrodynamic force In the case of unknown parameters, realize the tracking to expected path；

First, first design adaptive law for the uncertain parameter in Angle of Trim control law, then control law (15) is rewritten as：

$\begin{array}{c}{M}_{prop}=\frac{1}{b_4}\left(-b_1\left(u-u_c\right)\left(w-w_c\right)+b_{2}q+b_3\sin \mathrm{\θ}+f\right),\\ f=-c{\stackrel{\·}{\mathrm{\θ}}}_e-{\mathrm{\ϵ}}_3{s}_{3ver}-k_3|s_{3ver}{|}^{{\mathrm{\α}}_3}\mathrm{sgn}\left(s_{3ver}\right)-\stackrel{\·\·}{\mathrm{\α}}+{\stackrel{\·\·}{\mathrm{\θ}}}_d\end{array}---\left(16\right)$

Wherein,

If the uncertain parameter b in (16)₁,b₂,b₃And b₄Estimated value be respectivelyWithDefine simultaneously

WithThen：

$\begin{array}{c}\stackrel{\·}{q}={\tilde{b}}_1(u-u_c)(w-w_c)-{\tilde{b}}_{2}q-{\tilde{b}}_{3}sin\mathrm{\θ}+{\tilde{b}}_4{M}_{prop}+{\hat{b}}_1-{\hat{b}}_{2}q-{\hat{b}}_3\sin \mathrm{\θ}+{\hat{b}}_4{M}_{prop}\\ ={\tilde{b}}_1(u-u_c)(w-w_c)-{\tilde{b}}_{2}q-{\tilde{b}}_{3}sin\mathrm{\θ}+{\tilde{b}}_4{M}_{prop}+f\end{array}---\left(17\right)$

To bow phase angle sliding-mode surface functionDerivation, hasIn conjunction with (17) formula, obtain：

$\begin{array}{c}{\stackrel{\·}{s}}_{3ver}=c{\stackrel{\·}{\mathrm{\θ}}}_e+{\tilde{b}}_1\left(u-u_c\right)\left(w-w_c\right)-{\tilde{b}}_{2}q-{\tilde{b}}_3\sin \mathrm{\θ}+{\tilde{b}}_4{M}_{prop}+f+\stackrel{\·\·}{\mathrm{\α}}-{\stackrel{\·\·}{\mathrm{\θ}}}_d\\ ={\tilde{b}}_1\left(u-u_c\right)\left(w-w_c\right)-{\tilde{b}}_{2}q-{\tilde{b}}_3\sin \mathrm{\θ}+{\tilde{b}}_4{M}_{prop}-{\mathrm{\ϵ}}_3{s}_{3ver}-k_3|s_{3ver}{|}^{{\mathrm{\α}}_3}\mathrm{sgn}\left(s_{3ver}\right)\end{array}---\left(18\right)$

Choose Lyapunov function：

$V=\frac{1}{2}{s}_{3ver}^2+\frac{1}{2}{\mathrm{\ρ}}_1{\tilde{b}}_1^2+\frac{1}{2}{\mathrm{\ρ}}_2{\tilde{b}}_2^2+\frac{1}{2}{\mathrm{\ρ}}_3{\tilde{b}}_3^2+\frac{1}{2}{\mathrm{\ρ}}_4{\tilde{b}}_4^2$

Obtain indeterminateAdaptive law as follows：

${\stackrel{\·}{\hat{b}}}_1=\frac{s_{3ver}(u-u_c)(w-w_c)}{{\mathrm{\ρ}}_1},{\stackrel{\·}{\hat{b}}}_2=-\frac{{\mathrm{qs}}_{3ver}}{{\mathrm{\ρ}}_2},{\stackrel{\·}{\hat{b}}}_3=-\frac{{\mathrm{sin\θs}}_{3ver}}{{\mathrm{\ρ}}_4},{\stackrel{\·}{\hat{b}}}_4=\frac{M_{prop}{s}_{3ver}}{{\mathrm{\ρ}}_4}---\left(19\right)$

Wherein, constant ρ₁＞ 0, ρ₂＞ 0, ρ₃＞ 0, ρ₄＞ 0；

The uncertain parameter adaptive law designing UUV speed of a ship or plane tracing control in the same manner is as follows：

$\begin{array}{c}\stackrel{\·}{u}=-b_{5}wq+b_6{\stackrel{\·}{u}}_c-b_7(u-u_c)+b_8{X}_{prop}\\ =-\frac{m_2}{m_1}wq+\frac{m_1-m_2}{m_1}{\stackrel{\·}{u}}_c-\frac{d_1}{m_1}\left(u-u_c\right)+\frac{1}{m_1}{X}_{prop}\end{array}---\left(20\right)$

Wherein：

$b_5=\frac{m_2}{m_1},b_6=\frac{m_1-m_2}{m_1},b_7=\frac{d_1}{m_1},b_8=\frac{1}{m_1}$

IndeterminateAdaptive law be expressed as：

${\stackrel{\·}{\hat{b}}}_5=-\frac{s_{1ver}wq}{{\mathrm{\ρ}}_5},{\stackrel{\·}{\hat{b}}}_6=\frac{s_{1ver}(-{\mathrm{qw}}_c)}{{\mathrm{\ρ}}_6},{\stackrel{\·}{\hat{b}}}_7=-\frac{s_{1ver}(u-u_c)}{{\mathrm{\ρ}}_7},{\stackrel{\·}{\hat{b}}}_8=\frac{s_{1ver}{X}_{prop}}{{\mathrm{\ρ}}_8}---\left(21\right)$

Thus, UUV vertical path trace adaptive sliding-mode observer system representation is：

$\left\{\begin{array}{c}{X}_{prop}=\frac{1}{{\hat{b}}_8}\[-k_1|s_{1ver}{|}^{{\mathrm{\α}}_1}sgn\left(s_{1ver}\right)-{\mathrm{\ϵ}}_1{s}_{1ver}+{\hat{b}}_{5}wq-{\hat{b}}_6{\stackrel{\·}{u}}_c+{\hat{b}}_7(u-u_c)\]\\ \stackrel{\·}{\mathrm{\μ}}=u{\mathrm{cos\θ}}_e+{\mathrm{\ϵ}}_2{s}_{2ver}+k_2|s_{2ver}{|}^{{\mathrm{\α}}_2}sgn\left(s_{2ver}\right)\\ M_{prop}=\frac{1}{{\hat{b}}_4}(-{\hat{b}}_1(u-u_c\left)\right(w-w_c)+{\hat{b}}_{2}q+{\hat{b}}_{3}sin\mathrm{\θ}-c{\stackrel{\·}{\mathrm{\θ}}}_e-\stackrel{\·\·}{\mathrm{\α}}+{\stackrel{\·\·}{\mathrm{\θ}}}_d)\end{array}\right.---\left(22\right).$

4. printenv drive lacking UUV vertical path trace sliding-mode control according to claim 3, is characterized in that walking Rapid five detailed process includes：

First, Sigmoid function is replaced the sign function in the adaptive sliding-mode observer function of design：

$X_{prop}=\frac{1}{{\hat{b}}_8}\[-k_1|s_{1ver}{|}^{{\mathrm{\α}}_1}\mathrm{\Φ}({\mathrm{\λ}}_1,s_{1ver})-{\mathrm{\ϵ}}_1{s}_{1ver}+{\hat{b}}_{5}wq-{\hat{b}}_6{\stackrel{\·}{u}}_c+{\hat{b}}_7(u-u_c)\]---\left(23\right)$

Wherein,λ₁Represent boundary layer thickness parameter；

Boundary layer thickness φ follows the tracks of steady-state error u with the speed of a ship or plane_essRelation can be expressed as：

φ=k_ess|u_ess| (24)

Wherein, proportionality coefficient k_ess＞ 0_UUVSpeed of a ship or plane tracking error u_eU can be converged to quickly in the presence of control law (22)_ess, because This thinks that (24) formula is：

φ≈k_ess|u_e| (25)

Fuzzy rule is written as：RULEi:If|u_e|isΔ_i,then

Wherein, Δ_i, i=1,2,3 represents fuzzy set Z, S, B respectively；Proportionality coefficient k_iess, i=1,2,3 is by the actual boat of UUV Fast numerical value is determining.