CN106986271B - Consider the marine hoist control method of lasting interference and parameter uncertainty - Google Patents

Abstract

A kind of marine hoist control method of consideration lasting interference and parameter uncertainty, belongs to the technical field that Underactuated Mechanical Systems automatically control.This method includes：For the marine hoist system dynamics model by lasting interference effect, consider that the Parameter uncertainties including load etc. influence, a kind of nonlinear control method is devised, can realize the control targe of marine hoist, while the gravity that can compensate for during lifting rope lifting and cantilever pitching influences.The experimental results showed that the method can handle the parameter uncertainty and interference effect of marine hoist system, effectively inhibit hunting of load, realizes being accurately positioned for load.

Description

Consider the marine hoist control method of lasting interference and parameter uncertainty

Technical field

The invention belongs to the technical fields that Underactuated Mechanical Systems automatically control, and are suitable for by sea more particularly to one kind The load for the marine hoist system that unrestrained persistent disturbances and systematic parameter uncertainty influence is accurately positioned and disappears pendulum control.

Background technology

For a long time, sea transport due to high-throughput, low cost, transportation range length etc. advantages, in national economy Play important role in development.Sea transport mainly realized by cargo-container ship, in the cargo handling process of container, no Avoidable ground will use marine hoist system.Different from land-bound crane, marine hoist is due to being mounted on freighter, working environment It is more complicated, it is more vulnerable to influence of many uncertain noises, such as wave, strong wind etc., this also substantially increases marine hoist System automatically controls the challenge of problem.Currently, the control of marine hoist is usually by manually realizing.But at the same time, manually There is some defects for operation, such as working efficiency is low, control accuracy is poor.Particularly, when marine hoist system context compared with When being severe, even the worker to know a thing or two is also difficult to realize preferably control the system.Therefore, using automatically controlling skill Art, it has been the task of top priority to design suitable and efficient autocontrol method for marine hoist system.

To crane system, including land and marine hoist system, a most important challenge is the drive lacking characteristic of system, That is the control input number of system is less than system degree of freedom number to be controlled.Between past decades, underactuated system is asked The research of topic has received widespread attention^[1],[2].Specifically, for land-bound crane system, it has been proposed that serial of methods Carry out the hunting of load inhibition problem during processing work, such as input shaper method^[3]-[5], method for planning track^[6]-[8]Equal open loops Control method.In addition to this, better robustness, some scholars devise corresponding Closed-loop Control Strategy in order to obtain^[9]-[12]。

Unlike land-bound crane system, for marine hoist system due to being fixed on hull, its pedestal is can to move It is dynamic, at the same be more vulnerable to include the various interference such as wave, strong wind influence.In other words, marine hoist system is operated in non- In inertial system, this is also the main distinction with land-bound crane.On the other hand, the interference that marine hoist is subject to include matching interference with Non-matching two kinds of interference, increases the difficulty of design of control method.For these reasons, for the control method of land-bound crane without Method is applied to marine hoist system, therefore, suitable Automatic Control Strategy is designed for marine hoist system, has theoretical and reality Meaning, at the same it is also extremely challenging.

Although the automatic control problem of land-bound crane system has been widely studied, the research of marine hoist system control is still located In the stage of opposing primary.So far, the control method for being directed to the system on a small quantity is only proposed.Rauh et al.^[13]It proposes A method of based on linear matrix inequality, to handle external interference, be controlled effectively result.Document [14] proposes A kind of variable-gain observer and Gain-scheduling control rule control Maryland marine hoist system.Qian et al.^[15]Propose one kind Repetitive study control strategy, for inhibiting periodic sea wave disturbance.Document [16] proposes a kind of linear based on partial feedback The method of change can obtain the control result of final Uniformly stable.Some control methods based on sliding formwork^[17]-[19]Also by success Ground is applied to marine hoist system, has obtained better robust control effect.In addition, the control method based on fuzzy logic^[20] It can also be used for marine hoist and obtain effective control effect.

Currently, for the control of marine hoist system, there are still some urgent problems to be solved.First, it is hung in view of peculiar to vessel There are the pitching of cantilever and the lifting of load in vehicle system work process, need precisely to mend the gravity of cantilever and load It repays；However, in practice, it is difficult to accurately measure cantilever quality etc.；Secondly, existing major part method is required to hang to peculiar to vessel Vehicle system model carries out certain approximate processing, and when the condition that approximation needs cannot be satisfied, the effect of these methods may It has a greatly reduced quality；Finally, part control method can only obtain the control result of ultimately uniform boundary, can not ensure that error convergence arrives Zero, meanwhile, certain methods do not account for the elevating movement of load, application field relative narrower.

In conclusion for processing at present there are still these problems, obtain better marine hoist system control effect, it is anxious Suitable autocontrol method need to be designed.

Invention content

Present invention aim to address in place of current marine hoist system control method above shortcomings, one kind is provided Consider the marine hoist control method of lasting interference and parameter uncertainty.

This invention address that by constructing and analyzing new stored-energy function, propose a kind of novel to be directed to parameter uncertainty Marine hoist control method, and consider lifting rope length constraint, may be implemented to unknown cantilever and load the effective compensation of gravity, Ensure that lifting rope length is in effective range in the course of work simultaneously.This method is not necessarily to carry out approximate processing to model, and can be with Asymptotically stable control effect is obtained, is applied to practical marine hoist platform and is tested, it can be uncertain in systematic parameter In the case of, preferable control effect is obtained, working efficiency is improved.

The marine hoist control method of consideration lasting interference and parameter uncertainty provided by the invention：

1st, system control targe and corresponding constraint are determined

The control targe of marine hoist system includes following three part：1. in geodetic coordinatesUnder, adjust load situation Reach its target location [y_gd z_gd], wherein y_gd,z_gdIt respectively representsThe coordinate of load target position under coordinate system；2. inhibiting With elimination geodetic coordinatesUnder hunting of load；3. during entire control, the lifting rope length of marine hoist system, which should be in, to be had It imitates in range, i.e.,

L_min＜ L (t) ＜ L_max (13)

Wherein, L (t) indicates the lifting rope length of marine hoist system；T in bracket indicates the time, and (t) is indicated behind variable The variable is that it is subsequent (t) to omit most number variable for simplicity for the function about the time；L_min,L_maxIt indicates respectively effective The lower limit and the upper limit of lifting rope length.

2nd, error signal and auxiliary function are defined

Introduce following coordinate transform：

Wherein, subscript T representing matrixes/vector transposition, φ (t) indicate that the pitch angle of cantilever, L (t) indicate the length of lifting rope, θ (t) indicates that load pivot angle, ρ (t) indicate that hull roll angle caused by wave, ξ represent transformed state vector, ξ₁(t),ξ₂ (t),ξ₃(t) system state amount after representation transformation, the t in bracket indicate the time, behind variable (t) indicate the variable be about It is subsequent (t) to omit most number variable for simplicity for the function of time；Using above-mentioned coordinate transformation method, in conjunction with system Control targe, the target location of quantity of state is as follows after can must converting：

Wherein, arccos indicates inverse cosine function, y_gd,z_gdRepresent the target location coordinate of load, L_jRepresent the length of cantilever Degree, ξ_1d,ξ_2d,ξ_3dRespectively represent quantity of state ξ after converting₁(t),ξ₂(t),ξ₃(t) target location.

Further, error signal e is defined₁(t),e₂(t),e₃(t) as follows：

e₁=ξ₁-ξ_1d,e₂=ξ₂-ξ_2d,e₃=ξ₃-ξ_3d=ξ₃ (19)

Then error signal is about the derivative of time：

Wherein,Respectively represent ξ₁(t),ξ₂(t),ξ₃(t) about the derivative of time.Define auxiliary function γ₁(e₁),γ₂(e₂),γ₃(ξ₃) as follows：

Wherein,Indicate positive parameter, function s (*'s) is defined as follows：

Wherein, the independent variable of * representative functions s (*).

3rd, control law determines

Design cantilever pitch moment u_m(t) and lifting rope tractive force u_f(t) control law is as follows：

Wherein,For positive control gain.

4th, control method is realized

Using the sensor on marine hoist, the pitch angle φ (t) and angular speed of cantilever are measuredThe length L of lifting rope (t) and long change of rope speedHull roll angle ρ (t) and its angular speedUsing formula (24), control is calculated in real time Signal, for controlling corresponding driving motor, realization accurately controls marine hoist system.

The theoretical foundation and derivation of the method for the present invention:

1st, system model

For marine hoist system, useRespectively represent earth coordinates and hull coordinate system.z_gAxis and y_gAxis It is respectively perpendicular to and is parallel to ground level.z_sAxis and y_sAxis is respectively perpendicular to and is parallel to boat body plane.Utilize Lagrange Method, the kinetic model for obtaining marine hoist system are as follows：

Wherein, φ (t), L (t), θ (t) indicate cantilever pitch angle, lifting rope length and load pivot angle respectively, Indicate cantilever rate of pitch and angular acceleration,The speed and acceleration of long change of rope are represented,It is negative Pivot angle angular speed is carried,To load pivot angle angular acceleration；T indicates the time, and (t) indicates that the variable is about the time behind variable Function in the case where not producing ambiguity, (t) in most of variable is omitted in subsequent formula for simplicity； m_c,m_d,L_jRespectively indicate load quality, cantilever barycenter-pitching shaft distance and cantilever quality product and jib-length；J Cantilever rotary inertia is represented, g is acceleration of gravity；C_θ-φ,S_θ-φ,C_φ-ρ,C_θ-ρ,S_θ-ρIt is defined as follows：

C_θ-_φ=cos (θ-φ), S_θ-_φ=sin (θ-φ), C_φ-ρ=cos (φ-ρ), C_θ-_ρ=cos (θ-ρ), S_θ-_ρ=sin (θ-ρ)

ρ(t),Represent hull roll angle and corresponding angular speed, angular acceleration；u_m(t),u_f(t) it indicates respectively Cantilever torque and lifting rope tractive force, f_d1(t),f_d2(t),f_d3(t) external interference is represented, concrete form is as follows：

Wherein, c is resistance dependent constant.

Kinetic model (1)-(3) are rewritten into matrix form, it is specific as follows：

Wherein, q=[φ L θ]^TFor system mode vector, subscript T representing matrixes/vector transposition, u=[u_m(t) u_f(t) 0]^TExpression system input vector, G (q)=[(m_cL_j+m_d)gC_φ-ρ -m_cgC_θ-ρ m_cgLS_θ-ρ]^TExpression system gravity matrix, f_d= [f_d1(t) f_d2(t) f_d3(t)]^TIndicate that interference is vectorial, M (q),Indicate system inertia matrix and centripetal force-coriolis force Matrix, expression are as follows：

Wherein,

It is as follows to define coordinate transformation relation：

Wherein, ξ₁(t),ξ₂(t),ξ₃(t) system mode after representation transformation, ξ represent transformed state vector.It is based on This, motive power model (1)-(4) can be converted to following form：

Wherein,The interference vector after arranging is represented,WithIt is after indicating conversion respectively First derivatives and second dervative of the system state vector ξ about the time, are defined as follows：

Wherein,Represent system mode ξ after converting₁(t),ξ₂(t),ξ₃(t) it is led about the single order of time Number,Indicate system mode ξ after converting₁(t),ξ₂(t),ξ₃(t) about the second dervative of time.Generation Centripetal force-coriolis force matrix after table arrangement, concrete form are as follows：

Wherein,

Analysis can obtain, and transformed model has following property：

Property 1：Matrix M (q),Between meet following relationship,Wherein,Indicate first derivatives of the M (q) about the time.

Property 2：M (q) is positive definite matrix, and to arbitrary vectorThere is positive constant λ_m,λ_MMeet as follows Relationship：

λ_m||x||²≤x^TM(q)x≤λ_M||x||² (10)

In real work, it is difficult to measure m_c,m_dExact value, its bound can generally be estimated, i.e.,

Wherein, m _cIt indicates to load quality m_cThe bound of estimation, m _dIt indicates to m_dThe bound of estimation.

On the other hand, lifting rope length when marine hoist is started to work should be in effective range, i.e.,

L_min＜ L (0)=ξ₂(0) ＜ L_max, (12)

Wherein, L_min,L_maxThe minimum value and maximum value of effective lifting rope length are indicated respectively.It is similar with document [3]-[20], It is assumed that earth coordinatesUnder load pivot angle | ξ₃(t)|≤π/2。

It is an object of the present invention to design suitable control method, being accurately positioned and putting to marine hoist system load is realized It is dynamic to inhibit control.In terms of the target mainly includes following three：1. in geodetic coordinatesUnder, it adjusts load situation and reaches its target Position [y_gd z_gd], wherein y_gd,z_gdIt respectively representsThe y of load target position, z coordinate under coordinate system；2. inhibiting and eliminating Geodetic coordinatesUnder hunting of load；3. during entire control, the lifting rope length of marine hoist system should be in effective range It is interior, i.e.,

L_min＜ L (t) ＜ L_max. (13)

It can be geodetic coordinatesThe coordinate representation of lower load situation is as follows：

According to above-mentioned control targe, ξ is needed₃(t)=θ (t)-ρ (t) goes to zero, to inhibit earth coordinatesUnder it is negative It carries and swings.At this point, the target location coordinate of load can be expressed as form：

y_gd=L_j cos(ξ₁),z_gd=L_j sin(ξ₁)-ξ₂. (15)

Then, the control targe of system can indicate as follows：

y_g→y_gd,z_g→z_gd. (16)

Arrangement can obtain quantity of state ξ after coordinate transform₁(t),ξ₂(t),ξ₃(t) target is as follows：

Wherein, arccos indicates inverse cosine function；So, the control targe of marine hoist system is converted into：Design is suitable Control strategy so that ξ₁(t),ξ₂(t),ξ₃(t) its target location is converged to respectively, i.e.,

ξ₁→ξ_1d,ξ₂→ξ_2d,ξ₃→ξ_3d=0. (18)

2nd, design of control law

For the control targe for realizing described in formula (18), it is as follows to define error signal：

e₁=ξ₁-ξ_1d,e₂=ξ₂-ξ_2d,e₃=ξ₃-ξ_3d=ξ₃ (19)

In formula, e₁(t),e₂(t),e₃(t) quantity of state ξ is indicated respectively₁(t),ξ₂(t),ξ₃(t) position error.It is peculiar to vessel to hang The mechanical energy expression formula of vehicle system is as follows：

Wherein, E (t) indicates the mechanical energy of system.In next step, with ξ, ξ₂(t),ξ₃(t) q, L in E (t) are replaced respectively (t), θ (t) can construct following function：

Formula (21) arranges as follows time derivation：

Assuming that systematic parameter is it is known that can directly design the control law of following form at this time：

Wherein,Indicate positive control gain.Using the control law, the control of system may be implemented Target processed, while realizing to cantilever and loading the compensation of gravity.However, m_d,m_cExact value be often difficult to obtain, therefore nothing The control law (23) is applied in Practical Project by method.

To solve the above problems, The present invention gives a kind of control law considering parameter uncertainty, concrete form is such as Under：

Wherein,For positive control gain, L_max,L_minIndicate the upper of effective rope length Lower bound, γ₁(e₁),γ₂(e₂) indicate following auxiliary function：

γ₁(e₁)=α₁s(e₁),γ₂(e₂)=α₂s(e₂) (25)

Wherein,Positive parameter is represented, s (*) is a kind of saturation function, is defined as follows：

Wherein, the independent variable of * representative functions s (*).Analysis mode (25) and (26), it is known that following relationship is set up：

Theoretically, k_p1,k_d1,k_i1,k_p2,k_d2,k_i2,k_rMeet：

Wherein,It indicates to unknown m_cAnd m_dThe upper bound of estimation,m _cIt indicates to load quality m_cThe lower bound of estimation,Representative meets the normal number of relational expression (10),Indicate positive auxiliary parameter,Indicate auxiliary function γ₃(ξ₃) in parameter, γ₃(ξ₃) be defined as

Wherein, the definition of s (*) is referring to formula (26).

It is worth noting that being limited by the influence of Lyapunov analysis method conservative itself, provided in formula (28) Only theoretically k_p1,k_d1,k_i1,k_p2,k_d2,k_i2,k_rNeed the condition met.It is sent out with after experiment test by largely emulating It is existing, from the perspective of practical application, as long as choosing k_p1,k_d1,k_i1,k_p2,k_d2,k_i2,k_rFor just, control law (24) can be just The control to marine hoist system is realized in often work.

3rd, stability analysis

This part will prove that control law proposed by the invention (24) can be in lasting ship by stringent mathematical analysis In the case that body rolling disturbance and systematic parameter are unknown, make load running to it in earth coordinatesUnder target location, And simultaneously effective inhibit hunting of load, i.e.,

Meanwhile in whole process, lifting rope length L (t) will be remained in effective range, i.e.,

L_min＜ ξ₂(t)=L (t) ＜ L_max. (31)

To prove the conclusion, some lemma are provided first.

Lemma 1：To arbitrarily meeting k ＞ (m_cL_j+m_d) g positive real numberFollowing function f₁(ξ₁) it is positive definite integral form：

It proves：To f₁(ξ₁) about ξ₁Derivation utilizes relationship e₁=ξ₁-ξ_1d, obtain following result：

By formula (33) it is found that

Above formula shows ξ₁=ξ_1dIt is function f₁(ξ₁) a stationary point.Further, f₁(ξ₁) about ξ₁Second dervative such as Under：

By k ＞ (m_cL_j+m_d) g is it is found that following relationship is set up：

In summary, ξ₁=ξ_1dIt is function f₁(ξ₁) minimum point.On the other hand, formula (34) and (36) are it is found that ξ₁=ξ_1d For function f₁(ξ₁) unique stationary point.Therefore, ξ₁=ξ_1dIt is f₁(ξ₁) minimum point, f₁(ξ₁)≥f₁(ξ_1d)=0, i.e. function f₁ (ξ₁) it is positive definite integral form, formula (32) is set up.

Lemma 2：Work as ξ₂=L ＞ L_min, and when meeting the constraints in formula (28), if minor function W (t) is non-negative：

Wherein, γ (e)=[γ₁(e₁) γ₂(e₂) γ₃(ξ₃)]^T, γ₃(ξ₃) definition see formula (29).

It proves：By formula (10), (25)-(27), (29), the Section 2 in formula (37) can be organized into following form：

Work as ξ₂=L ＞ L_minWhen, Section 3 arranges as follows in formula (37)：

It can be obtained by formula (32),

To sum up, formula (37) can be rewritten as following form：

Therefore, when the constraints in formula (28) meets, W (t) is about e₁(t),e₂(t),e₃(t) positive function, draws Reason 2 is set up.

Lemma 3：WhenWhen, following inequality is set up：

|cos(ξ₁)-cos(ξ_1d)|≤k_g|ξ₁-ξ_1d|=k_g|e₁|. (42)

It proves：It is of equal value with following inequality to be apparent from formula (42)：

Ming Dynasty style (43) is set up as evidence, the auxiliary function being defined as follows：

f₂(ξ₁) to ξ₁Derivation obtains

By formula (45) it is found thatThat is ξ₁=ξ_1dIt is f₂(ξ₁) stationary point.f₂(ξ₁) to ξ₁Seek second order It leads, and according toIt can obtain

Therefore, ξ₁=ξ_1dIt is f₂(ξ₁) maximum point.Meanwhile by formula (46), ξ can be obtained₁=ξ_1dIt is f₂(ξ₁) uniquely stay Point, i.e. ξ₁=ξ_1dIt is f₂(ξ₁) maximum of points.So f₂(ξ₁)≥f₂(ξ_1d)=0 is set up, i.e. lemma 3 is set up.

It below will be to conclusion shown in formula (30), (31) into line justification.First, the scalar function being defined as follows：

Wherein,Indicate positive control gain, ψ₁(t),ψ_w(t) it represents as follows Auxiliary function：

Then, formula (47) is substituted into (24), and arranged, can be obtained to time derivation,

Formula (24) is substituted into formula (8), is arranged,

Wherein, m_n2r=k_r[(ξ_2d-L_max)/(ξ₂-L_max)³+(ξ_2d-L_min)/(ξ₂-L_min)³]e₂+m_cg[1-cos(ξ₃)],

m_n1r=(m_cL_j+m_d)g[cos(ξ₁)-cos(ξ_1d).Then, 6-7 in formula (49), it is rewritable as follows：

Formula (51) is substituted into formula (49), abbreviation can obtain

It is as follows that its upper bound can be obtained using Young inequality to the 7th on the right side of formula (52)：

In next step, using lemma 3, the 8th in formula (52) can carry out following processing：

In above formula, property shown in formula (27) has been used.On the other hand, 9-10 in formula (52) can be handled as follows：

To the 11st in formula (52), using formula (9), result as follows can be obtained：

Then, to the 12nd in formula (52), relationship as follows can be obtained：

Further, using formula (26), (27), (29), relationship as follows can be obtained：

In next step, formula (53)-(58) are substituted into formula (52), arrange abbreviation and obtains,

According to the control gain constraint condition in formula (28), it is known that first 6 on the right side of formula (47) are non-positve term, and the 7th Item still needs to further analyze.Since entire closed-loop system is continuous, it is known that the quantity of state of system can only consecutive variations, i.e. shape Saltus step will not occur for the track of state amount.In view of lifting rope length L (t)=ξ₂(t) initial value is in effective range, i.e. L_min ＜ L (0)=ξ₂(0) ＜ L_max[referring to formula (12)].Must then have moment T, when t ∈ [0, T) when, the coefficient before formula (59) the 7th It is negative, i.e.-k_r[(ξ_2d-L_max)/(ξ₂-L_max)³+(ξ_2d-L_min)/(ξ₂-L_min)³] ＜ 0.Therefore, when t ∈ [0, T) when, by formula (59) it can obtain,

Without loss of generality, it is assumed that ξ₂(t) t ∈ [0, T) when, have disengaging section (L_min,L_max) trend.In view of ξ₂(t) It is the variable of consecutive variations, needs the boundary for reaching the section first, i.e., as t=T, ξ₂(t)=L_minOr ξ₂(t)=L_max；This When, by the 7th in formula (47) it is found that V (t)=+ ∞.Simultaneously, it is contemplated that ξ₂(t) continuity, then have This and formula (60) conclusion contradiction.Therefore, it is known that ξ₂(t) without departing from section (L_min,L_max), i.e.,

By formula (61) it is found that in formula (59) the 7th be it is negative, in summary,

Next, formula (47) is rewritten into following form：

By analyzing it is found that first 8 of formula (63) are non-negative.Then, lemma 1 and lemma 2 are utilized, it is known that remaining in formula (63) Item is also positive definite.Therefore, function V (t) is positive definite integral form, can be used as Liapunov candidate functions.

Using formula (47) and (62), it can obtain and such as draw a conclusion：

Further, if e₂(t) → 0, then have IfThen basisWith It can obtainConvolution (64), it is known that

Due toIt is negative semidefinite, needs the asymptotic convergence using invariant set analytical proof closed-loop system.Definition is maximum constant Collect Φ, is included in following set omega

According to formula (62), it is known that in set Φ

Formula (67) is substituted into formula (8), (24), is obtained

This also just illustrates that designed control law can accurately compensate cantilever and the gravity of load.

Finally, by formula (67) it is found that maximum invariant set utilizes Russell's principle of invariance only comprising closed-loop system equalization point [11] provable formula (30) is set up.Meanwhile the result of formula (61) demonstrates rope length in whole process and is in effective range.By formula (68) it can obtain, the control of system inputs u_m(t),u_f(t) (m is finally converged to respectively_cL_j+m_d)gcos(ξ_1d),-m_cG, it was demonstrated that this Invention institute extracting method can handle m_d,m_cUncertainty.

The advantages of the present invention:

For marine hoist (abbreviation ship is hung) system, the present invention proposes a kind of pendulum position control method that effectively disappears.Phase Than existing method, this method is directed to the marine hoist system for being continued rolling interference by hull, considers parameter uncertainty, passes through Suitable control strategy compensation gravity is designed, that realizes load is accurately positioned and swings inhibition, before having good practical application Scape.

Description of the drawings：

Attached drawing 1 is the method for the present invention and control methods experimental result in 1 (embodiment 1) of experiment；ξ₁(t),ξ₂(t),ξ₃ (t) system mode after representation transformation is specifically defined and sees formula (7)；u_m(t),u_f(t) indicate that cantilever torque and lifting rope are led respectively Gravitation.

Specific implementation mode：

Embodiment 1：

1st, experimental procedure describes

1.1st, system control targe and corresponding constraint are determined

The control targe of marine hoist system includes following three part：1. in geodetic coordinatesUnder, adjust load situation Reach its target location [y_gd z_gd], wherein y_gd,z_gdIt respectively representsThe coordinate of load target position under coordinate system；2. inhibiting With elimination geodetic coordinatesUnder hunting of load；3. during entire control, the lifting rope length of marine hoist system, which should be in, to be had It imitates in range, i.e.,

L_min＜ L (t) ＜ L_max (13)

Wherein, L (t) indicates the lifting rope length of marine hoist system, the t expression times in bracket, and (t) is indicated behind variable The variable is the function about the time, L_min,L_maxThe lower limit and the upper limit of effective lifting rope length are indicated respectively.

1.2nd, error signal and auxiliary function are defined

Introduce following coordinate transform：

Wherein, subscript T representing matrixes/vector transposition, φ (t) indicate that the pitch angle of cantilever, L (t) indicate the length of lifting rope, θ (t) indicates that load pivot angle, ρ (t) indicate that hull roll angle caused by wave, ξ represent transformed state vector, ξ₁(t),ξ₂ (t),ξ₃(t) system state amount after representation transformation, the t in bracket indicate the time, behind variable (t) indicate the variable be about It is subsequent (t) to omit most number variable for simplicity for the function of time；Using above-mentioned coordinate transformation method, in conjunction with system Control targe, the target location of quantity of state is as follows after can must converting：

Wherein, arccos indicates inverse cosine function, y_gd,z_gdRepresent the target location coordinate of load, L_jRepresent the length of cantilever Degree, ξ_1d,ξ_2d,ξ_3dRespectively represent quantity of state ξ after converting₁(t),ξ₂(t),ξ₃(t) target location.

Further, error signal e is defined₁(t),e₂(t),e₃(t) as follows：

e₁=ξ₁-ξ_1d,e₂=ξ₂-ξ_2d,e₃=ξ₃-ξ_3d=ξ₃ (19)

Then error signal is about the derivative of time：

Wherein,Respectively represent ξ₁(t),ξ₂(t),ξ₃(t) about the derivative of time.Define auxiliary function γ₁(e₁),γ₂(e₂),γ₃(ξ₃) as follows：

Wherein,Indicate positive parameter；Function s (*'s) is defined as follows：

Wherein, the independent variable of * representative functions s (*).

1.3rd, control law determines

Design cantilever pitch moment u_m(t) and lifting rope tractive force u_f(t) control law is as follows：

Wherein,For positive control gain.

1.4th, control method is realized

Using the sensor on marine hoist, the pitch angle φ (t) and angular speed of cantilever are measuredThe length L of lifting rope (t) and long change of rope speedHull roll angle ρ (t) and its angular speedUsing formula (24), control is calculated in real time Signal, for controlling corresponding driving motor, realization accurately controls marine hoist system.

2nd, experimental result describes

To verify the validity of institute's extracting method of the present invention, according to above-mentioned steps, carried out on marine hoist experiment porch real It tests.Cantilever rotary inertia, jib-length in experiment porch etc. are as follows：

J=0.2457kgm²,L_j=0.65m, m_d=0.29kgm, g=9.8m/s²

The initial value of system mode is selected as ξ₁(0)=0rad, ξ₂(0)=0.6m, ξ₃(0)=0rad；Wherein, rad is indicated Radian, m indicate rice.The target location coordinate being supported under earth coordinates isz_gd=0.125m is utilized Corresponding system mode target can be calculated in formula (17)

ξ_1d=π/6rad (30deg), ξ_2d=0.2m, ξ_3d=0rad

Wherein, deg degree of a representations.The rolling disturbance of hull is set as

The Significant Change range of rope length is set as (L_min,L_max)=(0.18,1.0) [m].Assuming that m_dIt is unknown, and above and below it Boundary is estimated as m _d=0.2kgm.

2.1st, 1 is tested：It is compared with existing method.This experiment will be verified being accurately positioned in load of institute extracting method, be swung Validity in terms of inhibition, and itself and the method in document [16] are compared.This tests the essence of selected load quality Really value is m_c=0.34kg assumes that it is unknown in experiment, estimates of upper and lower bounds is m _c=0.2kg.By multiple It tests, the control gain in document [16] in control methods is selected as：

k₁=25.5, k₂=9.6, k₃=3.3, k_α=0.12, k_β=0.23, k_L1=20.7, k_L2=6.3, k_x=1.1, σ =0.015,

And the control gain of the method for the present invention is selected as：

k_p1=18, k_d1=9.9, k_i1=2, k_p2=27, k_d2=4.1, k_i2=0.4, α₁=0.1, α₂=0.02, k_r= 0.01。

Attached drawing 1 gives experimental result, wherein the system after coordinate transform is set forth in 5 subgraphs from top to bottom Quantity of state ξ₁(t),ξ₂(t),ξ₃(t) and system control inputs u_m(t),u_f(t) curve changed over time；Solid line in attached drawing 1 The method of the present invention and the experimental result of control methods are respectively represented with dotted line；1st subgraph and the 2nd (from top to bottom) in attached drawing 1 Dotted line in a subgraph indicates ξ respectively₁(t),ξ₂(t) target location ξ_1d,ξ_2d.Meanwhile experimental result is shown for convenience, ξ₁(t),ξ₃(t) unit of curve has been converted into angle (deg) from radian (rad).

As can be seen that two methods can be with driving condition amount ξ from attached drawing 1₁(t),ξ₂(t),ξ₃(t) it reaches corresponding Target, i.e. driving load reach its target location.But the experimental result of control methods is there are apparent overshoot, and regulating time compared with It is long；And the experimental result of the method for the present invention there's almost no overshoot.On the other hand, although can be seen that from curve shown in dotted line Control methods may be implemented the inhibition to hunting of load, but when loading the Residual oscillations after reaching target and continue for long Between；And in the range of hunting of load can be restricted to smaller by the experimental result (shown in solid) of the method for the present invention, while almost There is no Residual oscillations.From last two subgraphs it can also be seen that the control input curve of the method for the present invention is compared with control methods It is more smooth, it is easier to engineer application.

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Claims (1)

1. a kind of marine hoist control method of consideration lasting interference and parameter uncertainty, it is characterised in that this method includes：

1st, system control targe and corresponding constraint are determined

The control targe of marine hoist system includes following three part：1. in geodetic coordinatesUnder, it adjusts load situation and reaches Its target location [y_gd z_gd], wherein y_gd,z_gdIt respectively representsThe coordinate of load target position under coordinate system；2. inhibiting and disappearing Except geodetic coordinatesUnder hunting of load；3. during entire control, the lifting rope length of marine hoist system should be in effective model In enclosing, i.e.,

L_min＜ L (t) ＜ L_max (13)

Wherein, L (t) indicates the lifting rope length of marine hoist system；T in bracket indicates the time, and (t) indicates the change behind variable It is subsequent (t) to omit most number variable for simplicity for the function about the time for amount；L_min,L_maxEffective lifting rope is indicated respectively The lower limit and the upper limit of length；

2nd, error signal and auxiliary function are defined

Introduce following coordinate transform：

Wherein, subscript T representing matrixes/vector transposition, φ (t) indicate that the pitch angle of cantilever, L (t) indicate the length of lifting rope, θ (t) Indicate that load pivot angle, ρ (t) indicate that hull roll angle caused by wave, ξ represent transformed state vector, ξ₁(t),ξ₂(t),ξ₃ (t) system state amount after representation transformation, the t in bracket indicate the time, and (t) indicates that the variable is about the time behind variable It is subsequent (t) to omit most number variable for simplicity for function；Using above-mentioned coordinate transformation method, in conjunction with the control mesh of system Mark, the target location of quantity of state is as follows after can must converting：

Wherein, arccos indicates inverse cosine function, y_gd,z_gdRepresent the target location coordinate of load, L_jThe length of cantilever is represented, ξ_1d,ξ_2d,ξ_3dRespectively represent quantity of state ξ after converting₁(t),ξ₂(t),ξ₃(t) target location；

Further, error signal e is defined₁(t),e₂(t),e₃(t) as follows：

e₁=ξ₁-ξ_1d,e₂=ξ₂-ξ_2d,e₃=ξ₃-ξ_3d=ξ₃ (19)

Then error signal is about the derivative of time：

Wherein,Respectively represent ξ₁(t),ξ₂(t),ξ₃(t) about the derivative of time；It is defined as follows auxiliary function γ₁(e₁),γ₂(e₂),γ₃(ξ₃)：

Wherein, α₁,α₂,Indicate positive parameter, function s (*'s) is defined as follows：

Wherein, the independent variable of * representative functions s (*)；

3rd, control law determines

Design cantilever pitch moment u_m(t) and lifting rope tractive force u_f(t) control law is as follows：

Wherein, k_p1,k_d1,k_i1,k_p2,k_d2,k_i2,For positive control gain；

4th, control method is realized

Using the sensor on marine hoist, the pitch angle φ (t) and angular speed of cantilever are measuredThe length L (t) of lifting rope and Long change of rope speedHull roll angle ρ (t) and its angular speedUsing formula (24), control signal is calculated in real time, For controlling corresponding driving motor, realization accurately controls marine hoist system.