CN104129713A - Offline bridge crane locus control method - Google Patents

Abstract

A kind of offline overhead crane method for controlling trajectory,Have constrained drive lacking overhead crane acceleration trajectory control method,Include the following steps: step 1,Trajectory planning scheme,Using smooth acceleration movement track; Step 2,Determine trajectory parameters,For arbitrarily transporting process,By solving the kinematical equation of crane system,The coupled relation between trolley acceleration and hunting of load is analyzed,Calculate practical peak acceleration amax,It is even to accelerate ta time and at the uniform velocity time tc that the performance indicator that a kind of ideal acceleration trajectory meets the following core can be obtained; Step 3,The realization of control method,The trolley displacement signal x (t) and speed signal obtained in real time by sensor Calculating x (t) in real time, With acceleration signal Continuous integral signal xv (t), Between deviation, generate the control command of corresponding driving motor using traditional PD control device, realize the control to crane, complete transport task.

Description

A kind of traverse crane method for controlling trajectory of off-line

Technical field

The present invention relates to a kind of for owing to drive the method for controlling trajectory in bridge-type overhead crane control field, a kind of control method of traverse crane acceleration movement track specifically.

Background technology

Traverse crane is a kind of nonlinear system of typically owing to drive, and is widely used in the places such as harbour, workshop, building ground, warehouse for the transportation of goods.In the course of the work, chassis can move along the track on crane span structure, and goods is transported to target location safely and fast from reference position.But due to the drive performance of owing of system, the sport of chassis causes and the swing of load has potential safety hazard, and it may be bumped with other goods or operating personal around.Moreover, the swing of load has greatly reduced the work efficiency of crane.Therefore, for owing to drive bridge type crane system, urgently propose a kind of actv. method for planning track, make crane to arrive rapidly target location along this track, and without remaining, swing after chassis arrives target location.

For now, existing most methods are all that the adjusting of traverse crane is controlled, and very few for the path of motion planning aspect of traverse crane.And, for existing adjustment control method, cannot guarantee some constraints of crane system, mainly comprise the constraints such as maximum speed/acceleration/accel, the load amplitude of oscillation of chassis.In addition, existing method for planning track majority all cannot guarantee some important indicators of system.

Summary of the invention

The present invention will solve existing adjusting and controls and have the shortcoming that method for planning track cannot guarantee the important restrictions of crane system, proposes that a kind of tool is constrained owes to drive traverse crane acceleration trajectory control method.

Compared with prior art, the present invention is in the situation that taking into full account the constraint conditions such as the available peak acceleration of crane platform, maximum speed, proposed that a kind of tool is constrained owes to drive traverse crane acceleration trajectory planing method, met some performance figure of system.Compare existing method, main contributions of the present invention is as follows: 1) to transporting arbitrarily process, all can guarantee that chassis peak acceleration/speed, load maximum pendulum angle etc. remain in setting range, and load swings without remnants; 2) can predict in advance the required time of the process of transporting; 3) track of planning is simple and practical, is convenient to very much practical application.

Tool provided by the present invention is constrained owes to drive traverse crane acceleration trajectory control method, comprises the steps:

Step 1, trajectory planning scheme

For traditional traverse crane, generally adopt syllogic acceleration/accel (even acceleration-at the uniform velocity-even deceleration) track to transport, shown in accompanying drawing 2.Yet the discountinuity of acceleration/accel may cause certain infringement to crane equipment; And, in actual application, in strict accordance with syllogic acceleration movement track, there is certain challenge.Therefore, the present invention proposes a kind of smooth acceleration movement track, its expression formula is as follows:

Wherein, a _maxfor the actual peak acceleration adopting in process of transporting, and τ ∈ (0, T4), t ₁=τ, t ₂=τ+t _a, t ₃=2 τ+t _a, t ₄=2 τ+t _a+ t _c, t ₅=3 τ+t _a+ t _c, t ₆=3 τ+2t _a+ t _c, t ₇=4 τ+2t _a+ t _c, τ, t _a, t _crepresent to become accelerate respectively (become and slow down), even acceleration (even deceleration) and time constant at the uniform velocity, T is the period of vibration loading under constant acceleration.

Step 2, determine trajectory parameters

For transporting arbitrarily process, by solving the kinematical equation of crane system, analyze the coupled relation between chassis acceleration/accel and hunting of load, calculate actual peak acceleration a _max, even acceleration t _atime and at the uniform velocity time t _ccan obtain the performance figure that a kind of desirable acceleration trajectory meets the following core:

A) chassis arrives target location p within the limited time _d∈ R,

$\underset{t\→\∞}{\lim }x\left(t\right)=p_d---\left(3\right)$

The displacement that wherein x (t) is chassis.

B), in the process of transporting, machine speed and acceleration/accel meet

$\left|\stackrel{.}{x}\left(t\right)\right|\≤v_{\mathrm{ub}},\left|\stackrel{..}{x}\left(t\right)\right|\≤a_{\mathrm{ub}}---\left(4\right)$

Wherein be respectively chassis and transport the velocity and acceleration in process, v _ub, a _ub∈ R ⁺be respectively maximum speed and peak acceleration that crane platform can reach.

C), in the process of transporting, load maximum pendulum angle meets

|θ(t)|≤θ _ub (5)

Wherein θ (t) transports the pivot angle of load in process, θ for chassis _ub∈ R ⁺be respectively the maximum pendulum angle that crane system can allow.

D) when chassis travels at the uniform speed or arrive target location after, load and chassis on same vertical curve, i.e. between load and chassis without relative motion

$\mathrm{\θ}\left(t\right)=0,\∀t\≥t_f---\left(6\right)$

T wherein _ffor the time of chassis arrival target location.

The realization of step 3, control method

The chassis displacement signal x (t) and the speed signal that by sensor, obtain in real time real-time calculating x (t), with acceleration signal continuous integration signal x _v(t), between deviation, use traditional PD controller to produce the control command of corresponding drive motor, realize the control to crane, complete transportation burden.

Theoretical Analysis of the present invention

1, the kinematics model of crane

$\stackrel{..}{\mathrm{\θ}}+{\mathrm{\ω}}_n^2\mathrm{\θ}=-\frac{{\mathrm{\ω}}_n^2}{g}\stackrel{..}{x}---\left(1\right)$

Wherein, θ (t) represents the pivot angle of load and vertical direction, for angular acceleration; T represents the time, and (t) after variable represents when this parameter is to become, and for simplicity's sake, in formula, omits (t); for chassis acceleration/accel; the natural frequency of expression system; L is the length of lifting rope; G represents acceleration due to gravity.

This equation has reflected the dynamic coupling relation between chassis and load pivot angle, is the basis of trajectory planning next.

2, method for planning track

For existing bridge car crane method for planning track, some important constraints (as maximum pendulum angle of load etc.) cannot be guaranteed, and the track obtaining does not have analytical expression.In addition, existing method for planning track cannot meet some performance figure of system, such as acceptable load amplitude of oscillation in the available peak acceleration/speed of crane, motion process etc.

Novel method for controlling trajectory provided by the invention comprises:

1st, the overall plan of trajectory planning

In order to realize the continuous variation of crane acceleration/accel, the present invention, using opening upwards or Open Side Down a parabolical part as transitional link, reaches acceleration/accel continually varying object.For this reason, we construct acceleration trajectory as shown in Figure 3, and its expression formula can be expressed from the next

Wherein, a _maxfor the actual peak acceleration adopting in process of transporting, and τ ∈ (0, T/4), t ₁=τ, t ₂=τ+t _a, t ₃=2 τ+t _a, t ₄=2 τ+t _a+ t _c, t ₅=3 τ+t _a+ t _c, t ₆=3 τ+2t _a+ t _c, t ₇=4 τ+2t _a+ t _c, τ, t _a, t _crepresent to become accelerate respectively (become and slow down), even acceleration (even deceleration) and time constant at the uniform velocity, T is the period of vibration loading under constant acceleration.

By solving the kinematical equation of crane system, analyze the coupled relation between chassis acceleration/accel and hunting of load, calculate actual peak acceleration a _max, even acceleration t _atime and at the uniform velocity time t _ccan obtain the performance figure that a kind of desirable acceleration trajectory meets the following core:

A) chassis arrives target location p within the limited time _d∈ R,

$\underset{t\→\∞}{\lim }x\left(t\right)=p_d---\left(3\right)$

The displacement that wherein x (t) is chassis.

B), in the process of transporting, machine speed and acceleration/accel meet

$\left|\stackrel{.}{x}\left(t\right)\right|\≤v_{\mathrm{ub}},\left|\stackrel{..}{x}\left(t\right)\right|\≤a_{\mathrm{ub}}---\left(4\right)$

Wherein be respectively chassis and transport the velocity and acceleration in process, v _ub, a _ub∈ R ⁺be respectively maximum speed and peak acceleration that crane platform can reach.

C), in the process of transporting, load maximum pendulum angle meets

|θ(t)|≤θ _ub (5)

Wherein θ (t) transports the pivot angle of load in process, θ for chassis _ub∈ R ⁺be respectively the maximum pendulum angle that crane system can allow.

D) when chassis travels at the uniform speed or arrive target location after, load and chassis on same vertical curve, i.e. between load and chassis without relative motion

$\mathrm{\θ}\left(t\right)=0,\∀t\≥t_f---\left(6\right)$

T wherein _ffor the time of chassis arrival target location.

2nd, actual parameter determines

As 0≤t≤t ₁time, degree of will speed up substitution equation (1) can obtain:

${\stackrel{..}{\mathrm{\θ}}}_v+{\mathrm{\ω}}_n^2{\mathrm{\θ}}_v=-\frac{{\mathrm{\ω}}_n^2}{g}(2t-\frac{t^2}{\mathrm{\τ}})\frac{a_{\max }}{\mathrm{\τ}}---\left(7\right)$

According to initial condition (IC) can obtain the solution of above formula

$\begin{array}{c}{\mathrm{\θ}}_v\left(t\right)=\frac{2a_{\max }}{g{\mathrm{\ω}}_n^2{\mathrm{\τ}}^2}\cos \left({\mathrm{\ω}}_{n}t\right)+\frac{2a_{\max }}{\mathrm{g\τ}}\sin \left({\mathrm{\ω}}_{n}t\right)+\frac{a_{\max }}{g{\mathrm{\τ}}^2}{t}^2-\frac{2a_{\max }}{\mathrm{g\τ}}t-\frac{2a_{\max }}{g{\mathrm{\ω}}_n^2{\mathrm{\τ}}^2}\\ {\stackrel{.}{\mathrm{\θ}}}_v\left(t\right)=-\frac{2a_{\max }}{g{\mathrm{\ω}}_n^2{\mathrm{\τ}}^2}{\mathrm{\ω}}_n\sin \left({\mathrm{\ω}}_{n}t\right)+\frac{2a_{\max }}{\mathrm{g\τ}}{\mathrm{\ω}}_n\cos \left({\mathrm{\ω}}_{n}t\right)+\frac{2a_{\max }}{g{\mathrm{\τ}}^2}t-\frac{2a_{\max }}{\mathrm{g\τ}}\end{array}---\left(8\right)$

Wherein represent cireular frequency.

When t=τ, θ in the time of can obtaining the even acceleration of chassis _v(t), initial value be

$\begin{array}{c}{\mathrm{\θ}}_v\left(\mathrm{\τ}\right)=\frac{2a_{\max }}{g{\mathrm{\ω}}_n^2{\mathrm{\τ}}^2}\cos \left({\mathrm{\ω}}_n\mathrm{\τ}\right)+\frac{2a_{\max }}{\mathrm{g\τ}}\sin \left({\mathrm{\ω}}_n\mathrm{\τ}\right)-\frac{a_{\max }}{g}-\frac{2a_{\max }}{g{\mathrm{\ω}}_n^2{\mathrm{\τ}}^2}\\ {\stackrel{.}{\mathrm{\θ}}}_v\left(\mathrm{\τ}\right)=-\frac{2a_{\max }}{g{\mathrm{\ω}}_n^2{\mathrm{\τ}}^2}{\mathrm{\ω}}_n\sin \left({\mathrm{\ω}}_n\mathrm{\τ}\right)+\frac{2a_{\max }}{\mathrm{g\τ}}{\mathrm{\ω}}_n\cos \left({\mathrm{\ω}}_n\mathrm{\τ}\right)\end{array}---\left(9\right)$

By τ ∈ (0, T/4) known

${\mathrm{\&theta;}}_v\left(\mathrm{\&tau;}\right)<0,{\stackrel{.}{\mathrm{\&theta;}}}_v\left(\mathrm{\&tau;}\right)<0---\left(10\right)$

Further known load does not reach negative direction maxim.

Next, chassis will be with even acceleration a _maxoperation, the time dependent expression formula of load pivot angle and cireular frequency is as follows:

$\begin{array}{c}{\mathrm{\&theta;}}_v\left(t\right)={\mathrm{\&theta;}}_v\left(\mathrm{\&tau;}\right)\cos {\mathrm{\&omega;}}_n(t-\mathrm{\&tau;})+\frac{{\stackrel{.}{\mathrm{\&theta;}}}_v\left(\mathrm{\&tau;}\right)}{{\mathrm{\&omega;}}_n}\sin {\mathrm{\&omega;}}_n(t-\mathrm{\&tau;})-\frac{a_{\max }}{g}(1-\cos {\mathrm{\&omega;}}_n(t-\mathrm{\&tau;}))\\ {\stackrel{.}{\mathrm{\&theta;}}}_v\left(t\right)={\stackrel{.}{\mathrm{\&theta;}}}_v\left(\mathrm{\&tau;}\right)\cos {\mathrm{\&omega;}}_n(t-\mathrm{\&tau;})-({\mathrm{\&theta;}}_v\left(\mathrm{\&tau;}\right)+\frac{a_{\max }}{g}){\mathrm{\&omega;}}_n\sin {\mathrm{\&omega;}}_n(t-\mathrm{\&tau;})\end{array}---\left(11\right)$

Arrange

${\stackrel{.}{\mathrm{\&theta;}}}_v\left(t\right)=-\mathrm{\&Delta;}[\frac{({\mathrm{\&theta;}}_v\left(\mathrm{\&tau;}\right)+a_{\max }/g){\mathrm{\&omega;}}_n}{\mathrm{\&Delta;}}\sin {\mathrm{\&omega;}}_n(t-\mathrm{\&tau;})-\frac{{\stackrel{.}{\mathrm{\&theta;}}}_v\left(\mathrm{\&tau;}\right)}{\mathrm{\&Delta;}}\cos {\mathrm{\&omega;}}_n(t-\mathrm{\&tau;})]---\left(12\right)$

Wherein:

$\mathrm{\&Delta;}=\sqrt{{\stackrel{.}{\mathrm{\&theta;}}}_v^2\left(\mathrm{\&tau;}\right)+{({\mathrm{\&theta;}}_v\left(\mathrm{\&tau;}\right)+a_{\max }/g)}^2{\mathrm{\&omega;}}_n^2}>0---\left(13\right)$

Further abbreviation can obtain

Wherein:

When time, θ (t) can obtain extreme value, and now obtained extreme value is maxim or the minimum value of load pivot angle.When cireular frequency is zero first, load reaches negative direction wobble amplitude maxim, and it reaches the negative direction maxim time used and can be calculated by following formula:

Reaching for the first time peaked total time is:

The total time of formula (17) gained is updated to the maxim that equation (11) can obtain hunting of load angle

Periodicity by angle and cireular frequency can be regarded as to obtain the even acceleration of the chassis time used:

As time t=t ₃time, machine speed reaches maxim and is:

$v_{\max }=a_{\max }(\frac{4}{3}\mathrm{\&tau;}+t_a)---\left(20\right)$

Through above-mentioned analysis, draw the expression formula of even acceleration and even deceleration required time, next will calculate the at the uniform velocity required time.The acceleration trajectory that the present invention is proposed can obtain about twice integration of Time Continuous

$\begin{array}{c}{p}_d=a_{\max }(\frac{4}{3}\mathrm{\&tau;}+t_a)(2\mathrm{\&tau;}+t_a+t_c)\\ =v_{\max }(2\mathrm{\&tau;}+t_a+t_c)\end{array}---\left(21\right)$

Wherein: p _drepresent target location, t _cfor the chassis time at the uniform velocity used.

At the uniform velocity at the uniform velocity the time meets t to chassis in process _c>=0, so

$v_{\max }\&le;\frac{p_d}{2\mathrm{\&tau;}+t_a}---\left(22\right)$

Next, the important restrictions and the target that consider chassis are obtained peak acceleration a _max, even pick-up time t _atime t at the uniform velocity _c.If the acceptable load maximum pendulum angle of system is θ _ub, by the known load pivot angle of formula (18) maxim, should be met

$\left|{\mathrm{\&theta;}}_{\max }\right|=\frac{\mathrm{\&Delta;}}{{\mathrm{\&omega;}}_n}+\frac{a_{\max }}{g}\&le;{\mathrm{\&theta;}}_{\mathrm{ub}}---\left(23\right)$

By equation (23) and the known peak acceleration of system performance index, need be met

$a_{\max }\&le;a_{\mathrm{mub}}=\min (a_{\mathrm{ub}},\frac{g{\mathrm{\&omega;}}_n{\mathrm{\&theta;}}_{\mathrm{ub}}}{\mathrm{g\&Delta;}/a_{\max }+{\mathrm{\&omega;}}_n})---\left(24\right)$

In conjunction with (20), (21) and the known maximum speed of system performance index, need meet

$v_{\max }=\min (v_{\mathrm{ub}},\frac{p_d}{2\mathrm{\&tau;}+t_a},a_{\mathrm{mub}}(\frac{4}{3}\mathrm{\&tau;}+t_a))---\left(25\right)$

Further combined with equation (21), can try to achieve the actual peak acceleration adopting in process of transporting of system is

$a_{\max }=\frac{v_{\max }}{4\mathrm{\&tau;}/3+t_a}---\left(26\right)$

Finally, from formula (21) and formula (26) gained peak acceleration, can obtain the chassis uniform movement time is

$t_c=\frac{p_d}{v_{\max }}-2\mathrm{\&tau;}-t_a---\left(27\right)$

Based on above-mentioned theory, analyze resulting peak acceleration (26) a _max, even pick-up time (19) t _atime (27) t at the uniform velocity _cin conjunction with acceleration trajectory of the present invention can proof load maximum pendulum angle, machine speed/acceleration/accel etc. remains in the scope of setting, and when arriving target location, chassis swings without remnants with back loading, and acceleration trajectory of the present invention continuously smooth being easy to is followed the tracks of, there is simple analytical expression, be convenient to very much the application of Practical Project.

The object of the invention is to discontinuous for existing traverse crane method for planning track acceleration/accel, path of motion is difficult to tracking, easy excitated system oscillation, can not meet the deficiencies such as some core capabilities constraints (comprising chassis maximum speed/acceleration/accel, the load amplitude of oscillation, chassis operating efficiency), propose a kind of smooth chassis acceleration/accel and transported track, the smoothness run of table system can not only be guaranteed, and some important restrictions of system can be guaranteed to meet.

Advantage of the present invention and beneficial effect:

The trolley movement track that the present invention plans has analytical form, changes continuously, is convenient to very much the application of actual crane system; Compared with prior art, institute's invention track can proof load maximum pendulum angle, machine speed/acceleration/accel etc. remains in setting range, and load swings without remnants.Moreover, the trolley movement track that the present invention plans can be predicted the required time of the process of transporting in advance; The track of planning is simple and practical, is convenient to very much practical application.

Accompanying drawing explanation

Fig. 1 is the workflow diagram that adopts the inventive method

Fig. 2 is traditional syllogic acceleration trajectory

Fig. 3 is the acceleration trajectory of the inventive method

Fig. 4 is two-dimentional crane system constructional drawing

Fig. 5 is checking experiment porch of the present invention

Fig. 6 is actual emulation performance of the present invention

Fig. 7 is the experimental result of the present invention on true experiment porch

The specific embodiment

Below in conjunction with accompanying drawing, further illustrate the present invention.

Tool provided by the present invention is constrained owes to drive traverse crane acceleration trajectory control method, comprises the steps:

1st, experimental procedure is described

Step 1, trajectory planning scheme

For traditional traverse crane, generally adopt syllogic acceleration/accel (even acceleration-at the uniform velocity-even deceleration) track to transport, shown in accompanying drawing 2.Yet the discountinuity of acceleration/accel may cause certain infringement to crane equipment; And, in actual application, in strict accordance with syllogic acceleration movement track, there is certain challenge.Therefore, the present invention proposes a kind of smooth acceleration movement track, its expression formula is as follows:

Wherein, a _maxfor the actual peak acceleration adopting in process of transporting, and τ ∈ (0, T/4), t ₁=τ, t ₂=τ+t _a, t ₃=2 τ+t _a, t ₄=2 τ+t _a+ t _c, t ₅=3 τ+t _a+ t _c, t ₆=3 τ+2t _a+ t _c, t ₇=4 τ+2t _a+ t _c, τ, t _a, t _crepresent to become accelerate respectively (become and slow down), even acceleration (even deceleration) and time constant at the uniform velocity, T is the period of vibration loading under constant acceleration.

Step 2, determine trajectory parameters

For transporting arbitrarily process, by solving the kinematical equation of crane system, analyze the coupled relation between chassis acceleration/accel and hunting of load, calculate actual peak acceleration a _max, even acceleration t _atime and at the uniform velocity time t _ccan obtain the performance figure that a kind of desirable acceleration trajectory meets the following core:

A) chassis arrives target location p within the limited time _d∈ R,

$\underset{t\&RightArrow;\&infin;}{\lim }x\left(t\right)=p_d---\left(3\right)$

The displacement that wherein x (t) is chassis.

B), in the process of transporting, machine speed and acceleration/accel meet

$\left|\stackrel{.}{x}\left(t\right)\right|\&le;v_{\mathrm{ub}},\left|\stackrel{..}{x}\left(t\right)\right|\&le;a_{\mathrm{ub}}---\left(4\right)$

Wherein be respectively chassis and transport the velocity and acceleration in process, v _ub, a _ub∈ R ⁺be respectively maximum speed and peak acceleration that crane platform can reach.

C), in the process of transporting, load maximum pendulum angle meets

|θ(t)|≤θ _ub (5)

Wherein θ (t) transports the pivot angle of load in process, θ for chassis _ub∈ R ⁺be respectively the maximum pendulum angle that crane system can allow.

D) when chassis travels at the uniform speed or arrive target location after, load and chassis on same vertical curve, i.e. between load and chassis without relative motion

$\mathrm{\&theta;}\left(t\right)=0,\&ForAll;t\&GreaterEqual;t_f---\left(6\right)$

T wherein _ffor the time of chassis arrival target location.

The realization of step 3, control method

The chassis displacement signal x (t) and the speed signal that by sensor, obtain in real time real-time calculating x (t), with acceleration signal continuous integration signal x _v(t), between deviation, use the PD tracking control unit quote as follows friction force feedforward compensation:

$F\left(t\right)=-k_{p}e\left(t\right)-k_d\stackrel{.}{e}\left(t\right)+f_{r0}\tanh (\stackrel{.}{x}\left(t\right)/\mathrm{\&gamma;})-k_r\left|\stackrel{.}{x}\left(t\right)\right|\stackrel{.}{x}\left(t\right)---\left(28\right)$

Wherein, k _p, k _drepresent positive ride gain; E (t)=x (t)-x _v(t) be tracking error, x (t) represents chassis displacement, x _v(t) be chassis track (being the track that the present invention plans) to be tracked; for the derivative of e (t) about the time; for Friction Compensation item, f _r0, k _r, γ is friction parameter, by test experiment, demarcates in advance acquisition; Tanh () is hyperbolic tangent function; for machine speed.

2nd, simulation and experiment result is described

In order to verify that the present invention is at the actual behavior aspect overhead crane control, the present invention has carried out numerical simulation and actual experiment.

2.1st, simulating, verifying.Method for planning track proposed by the invention is used for to two-dimentional bridge type crane system as shown in Figure 4, feasibility and the actual behavior of check the inventive method on bridge type crane system.At this, will verify validity of the present invention from the angle of motion planning, do not consider the kinetics equation part of chassis.Only consider formula (1), the acceleration trajectory that planning is obtained as the input of formula (1), analyze its output situation.System parameter, target location and be constrained to:

l＝1.2m，τ＝0.25s，p _d＝2m，v _ub＝6m/s，a _ub＝0.8m/s ²，θ _ub＝3°

The length that wherein l is lifting rope.

Simulation result is accompanying drawing 6, the institute's Constrained that meets system from the known method for planning track of the present invention of result shown in accompanying drawing 6 (wherein dotted line represents that target location, solid line represent the constraint of simulation result, long and short dash line representative system), proof load swings and swings without remnants in default scope.

2.2nd, experimental verification.In order further to verify practical application performance of the present invention, method for planning track proposed by the invention, for true bridge type crane system shown in accompanying drawing 5, is checked to the inventive method actual behavior on bridge type crane system.The parameter of system, target location and be constrained to:

τ＝0.25s,p _d＝0.6m,v _ub＝0.2m/s，a _ub＝0.4m/s ²，θ _ub＝2°

M＝7kg,m＝1.025kg,l＝0.6m

M wherein, m is respectively the quality of chassis and load.

After fully debugging, the ride gain in contrail tracker of the present invention (28) is chosen for k _p=250, k _d=30.In addition,, through off-line calibration, obtaining formula (20) middle orbit friction parameter is f _r0=4.4, γ=0.01, k _r=-0.5.

Experimental result as shown in Figure 7.From the known method for planning track of the present invention of result shown in accompanying drawing 7 (wherein dotted line represents that simulation result, solid line represent the constraint of experimental result, long and short dash line representative system), be easy to follow the tracks of, load on and in default scope, swing and swing without remnants, can obtain good controller performance.Moreover, method for planning track proposed by the invention simple (workflow diagram by accompanying drawing 1 the inventive method can be found out) is convenient to the application of actual industrial crane very much.Therefore can be widely used in the crane in the places such as factory, harbour, workshop, enhance productivity.

Content described in this specification sheets embodiment is only enumerating the way of realization of inventive concept; protection scope of the present invention should not be regarded as only limiting to the concrete form that embodiment states, protection scope of the present invention is also forgiven those skilled in the art and according to the present invention, conceived the equivalent technologies means that can expect.

Claims (1)

1. tool is constrained owes to drive traverse crane acceleration trajectory control method, comprises the steps:

Step 1, trajectory planning scheme, adopt smooth acceleration movement track, and its expression formula is as follows:

Wherein, a _maxfor the actual peak acceleration adopting in process of transporting, and τ ∈ (0, T4), t ₁=τ, t ₂=τ+t _a, t ₃=2 τ+t _a, t ₄=2 τ+t _a+ t _c, t ₅=3 τ+t _a+ t _c, t ₆=3 τ+2t _a+ t _c, t ₇=4 τ+2t _a+ t _c, τ, t _a, t _crepresent to become accelerate respectively (become and slow down), even acceleration (even deceleration) and time constant at the uniform velocity, T is the period of vibration loading under constant acceleration;

Step 2, determine trajectory parameters

For transporting arbitrarily process, by solving the kinematical equation of crane system, analyze the coupled relation between chassis acceleration/accel and hunting of load, calculate actual peak acceleration a _max, even acceleration t _atime and at the uniform velocity time t _ccan obtain the performance figure that a kind of desirable acceleration trajectory meets the following core:

A) chassis arrives target location p within the limited time _d∈ R,

$\underset{t\&RightArrow;\&infin;}{\lim }x\left(t\right)=p_d---\left(3\right)$

The displacement that wherein x (t) is chassis;

B), in the process of transporting, machine speed and acceleration/accel meet

$\left|\stackrel{.}{x}\left(t\right)\right|\&le;v_{\mathrm{ub}},\left|\stackrel{..}{x}\left(t\right)\right|\&le;a_{\mathrm{ub}}---\left(4\right)$

Wherein be respectively chassis and transport the velocity and acceleration in process, v _ub, a _ub∈ R ⁺be respectively maximum speed and peak acceleration that crane platform can reach;

C), in the process of transporting, load maximum pendulum angle meets

|θ(t)|≤θ _ub (5)

Wherein θ (t) transports the pivot angle of load in process, θ for chassis _ub∈ R ⁺be respectively the maximum pendulum angle that crane system can allow;

D) when chassis travels at the uniform speed or arrive target location after, load and chassis on same vertical curve, i.e. between load and chassis without relative motion

$\mathrm{\&theta;}\left(t\right)=0,\&ForAll;t\&GreaterEqual;t_f---\left(6\right)$

T wherein _ffor the time of chassis arrival target location;

The realization of step 3, control method

The chassis displacement signal x (t) and the speed signal that by sensor, obtain in real time real-time calculating x (t), with acceleration signal continuous integration signal x _v(t), between deviation, use traditional PD controller to produce the control command of corresponding drive motor, realize the control to crane, complete transportation burden.