CN104129713B - A kind of traverse crane method for controlling trajectory of off-line - Google Patents

Abstract

A traverse crane method for controlling trajectory for off-line, tool constrained drive lacking traverse crane acceleration trajectory control method, comprises the steps: step 1, trajectory planning scheme, adopts smooth acceleration movement track; Step 2, determine trajectory parameters, for transporting process arbitrarily, by solving the kinematical equation of crane system, analyzing the coupled relation between chassis acceleration/accel and hunting of load, calculating actual peak acceleration a _max, even acceleration t _atime and at the uniform velocity time t _cthe performance figure that a kind of desirable acceleration trajectory meets the following core can be obtained; The realization of step 3, control method, chassis displacement signal x (t) obtained in real time by sensor and speed signal , calculate in real time 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, to the control of crane, completing transportation burden.

Description

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

Technical field

The present invention relates to a kind of method for controlling trajectory for drive lacking traverse crane control field, specifically a kind of control method of traverse crane acceleration movement track.

Background technology

Traverse crane is a kind of typical drive lacking nonlinear system, is widely used in the transport of the places such as harbour, workshop, building ground, warehouse for 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 lacking characteristic of system, the sport of chassis causes the swing of load, there is potential safety hazard, make it may collide with other goods of surrounding or operating personal.Moreover, the swing of load significantly reduces the work efficiency of crane.Therefore, for drive lacking bridge type crane system, urgently propose a kind of actv. method for planning track, make crane can arrive target location rapidly along this track, and without Residual oscillations after chassis arrives target location.

For now, existing most method is all the regulable control to traverse crane, and very few for the Motion trajectory aspect of traverse crane.And, some constraints of crane system cannot be ensured for existing adjustment control method, mainly comprise the constraints such as the maximum speed/acceleration/accel of chassis, the load amplitude of oscillation.In addition, existing method for planning track majority all cannot ensure some important indicators of system.

Summary of the invention

The present invention will solve the shortcoming that existing regulable control and existing method for planning track cannot ensure the important restrictions of crane system, proposes a kind of tool constrained drive lacking traverse crane acceleration trajectory control method.

Compared with prior art, the present invention is when taking into full account the constraint conditions such as the available peak acceleration of crane platform, maximum speed, propose a kind of tool constrained drive lacking traverse crane acceleration trajectory planing method, meet some performance figure of system.Compare existing method, main contributions of the present invention is as follows: 1) to transporting process arbitrarily, all can ensure that chassis peak acceleration/speed, load maximum pendulum angle etc. remain in setting range, and load is without Residual oscillations; 2) time needed for transport process can be predicted in advance; 3) track planned is simple and practical, is very convenient to practical application.

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

Step 1, trajectory planning scheme

For traditional traverse crane, general syllogic acceleration/accel (even acceleration-at the uniform velocity-even deceleration) track that adopts transports, namely shown in accompanying drawing 2.But 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 peak acceleration adopted in actual transport process, 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 respectively to become and accelerate (become slow down), even acceleration (even deceleration) and at the uniform velocity time constant, T is the period of vibration of load under constant acceleration.

Step 2, determine trajectory parameters

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

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

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

Wherein x (t) displacement that is chassis.

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

C) in transport process, load maximum pendulum angle meets

|θ(t)|≤θ _ub(5)

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

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

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

Wherein t _ffor chassis arrives the time of target location.

The realization of step 3, control method

Chassis displacement signal x (t) obtained in real time by sensor and speed signal 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, to the control of crane, completing 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, becomes, for simplicity's sake, omit (t) in formula when (t) after variable represents that this parameter is; 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 reflects the dynamic coupling relation between chassis and load pivot angle, is the basis of following trajectory planning.

2, method for planning track

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

Novel method for controlling trajectory provided by the invention comprises:

1st, the overall plan of trajectory planning

In order to realize the consecutive variations of crane acceleration/accel, opening upwards or Open Side Down a parabolical part as transitional link, are reached acceleration/accel continually varying object by the present invention.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 peak acceleration adopted in actual transport process, 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 respectively to become and accelerate (become slow down), even acceleration (even deceleration) and at the uniform velocity time constant, T is the period of vibration of load under constant acceleration.

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

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

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

Wherein x (t) displacement that is chassis.

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

C) in transport process, load maximum pendulum angle meets

|θ(t)|≤θ _ub(5)

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

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

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

Wherein t _ffor chassis arrives the time of target location.

2nd, the determination of actual parameter

As 0≤t≤t ₁time, degree of will speed up substitute into 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) the solution of above formula can be obtained

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

Wherein represent cireular frequency.

As t=τ, θ when can obtain chassis even acceleration _v(t), initial value be

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

Known by τ ∈ (0, T/4)

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

Further known load does not reach negative direction maxim.

Next, chassis will with even acceleration a _maxrun, load pivot angle and the time dependent expression formula of cireular frequency 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 namely now acquired 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:

The total time that first time reaches maxim is:

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

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

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

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

Draw the expression formula of even acceleration and even deceleration required time through above-mentioned analysis, next will calculate the at the uniform velocity required time.Can obtain about Time Continuous twice integration the acceleration trajectory that the present invention proposes

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

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 obtain peak acceleration a _max, even pick-up time t _aat the uniform velocity time t _c.If the acceptable load maximum pendulum angle of system is θ _ub, then should be met by formula (18) known load pivot angle maxim

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

Need be met by equation (23) and the known peak acceleration of system performance index

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

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

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

Can try to achieve further combined with equation (21) peak acceleration adopted in the actual transport process of system is

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

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

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

Based on peak acceleration (26) a that above-mentioned theory analysis obtains _max, even pick-up time (19) t _aat the uniform velocity time (27) t _ccan proof load maximum pendulum angle, machine speed/acceleration/accel etc. remain in the scope of setting in conjunction with acceleration trajectory of the present invention, and when chassis arrives target location with back loading without Residual oscillations, and acceleration trajectory continuous and derivable of the present invention is easy to follow 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 some core capabilities constraint deficiency such as (comprising chassis maximum speed/acceleration/accel, the load amplitude of oscillation, chassis operating efficiency), propose a kind of smooth chassis acceleration/accel and transport track, the smoothness run of table system can not only be ensured, and some important restrictions meeting system can be ensured.

Advantage of the present invention and beneficial effect:

The trolley movement track that the present invention plans has analytical form, consecutive variations, 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. remain in setting range, and load is without Residual oscillations.Moreover, the trolley movement track that the present invention plans can predict the time needed for transport process in advance; The track planned is simple and practical, is very convenient to practical application.

Accompanying drawing explanation

Fig. 1 is the workflow diagram adopting 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

Detailed description of the invention

The present invention is further illustrated below in conjunction with accompanying drawing.

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

1st, experimental procedure describes

Step 1, trajectory planning scheme

For traditional traverse crane, general syllogic acceleration/accel (even acceleration-at the uniform velocity-even deceleration) track that adopts transports, namely shown in accompanying drawing 2.But 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 peak acceleration adopted in actual transport process, 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 respectively to become and accelerate (become slow down), even acceleration (even deceleration) and at the uniform velocity time constant, T is the period of vibration of load under constant acceleration.

Step 2, determine trajectory parameters

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

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

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

Wherein x (t) displacement that is chassis.

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

C) in transport process, load maximum pendulum angle meets

|θ(t)|≤θ _ub(5)

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

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

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

Wherein t _ffor chassis arrives the time of target location.

The realization of step 3, control method

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

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

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

2nd, simulation and experiment result describes

In order to verify the actual behavior of the present invention in overhead crane control, invention has been numerical simulation and actual experiment.

2.1st, simulating, verifying.By method for planning track proposed by the invention for two-dimentional bridge type crane system as shown in Figure 4, the feasibility of inspection the inventive method on bridge type crane system and actual behavior.At this, angle from motion planning is verified validity of the present invention, namely do not consider the kinetics equation part of chassis.Only consider formula (1), will the acceleration trajectory obtained be planned 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°

Wherein l is the length of lifting rope.

Simulation result is accompanying drawing 6, meet institute's Constrained of system from the known method for planning track of the present invention of result shown in accompanying drawing 6 (wherein represented by dotted arrows target location, solid line represent the constraint of simulation result, long and short dash line representative system), proof load swings and without Residual oscillations in the scope preset.

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

Wherein M, m are 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.Be easy to follow the tracks of from the known method for planning track of the present invention of result shown in accompanying drawing 7 (wherein represented by dotted arrows simulation result, solid line represent the constraint of experimental result, long and short dash line representative system), load swings and without Residual oscillations, can obtain good controller performance in the scope preset.Moreover, method for planning track proposed by the invention simple (workflow diagram as can be seen from accompanying drawing 1 the inventive method), 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 being only limitted to the concrete form that embodiment is stated, protection scope of the present invention is also forgiven those skilled in the art and conceived the equivalent technologies means that can expect according to the present invention.

Claims (1)

1. a traverse crane method for controlling trajectory for off-line, comprises the steps:

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

Wherein, a _maxfor the peak acceleration adopted in actual transport process, 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 respectively to become and accelerate (become slow down), even acceleration (even deceleration) and at the uniform velocity time constant, T is the period of vibration of load under constant acceleration;

Step 2, determine trajectory parameters

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

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

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

Wherein x (t) displacement that is chassis;

B) in transport process, machine speed and acceleration/accel meet

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

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

C) in transport process, load maximum pendulum angle meets

|θ(t)|≤θ _ub(5)

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

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

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

Wherein t _ffor chassis arrives the time of target location;

The realization of step 3, control method

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