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
Wherein x (t) displacement that is chassis.
B) in transport process, machine speed and acceleration/accel meet
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
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
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
Wherein x (t) displacement that is chassis.
B) in transport process, machine speed and acceleration/accel meet
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
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:
According to initial condition (IC)
the solution of above formula can be obtained
Wherein
represent cireular frequency.
As t=τ, θ when can obtain chassis even acceleration
v(t),
initial value be
Known by τ ∈ (0, T/4)
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:
Arrange
Wherein:
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:
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
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
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
Need be met by equation (23) and the known peak acceleration of system performance index
Need meet in conjunction with (20), (21) and the known maximum speed of system performance index
Can try to achieve further combined with equation (21) peak acceleration adopted in the actual transport process of system is
Finally, can obtain the chassis uniform movement time from formula (21) and formula (26) gained peak acceleration is
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.
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
Wherein x (t) displacement that is chassis.
B) in transport process, machine speed and acceleration/accel meet
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
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:
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.