CN105388761B - Crane based on positive and negative POSICAST input shapers method is prevented shaking control method - Google Patents
Crane based on positive and negative POSICAST input shapers method is prevented shaking control method Download PDFInfo
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- CN105388761B CN105388761B CN201510916217.1A CN201510916217A CN105388761B CN 105388761 B CN105388761 B CN 105388761B CN 201510916217 A CN201510916217 A CN 201510916217A CN 105388761 B CN105388761 B CN 105388761B
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/041—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a variable is automatically adjusted to optimise the performance
Abstract
The present invention relates to a kind of cranes based on positive and negative POSICAST input shapers method to prevent shaking control method, including method one：Pivot angle after moment returns to zero forward and reverse POSICAST methods, method two：Pivot angle after the Td moment returns to zero forward and reverse POSICAST methods and method three：Pivot angle after moment returns to zero forward and reverse POSICAST methods.Wherein TdIt is the damped oscillation period of system.The present invention is suitable for having damping system, is also applied for undamped second-order system.Since the method is open-loop control method, it is an advantage of the invention that not needing to the measurement sensor for closed loop feedback.The present invention is inputted using step acceleration, is directed to the shaping of step acceleration output, compared with pulse acceleration input method, speed consecutive variations are easy to Project Realization.The present invention has the second-order system of damping suitable for any using step signal as input, for the anti-system waved or wanted a certain output and be eventually returned to home position.
Description
Technical field
Prevent shaking control method the present invention relates to portal crane, and in particular to one kind inputs whole based on positive and negative POSICAST
The crane of shape method is prevented shaking control method.
Background technology
Residual of the research in relation to input shaper technology earliest originating from the Oscillatory mode shape for inhibiting small damping servo-drive system is shaken
It swings.The emphasis of this method is to design input shaper controller the most suitable using the means of time delay to avoid pair
The oscillation of elephant is a kind of open-loop control method.Input shaper not only can be achieved with only with simple open-loop control method
Crane is prevented shaking effect, and avoids and inevitably held high using what measurement feedback signal during feedback control scheme to be used
Expensive measuring device so that this scheme is easily promoted.
Input shaper technology is applied to crane and prevents that the research in the field of shaking has much by the current country, and representative is
Shanghai Zhenhua heavy industry group.Shanghai Zhenhua heavy industry group uses two sections of accelerated process, two sections of accelerated process：Given trolley is carved at the beginning
One constant acceleration a, trolley are in boost phase；At the T/4 moment, to the acceleration of trolley superposition-a, at this time trolley from
Acceleration mode enters at the uniform velocity state (T is the cycle of oscillation of pivot angle)；At the T/2 moment, to the acceleration of trolley superposition a, trolley from
At the uniform velocity state enters acceleration mode；At the 3T/4 moment, then the acceleration to trolley superposition-a, at this time trolley again from accelerate transition into
Enter at the uniform velocity state, the speed of service of trolley is right up to preset speed at this time.In whole process, the pivot angle of load is also with trolley
The variation of speed and convert, load pivot angle output response be this superposition of four acceleration as the response of Stepped Impedance Resonators, institute
With the 3T/4 moment, pivot angle returns to zero.But two sections of accelerated methods of Shanghai Zhenhua heavy industry group are directed to undamped system.
Invention content
The defects of the purpose of the present invention is being directed to corresponding knowledge, solve based on input shaper method for there is anti-shake of damping to be
How the opened loop control method of system, make pivot angle return to zero within the shortest time.
Technical scheme is as follows：
A kind of crane based on positive and negative POSICAST input shapers method prevents shaking control method, and whole system is small by controlling
The acceleration a of vehiclec, and then adjust the speed of service V of trolleycSo that the pivot angle of load is controlled, to achieve the purpose that anti-shake.
Wherein, load quality m, lifting rope length are L, and load is connected by lifting rope with trolley, and tangential acceleration when load is waved is
am, tangential velocity Vm, amplitude when k finally stablizes for pivot angle, ωnTo shake frequency naturally, ξ is damping ratio, ωdFor damping
Frequency is shaken, lifting rope is θ with the angle of vertical aspect, and the step response of the system is：
It is characterized in that, the crane based on positive and negative POSICAST input shapers method prevents that it is method to shake control method
First, an optional method in method two and method three；Wherein TdIt is the damped oscillation week of the system of trolley and load composition
Phase, σ are overshoot,
Method one：Pivot angle after moment returns to zero forward and reverse POSICAST methods；
Specific method：Boost phase, in t1=0 moment gave positive acceleration step, and amplitude isIn t2=tpWhen
It carves again to positive acceleration step, amplitude isIn t1=0 moment and t2=tpMoment gives different acceleration respectively
Step is spent, this mode forms boost phase t1=0 moment and t2=tpThe positive POSICAST input shapers at moment；In t3=
2tpMoment gives negativeacceleration step, and amplitude isIn t4=3tpMoment is again to negativeacceleration step, amplitude
It isIn t3=2tpMoment and t4=3tpMoment gives different "Jerk's respectively, and this mode, which is formed, to be added
Fast stage t3=2tpMoment and t4=3tpThe reversed POSICAST input shapers at moment；Boost phase t1=0 moment and t2=tp
The positive POSICAST input shapers and boost phase t at moment3=2tpMoment and t4=3tpThe reversed POSICAST at moment is defeated
Enter shaping synergy so that pivot angle returns to 0 at the T moment；Decelerating phase, in the initial time t for entering the decelerating phase5=t4+0
Negativeacceleration step is given, amplitude isIn t6=t4+tpMoment, amplitude was again to backward acceleration stepIn the initial time t for entering the decelerating phase5=t4+ 0 and t6=t4+tpMoment gives different acceleration ranks respectively
Jump, this mode form decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment；
t7=t4+2tpMoment gives positive acceleration step, and amplitude isIn t8=t4+3tpMoment gives positive acceleration rank again
Jump, amplitude areIn the t for entering the decelerating phase7=t4+2tpMoment and t8=t4+3tpMoment gives different respectively
"Jerk', this mode form decelerating phase t7=t4+2tpMoment and t8=t4+3tpThe reversed POSICAST inputs at moment
Shaping；Decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers and decelerating phase t at moment7
=t4+2tpMoment and t8=t4+3tpThe reversed POSICAST input shapers synergy at moment so that pivot angle is entering deceleration rank
The T moment after section returns to 0.
Method two：T=TdPivot angle after moment returns to zero forward and reverse POSICAST methods；
Specific method：Boost phase, in t1=0 moment gave positive acceleration step, and amplitude isIn t2=tpWhen
It carves again to positive acceleration step, amplitude isIn t1=0 moment and t2=tpMoment gives different acceleration respectively
Step is spent, this mode forms boost phase t1=0 moment and t2=tpThe positive POSICAST input shapers at moment；In t3=
tpMoment gives negativeacceleration step, and amplitude isIn t4=2tpMoment, amplitude was again to negativeacceleration stepIn t3=tpMoment and t4=2tpMoment gives different "Jerk's respectively, and this mode, which is formed, accelerates rank
Section t3=tpMoment and t4=2tpThe reversed POSICAST input shapers at moment；Boost phase t1=0 moment and t2=tpMoment
Positive POSICAST input shapers and boost phase t3=tpMoment and t4=2tpThe reversed POSICAST input shapers at moment
Synergy so that pivot angle returns to 0 at the T moment；Decelerating phase, in the initial time t for entering the decelerating phase5=t4+ 0 gives negative sense
"Jerk', amplitude areIn t6=t4+tpMoment, amplitude was again to backward acceleration step
In the initial time t for entering the decelerating phase5=t4+ 0 and t6=t4+tpMoment gives different "Jerk's, this side respectively
Formula forms decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment；In t7=t4+tp
Moment gives positive acceleration step, and amplitude isIn t8=t4+2tpMoment, amplitude was again to positive acceleration stepIn the t for entering the decelerating phase7=t4+tpMoment and t8=t4+2tpMoment gives different acceleration ranks respectively
Jump, this mode form decelerating phase t7=t4+tpMoment and t8=t4+2tpThe reversed POSICAST input shapers at moment；Slow down
Stage initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers and decelerating phase t at moment7=t4+tpMoment
And t8=t4+2tpThe reversed POSICAST input shapers synergy at moment so that T moment of the pivot angle after the decelerating phase is entered
Return to 0.
Method three：Pivot angle after moment returns to zero forward and reverse POSICAST methods；
Specific method：Boost phase, in t1=0 moment gave positive acceleration step, and amplitude isIn t2=tpWhen
It carves again to positive acceleration step, amplitude isIn t1=0 moment and t2=tpMoment gives different acceleration respectively
Step is spent, this mode forms boost phase t1=0 moment and t2=tpThe positive POSICAST input shapers at moment；Moment gives negativeacceleration step, and amplitude is Moment is again to negativeacceleration step, width
Value is Moment andMoment gives different "Jerk's respectively, and this mode is formed
Boost phaseMoment andThe reversed POSICAST input shapers at moment；Boost phase t1=0 moment and t2=
tpThe positive POSICAST input shapers and boost phase at momentMoment andThe reversed POSICAST at moment is defeated
Enter shaping synergy so that pivot angle returns to 0 at the T moment；Decelerating phase, in the initial time t for entering the decelerating phase5=t4+0
Negativeacceleration step is given, amplitude isIn t6=t4+tpMoment, amplitude was again to backward acceleration stepIn the initial time t for entering the decelerating phase5=t4+ 0 and t6=t4+tpMoment gives different acceleration ranks respectively
Jump, this mode form decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment；Moment gives positive acceleration step, and amplitude is Moment gives positive acceleration rank again
Jump, amplitude areEntering the decelerating phaseMoment andMoment gives different respectively
"Jerk', this mode form the decelerating phaseMoment andThe reversed POSICAST inputs at moment
Shaping；Decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment and decelerating phaseMoment andThe reversed POSICAST input shapers synergy at moment so that pivot angle subtracts in entrance
The T moment after the fast stage returns to 0.
Description of the drawings
It is further illustrated the present invention below in conjunction with the drawings and specific embodiments.
Fig. 1 is present invention load moving of car model schematic.
Fig. 2 is the unit-step response schematic diagram of second-order under damped system of the present invention.
Fig. 3 is the input schematic diagram after the present invention is changed unit step input by POSICAST methods.
Fig. 4 be the present invention unit step as input when system response curve with according to POSICAST methods as defeated
The control schematic diagram of the system response curve entered.
Fig. 5 is the present invention according to POSICAST methods system response curve schematic diagram as input.
Fig. 6 is the present invention in TdAfter moment adds in reversed POSICAST control methods, the output response curve signal of system
Figure.
Fig. 7 is that the present invention carves the POSICAST controls of addition forward direction at the beginning, in TdMoment adds in reversed POSICAST controls
After system, the output response curve schematic diagram of system.
Fig. 8 is that first embodiment of the invention inputs schematic diagram according to the system that positive and negative POSICAST methods give.
Fig. 9 is the curve of output schematic diagram of the small vehicle speed of first embodiment of the invention and swing angle.
Figure 10 is that second embodiment of the invention inputs schematic diagram according to the system that positive and negative POSICAST methods give.
Figure 11 is the curve of output schematic diagram of the small vehicle speed of second embodiment of the invention and swing angle.
Figure 12 is that third embodiment of the invention inputs schematic diagram according to the system that positive and negative POSICAST methods give.
Figure 13 is the curve of output schematic diagram of the small vehicle speed of third embodiment of the invention and swing angle.
Specific embodiment
In order to be easy to understand the technical means, the creative features, the aims and the efficiencies achieved by the present invention, tie below
Conjunction is specifically illustrating, and the present invention is further explained.
Container crane facility has gantry crane, the trolley of field bridge, the steel wire rope of connection and load, can be by whole system
Similar to a mobile single pendulum system, as shown in Fig. 1.
Whole system is by controlling the acceleration a of trolleyc, and then adjust the speed of service V of trolleycSo that the pivot angle of load
It is controlled, to achieve the purpose that anti-shake.Wherein, load quality m, lifting rope length are L, and load passes through lifting rope and trolley phase
Even.Tangential acceleration when load is waved is am, tangential velocity Vm.For easy analysis, the present invention makees as above model above
Assuming that：
Assuming that 1：Regard trolley and load as known to quality particle；
Assuming that 2：Lifting rope is non-extensible, and elasticity and quality can be ignored.
It gains knowledge and more than mathematical model is analyzed according to Newton's second law and movement, which can use second order
System representation：
Amplitude when k finally stablizes for pivot angle in formula, ωnTo shake frequency naturally, ξ is damping ratio.Formula (1)
For input signal a (t) and output signal θ (t) to be carried out to the system transter after Laplace transformation.
The step response of the system is：
ω in formuladFor damped vibration frequency.
By giving different Stepped Impedance Resonators in different moments so that pivot angle is superposed to zero in output sometime,
Design A0,A1,A2…An, t0,t1,t2…tnSo that pivot angle is superposed to zero in output sometime.
In order to solve this problem, it is known as positive and negative POSICAST methods by the method that the present invention uses.Brief introduction one first
Lower POSICAST methods.The POSICAST controls that O.J.M.Smith (U.Calif.Berkeley lifetime professors) is proposed in the fifties
Method processed, the method can eliminate the overshoot of step response.Unit step is inputted into line delay and is superimposed, is carved into original at the beginning
The peak value moment of first step responseIn this period, TdIt is the damped oscillation period of system,Stepped Impedance Resonators
It is originalTimes, wherein σ is overshoot, Stepped Impedance Resonators are superimposed to 1 as defeated by the moment
Enter, as shown in Figure 3.The method that input progress shaping can be eliminated the overshoot of step response by this.Global concept such as Fig. 2, Fig. 3
And shown in Fig. 4.
Fig. 2 is the unit-step response figure of second-order under damped system, and σ is maximum overshoot,For time to peak, this sound
Should finally it stablize 1.
Fig. 3 is the input figure after unit step input is changed by POSICAST methods.
When dotted line in Fig. 4 is unit step as input, the response curve of system, solid line be with it is shown in Fig. 3 according to
POSICAST methods system response curve as input, it can be seen that POSICAST methods can eliminate the super of step response
It adjusts.
The input shaper controller of the system is designed based on the theory of POSICAST control methods, if will be above this
It inputs as positive method referred to as forward direction POSICAST, then basic thought of the invention is exactly positive and negative POSICAST methods
Delay superposition.In TdMoment adds in reversed POSICAST controls,Load pivot angle after moment can be offset, and be reached
To the effect of pivot angle back to zero.
Curve in Fig. 5 is according to POSICAST methods system response curve as input with shown in Fig. 3.In peak value
MomentWhen, the original overshoot of system disappears, and tends towards stability later.
What the curve in Fig. 6 represented is in TdMoment adds in reversed POSICAST control methods, i.e., in TdMoment adds in and figure
After similar reversed input shown in 3, the output response curve of system.In peak value momentWhen, the original overshoot of system disappears,
It tends towards stability later.
Fig. 7 adds in forward direction POSICAST controls to carve at the beginning, in TdAfter moment adds in reversed POSICAST controls, it is
The output response curve of system, can be regarded as the superposition of Fig. 5 and Fig. 6.
Technical solution of the present invention elaborates.
By further theory analysis, find not only in TdThe reversed POSICAST of moment addition can reach anti-and shake
Effect,Moment orMoment adds in reversed POSICAST, and system can also be made to reach good and prevent shaking effect.Under
Face by provide these three positive and negative POSICAST control methods elaborate and theory deduction process, and with when trolley it is last
The speed V of constant velocity stagedFor 4m/s, rope length L is 15 metersAnd schematic diagram during ξ=0.016.
Involved in derivation to some formulas that can simplify：
wdtp=π (5)
It is derived below as positive POSICAST and reversed POSICAST.
Method one：Pivot angle after moment returns to zero forward and reverse POSICAST methods；
Specific method：Boost phase, in t1=0 moment gave positive acceleration step, and amplitude isIn t2=tpWhen
It carves again to positive acceleration step, amplitude isIn t1=0 moment and t2=tpMoment gives different acceleration respectively
Step is spent, this mode forms boost phase t1=0 moment and t2=tpThe positive POSICAST input shapers at moment；In t3=
2tpMoment gives negativeacceleration step, and amplitude isIn t4=3tpMoment is again to negativeacceleration step, amplitude
It isIn t3=2tpMoment and t4=3tpMoment gives different "Jerk's respectively, and this mode, which is formed, to be added
Fast stage t3=2tpMoment and t4=3tpThe reversed POSICAST input shapers at moment；Boost phase t1=0 moment and t2=tp
The positive POSICAST input shapers and boost phase t at moment3=2tpMoment and t4=3tpThe reversed POSICAST at moment is defeated
Enter shaping synergy so that pivot angle existsMoment returns to 0；Decelerating phase, enter the decelerating phase it is initial when
Carve t5=t4+ 0 gives negativeacceleration step, and amplitude isIn t6=t4+tpMoment gives backward acceleration step again,
Amplitude isIn the initial time t for entering the decelerating phase5=t4+ 0 and t6=t4+tpMoment gives different add respectively
Velocity Step Technique, this mode form decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST inputs at moment
Shaping；In t7=t4+2tpMoment gives positive acceleration step, and amplitude isIn t8=t4+3tpMoment adds again to positive
Velocity Step Technique, amplitude areIn the t for entering the decelerating phase7=t4+2tpMoment and t8=t4+3tpMoment gives respectively
Different "Jerk's, this mode form decelerating phase t7=t4+2tpMoment and t8=t4+3tpMoment it is reversed
POSICAST input shapers；Decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment
With decelerating phase t7=t4+2tpMoment and t8=t4+3tpThe reversed POSICAST input shapers synergy at moment so that pivot angle
3t after the decelerating phase is enteredpMoment returns to 0；
Theoretical explanation：
(1) forward direction POSICAST is added in initial zero moment：
(2) in TdMoment, that is, 2tpMoment adds in reversed POSICAST：
In the at the uniform velocity section of this method, i.e.,After moment, the speed of trolley isA (t) is trolley
Acceleration.If the small vehicle speed expected is Vd, then the "Jerk' amplitude at each moment can be multiplied by COEFFICIENT K,So as to ensure, the at the uniform velocity section speed of trolley is Vd。
Method one is in 3tpI.e.Pivot angle after moment is zero.
As shown in figure 8, since schematic diagram is all the speed V according to the last constant velocity stage of trolleydFor 4m/s, rope length L is 15
RiceAnd the index of ξ=0.016 illustrates, so some parameter declarations are as follows：It is carved into the peak value moment of original step response at the beginningAt this section
In, Stepped Impedance Resonators are originalTimes, wherein σ is overshoot,Again since it is desired that ensureing trolley
The speed V of last constant velocity stagedFor 4m/s, so the "Jerk' amplitude at each moment is multiplied by COEFFICIENT K,K=0.5 can be calculated, i.e. Stepped Impedance Resonators are originalTimes,
Then existMoment, amplitude was again to positive acceleration stepIn Td=8s the moment adds in reversed
POSICAST is controlled, and gives negativeacceleration step, and amplitude is Moment adds again to negative sense
Velocity Step Technique, amplitude areIt is 0 to be superimposed post-acceleration input.Hereafter, it allows trolley at the uniform velocity 10 seconds, enters back into
Decelerating phase, the acceleration input in decelerating phase are given consistent with the principle in acceleration stage.
As shown in figure 9, the explanation of trolley rate curve is as follows：From initial time toMoment trolley, which is in, accelerates rank
Section, 12 seconds to 22 seconds, this 10 seconds time trolley was in constant velocity stage, and 22 seconds to 34 seconds, this 12 seconds trolleies were in the decelerating phase.
Swing angle curve explains as follows：From initial time toMoment, swing angle are responded according to principle shown in Fig. 7,
Swing angle returns to zero later, and so as to achieve the effect that prevent to shake, equally in the decelerating phase of trolley, swing angle is also according to just
The control principle output of anti-POSICAST.
Method two：T=TdPivot angle after moment returns to zero forward and reverse POSICAST methods；
Specific method：Boost phase, in t1=0 moment gave positive acceleration step, and amplitude isIn t2=tpWhen
It carves again to positive acceleration step, amplitude isIn t1=0 moment and t2=tpMoment gives different acceleration respectively
Step is spent, this mode forms boost phase t1=0 moment and t2=tpThe positive POSICAST input shapers at moment；In t3=
tpMoment gives negativeacceleration step, and amplitude isIn t4=2tpMoment, amplitude was again to negativeacceleration stepIn t3=tpMoment and t4=2tpMoment gives different "Jerk's respectively, and this mode, which is formed, accelerates rank
Section t3=tpMoment and t4=2tpThe reversed POSICAST input shapers at moment；Boost phase t1=0 moment and t2=tpMoment
Positive POSICAST input shapers and boost phase t3=tpMoment and t4=2tpThe reversed POSICAST input shapers connection at moment
Cooperation is used so that pivot angle is in T=Td=2tpMoment returns to 0；Decelerating phase, in the initial time t for entering the decelerating phase5=t4+0
Negativeacceleration step is given, amplitude isIn t6=t4+tpMoment, amplitude was again to backward acceleration stepIn the initial time t for entering the decelerating phase5=t4+ 0 and t6=t4+tpMoment gives different acceleration respectively
Step, this mode form decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment；
In t7=t4+tpMoment gives positive acceleration step, and amplitude isIn t8=t4+2tpMoment gives positive acceleration rank again
Jump, amplitude areIn the t for entering the decelerating phase7=t4+tpMoment and t8=t4+2tpMoment gives different respectively
"Jerk', this mode form decelerating phase t7=t4+tpMoment and t8=t4+2tpThe reversed POSICAST inputs at moment
Shaping；Decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers and decelerating phase t at moment7
=t4+tpMoment and t8=t4+2tpThe reversed POSICAST input shapers synergy at moment so that pivot angle is entering deceleration rank
2t after sectionpMoment returns to 0；
Theoretical explanation：
(1) forward direction POSICAST is added in initial zero moment：
(2) existMoment, that is, tpMoment adds in reversed POSICAST：
In the at the uniform velocity section of this method, i.e. TdAfter moment, the speed of trolley isIf the trolley expected
Speed is Vd, then the "Jerk' amplitude at each moment can be multiplied by COEFFICIENT K,So as to ensure, trolley is at the uniform velocity
Duan Sudu is Vd。
Method two is in 2tpThat is TdPivot angle after moment is zero.
As shown in Figure 10, difference lies in method two exists Figure 10 and Fig. 8Moment adds in reversed POSICAST controls.Figure
10 explanation is as follows：Since schematic diagram is all the speed V according to the last constant velocity stage of trolleydFor 4m/s, rope length L is 15 metersAnd the index of ξ=0.016 illustrates, so some parameter declarations are as follows：It is carved into the peak value moment of original step response at the beginningAt this section
In, Stepped Impedance Resonators are originalTimes, wherein σ is overshoot,Again since it is desired that ensureing trolley most
The speed V of constant velocity stage afterwardsdFor 4m/s, so the "Jerk' amplitude at each moment is multiplied by COEFFICIENT K,K=1 can be calculated, i.e. Stepped Impedance Resonators are originalTimes, then
Moment, amplitude was again to positive acceleration step Moment adds in reversed
POSICAST is controlled, and gives negativeacceleration step, and amplitude isIn Td=8s the moment accelerates again to negative sense
Step is spent, amplitude isIt is 0 to be superimposed post-acceleration input.Hereafter, it allows trolley at the uniform velocity 10 seconds, enters back into and subtract
Fast stage, the acceleration input in decelerating phase are given consistent with the principle in acceleration stage.
Figure 11 is the curve of output schematic diagram of the small vehicle speed of second embodiment of the invention and swing angle, the area with Fig. 9
It is not, method two existsMoment adds in reversed POSICAST controls.Trolley rate curve in Figure 11 explains as follows：From first
The moment begin to Td=8s moment trolley is in boost phase, 8 seconds to 18 seconds, this 10 seconds time trolley is in constant velocity stage, and 18
Second, this 8 seconds trolleies were in the decelerating phase to 26 seconds.Swing angle curve explains as follows：From initial time to TdIt at=8s the moment, shakes
Swinging is responded according to principle shown in Fig. 7, and swing angle returns to zero later, so as to achieve the effect that prevent to shake, equally in trolley
Decelerating phase, swing angle is also to be exported according to the control principle of positive and negative POSICAST.
Method three：Pivot angle after moment returns to zero forward and reverse POSICAST methods；
Specific method：Boost phase, in t1=0 moment gave positive acceleration step, and amplitude isIn t2=tpWhen
It carves again to positive acceleration step, amplitude isIn t1=0 moment and t2=tpMoment gives different acceleration respectively
Step is spent, this mode forms boost phase t1=0 moment and t2=tpThe positive POSICAST input shapers at moment；Moment gives negativeacceleration step, and amplitude is Moment is again to negativeacceleration step, width
Value is Moment andMoment gives different "Jerk's respectively, and this mode, which is formed, to be added
The fast stageMoment andThe reversed POSICAST input shapers at moment；Boost phase t1=0 moment and t2=tpWhen
The positive POSICAST input shapers and boost phase at quarterMoment andThe reversed POSICAST inputs at moment are whole
Shape synergy so that pivot angle existsMoment returns to 0；Decelerating phase, in the initial time t for entering the decelerating phase5
=t4+ 0 gives negativeacceleration step, and amplitude isIn t6=t4+tpMoment is again to backward acceleration step, amplitude
It isIn the initial time t for entering the decelerating phase5=t4+ 0 and t6=t4+tpMoment gives different acceleration respectively
Step, this mode form decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST inputs at moment are whole
Shape；Moment gives positive acceleration step, and amplitude is Moment accelerates again to positive
Step is spent, amplitude isEntering the decelerating phaseMoment andMoment gives not respectively
Same "Jerk', this mode form the decelerating phaseMoment andThe reversed POSICAST at moment
Input shaper；Decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment and deceleration rank
SectionMoment andThe reversed POSICAST input shapers synergy at moment so that pivot angle subtracts in entrance
After the fast stageMoment returns to 0；
Theoretical explanation：
(1) forward direction POSICAST is added in initial zero moment：
(2) existMoment isMoment adds in reversed POSICAST：
In the at the uniform velocity section of this method, i.e.,After moment, the speed of trolley isIf that expects is small
Vehicle speed is Vd, then the "Jerk' amplitude at each moment can be multiplied by COEFFICIENT K,So as to ensure, trolley it is even
Fast section speed is Vd。
Method three existsI.e.Pivot angle after moment is zero.
As shown in figure 12, the difference of Figure 12 and Fig. 8 is that method three existsMoment adds in reversed POSICAST controls.Figure 12
Explanation it is as follows：Since schematic diagram is all the speed V according to the last constant velocity stage of trolleydFor 4m/s, rope length L is 15 metersAnd the index of ξ=0.016 illustrates, so some parameter declarations are as follows：It is carved into the peak value moment of original step response at the beginningAt this section
In, Stepped Impedance Resonators are originalTimes, wherein σ is overshoot,Again since it is desired that ensureing trolley
The speed V of last constant velocity stagedFor 4m/s, so the "Jerk' amplitude at each moment is multiplied by COEFFICIENT K,K=2 can be calculated, i.e. Stepped Impedance Resonators are originalTimes, so
Exist afterwardsMoment, amplitude was again to positive acceleration step Moment adds in reversed
POSICAST is controlled, and gives negativeacceleration step, and amplitude is Moment adds again to negative sense
Velocity Step Technique, amplitude areIt is 0 to be superimposed post-acceleration input.Hereafter, it allows trolley at the uniform velocity 10 seconds, enters back into
Decelerating phase, the acceleration input in decelerating phase are given consistent with the principle in acceleration stage.
Figure 13 is the curve of output schematic diagram of the small vehicle speed of third embodiment of the invention and swing angle.Figure 13 and Fig. 9
Difference be that method three existsMoment adds in reversed POSICAST controls.Trolley rate curve in Figure 11 explains as follows：From
Initial time is extremelyMoment trolley is in boost phase, and 6 seconds to 16 seconds, this 10 seconds time trolley was in constant velocity stage,
16 seconds to 22 seconds, this 6 seconds trolleies were in the decelerating phase.Swing angle curve explains as follows：From initial time toWhen
It carves, swing angle is responded according to principle shown in Fig. 7, and swing angle returns to zero later, so as to achieve the effect that prevent to shake, is equally existed
The decelerating phase of trolley, swing angle are also to be exported according to the control principle of positive and negative POSICAST.
So either in TdMoment,Moment still existsMoment adds in reversed POSICAST, can with initial
The positive POSICAST that zero moment adds in is offseted so that final pivot angle returns to zero, and corresponding, pivot angle exists respectivelyMoment,
TdMoment andMoment returns to zero.
It can be seen that from the analogous diagram of three cases aboveMoment isMoment adds in reversed POSICAST, load
Time of pivot angle back to zero be shortest, but the maximum value of its pivot angle is also maximum in these three situations.
Advantages and advantages of the invention are as follows：
1) the present invention is directed there is the second-order system of damping, under different damping sizes, conclusion of the invention all into
It is vertical.
2) present invention is inputted using step acceleration, the shaping of step acceleration output is directed to, with pulse acceleration
Input method compares, and speed consecutive variations are easy to Project Realization.
3) there are three types of the positive and negative POSICAST control methods of different moments, each method in the present invention effectively to control
System so that the pivot angle back to zero of load, and have rigorous theory deduction, and also by analog simulation and physical system into
Verification is gone.
4) in the present invention, the acceleration of trolley is regard as output as input, the speed of trolley and the pivot angle of load, this
Sample in actual production, according to the rate curve of the trolley of design, directly controls the speed of service of trolley, without any measurement
The sensor of pivot angle or trolley velocity of displacement, it will be able to directly reach and prevent shaking effect.
5) present invention is applicable not only to undamped system, and has been also applied for damping second-order system, and in practical life
It produces in operation process, due to the influence of various factors, system there will necessarily be damping, so the invention is than existing opened loop control skill
Art, which has, preferably promotes power.Certainly, many scholars' researchs now be closed loop control method, then bigger of the present invention it is excellent
Point is exactly measurement sensor for closed loop feedback that should not be any.
6) present invention be suitable for it is any using step signal as inputting, have the second-order system of damping, for preventing waving or
Want a certain system for exporting and being eventually returned to home position.
Basic principle, main feature and the advantages of the present invention of the present invention has been shown and described above.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and the above embodiments and description only describe this
The principle of invention, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes
Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appended claims and its
Equivalent thereof.
Claims (3)
1. a kind of crane based on positive and negative POSICAST input shapers method is prevented shaking control method, system is by controlling adding for trolley
Speed ac, and then adjust the speed of service V of trolleyc；Wherein, load quality m, lifting rope length are L, and load passes through lifting rope and small
Vehicle is connected, and tangential acceleration when load is waved is am, tangential velocity Vm, amplitude when k finally stablizes for pivot angle, ωnFor certainly
So concussion frequency, ξ are damping ratio, ωdFor damped vibration frequency, lifting rope is θ with the angle of vertical aspect, the step of the system
Response is：
TdIt is the damped oscillation period of the system of trolley and load composition；Time to peak for step response；σ is overshoot
Amount,
It is characterized in that, the crane based on positive and negative POSICAST input shapers method prevents that shaking control method isMoment
Pivot angle later returns to zero forward and reverse POSICAST methods, and specific method is as follows：
Boost phase, in t1=0 moment gave positive acceleration step, and amplitude isIn t2=tpMoment adds again to positive
Velocity Step Technique, amplitude areIn t1=0 moment and t2=tpMoment gives different "Jerk's, this side respectively
Formula forms boost phase t1=0 moment and t2=tpThe positive POSICAST input shapers at moment；In t3=2tpMoment adds to negative sense
Velocity Step Technique, amplitude areIn t4=3tpMoment, amplitude was again to negativeacceleration stepIn t3
=2tpMoment and t4=3tpMoment gives different "Jerk's respectively, and this mode forms boost phase t3=2tpMoment
And t4=3tpThe reversed POSICAST input shapers at moment；Boost phase t1=0 moment and t2=tpThe positive POSICAST at moment
Input shaper and boost phase t3=2tpMoment and t4=3tpThe reversed POSICAST input shapers synergy at moment so that
Pivot angle returns to 0 at the T moment；Decelerating phase, in the initial time t for entering the decelerating phase5=t4+ 0 gives negativeacceleration step, width
Value isIn t6=t4+tpMoment, amplitude was again to backward acceleration stepInto the decelerating phase
Initial time t5=t4+ 0 and t6=t4+tpMoment gives different "Jerk's respectively, and this mode forms the decelerating phase
Initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment；In t7=t4+2tpMoment accelerates to positive
Step is spent, amplitude isIn t8=t4+3tpMoment, amplitude was again to positive acceleration stepEntering
The t in decelerating phase7=t4+2tpMoment and t8=t4+3tpMoment gives different "Jerk's respectively, and this mode, which is formed, to be subtracted
Fast stage t7=t4+2tpMoment and t8=t4+3tpThe reversed POSICAST input shapers at moment；Decelerating phase initial time t5=
t4+ 0 and t6=t4+tpThe positive POSICAST input shapers and decelerating phase t at moment7=t4+2tpMoment and t8=t4+3tpWhen
The reversed POSICAST input shapers synergy carved so that T moment of the pivot angle after the decelerating phase is entered returns to 0.
2. a kind of crane based on positive and negative POSICAST input shapers method is prevented shaking control method, system is by controlling adding for trolley
Speed ac, and then adjust the speed of service V of trolleyc；Wherein, load quality m, lifting rope length are L, and load passes through lifting rope and small
Vehicle is connected, and tangential acceleration when load is waved is am, tangential velocity Vm, amplitude when k finally stablizes for pivot angle, ωnFor certainly
So concussion frequency, ξ are damping ratio, ωdFor damped vibration frequency, lifting rope is θ with the angle of vertical aspect, the step of the system
Response is：
TdIt is the damped oscillation period of the system of trolley and load composition；Time to peak for step response；σ is overshoot
Amount,
It is characterized in that, the crane based on positive and negative POSICAST input shapers method prevents that it is T=T to shake control methoddMoment it
Pivot angle afterwards returns to zero forward and reverse POSICAST methods, and specific method is as follows：
Boost phase, in t1=0 moment gave positive acceleration step, and amplitude isIn t2=tpMoment adds again to positive
Velocity Step Technique, amplitude areIn t1=0 moment and t2=tpMoment gives different "Jerk's, this side respectively
Formula forms boost phase t1=0 moment and t2=tpThe positive POSICAST input shapers at moment；In t3=tpMoment adds to negative sense
Velocity Step Technique, amplitude areIn t4=2tpMoment, amplitude was again to negativeacceleration stepIn t3
=tpMoment and t4=2tpMoment gives different "Jerk's respectively, and this mode forms boost phase t3=tpMoment and
t4=2tpThe reversed POSICAST input shapers at moment；Boost phase t1=0 moment and t2=tpThe positive POSICAST at moment is defeated
Enter shaping and boost phase t3=tpMoment and t4=2tpThe reversed POSICAST input shapers synergy at moment so that pivot angle
0 is returned at the T moment；Decelerating phase, in the initial time t for entering the decelerating phase5=t4+ 0 gives negativeacceleration step, and amplitude isIn t6=t4+tpMoment, amplitude was again to backward acceleration stepEntering the first of decelerating phase
Begin moment t5=t4+ 0 and t6=t4+tpMoment gives different "Jerk's respectively, and it is initial that this mode forms the decelerating phase
Moment t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment；In t7=t4+tpMoment gives positive acceleration rank
Jump, amplitude areIn t8=t4+2tpMoment, amplitude was again to positive acceleration stepSlow down entering
The t in stage7=t4+tpMoment and t8=t4+3tpMoment gives different "Jerk's respectively, and this mode forms deceleration rank
Section t7=t4+tpMoment and t8=t4+2tpThe reversed POSICAST input shapers at moment；Decelerating phase initial time t5=t4+ 0 and
t6=t4+tpThe positive POSICAST input shapers and decelerating phase t at moment7=t4+tpMoment and t8=t4+2tpMoment it is reversed
POSICAST input shaper synergy so that T moment of the pivot angle after the decelerating phase is entered returns to 0.
3. a kind of crane based on positive and negative POSICAST input shapers method is prevented shaking control method, system is by controlling adding for trolley
Speed ac, and then adjust the speed of service V of trolleyc；Wherein, load quality m, lifting rope length are L, and load passes through lifting rope and small
Vehicle is connected, and tangential acceleration when load is waved is am, tangential velocity Vm, amplitude when k finally stablizes for pivot angle, ωnFor certainly
So concussion frequency, ξ are damping ratio, ωdFor damped vibration frequency, lifting rope is θ with the angle of vertical aspect, the step of the system
Response is：
TdIt is the damped oscillation period of the system of trolley and load composition；Time to peak for step response；σ is overshoot
Amount,
It is characterized in that, the crane based on positive and negative POSICAST input shapers method prevents that shaking control method isMoment
Pivot angle later returns to zero forward and reverse POSICAST methods, and specific method is as follows：
Boost phase, in t1=0 moment gave positive acceleration step, and amplitude isIn t2=tpMoment adds again to positive
Velocity Step Technique, amplitude areIn t1=0 moment and t2=tpMoment gives different "Jerk's, this side respectively
Formula forms boost phase t1=0 moment and t2=tpThe positive POSICAST input shapers at moment；Moment adds to negative sense
Velocity Step Technique, amplitude are Moment, amplitude was again to negativeacceleration step Moment andMoment gives different "Jerk's respectively, and this mode forms boost phaseMoment
WithThe reversed POSICAST input shapers at moment；Boost phase t1=0 moment and t2=tpThe forward direction at moment
POSICAST input shapers and boost phaseMoment andThe reversed POSICAST input shapers joint at moment is made
With so that pivot angle returns to 0 at the T moment；Decelerating phase, in the initial time t for entering the decelerating phase5=t4+ 0 gives negativeacceleration
Step, amplitude areIn t6=t4+tpMoment, amplitude was again to backward acceleration stepEntering
The initial time t in decelerating phase5=t4+ 0 and t6=t4+tpMoment gives different "Jerk's respectively, and this mode is formed
Decelerating phase initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment；Moment is given
Positive acceleration step, amplitude are Moment, amplitude was again to positive acceleration stepEntering the decelerating phaseMoment andMoment gives different acceleration ranks respectively
Jump, this mode form the decelerating phaseMoment andThe reversed POSICAST input shapers at moment；Subtract
Fast stage initial time t5=t4+ 0 and t6=t4+tpThe positive POSICAST input shapers at moment and decelerating phase
Moment andThe reversed POSICAST input shapers synergy at moment so that pivot angle is after the decelerating phase is entered
The T moment returns to 0.
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