CN105388761A - Positive and negative POSICAST input shaping method-based crane anti-swing control method - Google Patents

Abstract

The invention relates to a positive and negative POSICAST input shaping method-based crane anti-swing control method. The method includes a positive and negative POSICAST method adopted when a swing angle returns to zero after a time point 3Td/2, a positive and negative POSICAST method adopted when the swing angle returns to zero after a time point Td, and a positive and negative POSICAST method adopted when the swing angle returns to zero after a time point 3Td/4, wherein Td is the damped oscillation period of a system. The method of the invention is either applicable to a damped system or an un-damped two-order system. The method of the invention is an open-loop control method. With the method adopted, a measuring sensor for closed-loop feedback is not required. According to the method of the invention, step acceleration input is utilized, and the shaping of step acceleration output is targeted. Compared with a pulse acceleration input method, the method has the advantages of continuous speed change and easiness in engineering realization. The method of the invention is applicable to any damped two-order systems adopting step signals as input, and is used for an anti-swing system or a system of which the output of a certain item is expected to return to an original position.

Description

Crane based on positive and negative POSICAST input shaper method is anti-shakes control method

Technical field

The present invention relates to portal crane to prevent shaking control method, be specifically related to a kind of crane based on positive and negative POSICAST input shaper method and prevent shaking control method.

Background technology

Research about input shaper technology originates from the residual oscillations of the Oscillatory mode shape suppressing little damping servo-drive system the earliest.The emphasis of this method utilizes the means of time delay to design input shaper controller the most suitable to avoid the vibration of object, is a kind of open-loop control method.Input shaper not only only adopt simple open-loop control method just can realize crane is anti-shakes effect, and avoid the measurement mechanism measuring the inevitable costliness that feedback signal will be used when adopting feedback control scheme, this scheme easily promoted.

The domestic crane that input shaper technology is applied to prevents that the research in the field of shaking has a lot at present, and representative is Shanghai Zhenhua heavy industry group.Shanghai Zhenhua heavy industry group adopts two sections of accelerated process, two sections of accelerated process: at the acceleration a that one, the given dolly of initial time is constant, dolly is in boost phase; In the T/4 moment, to the acceleration of dolly superposition-a, now dolly enters at the uniform velocity state (T is the oscillation period of pivot angle) from acceleration mode; In the T/2 moment, to the acceleration of dolly superposition a, dolly enters acceleration mode from the uniform velocity state; In the 3T/4 moment, then superpose the acceleration of-a to dolly, now dolly enters at the uniform velocity state from acceleration transition again, and now the travelling speed of dolly just in time reaches default speed.In whole process, the pivot angle of load also converts with the change of little vehicle speed, and the output response of load pivot angle is the superpositions of these four acceleration as the response of Stepped Impedance Resonators, so the 3T/4 moment, pivot angle gets back to zero.But two sections of accelerated methods of Shanghai Zhenhua heavy industry group for be undamped system.

Summary of the invention

The object of the invention is the defect for corresponding knowledge, solve based on input shaper method for the opened loop control method having damping anti-sway system, how to make pivot angle get back to zero within the shortest time.

Technical scheme of the present invention is as follows:

Crane based on positive and negative POSICAST input shaper method is anti-shakes a control method, and whole system is by controlling the acceleration a of dolly _c, and then regulate the travelling speed V of dolly _c, the pivot angle of load is controlled, to reach anti-object of shaking.Wherein, load quality is m, and lifting rope length is L, and load is connected with dolly by lifting rope, and tangential acceleration when load is waved is a _m, tangential velocity is V _m, k is the amplitude of pivot angle when finally stablizing, ω _nfor naturally shaking frequency, ξ is damping ratio, ω _dfor damped vibration frequency, lifting rope is θ with the angle of vertical aspect, and the step response of described system is:

It is characterized in that, it is an optional method in method one, method two and method three that the described crane based on positive and negative POSICAST input shaper method prevents shaking control method; Wherein T _dbe the damped oscillation cycle of the system that dolly and load are formed, σ is overshoot,

Method one: pivot angle after moment gets back to forward and reverse POSICAST method of zero;

Concrete grammar: boost phase, at t ₁=0 moment, amplitude was to positive acceleration step at t ₂=t _pmoment gives positive acceleration step again, and amplitude is at t ₁=0 moment and t ₂=t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment; At t ₃=2t _pmoment, amplitude was to negativeacceleration step at t ₄=3t _pmoment gives negativeacceleration step again, and amplitude is at t ₃=2t _pmoment and t ₄=3t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₃=2t _pmoment and t ₄=3t _pthe reverse POSICAST input shaper in moment; Boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment and boost phase t ₃=2t _pmoment and t ₄=3t _pthe reverse POSICAST input shaper synergy in moment, makes pivot angle get back to 0 in the T moment; In the decelerating phase, entering the initial time t in decelerating phase ₅=t ₄+ 0 gives negativeacceleration step, and amplitude is at t ₆=t ₄+ t _pmoment gives backward acceleration step again, and amplitude is entering the initial time t in decelerating phase ₅=t ₄+ 0 and t ₆=t ₄+ t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment; At t ₇=t ₄+ 2t _pmoment, amplitude was to positive acceleration step at t ₈=t ₄+ 3t _pmoment gives positive acceleration step again, and amplitude is entering the t in decelerating phase ₇=t ₄+ 2t _pmoment and t ₈=t ₄+ 3t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase t ₇=t ₄+ 2t _pmoment and t ₈=t ₄+ 3t _pthe reverse POSICAST input shaper in moment; Decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment and decelerating phase t ₇=t ₄+ 2t _pmoment and t ₈=t ₄+ 3t _pthe reverse POSICAST input shaper synergy in moment, makes the T moment of pivot angle after entering the decelerating phase get back to 0.

Method two: T=T _dpivot angle after moment gets back to forward and reverse POSICAST method of zero;

Concrete grammar: boost phase, at t ₁=0 moment, amplitude was to positive acceleration step at t ₂=t _pmoment gives positive acceleration step again, and amplitude is at t ₁=0 moment and t ₂=t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment; At t ₃=t _pmoment, amplitude was to negativeacceleration step at t ₄=2t _pmoment gives negativeacceleration step again, and amplitude is at t ₃=t _pmoment and t ₄=2t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₃=t _pmoment and t ₄=2t _pthe reverse POSICAST input shaper in moment; Boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment and boost phase t ₃=t _pmoment and t ₄=2t _pthe reverse POSICAST input shaper synergy in moment, makes pivot angle get back to 0 in the T moment; In the decelerating phase, entering the initial time t in decelerating phase ₅=t ₄+ 0 gives negativeacceleration step, and amplitude is at t ₆=t ₄+ t _pmoment gives backward acceleration step again, and amplitude is entering the initial time t in decelerating phase ₅=t ₄+ 0 and t ₆=t ₄+ t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment; At t ₇=t ₄+ t _pmoment, amplitude was to positive acceleration step at t ₈=t ₄+ 2t _pmoment gives positive acceleration step again, and amplitude is entering the t in decelerating phase ₇=t ₄+ t _pmoment and t ₈=t ₄+ 2t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase t ₇=t ₄+ t _pmoment and t ₈=t ₄+ 2t _pthe reverse POSICAST input shaper in moment; Decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment and decelerating phase t ₇=t ₄+ t _pmoment and t ₈=t ₄+ 2t _pthe reverse POSICAST input shaper synergy in moment, makes the T moment of pivot angle after entering the decelerating phase get back to 0.

Method three: pivot angle after moment gets back to forward and reverse POSICAST method of zero;

Concrete grammar: boost phase, at t ₁=0 moment, amplitude was to positive acceleration step at t ₂=t _pmoment gives positive acceleration step again, and amplitude is at t ₁=0 moment and t ₂=t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment; ? moment, amplitude was to negativeacceleration step ? moment gives negativeacceleration step again, and amplitude is ? moment and moment is given different "Jerk' respectively, and this mode forms boost phase moment and the reverse POSICAST input shaper in moment; Boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment and boost phase moment and the reverse POSICAST input shaper synergy in moment, makes pivot angle get back to 0 in the T moment; In the decelerating phase, entering the initial time t in decelerating phase ₅=t ₄+ 0 gives negativeacceleration step, and amplitude is at t ₆=t ₄+ t _pmoment gives backward acceleration step again, and amplitude is entering the initial time t in decelerating phase ₅=t ₄+ 0 and t ₆=t ₄+ t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment; ? moment, amplitude was to positive acceleration step ? moment gives positive acceleration step again, and amplitude is entering decelerating phase moment and moment is given different "Jerk' respectively, and this mode forms the decelerating phase moment and the reverse POSICAST input shaper in moment; Decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment and decelerating phase moment and the reverse POSICAST input shaper synergy in moment, makes the T moment of pivot angle after entering the decelerating phase get back to 0.

Accompanying drawing explanation

The present invention is further illustrated below in conjunction with the drawings and specific embodiments.

Fig. 1 is load moving of car model schematic of the present invention.

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 unit step input changes by POSICAST method by the present invention.

To be unit step of the present invention contrast schematic diagram with according to POSICAST method as the system responses curve inputted as the response curve of system during input to Fig. 4.

Fig. 5 is that the present invention is according to the system responses curve synoptic diagram of POSICAST method as input.

Fig. 6 is that the present invention is at T _dafter moment adds reverse POSICAST control method, the output response curve schematic diagram of system.

Fig. 7 is that the present invention adds forward POSICAST at initial time and controls, at T _dmoment add reverse POSICAST control after, 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 method is given.

Fig. 9 is the curve of output schematic diagram of the little 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 method is given.

Figure 11 is the curve of output schematic diagram of the little 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 method is given.

Figure 13 is the curve of output schematic diagram of the little vehicle speed of third embodiment of the invention and swing angle.

Embodiment

The technological means realized to make the present invention, creation characteristic, reaching object and effect is easy to understand, below in conjunction with concrete diagram, setting forth the present invention further.

Container crane facility has An Qiao, the dolly of field bridge, the wire rope of connection and load, whole system can be approximated to the single pendulum system of a movement, as shown in Figure 1.

Whole system is by controlling the acceleration a of dolly _c, and then regulate the travelling speed V of dolly _c, the pivot angle of load is controlled, to reach anti-object of shaking.Wherein, load quality is m, and lifting rope length is L, and load is connected with dolly by lifting rope.Tangential acceleration when load is waved is a _m, tangential velocity is V _m.In order to easy analysis, the present invention does as above to suppose to above model:

Suppose 1: dolly and load are regarded as the particle that quality is known;

Suppose 2: lifting rope is not tensile, its elasticity and quality negligible.

Analyze above mathematical model according to Newton second law and kinematics knowledge, this system can represent by second-order system:

In formula, k is the amplitude of pivot angle when finally stablizing, ω _nfor naturally shaking frequency, ξ is damping ratio.Formula (1)

For input signal a (t) and output signal θ (t) are carried out the system transter after Laplace transformation.

The step response of this system is:

ω in formula _dfor damped vibration frequency.

By at not given different Stepped Impedance Resonators in the same time, pivot angle is made to be superposed to zero in output sometime,

Namely A is designed ₀, A ₁, A ₂a _n, t ₀, t ₁, t ₂t _n, make pivot angle be superposed to zero in output sometime.

And

In order to address this problem, it is called positive and negative POSICAST method by the method that the present invention adopts.First brief introduction POSICAST method once.The POSICAST control method that O.J.M.Smith (U.Calif.Berkeley lifetime professor) proposed in the fifties, the method can eliminate the overshoot of step response.Unit step input is carried out time delay superposition, in the peak value moment of initial time to original step response during this period of time, T _dthe damped oscillation cycle of system, stepped Impedance Resonators is original doubly, wherein σ is overshoot, ? stepped Impedance Resonators is superimposed to 1 as input by the moment, as shown in Figure 3.This method of input being carried out shaping can eliminate the overshoot of step response.Global concept is as shown in Fig. 2, Fig. 3 and Fig. 4.

Fig. 2 is the unit-step response figure of second-order under damped system, σ is maximum overshoot, for time to peak, this response is finally stabilized in 1.

Fig. 3 is the input figure after unit step input being changed by POSICAST method.

When dotted line in Fig. 4 is unit step as input, the response curve of system, solid line be using shown in Fig. 3 according to the system responses curve of POSICAST method as input, can see, POSICAST method can eliminate the overshoot of step response.

Theory based on POSICAST control method designs the input shaper controller of this system, if be input as positive method be called forward POSICAST by this above, basic thought so of the present invention is exactly, the time delay superposition of positive and negative POSICAST method.At T _dmoment adds reverse POSICAST and controls, load pivot angle after moment can be offset, and reaches the effect of pivot angle back to zero.

Curve in Fig. 5 be using shown in Fig. 3 according to POSICAST method as input system responses curve.In peak value moment time, the overshoot disappearance that system is original, tends towards stability afterwards.

What the curve in Fig. 6 represented is at T _dmoment adds reverse POSICAST control method, namely at T _dmoment add with reverse input similar shown in Fig. 3 after, the output response curve of system.In peak value moment time, the overshoot disappearance that system is original, tends towards stability afterwards.

Fig. 7 controls for adding forward POSICAST at initial time, at T _dmoment add reverse POSICAST control after, the output response curve of system, can be regarded as the superposition of Fig. 5 and Fig. 6.

Elaborating of technical solution of the present invention.

Through further theoretical analysis, find not only at T _dmoment adds reverse POSICAST and can reach anti-and shake effect, moment or moment adds reverse POSICAST, system also can be made to reach good and anti-ly shake effect.To elaborating and theory deduction process of these three kinds positive and negative POSICAST control methods be provided below, and with the speed V as the last constant velocity stage of dolly _dfor 4m/s, the long L that restricts is 15 meters and schematic diagram during ξ=0.016.

Some formulas that can simplify related in derivation:

w _dt _p＝π(5)

Derive according to forward POSICAST and reverse POSICAST below.

Method one: pivot angle after moment gets back to forward and reverse POSICAST method of zero;

Concrete grammar: boost phase, at t ₁=0 moment, amplitude was to positive acceleration step at t ₂=t _pmoment gives positive acceleration step again, and amplitude is at t ₁=0 moment and t ₂=t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment; At t ₃=2t _pmoment, amplitude was to negativeacceleration step at t ₄=3t _pmoment gives negativeacceleration step again, and amplitude is at t ₃=2t _pmoment and t ₄=3t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₃=2t _pmoment and t ₄=3t _pthe reverse POSICAST input shaper in moment; Boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment and boost phase t ₃=2t _pmoment and t ₄=3t _pthe reverse POSICAST input shaper synergy in moment, makes pivot angle exist moment gets back to 0; In the decelerating phase, entering the initial time t in decelerating phase ₅=t ₄+ 0 gives negativeacceleration step, and amplitude is at t ₆=t ₄+ t _pmoment gives backward acceleration step again, and amplitude is entering the initial time t in decelerating phase ₅=t ₄+ 0 and t ₆=t ₄+ t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment; At t ₇=t ₄+ 2t _pmoment, amplitude was to positive acceleration step at t ₈=t ₄+ 3t _pmoment gives positive acceleration step again, and amplitude is entering the t in decelerating phase ₇=t ₄+ 2t _pmoment and t ₈=t ₄+ 3t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase t ₇=t ₄+ 2t _pmoment and t ₈=t ₄+ 3t _pthe reverse POSICAST input shaper in moment; Decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment and decelerating phase t ₇=t ₄+ 2t _pmoment and t ₈=t ₄+ 3t _pthe reverse POSICAST input shaper synergy in moment, makes the 3t of pivot angle after entering the decelerating phase _pmoment gets back to 0;

Theoretical explanation:

(1) forward POSICAST is added in initial zero moment:

(2) at T _dmoment and 2t _pmoment adds reverse POSICAST:

In the at the uniform velocity section of this method, namely after moment, the speed of dolly is the acceleration that a (t) is dolly.If the little vehicle speed expected is V _d, then the "Jerk' amplitude in each moment can be multiplied by COEFFICIENT K, thus ensure, the at the uniform velocity section speed of dolly is V _d.

Method one is at 3t _pnamely pivot angle after moment is zero.

As shown in Figure 8, due to speed V that schematic diagram is all according to the last constant velocity stage of dolly _dfor 4m/s, the long L that restricts is 15 meters and the index of ξ=0.016 is described, so some parameter declaration is as follows: in the peak value moment of initial time to original step response during this period of time, Stepped Impedance Resonators is original doubly, wherein σ is overshoot, again because need the speed V ensureing the last constant velocity stage of dolly _dfor 4m/s, so the "Jerk' amplitude in each moment is multiplied by COEFFICIENT K, can calculate K=0.5, namely Stepped Impedance Resonators is original doubly, then exist moment gives positive acceleration step again, and amplitude is at T _din=8s the moment, add reverse POSICAST and control, given negativeacceleration step, amplitude is ? moment gives negativeacceleration step again, and amplitude is superposition post-acceleration is input as 0.After this, allow dolly at the uniform velocity 10 seconds, then enter the decelerating phase, the acceleration input in decelerating phase is given consistent with the principle in acceleration stage.

As shown in Figure 9, the explanation of dolly rate curve is as follows: from initial time to moment dolly is in boost phase, 12 seconds to 22 seconds, and this time dolly of 10 seconds is in constant velocity stage, 22 seconds to 34 seconds, and this 12 seconds dollies are in the decelerating phase.The explanation of swing angle curve is as follows: from initial time to in the moment, swing angle is according to the principle response shown in Fig. 7, and swing angle gets back to zero afterwards, thus reaches anti-effect of shaking, and equally in the decelerating phase of dolly, swing angle is also export according to the control principle of positive and negative POSICAST.

Method two: T=T _dpivot angle after moment gets back to forward and reverse POSICAST method of zero;

Concrete grammar: boost phase, at t ₁=0 moment, amplitude was to positive acceleration step at t ₂=t _pmoment gives positive acceleration step again, and amplitude is at t ₁=0 moment and t ₂=t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment; At t ₃=t _pmoment, amplitude was to negativeacceleration step at t ₄=2t _pmoment gives negativeacceleration step again, and amplitude is at t ₃=t _pmoment and t ₄=2t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₃=t _pmoment and t ₄=2t _pthe reverse POSICAST input shaper in moment; Boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment and boost phase t ₃=t _pmoment and t ₄=2t _pthe reverse POSICAST input shaper synergy in moment, makes pivot angle at T=T _d=2t _pmoment gets back to 0; In the decelerating phase, entering the initial time t in decelerating phase ₅=t ₄+ 0 gives negativeacceleration step, and amplitude is at t ₆=t ₄+ t _pmoment gives backward acceleration step again, and amplitude is entering the initial time t in decelerating phase ₅=t ₄+ 0 and t ₆=t ₄+ t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment; At t ₇=t ₄+ t _pmoment, amplitude was to positive acceleration step at t ₈=t ₄+ 2t _pmoment gives positive acceleration step again, and amplitude is entering the t in decelerating phase ₇=t ₄+ t _pmoment and t ₈=t ₄+ 2t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase t ₇=t ₄+ t _pmoment and t ₈=t ₄+ 2t _pthe reverse POSICAST input shaper in moment; Decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment and decelerating phase t ₇=t ₄+ t _pmoment and t ₈=t ₄+ 2t _pthe reverse POSICAST input shaper synergy in moment, makes the 2t of pivot angle after entering the decelerating phase _pmoment gets back to 0;

Theoretical explanation:

(1) forward POSICAST is added in initial zero moment:

(2) exist moment and t _pmoment adds reverse POSICAST:

In the at the uniform velocity section of this method, i.e. T _dafter moment, the speed of dolly is if the little vehicle speed expected is V _d, then the "Jerk' amplitude in each moment can be multiplied by COEFFICIENT K, thus ensure, the at the uniform velocity section speed of dolly is V _d.

Method two is at 2t _pi.e. T _dpivot angle after moment is zero.

As shown in Figure 10, the difference of Figure 10 and Fig. 8 is, method two exists moment adds reverse POSICAST and controls.The explanation of Figure 10 is as follows: because schematic diagram is all the speed V according to the last constant velocity stage of dolly _dfor 4m/s, the long L that restricts is 15 meters and the index of ξ=0.016 is described, so some parameter declaration is as follows: in the peak value moment of initial time to original step response during this period of time, Stepped Impedance Resonators is original doubly, wherein σ is overshoot, again because need the speed V ensureing the last constant velocity stage of dolly _dfor 4m/s, so the "Jerk' amplitude in each moment is multiplied by COEFFICIENT K, can calculate K=1, namely Stepped Impedance Resonators is original doubly, then exist moment gives positive acceleration step again, and amplitude is ? in the moment, add reverse POSICAST and control, given negativeacceleration step, amplitude is at T _d=8s the moment gives negativeacceleration step again, and amplitude is superposition post-acceleration is input as 0.After this, allow dolly at the uniform velocity 10 seconds, then enter the decelerating phase, the acceleration input in decelerating phase is given consistent with the principle in acceleration stage.

Figure 11 is the curve of output schematic diagram of the little vehicle speed of second embodiment of the invention and swing angle, and be with the difference of Fig. 9, method two exists moment adds reverse POSICAST and controls.Dolly rate curve explanation in Figure 11 is as follows: from initial time to T _d=8s moment dolly is in boost phase, 8 seconds to 18 seconds, and this time dolly of 10 seconds is in constant velocity stage, 18 seconds to 26 seconds, and this 8 seconds dollies are in the decelerating phase.The explanation of swing angle curve is as follows: from initial time to T _din=8s the moment, swing angle is according to the principle response shown in Fig. 7, and swing angle gets back to zero afterwards, thus reaches anti-effect of shaking, and equally in the decelerating phase of dolly, swing angle is also export according to the control principle of positive and negative POSICAST.

Method three: pivot angle after moment gets back to forward and reverse POSICAST method of zero;

Concrete grammar: boost phase, at t ₁=0 moment, amplitude was to positive acceleration step at t ₂=t _pmoment gives positive acceleration step again, and amplitude is at t ₁=0 moment and t ₂=t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment; ? moment, amplitude was to negativeacceleration step ? moment gives negativeacceleration step again, and amplitude is ? moment and moment is given different "Jerk' respectively, and this mode forms boost phase moment and the reverse POSICAST input shaper in moment; Boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment and boost phase moment and the reverse POSICAST input shaper synergy in moment, makes pivot angle exist moment gets back to 0; In the decelerating phase, entering the initial time t in decelerating phase ₅=t ₄+ 0 gives negativeacceleration step, and amplitude is at t ₆=t ₄+ t _pmoment gives backward acceleration step again, and amplitude is entering the initial time t in decelerating phase ₅=t ₄+ 0 and t ₆=t ₄+ t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment; ? moment, amplitude was to positive acceleration step ? moment gives positive acceleration step again, and amplitude is entering decelerating phase moment and moment is given different "Jerk' respectively, and this mode forms the decelerating phase moment and the reverse POSICAST input shaper in moment; Decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment and decelerating phase moment and the reverse POSICAST input shaper synergy in moment, makes pivot angle after entering the decelerating phase moment gets back to 0;

Theoretical explanation:

(1) forward POSICAST is added in initial zero moment:

(2) exist moment namely moment adds reverse POSICAST:

In the at the uniform velocity section of this method, namely after moment, the speed of dolly is if the little vehicle speed expected is V _d, then the "Jerk' amplitude in each moment can be multiplied by COEFFICIENT K, thus ensure, the at the uniform velocity section speed of dolly is V _d.

Method three exists namely pivot angle after moment is zero.

As shown in figure 12, the difference of Figure 12 and Fig. 8 is, method three exists moment adds reverse POSICAST and controls.The explanation of Figure 12 is as follows: because schematic diagram is all the speed V according to the last constant velocity stage of dolly _dfor 4m/s, the long L that restricts is 15 meters and the index of ξ=0.016 is described, so some parameter declaration is as follows: in the peak value moment of initial time to original step response during this period of time, Stepped Impedance Resonators is original doubly, wherein σ is overshoot, again because need the speed V ensureing the last constant velocity stage of dolly _dfor 4m/s, so the "Jerk' amplitude in each moment is multiplied by COEFFICIENT K, can calculate K=2, namely Stepped Impedance Resonators is original doubly, then exist moment gives positive acceleration step again, and amplitude is ? in the moment, add reverse POSICAST and control, given negativeacceleration step, amplitude is ? moment gives negativeacceleration step again, and amplitude is superposition post-acceleration is input as 0.After this, allow dolly at the uniform velocity 10 seconds, then enter the decelerating phase, the acceleration input in decelerating phase is given consistent with the principle in acceleration stage.

Figure 13 is the curve of output schematic diagram of the little vehicle speed of third embodiment of the invention and swing angle.The difference of Figure 13 and Fig. 9 is, method three exists moment adds reverse POSICAST and controls.Dolly rate curve explanation in Figure 11 is as follows: from initial time to moment dolly is in boost phase, 6 seconds to 16 seconds, and this time dolly of 10 seconds is in constant velocity stage, 16 seconds to 22 seconds, and this 6 seconds dollies are in the decelerating phase.The explanation of swing angle curve is as follows: from initial time to in the moment, swing angle is according to the principle response shown in Fig. 7, and swing angle gets back to zero afterwards, thus reaches anti-effect of shaking, and equally in the decelerating phase of dolly, swing angle is also export according to the control principle of positive and negative POSICAST.

So no matter be at T _dmoment, moment still exists moment adds reverse POSICAST, can offset, make final pivot angle get back to zero with the forward POSICAST added in initial zero moment, corresponding, pivot angle exists respectively moment, T _dmoment and moment gets back to zero.

As can be seen from the analogous diagram of above three kinds of situations, moment namely moment adds reverse POSICAST, and the time of the pivot angle back to zero of load is the shortest, but the maximal value of its pivot angle is also maximum in these three kinds of situations.

Beneficial effect of the present invention and advantage as follows:

1) the present invention is directed there is the second-order system of damping, under different damping sizes, conclusion of the present invention is all set up.

2) the present invention uses step acceleration to input, for be step acceleration export shaping, compare with pulse acceleration input method, speed consecutive variations, is easy to Project Realization.

3) have three kinds of not positive and negative POSICAST control methods in the same time in the present invention, often kind of method can effectively control, and makes the pivot angle back to zero of load, and has rigorous theory deduction, and also verified by analog simulation and physical system.

4) in the present invention, using the acceleration of dolly as input, the speed of dolly and the pivot angle of load are as output, like this, in actual production, according to the rate curve of the dolly of design, directly control the travelling speed of dolly, without the need to the sensor of any measurement pivot angle or dolly velocity of displacement, just directly can reach anti-and shake effect.

5) the present invention is not only applicable to undamped system, and be applicable to damping second-order system, and in actual production operation process, due to the impact of various factors, must there is damping in system, so this invention has better popularization power than existing open-loop control technology.Certainly, now a lot of scholar's research is the control method of closed loop, and the advantage that so the present invention is larger is exactly not any survey sensor for close-loop feedback.

6) the present invention is applicable to any using step signal as input, has the second-order system of damping, waves for anti-or want a certain output finally to get back to the system in original position.

More than show and describe ultimate principle of the present invention, principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; what describe in above-described embodiment and instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.Application claims protection domain is defined by appending claims and equivalent thereof.

Claims (3)

1. the crane based on positive and negative POSICAST input shaper method is prevented shaking a control method, by controlling the acceleration a of dolly _c, and then regulate the travelling speed V of dolly _c; Wherein, load quality is m, and lifting rope length is L, and load is connected with dolly by lifting rope, and tangential acceleration when load is waved is a _m, tangential velocity is V _m, k is the amplitude of pivot angle when finally stablizing, ω _nfor naturally shaking frequency, ξ is damping ratio, ω _dfor damped vibration frequency, lifting rope is θ with the angle of vertical aspect, and the step response of described system is:

$\mathrm{\θ}\left(t\right)=k\[1-e^{-{\mathrm{\ξ\ω}}_{n}t}({\mathrm{cos\ω}}_{d}t+\frac{\mathrm{\ξ}}{\sqrt{1-{\mathrm{\ξ}}^2}}{\mathrm{sin\ω}}_{d}t)\],$

T _dbe the damped oscillation cycle of the system that dolly and load are formed, σ is overshoot,

It is characterized in that, the described crane based on positive and negative POSICAST input shaper method prevents that shaking control method is pivot angle after moment gets back to forward and reverse POSICAST method of zero, and concrete grammar is as follows:

Boost phase, at t ₁=0 moment, amplitude was to positive acceleration step at t ₂=t _pmoment gives positive acceleration step again, and amplitude is at t ₁=0 moment and t ₂=t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment; At t ₃=2t _pmoment, amplitude was to negativeacceleration step at t ₄=3t _pmoment gives negativeacceleration step again, and amplitude is at t ₃=2t _pmoment and t ₄=3t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₃=2t _pmoment and t ₄=3t _pthe reverse POSICAST input shaper in moment; Boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment and boost phase t ₃=2t _pmoment and t ₄=3t _pthe reverse POSICAST input shaper synergy in moment, makes pivot angle get back to 0 in the T moment; In the decelerating phase, entering the initial time t in decelerating phase ₅=t ₄+ 0 gives negativeacceleration step, and amplitude is at t ₆=t ₄+ t _pmoment gives backward acceleration step again, and amplitude is entering the initial time t in decelerating phase ₅=t ₄+ 0 and t ₆=t ₄+ t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment; At t ₇=t ₄+ 2t _pmoment, amplitude was to positive acceleration step at t ₈=t ₄+ 3t _pmoment gives positive acceleration step again, and amplitude is entering the t in decelerating phase ₇=t ₄+ 2t _pmoment and t ₈=t ₄+ 3t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase t ₇=t ₄+ 2t _pmoment and t ₈=t ₄+ 3t _pthe reverse POSICAST input shaper in moment; Decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment and decelerating phase t ₇=t ₄+ 2t _pmoment and t ₈=t ₄+ 3t _pthe reverse POSICAST input shaper synergy in moment, makes the T moment of pivot angle after entering the decelerating phase get back to 0.

2. the crane based on positive and negative POSICAST input shaper method is prevented shaking a control method, by controlling the acceleration a of dolly _c, and then regulate the travelling speed V of dolly _c; Wherein, load quality is m, and lifting rope length is L, and load is connected with dolly by lifting rope, and tangential acceleration when load is waved is a _m, tangential velocity is V _m, k is the amplitude of pivot angle when finally stablizing, ω _nfor naturally shaking frequency, ξ is damping ratio, ω _dfor damped vibration frequency, lifting rope is θ with the angle of vertical aspect, and the step response of described system is:

$\mathrm{\θ}\left(t\right)=k\[1-e^{-{\mathrm{\ξ\ω}}_{n}t}({\mathrm{cos\ω}}_{d}t+\frac{\mathrm{\ξ}}{\sqrt{1-{\mathrm{\ξ}}^2}}{\mathrm{sin\ω}}_{d}t)\],$

T _dbe the damped oscillation cycle of the system that dolly and load are formed, σ is overshoot,

It is characterized in that, the described crane based on positive and negative POSICAST input shaper method prevents that shaking control method is T=T _dpivot angle after moment gets back to forward and reverse POSICAST method of zero, and concrete grammar is as follows:

Boost phase, at t ₁=0 moment, amplitude was to positive acceleration step at t ₂=t _pmoment gives positive acceleration step again, and amplitude is at t ₁=0 moment and t ₂=t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment; At t ₃=t _pmoment, amplitude was to negativeacceleration step at t ₄=2t _pmoment gives negativeacceleration step again, and amplitude is at t ₃=t _pmoment and t ₄=2t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₃=t _pmoment and t ₄=2t _pthe reverse POSICAST input shaper in moment; Boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment and boost phase t ₃=t _pmoment and t ₄=2t _pthe reverse POSICAST input shaper synergy in moment, makes pivot angle get back to 0 in the T moment; In the decelerating phase, entering the initial time t in decelerating phase ₅=t ₄+ 0 gives negativeacceleration step, and amplitude is at t ₆=t ₄+ t _pmoment gives backward acceleration step again, and amplitude is entering the initial time t in decelerating phase ₅=t ₄+ 0 and t ₆=t ₄+ t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment; At t ₇=t ₄+ t _pmoment, amplitude was to positive acceleration step at t ₈=t ₄+ 2t _pmoment gives positive acceleration step again, and amplitude is entering the t in decelerating phase ₇=t ₄+ t _pmoment and t ₈=t ₄+ 3t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase t ₇=t ₄+ t _pmoment and t ₈=t ₄+ 2t _pthe reverse POSICAST input shaper in moment; Decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment and decelerating phase t ₇=t ₄+ t _pmoment and t ₈=t ₄+ 2t _pthe reverse POSICAST input shaper synergy in moment, makes the T moment of pivot angle after entering the decelerating phase get back to 0.

3. the crane based on positive and negative POSICAST input shaper method is prevented shaking a control method, by controlling the acceleration a of dolly _c, and then regulate the travelling speed V of dolly _c; Wherein, load quality is m, and lifting rope length is L, and load is connected with dolly by lifting rope, and tangential acceleration when load is waved is a _m, tangential velocity is V _m, k is the amplitude of pivot angle when finally stablizing, ω _nfor naturally shaking frequency, ξ is damping ratio, ω _dfor damped vibration frequency, lifting rope is θ with the angle of vertical aspect, and the step response of described system is:

$\mathrm{\θ}\left(t\right)=k\[1-e^{-{\mathrm{\ξ\ω}}_{n}t}({\mathrm{cos\ω}}_{d}t+\frac{\mathrm{\ξ}}{\sqrt{1-{\mathrm{\ξ}}^2}}{\mathrm{sin\ω}}_{d}t)\],$

T _dbe the damped oscillation cycle of the system that dolly and load are formed, σ is overshoot,

It is characterized in that, the described crane based on positive and negative POSICAST input shaper method prevents that shaking control method is pivot angle after moment gets back to forward and reverse POSICAST method of zero, and concrete grammar is as follows:

Boost phase, at t ₁=0 moment, amplitude was to positive acceleration step at t ₂=t _pmoment gives positive acceleration step again, and amplitude is at t ₁=0 moment and t ₂=t _pmoment is given different "Jerk' respectively, and this mode forms boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment; ? moment, amplitude was to negativeacceleration step ? moment gives negativeacceleration step again, and amplitude is ? moment and moment is given different "Jerk' respectively, and this mode forms boost phase moment and the reverse POSICAST input shaper in moment; Boost phase t ₁=0 moment and t ₂=t _pthe forward POSICAST input shaper in moment and boost phase moment and the reverse POSICAST input shaper synergy in moment, makes pivot angle get back to 0 in the T moment; In the decelerating phase, entering the initial time t in decelerating phase ₅=t ₄+ 0 gives negativeacceleration step, and amplitude is at t ₆=t ₄+ t _pmoment gives backward acceleration step again, and amplitude is entering the initial time t in decelerating phase ₅=t ₄+ 0 and t ₆=t ₄+ t _pmoment is given different "Jerk' respectively, and this mode forms decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment; ? moment, amplitude was to positive acceleration step ? moment gives positive acceleration step again, and amplitude is entering decelerating phase moment and moment is given different "Jerk' respectively, and this mode forms the decelerating phase moment and the reverse POSICAST input shaper in moment; Decelerating phase initial time t ₅=t ₄+ 0 and t ₆=t ₄+ t _pthe forward POSICAST input shaper in moment and decelerating phase moment and the reverse POSICAST input shaper synergy in moment, makes the T moment of pivot angle after entering the decelerating phase get back to 0.