CN106227149B - A kind of galvanometer motor motion planning method shortening idle stroke positioning time - Google Patents
A kind of galvanometer motor motion planning method shortening idle stroke positioning time Download PDFInfo
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- CN106227149B CN106227149B CN201610547833.9A CN201610547833A CN106227149B CN 106227149 B CN106227149 B CN 106227149B CN 201610547833 A CN201610547833 A CN 201610547833A CN 106227149 B CN106227149 B CN 106227149B
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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
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
Abstract
The invention discloses a kind of galvanometer motor motion planning methods shortening idle stroke positioning time, including step to establish the assembly finite element model and nonlinear dynamic response finite element model for including kinematics degree of freedom；Setup parameter movement function, and be applied in the non-linear assembly finite element model comprising kinematics degree of freedom as boundary condition；The resolving of galvanometer mechanism nonlinear finite element model is carried out, galvanometer mechanism kinematic response curve is obtained, calculates the displacement relative to positioning final position, velocity information in real time；Judge whether galvanometer mechanism meets positioning accuracy request and obtain termination residual oscillation die-away time length used；It obtains mass motion positioning time, and mass motion time target as an optimization will be minimized；Obtain the optimized parameter of motion planning parameter.Compared with prior art, the requirement on both side that final positioning accuracy and minimum positioning time have been taken into account to optimum results of present invention gained.
Description
Technical field
The present invention relates to galvanometer mechanism kinematic planning field more particularly to a kind of galvanometer electricity shortening idle stroke positioning time
Machine motion planning method.
Background technology
In field of laser processing such as laser markings, galvanometer motor is a kind of common driving part.Galvanometer motor is a kind of spy
Different oscillating motor can only execute deflection action.In field of laser processing, galvanometer piece is fixed on the axis of galvanometer motor, passes through
Galvanometer motor swings to realize the adjustment of optical path direction, and realizes laser processing.Since in laser processing procedure, laser adds
, often there are some interruption parts that need not be laser machined in the not necessarily global continuous path in work hot spot path.It is above-mentioned not
The interruption laser machined is needed to partly belong to the idle stroke of laser process equipment.Reduce the above-mentioned idle stroke movement consumed time
Working efficiency for improving laser process equipment plays an important role.Due in laser machining idle stroke section, intermediary movements section
Motion conditions laser processing precision etc. is not influenced, only the motion positions precision of the end of idle stroke just swashs to subsequent
There is influence in light process.Therefore, it should be used in above-mentioned idle stroke section total to meet the minimum of end positioning accuracy request
The motion planning model of body positioning time.
Since the galvanometer piece of the small quality when high speed emergency stop is swung is easy to happen shake, the shake of above-mentioned galvanometer piece can be in light
Lead to the shake of laser beam bigger on working face under the enlarge-effect effect of road, and reducing the residual jitter in above-mentioned position fixing process needs
Expend certain galvanometer piece residual oscillation die-away time.Therefore, how to shake in preventing fast idle point motion process
Eyeglass reduces galvanometer piece general location time while generating excessive residual oscillation becomes one that raising laser machines efficiency
Critical issue.
Since the idle stroke movement of galvanometer piece belongs to typical point movement, S type motion planning curves usually can be all used
Motion planning as galvanometer motor.But since classical S type motion planning curves are bent merely by considering to move
The geometric smoothness of line carries out mechanism kinematic planning and designing, does not fully consider that execution unit during mechanism kinematic is deposited
In elastic vibration problem, motion will be caused to need certain residual oscillation die-away time that could meet required precision, it can not
Take into account the minimum of the stationarity and general location time of movement.
Patent 201310460878.9 proposes a kind of S type curve movements planning side of high-speed mechanism reduction residual oscillation
Method by increasing by one section of die-away time section for considering that residual oscillation influences in conventional S type curve movement planing methods, and is built
It stands accordingly with the Optimized model of the motion planning time+die-away time minimum target of section.When decaying described in patent
Between section be mechanism with high speed motion be after motion planning end time ensure residual oscillation amplitude be less than position error institute allowable
The time quantum needed.Above-mentioned die-away time section passes through abs (s-s*)+abs (v)<ε (wherein s, s*, v, ε be respectively moving displacement,
It is expected that displacement, movement velocity, position error allowable) it obtains.Patent 201310460878.9 is moving song based on traditional S types
The residual oscillation die-away time that above-mentioned acquisition is contained in the Optimized model that line gauge is drawn, it is excellent to obtain revised integrated motion planning
Change model.
Patent 201410255068.4 proposes a kind of asymmetric fluctuating acceleration rule based on dominant frequency energy time domain Optimal Distribution
The method of drawing analyzes the positioning for obtaining the motion under parametrization asymmetrical movement function drive using Nonlinear FEM Simulation
Residual oscillation responds course, and utilizes abs (s-s*)+abs (v)<(wherein s, s*, v, ε are respectively moving displacement, it is expected position ε
Shifting, movement velocity, position error allowable) judgment criterion determines that executing agency's residual oscillation meets the remnants needed for required precision
Vibrate die-away time.Patent 201410255068.4 is necessarily less than residual oscillation amplitude by being introduced in optimizing and analyzing model
The analysis constraint of position error allowable obtains comprehensive optimal motion planning function parameter.
The integrated motion plan optimization algorithm that patent 201310460878.9 and patent 201410255068.4 are provided is equal
It can be used for obtaining the optimal motion planning for meeting positioning accuracy and minimizing the requirements such as general location time needed for galvanometer mechanism
Parameter.The core point of above-mentioned patent is the judgement measured to the residual oscillation die-away time for meeting positioning accuracy request.Upper
It states in patent, used acquisition meets the positioning allowable employed in the judgment criterion used in motion positioning accuracy request
Error ε does not have direct physical significance, belongs to and a kind of true relevant approximate relative indicatrix of positioning displacement error allowable.
Since the position error ε allowable in above-mentioned patent is only a kind of relative indicatrix, and the same accuracy in actual complex operating mode
It is required that motion used in ε be not necessarily the same, i.e., the ε in judgment criterion used in above-mentioned patent with true position error allowable simultaneously
There is no a specific functional relations, this not necessarily matches the motion planning optimum results for causing above-mentioned patent final
The optimal motion planning of true positioning accuracy request.
Invention content
In order to overcome the deficiencies of the prior art, the present invention proposes a kind of galvanometer mechanism kinematic rule for shortening idle stroke positioning time
The method of drawing, the optimized parameter for obtaining general location time shortest motion planning function used.
The technical scheme is that such：A kind of galvanometer motor motion planning side for shortening idle stroke positioning time
Method, including step
S1：According to the geometrical model of galvanometer mechanism, the assembly finite element model for including kinematics degree of freedom is established, and create
Build the nonlinear dynamic response finite element model of the degree of freedom containing kinematics；
S2：Setup parameter movement function, and it includes kinematics degree of freedom to be applied to described as boundary condition
In non-linear assembly finite element model；
S3：Utilize the nonlinear dynamic response finite element model of galvanometer mechanism degree of freedom containing kinematics and the ginseng
Numberization movement function boundary condition, and the resolving of galvanometer mechanism nonlinear finite element model is carried out, it obtains the galvanometer mechanism and exists
Motion picture response curve under the Parametric motion functional boundary conditioning calculates the position relative to positioning final position in real time
It moves, velocity information；
S4：Determined come whether real-time judge galvanometer mechanism meets relative to the displacement of positioning final position, speed using described
Position required precision, the galvanometer mechanism nonlinear finite element model repeated in step S3 are resolved, are wanted until meeting positioning accuracy
It asks, and the difference for obtaining the end time and motion planning end time is residual oscillation die-away time length T usedres；
S5：By the residual oscillation die-away time TresAnd movement driving time TplanSummation obtains mass motion positioning
Time Ttotal(=Tres+Tplan), and T will be minimizedtotalTarget as an optimization；
S6：Judge T by iteration convergencetotalWhether it is minimum value, if TtotalFor minimum value, then correspond in iterative process
Motion planning parameter be optimized parameter, if TtotalIt is not minimum value, then the excellent of kinematic parameter is calculated based on gradient optimal method
Change the direction of search and step-size in search, and update the Parametric motion function in S3 steps, returns to S3 steps and be iterated calculating.
Further, the method packet of the nonlinear dynamic response finite element model of the degree of freedom containing kinematics is created in step S1
Include step
S11：FEM meshing and material properties defining operation are carried out according to the 3-D geometric model of galvanometer mechanism, is built
The finite element model of vertical galvanometer mechanism；
S12：Constraint of kinematic pair is created at the movable joint of mechanism part, is shaken to be established in finite element analysis environment
Illuminating apparatus structure includes the assembly finite element model of kinematics degree of freedom；
S13：Apply Parametric motion functional boundary condition in driving joint；
S14：It creates complete non linear finite element analysis and resolves model.
Further, judge that the method whether galvanometer mechanism meets positioning accuracy request includes step in step S4
S41：The displacement of the residual oscillation course of the galvanometer mechanism located terminal end obtained in step S3, velocity information are carried out
Fast Fourier Transform (FFT) and bandpass filtered signal processing (or measuring each modal information in simulation model respectively), obtain galvanometer machine
Each rank natural frequency ω of structurei(i=1..n) and its displacement s in corresponding galvanometer mechanism residual oscillation coursei(t), speed
vi(t) signal；
S42：Utilize the natural frequency ωiWith displacement si(t), speed vi(t) signal obtains each rank natural frequency ωiInstitute
Corresponding displacement si(t) and speed vi(t) time domain course curve, and utilize formulaObtain each rank
Natural frequency ωiCorresponding energy envelope line Ei(t), the energy envelope line Ei(t) amplitude is galvanometer mechanism in t moment
Natural frequency ωiThe equivalent potential energy maximum displacement of corresponding temporal motion course energy；
S43：To each rank natural frequency ωiCorresponding energy envelope line Ei(t) it is overlapped, obtains gross energy envelope
Line ESum(t)；
S44：By the gross energy envelope ESum(t) amplitude works as total energy compared with motion displacement error value allowable
Measure envelope ESum(t) when amplitude is less than motion displacement error allowable, then meet positioning accuracy in the moment galvanometer mechanism
It is required that.
The beneficial effects of the present invention are compared with prior art, the present invention has fully considered the null in galvanometer mechanism
Journey point moves the design constraint of operating mode, and obtained optimum results have taken into account final positioning accuracy and minimized positioning time
It requires on both side, the optimization process can be further applied the complex optimum of control and structure；Meanwhile institute of the present invention
Final positioning accuracy decision criteria has specific physical significance, and uses the expression-form based on equivalent energy, keeps away
Exempt from only to consider to judge by accident caused by vibration displacement curve；Again, the final positioning accuracy decision criteria used in the present invention meets real
When judge demand, be conducive to use calculating in the high occasion of requirement of real-time in motion control card etc..
Description of the drawings
Fig. 1 is that the present invention is based on positioning time shortest galvanometer mechanism kinematic planing method flow charts；
Fig. 2 is the algorithm flow chart of the present invention；
Fig. 3 is that the present invention judges residual oscillation schematic diagram of the positioning accuracy under multi-modal operating mode；
Fig. 4 is the corresponding residual oscillation analysis schematic diagram of 1 rank basic frequency under multi-modal operating mode shown in Fig. 3；
Fig. 5 is the corresponding residual oscillation analysis schematic diagram of 2 rank basic frequencies under multi-modal operating mode shown in Fig. 3；
Fig. 6 is the corresponding residual oscillation analysis schematic diagram of 3 rank basic frequencies under multi-modal operating mode shown in Fig. 3.
Specific implementation mode
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation describes, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other without creative efforts
Embodiment shall fall within the protection scope of the present invention.
Fig. 1 is referred to, one kind being based on positioning time shortest galvanometer mechanism kinematic planing method, including step
S1：According to the geometrical model of galvanometer mechanism, the assembly finite element model for including kinematics degree of freedom is established, and create
Build the nonlinear dynamic response finite element model of the degree of freedom containing kinematics；
S2：Setup parameter movement function, and it includes kinematics degree of freedom to be applied to described as boundary condition
In non-linear assembly finite element model；
S3：Utilize the nonlinear dynamic response finite element model of galvanometer mechanism degree of freedom containing kinematics and the ginseng
Numberization movement function boundary condition obtains the galvanometer mechanism in the Parametric motion functional boundary conditioning by emulating
Under motor imagination, and calculate relative to the positioning displacement of final position, speed；
S4：Determined come whether real-time judge galvanometer mechanism meets relative to the displacement of positioning final position, speed using described
Position required precision, repeats the nonlinear dynamic response finite element model of galvanometer mechanism degree of freedom containing kinematics in step S3
It resolves, until meeting positioning accuracy determination requirement, and it is remnants used to obtain difference between the end time and motion planning time
Vibrate die-away time Tres；
S5：By the residual oscillation die-away time TresAnd movement driving time TplanSummation obtains mass motion positioning
Time Ttotal(=Tres+Tplan), and T will be minimizedtotalTarget as an optimization；
S6：By iteration convergence judgement currently with previous TtotalWhether approach, if TtotalRelative deviation is less than a certain
Error, then it is optimized parameter to correspond to the motion planning parameter in iterative process, otherwise, is then based on gradient optimal method and calculates movement
The Optimizing Search direction of parameter and step-size in search, and the Parametric motion function in S3 steps is updated, it returns to S3 steps and changes
In generation, calculates.
The method for creating the nonlinear dynamic response finite element model of the degree of freedom containing kinematics in step sl includes step
S11：FEM meshing and material properties defining operation are carried out according to the 3-D geometric model of galvanometer mechanism, is built
The finite element model of vertical galvanometer mechanism；
S12：Constraint of kinematic pair is created at the movable joint of mechanism part, is shaken to be established in finite element analysis environment
Illuminating apparatus structure includes the assembly finite element model of kinematics degree of freedom；
S13：Apply Parametric motion functional boundary condition in driving joint；
S14：It creates complete nonlinear response finite element analysis and resolves model.
Judge that the method whether galvanometer mechanism meets positioning accuracy request includes step in step s 4
S41：Fast Fourier is carried out to the displacement of the galvanometer mechanism located terminal end obtained in step S3, velocity-response curve
The signal processing of transformation and bandpass filtering obtains each rank natural frequency ω of galvanometer mechanismi(i=1..n) and its corresponding galvanometer
Displacement s in mechanism residual oscillation coursei(t) and speed vi(t) motor message；
S42：According to the natural frequency ωiWith displacement si(t), speed vi(t) signal utilizes formula
Obtain each rank natural frequency ωiCorresponding energy envelope line Ei(t), the energy envelope line Ei(t) amplitude is galvanometer mechanism
In t moment natural frequency ωiThe equivalent potential energy maximum displacement of corresponding temporal motion course energy；
S43：To each rank natural frequency ωiCorresponding energy envelope line Ei(t) it is overlapped, obtains gross energy envelope
Line ESum(t)；
S44：By the gross energy envelope ESum(t) amplitude works as total energy compared with motion displacement error value allowable
Measure envelope ESum(t) when amplitude is less than motion displacement error allowable, then meet positioning accuracy in the moment galvanometer mechanism
It is required that.
The principle of end positioning accuracy judgment criterion is as follows in the present invention：
According to Fourier transform principle, complicated Vibration Condition can be decomposed into the superposition of several simple harmonic oscillations.It is assumed that fortune
Each rank THE CURVES ON WHICH A POINT MASS OSCILLATES HARMONICALLY equation in dynamic end residual oscillation is si(t)=Aie-αtsin(ωiT), wherein AiFor vibration frequency
ωiThe amplitude of oscillating curve, α damp for system structure.The vibration velocity equation of above-mentioned each rank simple harmonic oscillation isIn above-mentioned simple harmonic oscillation course, the vibrational energy of each moment point is equal
For the kinetic energy and the sum of potential energy at the moment point, i.e.,Above-mentioned total energy expression is converted to
Equal potential energy expression-form can obtain
Pass through the general potential energy expression formula of analogyIt can be seen thatFor gross energy in simple harmonic oscillation course
Corresponding equal potential energy maximum displacement.And it is substantial,Energy envelope curve is ω i frequency simple harmonic oscillations
The high accuracy approximation approximating curve of vibration displacement envelope curve.Therefore it may be usedEnergy envelope curve
As the displacement envelope curve of ω i frequency simple harmonic oscillations, for vibrating precision judgement.
Due toIt is to be derived from energy point of view, according to the scalar nature of energy, multiple frequency letters
The corresponding gross energy envelope of complex vibration curve after harmonic motion superposition is the corresponding energy envelope line of each rank vibration frequency
Superposition and, i.e.,According to ESum(t) amplitude can carry out the vibrational energy of complex vibration
Quickly judgement, and then judge whether the residual oscillation amplitude at the moment meets positioning accuracy request.
One embodiment of positioning accuracy judgement used in the carried motion planning of the present invention is as seen in figures 3-6.
S (t) residual oscillation displacement curve shown in Fig. 3 is that positioning of the motion under set motion planning model cootrol is remaining
Vibration course curve.Solid line represents s (t) residual oscillation displacement curves in Fig. 3, and dotted line represents gross energy envelope.The s (t)
The time zero of displacement curve is the end time of former setting motion planning curve, and the vibration displacement is that motion is opposite
The displacement of locating endpoints.Also due to the factors such as structural damping existing for motion itself, the energy of motion with when
Between course gradually decay.In the present embodiment, motion includes mainly 3 intrinsic frequencies.3 intrinsic frequencies can be with
It is obtained by carrying out Fourier transformation analysis to s (t) residual oscillation displacement curves.As shown in figure 3, due in multi-modal operating mode
Motion includes multiple intrinsic frequencies, causes to be difficult directly directly to utilize s (t) to original s (t) residual oscillation displacement curves
Residual oscillation displacement curve carries out positioning accuracy judgement.
In the 3 mode operating mode embodiments described in Fig. 3, obtained first with the signals analysis means such as Fast Fourier Transform (FFT)
Then each rank basic frequency extracts each rank dominant frequency in the way of bandpass filtering etc. from original s (t) residual oscillation displacement curves
Rate ωi(i=1,2,3) corresponding vibration response curve, the s in respectively Fig. 4-Fig. 6i(t) (i=1,2,3) vibration displacement responds
Curve.Solid line represents each rank dominant frequency displacement response curve in Fig. 4-Fig. 6, and long phantom line segments represent each order frequency/intrinsic frequency
Displacement curve, short dash line section represent each rank equivalent energy envelope.Due to each vibration position isolated according to each rank basic frequency
Several single mode operating modes etc. can essentially be equivalent to by moving response curve, therefore can utilize processing identical with single mode operating mode
Method is obtained to si(t) the corresponding energy envelope line of (i=1,2,3) vibration displacement response curve
(i=1,2,3).Finally by above-mentioned each rank basic frequency ωiCorresponding energy envelope line Ei(t) displacement envelope carries out amplitude superposition
Obtain gross energy envelope ESum(t).Pass through gross energy envelopeAmplitude is shaken with allowable
Whether the comparison between dynamic displacement error positions completion come the motion judged under multi-modal operating mode.
The above is the preferred embodiment of the present invention, it is noted that for those skilled in the art
For, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also considered as
Protection scope of the present invention.
Claims (3)
1. a kind of galvanometer motor motion planning method shortening idle stroke positioning time, which is characterized in that including step
S1：According to the geometrical model of galvanometer mechanism, the assembly finite element model for including kinematics degree of freedom is established, and create and contain
The nonlinear dynamic response finite element model of kinematics degree of freedom；
S2：Setup parameter movement function, and it includes the non-thread of kinematics degree of freedom to be applied to described as boundary condition
In property assembly finite element model；
S3：Utilize the nonlinear dynamic response finite element model of galvanometer mechanism degree of freedom containing kinematics and the parametrization
Movement function boundary condition, and the resolving of galvanometer mechanism nonlinear finite element model is carried out, the galvanometer mechanism is obtained described
Motion picture response curve under Parametric motion functional boundary conditioning, in real time calculate relative to positioning final position displacement,
Velocity information；
S4：Whether meet positioning accurate relative to the displacement of positioning final position, speed come real-time judge galvanometer mechanism using described
Degree requires, and the galvanometer mechanism nonlinear finite element model repeated in step S3 resolves, until meeting positioning accuracy request, and
The difference for obtaining the end time and motion planning end time is residual oscillation die-away time length T usedres；
S5：By the residual oscillation die-away time TresAnd movement driving time TplanSummation obtains mass motion positioning time
Ttotal(=Tres+Tplan), and T will be minimizedtotalTarget as an optimization；
S6：Judge T by iteration convergencetotalWhether it is minimum value, if TtotalFor minimum value, then the movement in iterative process is corresponded to
Projecting parameter is optimized parameter, if TtotalIt is not minimum value, then calculates the Optimizing Search of kinematic parameter based on gradient optimal method
Direction and step-size in search, and the Parametric motion function in S3 steps is updated, it returns to S3 steps and is iterated calculating.
2. shortening the galvanometer motor motion planning method of idle stroke positioning time as described in claim 1, which is characterized in that step
It includes step to create the method for the nonlinear dynamic response finite element model of the degree of freedom containing kinematics in rapid S1
S11：FEM meshing is carried out according to the 3-D geometric model of galvanometer mechanism and material properties defining operation, foundation are shaken
The finite element model of illuminating apparatus structure；
S12：Constraint of kinematic pair is created at the movable joint of mechanism part, to establish galvanometer machine in finite element analysis environment
Structure includes the assembly finite element model of kinematics degree of freedom；
S13：Apply Parametric motion functional boundary condition in driving joint；
S14：It creates complete non linear finite element analysis and resolves model.
3. shortening the galvanometer motor motion planning method of idle stroke positioning time as described in claim 1, which is characterized in that step
Judge that the method whether galvanometer mechanism meets positioning accuracy request includes step in rapid S4
S41：The displacement of the residual oscillation course of the galvanometer mechanism located terminal end obtained in step S3, velocity information are carried out quick
Fourier transformation and bandpass filtered signal processing (or measuring each modal information in simulation model respectively), obtain galvanometer mechanism
Each rank natural frequency ωi(i=1..n) and its displacement s in corresponding galvanometer mechanism residual oscillation coursei(t), speed vi(t)
Signal；
S42：Utilize the natural frequency ωiWith displacement si(t), speed vi(t) signal obtains each rank natural frequency ωiCorresponding
Displacement si(t) and speed vi(t) time domain course curve, and utilize formulaObtain the intrinsic frequency of each rank
Rate ωiCorresponding energy envelope line Ei(t), the energy envelope line Ei(t) amplitude is galvanometer mechanism in the intrinsic frequency of t moment
Rate ωiThe equivalent potential energy maximum displacement of corresponding temporal motion course energy；
S43：To each rank natural frequency ωiCorresponding energy envelope line Ei(t) it is overlapped, obtains gross energy envelope ESum
(t)；
S44：By the gross energy envelope ESum(t) amplitude is compared with motion displacement error value allowable, when gross energy packet
Winding thread ESum(t) when amplitude is less than motion displacement error allowable, then meets positioning accuracy in the moment galvanometer mechanism and want
It asks.
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| CN107351087A (en) * | 2017-08-29 | 2017-11-17 | 成都乐创自动化技术股份有限公司 | A kind of crawl response control mehtod and system |
| CN113241319B (en) * | 2021-05-31 | 2021-11-30 | 广东工业大学 | Rapid positioning method and system |
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|---|---|---|---|---|
| JPS58223807A (en) * | 1982-06-22 | 1983-12-26 | Kobe Steel Ltd | Preventing method of gunshot vibration of robot at stopping |
| JPS6383807A (en) * | 1986-09-29 | 1988-04-14 | S G:Kk | Compensating system for angle of lead in position control |
| CN103513575A (en) * | 2013-10-08 | 2014-01-15 | 广东工业大学 | S-shaped movement curve planning method for reducing residual oscillation of high-speed mechanism |
| CN103530272A (en) * | 2013-09-26 | 2014-01-22 | 广东工业大学 | Determining method used for defining mechanism motion high-speed area |
| CN104008250A (en) * | 2014-06-10 | 2014-08-27 | 广东工业大学 | Planning method of asymmetric variable acceleration based on optimal distribution in the time-domain of main frequency energy |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP1380000A2 (en) * | 2001-03-26 | 2004-01-14 | Cymer, Inc. | Method and device for vibration control |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS58223807A (en) * | 1982-06-22 | 1983-12-26 | Kobe Steel Ltd | Preventing method of gunshot vibration of robot at stopping |
| JPS6383807A (en) * | 1986-09-29 | 1988-04-14 | S G:Kk | Compensating system for angle of lead in position control |
| CN103530272A (en) * | 2013-09-26 | 2014-01-22 | 广东工业大学 | Determining method used for defining mechanism motion high-speed area |
| CN103513575A (en) * | 2013-10-08 | 2014-01-15 | 广东工业大学 | S-shaped movement curve planning method for reducing residual oscillation of high-speed mechanism |
| CN104008250A (en) * | 2014-06-10 | 2014-08-27 | 广东工业大学 | Planning method of asymmetric variable acceleration based on optimal distribution in the time-domain of main frequency energy |
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