Implementation of Input Shaping Control to Reduce Residual Vibration in Industrial Network Motion System

Transcription

1 015 15th Iteratioal Coferece o Cotrol, Automatio ad Systems (ICCAS 015) Oct. 1-16, 015 i BEXCO, Busa, orea Implemetatio of Iput Shapig Cotrol to educe esidual Vibratio i Idustrial Network Motio System Ha-Quag-Thih Ngo 1, Quoc-Chi Nguye * ad Wo-Ho im 1 Cotrol ad Automatio Lab, Departmet of Mechatroics Egieerig, Ho Chi Mih City Uiversity of Techology, Ho Chi Mih, Vietam ( thihpfiev00@yahoo.com) Departmet of Mechatroics Egieerig, Ho Chi Mih City Uiversity of Techology, Ho Chi Mih, Vietam ( qchi@hcmut.edu.v) * Correspodig author Departmet of Itelliget System Egieerig, Dog-Eui Uiversity, Busa, orea ( kwh@deu.ac.kr) Abstract: I this paper, a method to implemet the iput shapig cotrol i Mechatrolik-III motio system is itroduced. Firstly, the uderdamped system is theoretically built by modelig. The, the motio cotroller of Mechatrolik-III etwork is desiged to apply the iput shaper for reducig residual vibratio i maufacturig machie. Later, the experimetal beam is set-up to verify the effective performace of iput shapig techique. The validity of the cotrol strategy is practically performed by testig ZV, ZVD ad ZVDD iput shapers. Especially, the successful implemetatio provides a opportuity to apply the iput shaper for multi-axes sice Mechatrolik-III motio cotroller supports up to axes. eywords: motio cotrol; iput shapig; mechatrolik-iii; idustrial etwork, residual vibratio. 1. INTODUCTION For idustrial motio system, the vibratio suppressio is oe of key techiques which researchers ad egieers wat to address the problem. Especially, with growth of accuracy maufacturig system, a eed for the developmet of residual vibratio techique has therefore arise. Oe of efforts to suppress residual vibratios has bee tried by modifyig the motio profile. The proposed iput motio desig procedure i [1] was to defie asymmetrical S-curve velocity profiles with fast acceleratio ad slow deceleratio of AC servo motors which itermittetly move the puchig machie to desired positios with the reduced amplitude of residual vibratios. The authors i [] developed a asymmetric S-curve profile method with jerk bouded to obtai high precisio ad reduce the residual vibratio. Ha et al. [] itroduced a jerk ratio to scale dow the jerks durig the deceleratio period. Whe the jerk ratio icreases, the residual vibratio decreases i motio system. Particularly, the high ruig speed ca cause strog excitatios i precisio positioig machies. Thus, i [4], a low-vibratio motio profile geeratio method to lesse systematic excitatios was preseted. The acceleratio profile is desiged by usig a level-shifted siusoidal waveform to have a s-shape i order to cotrol its chage rate. Iput shapig strategy is a attractive issue for reducig residual vibratio i motio cotrol system due to the robustess ad effectiveess. Sice Sighose et al. i [5] described a method for limitig vibratio by addig costraits o the derivative of residual vibratio magitudes, various approaches to suppress the residual vibratios has bee achieved such as hybrid iput shapig [6], a three-impulse sequece iput shaper [7] or lookup table cotrol method [8]. However, Sighose s work performs the robustess to modelig errors ad effectiveess to apply i the idustrial motio system. I this method, egieer eeds to determie the atural frequecy ad dampig ratio i order to build a iput shapig cotroller. ecetly, researchers i [9] studied the effect of atural frequecy error to residual vibratio i three iput shapig cotroller. ZVD ad ZVDD shaper are more robust tha ZV shaper if the error i atural frequecy of flexible beam exists. Mechatrolik-III protocol is a real-time protocol that is based o Etheret techology ad was developed by Yaskawa [10]. Mechatrolik-III is chose to ivestigate because of their advatages such as fast commuicatio, high reliability ad rapid desig. The performace of Mechatrolik-III was aalyzed i [11] ad slave statio was desiged i [1]. The protocol guaratees the short cycle time which is cosidered as a typical factor i motio cotrol fields. This paper is orgaized as follows. I Sectio, the model formulatio of flexible beam is preseted. Sectio proposes the implemetatio of iput shaper as a egieer solutio. I Sectio 4, the hardware developmet ad software developmet of Mechatrolik-III motio cotroller are show. I Sectio 5, the experimetal verificatios ad results are carried out. Fially, this paper eds with coclusios i Sectio 6.. MODEL FOMULATION Cosider a mass mouted o the ed of flexible beam as Fig.1 (a). Both of them are made from alumium alloy which the modulus of elasticity is E. The beam has legth L, mass per legth ad sizes as Fig.1 (b). Assume that the ed-mass is much greater tha the mass of the beam. The free-body diagram of beam is described i Fig.1 (c). Aalytically, is the reactio force; M is the reactio bedig momet. Apply Newto s law for static equilibrium poit; the followig equatio ca be obtaied. 169

2 mg 0 (1) mg () At the left boudary, the equatio of momet is illustrated. Fig.1 (a) Catilever beam model; (b) sizes of beam; (c) free-body diagram; (d) a sectio of beam. M M mgl 0 () mgl (4) I Fig.1 (d), startig from the left boudary i a sectio of flexible beam, we ca acquire the sum of momets at the right side. M x M 0 (5) M M x (6) The momet M ad the deflectio y of flexible beam are formed. M EIy" (7) Substitute equatio (6) ito equatio (7), we have equatio. mg y" L x EI (8) Itegratig equatio (8) i two times ad usig the boudary coditios at the left ed, we have the resultig deflectio at the right ed. mgl yl ( ) EI (9) Apply Hooke s law for flexible beam with cosiderig that flexible beam with mass at the ed as a liear sprig with stiffess k. The force at the ed of the beam is mg. The stiffess at the ed of the beam is expressed. k EI L (10) The formula to compute the atural frequecy the catilever beam with the ed-mass is foud. 1 EI ml of (11) Assume that both the beam mass ad the ed-mass are sigificat ad the beam has a uiform cross sectio. The, the mass of beam at the ed is thus. m 0.5 L (1) beam The total mass m t ca be calculated. m m m (1) t beam Agai, the stiffess at the free of the catilever beam is. k EI L (14) The atural frequecy of beam is thus. 1 EI ml (15) t The parameters, which are the key factors to demostrate a iput shapig scheme are atural frequecy ad dampig ratio. Theoretically, dampig ratio of a uderdamped system i the time domai ca be idetified by usig logarithmic decremet method i Fig.. The amout of logarithmic decremet is the atural log of the ratio of the amplitudes x, x of ay two successive peaks at time sequece i i i ad i+. 1 x l i x (16) i The, the dampig ratio is foud from the logarithmic decremet. (17) Fig. Illustratio of Logarithmic decremet method to calculate the dampig ratio.. INPUT SHAPE DESIGN The trasfer fuctio G(s) of uderdamped secod order system ca be expressed i Laplace trasform. Ys () Gs () U( s) s s (18) The vibratio system ca be modeled as equatio (18). I the time domai, the impulse respose of the system is validated. A ( 0 ) ( ) t y t e t si 1 t t 1 (19) Where A ad t 0 are amplitude ad the time of impulse respectively

3 To achieve zero vibratio after the last impulse, y(t) should be zero. The desig objectives of iput shapig cotroller are to determie the amplitude ad time locatio of impulse. For two impulse sequece, the parameters are required. 1 t1 0 A1 1 t A d 1 Where d 1 ad 1 e. (0) Ad three impulse sequeces with parameters ca be yielded. 1 t 0 A 1 t A t A 1 1 d 1 d 1 A four-impulse-sequece ca be established. 1 t 0 A 1 t A t A t A 1 1 d 1 d d 1 4. IMPLEMENTATION IN MECHATOLIN-III CONTOLLE (1) () The Mechatrolik-III etwork compoets cosist of oe C1 master ad various slaves which ca be servo drive, steppig motor ad I/O module. They ca be coected i cascade, star or mix topology if usig hub. I the etwork, C1 master receives commad profiles from slaves ad determies the kid of devices. After master seds commads, slaves receive ad execute commads, ad later slaves reply their moitorig iformatio. The speed of etwork to trasmit data is at 100 Mbps. The Mechatrolik-III protocol supports both sychroous ad asychroous commuicatio modes. I sychroous mode, master statio seds the commad data at ay required timig ad the slave statio respods to the set commad data. Asychroous commuicatio ca be used i a system where sychroous operatio is ot eeded, i.e. collectig ecessary iformatio for sychroous commuicatio from slaves. 4.1 Hardware developmet I this sectio, the desig of Mechatrolik-III master device is itroduced. Fig. presets the block diagram of hardware desig. The cotroller commuicates with host PC by PCI iterface. The, FPGA chipset is used for timig sychroizatio of cotroller. Based o the powerful ad fast computatio, motio geerator ad other calculatios of sigals are embedded ito DSP. I this diagram, AM CPU plays a importat role. It hadles data betwee iteral cotroller ad Mechatrolik-III etwork. Lastly, ASIC JL-100A chip cotrol Mechatrolik-III sedig/receivig frame iside etwork. I Table 1, specificatios of Mechatrolik-III cotroller are listed. Fig. Block diagram of hardware desig. 4. Software developmet I Widows platform, the static library -bit is programmed to iput data from ed-user. The essetial parameters to apply iput shapig are show. AxmAdvISTSetParameter(lAxis,dFreq,dDampigatio, dimpulsecout) Where laxis is the axis umber; dfreq ad ddampigatio are atural frequecy ad dampig ratio. dimpulsecout displays the umber of impulse. dimpulsecout = : ZV cotrol scheme dimpulsecout = : ZVD cotrol scheme dimpulsecout = 4: ZVDD cotrol scheme AxmAdvISTEable(lAxis,dEable) Where laxis is the umber of axis to cotrol. The value TUE of deable is to activate the iput shapig techology, otherwise ormal motio is execute. Oce, atural frequecy ad dampig ratio are iput, amplitude ad time cycle of impulse are kow. A umber of impulses deped o iput shapig modes. Whe iput shapig cotrol is activated, a referece data from profile geerator is drive ito ZV, ZVD or ZVDD shaper scheme. Table 1 Specificatios of Mechatrolik-III cotroller. Form Factor Protocol Commuicatio Speed Trasmissio Cycle Data Frame Support Commuicatio Mechatrolik-III Chipset PCI ( bit/ MHz) Mechatrolik-III 100Mbps 50us 48byte Cyclic, Evet-drive JL100A 1695

4 I low level, i Fig. 4, a loop which is resposible for the real-time cotrol of data exchage is defied. The firmware icludes the mai program ad iterrupt service routie. I the first stage, PLL clock, timer, system cotrol register, iterrupt service routie ad motio parameters are predetermied. Later, ASIC JL-100A is iitialized i three times. If error still occurs, LED displays to otify. Otherwise, ifiite loop that switches betwee asychroous ad sychroous mode is used to update data. As show i Fig. 5, the iput shapig strategies are implemeted i IS. After cofirmig the error system is i a rage, motio profile is geerated. Value of time is computed ad compared with samplig time i system to determie the period of impulse. The, a mathematical operatio is covolved betwee two sigals as a output of iput shaper. The result is trasmitted to slave statio i Mechatrolik-III etwork i order to execute commad profile. Fig. 6 Iput shapig for S-curve profile. The iput shapig for S-curve profile is illustrated i Fig. 6. The effect of iput shapig is smoother ad reduced residual vibratio sigificatly. 5. EXPEIMENTAL ESULTS Experimets were coducted with proposed Mechatrolik-III cotroller ad slave servo drive as show i Fig. 7 ad its correspodig parameters ca be see i Table. A alumium ruler is used as flexible beam. Two bolts are haged i each side of beam as mass or load. The ruler is directly mouted with motor shaft which is vertically suspeded o frame. Fig. 4 Flowchart of mai program. Fig. 7 Experimetal system is set-up. Fig. 8 Spectrum frequecy measured by laser sesor. Fig. 5 Flowchart of iterrupt service routie. Fig. 9 System vibratio measured by laser sesor. 1696

5 I order to idetify exact atural frequecy of beam, a laser sesor is used to measure. The flexible beam rotates aroud vertical directio ad the, laser sesor detects residual vibratio of beam. I Fig. 8 ad 9, spectrum frequecy ad system vibratio that measured by laser sesor are displayed. The measured atural frequecy is. Hz. Hece, the calculated dampig ratio based o logarithmic decremet method is These parameters are used i all tests. However, depedig o each kid of iput shapers, impulse couts are selected as, or 4. Fig. 10 Experimetal speed profile without iput shaper. Fig. 14 Experimetal torque cotrol with ZV shaper, ZVD shaper, ZVDD shaper ad without iput shaper. The experimetal results with ZV, ZVD ad ZVDD shapers ad without iput shaper are described i Fig. 10, 11, 1 ad 1 respectively. It ca be see clearly that speed profile sustais vibratio i case of without iput shaper. Whe applyig ZV, ZVD ad ZVDD shaper, the profiles are smoother ad reduced residual vibratio sigificatly. Fig. 14 shows experimetal data of torque cotrol i ZV, ZVD ad ZVDD iput shaper ad without iput shaper. The experimet tests result that iput shapig techique has good performace i Mechatrolik-III motio cotrol system. Table Parameters of experimetal motio system. Youg s modulus of beam 70GPa Mass per legth.7 g/cm Legth of beam 85mm Width of beam 15mm Height of beam 1.8mm Mass of two bolts 1.g Fig. 11 Experimetal speed profile with ZV shaper. Fig. 1 Experimetal speed profile with ZVD shaper. Fig. 1 Experimetal speed profile with ZVDD shaper. 6. CONCLUSIONS The implemetatio of iput shapig method i Mechatrolik-III etwork has bee preseted. A mathematical model of beam has bee used to aalyze atural frequecy ad dampig ratio. Accordig to the experimetal results, the motio profiles are smooth ad reduced residual vibratio. It is idicated that Mechatrolik-III motio cotroller with iput shaper has good performace. With large buffer eough, this successful implemetatio provides a opportuity to apply the iput shaper for multi-axes i idustrial etwork motio system. EFEENCES [1] D. M. Tsay ad C. F. Li, Asymmetric Iputs for Miimizig esidual espose, Proc. of the Iteratioal Coferece o Mechatroics, pp. 5-40, 005. [] F. Zou, D. Qu, ad F. Su, Asymmetric S-curve Trajectory Plaig for obot Poit-to-Poit Motio, Proc. of the Iteratioal Coferece o obotics ad Biomimetics, pp , 009. [] C. W. Ha,. H. ew, ad. S. im, A Complete Solutio to Asymmetric S-curve Motio Profile: Theory & Experimets, Proc. of the Iteratioal Coferece o Cotrol, Automatio ad Systems, pp , 008. [4] H. Li, M. D. Le, Z. M. Gog, ad W. Li, Motio 1697

6 Profile Desig to educe esidual Vibratio of High-Speed Positioig Stages, IEEE/ASME Trasactios o Mechatroics, Vol. 14, No., pp , 009. [5] W. Sighose, W. Seerig ad N. Siger, esidual Vibratio eductio Usig Vector Diagrams to Geerate Shaped Iputs, Joural of Mechaical Desig, Vol. 116, No., pp , [6] M. A. Ahmad, A. N.. Nasir,. M. T. aja Ismail ad M. S. amli, Compariso of Hybrid Cotrol Schemes for Vibratio Suppressio of Flexible obot Maipulator, Iteratioal Coferece o Computer Modelig ad Simulatio, pp , 009. [7] S. S. Gurleyuk ad S. Cial, obust Three-Impulse Sequece Iput Shaper Desig, Joural of Vibratio ad Cotrol, Vol. 1, No. 1, pp , 007. [8] V. P. Pha, N. S. Goo,. J. Yoo, ad D. S. Hwag, Lookup Table Cotrol Method for Vibratio Suppressio of a Flexible Maipulator with Optimizatio of the Miimum Settlig Time ad Eergy Cosumptio, Asia Joural of Cotrol, Vol. 14, No., pp , 01. [9] M. T. Ha, C. G. ag, Experimetal Aalysis of Natural Frequecy Error to esidual Vibratio i ZV, ZVD ad ZVDD Shapers, Iteratioal Coferece o Ubiquitious obots ad Ambiet Itelligece, pp , 01. [10] [11] T. T. Dag, J. H. im ad J. W. Jeo, Performace Aalysis of Mechatrolik-III, Iteratioal Coferece o Idustrial Iformatics, pp , 01. [1] X. Xu, F. He, Y. Tao, Z. Wag ad J. Xig, Desig ad Implemetatio of Mechatrolik-III Bus Slave Statio Based o SOPC, Iteratioal Coferece o Computatioal ad Iformatio Scieces, pp ,