Study on Active Micro-vibration Isolation System with Linear Motor Actuator. Gong-yu PAN, Wen-yan GU and Dong LI

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1 2017 2nd Internatonal Conference on Electrcal and Electroncs: echnques and Applcatons (EEA 2017) ISBN: Study on Actve Mcro-vbraton Isolaton System wth Lnear Motor Actuator Gong-yu PAN, Wen-yan GU and Dong LI School of Automotve and raffc Engneerng, Jangsu Unversty, henjang, Jangsu, Chna, Keywords: Mcro-vbraton solaton, Actve control, Lnear motor actuator, Optmal control algorthm. Abstract. An actve mcro-vbraton solaton control system wth lnear motor actuators has been proposed and studed. he system s supported by the ar sprngs and symmetrcally placed lnear motor actuators. A mathematcal model of the mcro-vbraton solaton platform s establshed, and the optmal control algorthm s desgned for solatng vbraton system. Smulaton and experment s carred out to verfy the effectveness of actve mcro-vbraton control system. he results demonstrate that the proposed mcro-vbraton control system has good solaton performance and the lnear motor can be used as the actve actuator. Introducton he lnear motor can produce lnear moton drectly wthout ntermedate converson mechansm, whch can smplfy the structure, reduce the moton nerta and mprove dynamc performance and postonng accuracy greatly. And the fast response and hgh senstvty make t wde applcaton n precson moton control. On the other hand, wth the rapd development of mcro fabrcaton technology and precson measurement technology, mcro vbraton control technology has become a very mportant research subject. Although the tradtonal ar sprng passve vbraton solaton devce can make the natural frequency of the system low, but n some feld the passve vbraton solaton technology s dffcult to effectvely to solate the low-frequency vbraton. In order to make full use of the advantages of ar sprng and lnear motor, ths paper establshes a precson vbraton solaton platform of 6 degrees of freedom wth the combnaton of passve vbraton solaton and actve vbraton solaton technology. In ths system, ar sprngs are used as passve vbraton solaton components, 8 lnear motors are used as the actve components, and the performance of the system s smulated and tested by usng the optmal control algorthm. he results of smulaton and experment show that the actve vbraton control system has good vbraton solaton effect both on the low and hgh frequency dsturbance. Actve Mcro-Vbraton Platform Basc Structure of the System he dagram of the actve vbraton solaton system s shown n fgure 1. Actve vbraton control platform uses ar sprngs as passve vbraton solaton components, wth the lnear motor as the actve touch element. By detectng the ground acceleraton sensor, platform acceleraton sensor, dsplacement sensor, the controller system wth the optmal control algorthm can nput a control sgnal to lnear motor and lnear motor produce a control force to solate the vbraton from the ground nterference and platform nterference. he closed-loop actve vbraton control system not only has the characterstcs of the ar sprng, but also has the characterstcs of fast response, hgh senstvty of the lnear motor. 248

2 z x y Fgure 1. Dagram of the mcro-vbraton solaton platform. Equaton of the Isolaton System In the actve vbraton control system shown n fgure 1, f the vbraton platform s assumed as a rgd body, the system can be descrbed as 6 degrees freedom system wth the followng 6 varables: xg yg zg x y z the translatonal dsplacement and rotatonal angular dsplacement. Assumng that the ar sprngs has the same the performance, the equaton of moton of the table s as follows. M x C x K x C x K x K u 0 a (1) Where: [M] s the mass matrx (6 6); [M]=dag m m m J J Y J, m s the mass of the platform, and J, JY, J are the moments of nerta of the vbraton solaton platform around the axs; C s the dampng matrx (6 6); C =dag C C C C C Y Y C ; K s the stffness matrx(6 6); K = dag K KY K K K center of the table (6 1); x x x x x x x x y z ; g g g 5 Y Y 0 x 0 x x x x x K x s nterference dsplacement vector 1 x ; ; x s the dsplacement at the gravtatonal ; u s the control the current vector of the lnear motor 81 u k n1i1 kn2i2 kn3i3 kn4i4 kn5i5 kn6i6 kn7i7 kn8i K 8 a s the output power factor of lnear motor related to nstallaton poston of the lnear actuator, and k n s the force factor of the lnear actuator. Accordng of the coordnate transformaton, equaton (1) can be expressed as the followng. x 2 t 2 x t x t u t t, 1,2,, 6 where: s the dampng rato; (2) 249

3 s the natural frequency; u t s the control sgnal; 1 u t M K u ; a ( s the ground nterference; 2 t 2 x0 x0. Desgn of Control System It s known that the mcro vbraton platform s manly affected by the two knds of nterference. One s a class of basc nterference, ncludng the bass of the vbraton dsplacement and vbraton velocty; the other s the drect nterference of mcro manufacturng equpment. hese dsturbances are random dsturbances, and the correspondng performance ndexes are naturally random varables, so the optmal control of mcro vbraton of mcro manufacturng platform s taken as the performance ndex. J u E[ x ( ) Q0 x( )] [ x ( Qx( u ( Ru( ] dt 0 (3) where, Q 0, Q, R are the weghted symmetrc matrx. Accordng to the separaton theorem, the stochastc optmal control law s as the follow. u( Lxˆ( Frst, the feedback gan matrx s obtaned by the determnstc optmal control problem. (4) L 1 R B S (5) where the S can be obtaned by solvng the followng Rccat algebrac equaton. 1 SA A S SBR B S Q 0 (6) As the mcro vbraton platform solaton system s completely observed, the state estmaton of the equaton (4) can be obtaned by Kalman flterng. x ˆ( Axˆ( Bu( K[ y( Cxˆ( ] where K s the estmated gan matrx. K PC Q 1 v P n the equaton (8) wll be ft to the followng Raccat algebrac equaton. (7) (8) AP PA PC Q CP HQ H 1 v 0 w (9) After obtanng the state estmaton and optmal control feedback gan matrx, the feedback control loop can be made by flterng estmaton and seral optmal control, and the optmal control law can be acheved. Smulaton and Experment Smulaton he natural frequency of, Y, drecton of the mcro-vbraton solatng system n the passve state s desgned as 3.0Hz, 3.0Hz and 4.5Hz respectvely. And usng the above control law, the 250

4 optmal control force can be got by the Matlab, Control oolbox and Robust Control oolbox. Fgures 2-4 show the transmsson functon of,y, drecton n whch the sold lne s the smulaton result of actve state and the dot lnes the smulaton result of passve state. It clearly shows the actve state has better solaton performance than passve one. Fgure 2. drecton s passve and actve transmssblty. Fgure 3. Y drecton s passve and actve transmssblty. Fgure 4. drecton s passve and actve transmssblty. 251

5 Experment Fgure 5 shows the expermental block dagram of the actve vbraton control system. Here the ground acceleraton sensor, platform acceleraton sensor and dsplacement sensor wll detect the state of the platform. hese sgnals wll transfer to the controller by the measurement system. he controller wll output a control sgnal to lnear motor by the optmal control algorthm and lnear motor produce a control force to solate the vbraton from the ground nterference and platform nterference. Fgure 6 shows expermental dagram. Fgure 5. Block dagram of the actve vbraton control system. Fgure 6. Expermental dagram. 252

6 Fgure 7. Acceleraton n drecton on the ground and platform. Fgure 8. Acceleraton n drecton Y on the ground and platform. Wth the expermental devce showed n fgure 6, the acceleraton on the platform and ground n the actve state and passve state can be obtaned. Fgures 7-9 show the, Y, drecton acceleraton on the platform and ground n the actve and passve state. he expermental results show that the ground vbraton sgnal can be effectvely solated wth the actve solaton system. 253

7 he ground acceleraton n the and Y drecton can be reduced about 20dB, and the ground acceleraton n the drecton can be reduced about 30dB. he expermental results also ndcate that the actve solaton system can not only solate the hgh frequency vbraton, t can also solate the low frequency vbraton. Fgure 9. Acceleraton n drecton on the ground and platform. Concluson A comprehensve vbraton solaton system combned the ar sprng passve vbraton solaton and the actve vbraton solaton technology wth lnear actuator s proposed and used n a precson solaton platform. he smulaton and expermental show the actve solaton system can effectvely solate the ground dsturbance n wde frequency range. Acknowledgment hs work was supported by the Sx alent Peaks Project of Jangsu Provnce under Grant No B-024, the natonal Natural Foundaton of Chna under Grant No References [1] Wllam. homson, Mare Dllon Dahleh, heory of Vbraton wth Applcaton, Prentce-hall, nc [2] Gardono P., Ellott S.J., Pnnngton R.J. Actve solaton of structural vbraton on a multple degree of freedom system, Part I: he dynamcs of the system, Journal of Sound and Vbraton, 1997, 207 (1): [3] Nakamura Y., Nakayama M., Kura M., Yasuda M., Fujta., Applcaton of actve mcrovbraton control system usng a gant magnetostrcton actuator, Intellgent Materal Systems and Structures, 2007, 18(11):