Active Vibration Control Experiments on an. AgustaWestland W30 Helicopter Airframe

Transcription

1 Active Vibration Control Experiment on an AgutaWetland W30 Helicopter Airrame Jon E Motteread, Maryam Gandci Terani, Simon Jame and Peter Court 3 Centre or Engineering Dynamic, Univerity o Liverpool L69 3GH, UK. Intitute o Sound and Vibration Reearc, Soutampton Univerity SO7 BJ, UK. 3 AgutaWetland Helicopter, Lyander Road, Yeovil BA0 YB, UK. j.e.motteread@liv.ac.uk Abtract Ti article decribe te practical application o a vibration control tecnique, developed by te autor and known a te receptance metod, to te AgutaWetland W30 elicopter airrame in te vibration tet oue at Yeovil. Te experimental work wa carried out over a total o ive day in two viit to te Yeovil ite during February and Marc 0. In te experiment, ue wa made o exiting electro-ydraulic actuator, built into te airrame tructure and originally deigned or vibration uppreion by te metodology known a ACSR Active Control o Structural Repone developed at te AgutaWetland Helicopter ite in Yeovil. Accelerometer were placed at a large number o point around te airame and an initial open-loop modal tet wa carried out. In a ubequent tet, at iger actuator input voltage, coniderable nonlinearity wa dicovered, to te extent tat te ordering o te certain mode ad canged. Te vibration mode were generally eavily damped. Control wa implemented uing meaured requency repone unction obtained at te iger input level. Ater acquiring te neceary meaurement, imulation were carried out and te controller wa implemented uing MATLAB/Simulink and dspace. Te cloed-loop pole were motly aigned wit mall real part o tat te ytem would be ligtly damped and arp peak would be clearly apparent in te meaured cloed-loop requency repone unction. Location o te open- and cloed-loop pole in te complex -plane were obtained to veriy tat te required aignment o pole ad taken place.. Introduction Ti paper decribe te active vibration control o an AgutaWetland Helicopter W30 airrame baed on vibration tet meaurement in te orm o input-output requency repone unction meaurement. Te teoretical bai o te receptance metod a been preented in

2 a erie o paper [-4] including tudie carried out on experimental rig in te laboratory. In ti article te irt application o te metod to an indutrial ied tructure i decribed. Te general procedure involve te contruction o a receptance matrix or requency repone unction matrix between any input and output meaurement or multiple actuator and enor, eac term being a unction o requency. Rational raction polynomial are itted to te meaurement and in ti way a matrix o receptance traner unction are ormed, eac being a unction o te Laplacian complex requency. Ti matrix i te matematical model; in teory it i te invere o te dynamic tine, M C K H, owever tere i no need to know or to evaluate te matrice, M, C, K, wic generally contain error and approximation not preent in te meaured receptance. Anoter important advantage i apparent wen te more general traner unction matrix i conidered, typically output voltage rom enor / input voltage to actuator. In ti cae tere i no need to model te dynamic o te actuator and enor, wic ten become included in te meaurement. Te teoretical bai i provided rom te linear algebra by te Serman-Morrion ormula [5], wic enable te invere o a modiied matrix to be determined rom a te original invere matrix and b a known modiication. In ti cae te modiication i provided by te controller and te original invere matrix i te meaured H. It a been demontrated ow natural requencie, damping value and antireonance may be aigned to a tructure by ti metod [,]. Tecnique or te aignment o pole natural requencie and damping tat are robut to meaurement noie on te data were explained by Gandci Terani et al. [4]. Anoter apect o te work i te o-called partial pole placement, wen certain natural requencie and damping value are aigned wile oter are coen to remain uncanged by te control action. Ti i acieved by electing te excitation o tat te uncanged pole are uncontrollable [3]. It require a particular arrangement o te enor to excite only a ubet o coen mode; a acility tat wa not available to te preent tudy a will be explained preently wen dicuing te availability o actuator.. Experimental Arrangement Te W30 airrame, upported on it weel wit inlated tyre, i own in Figure at te time te tet decribed in ti article were conducted. Te engine and main gearbox are mounted on a teel ramework wic i itel upported by our elatomeric mount on te roo o te cabin. An electro-ydraulic actuator [6, 7] orm an integral part o te upport ytem and impart an internal orce between te rat and te uelage in parallel wit eac o te our elatomeric mount. Ti coniguration, own in Figure a and b, orm part o te original AgutaWetland ACSR tructural vibration control ytem, te purpoe being to iolate te uelage rom blade-induced vibration at armonic o te blade paing peed. Operation o te ytem, baed on te ue o a reerence ignal to detect te armonic concerned, wa baed on adjuting te magnitude and pae o te actuator orce o tat a quadratic cot unction wa minimied. Ti procedure, o te eed-orward type, i decribed

3 by Fuller et al. [8] and alo by Pearon and Goodall [9]. Implementation o te ACSR ytem i decribed by Staple [6,7]. In ti exercie a eedback ytem wa applied uing te receptance metod. Te work wa carried out over a period o ive day during two viit to te AgutaWetland ite at Yeovil in February and Marc 0. Te main gearbox wa preent but te engine ad been removed. Conequently tere wa inuicient ma over te two rear actuator or reacting te uelage orce. It wa decided tat tee two actuator would be preuried and ued paively. Tu, only te two ront actuator were available or active vibration control. Rat Actuator a Overview o te tet arrangement. b Cloe-up o te gearbox, rat and actuator. Figure. W30 airrame during teting. a Rat and it poition on te aircrat Figure. Rat and Electro-ydraulic actuator b Electro-ydraulic actuator wit parallel elatomeric upport During te irt viit a preliminary open-loop modal tet wa carried out uing twenty tri-axial accelerometer 60 cannel wit low level excitation applied independently to te two electro-ydraulic actuator - ero-mean random input to te ampliier in te range 0.V. Te requency range wa 0-50 H and te ampling requency wa 00 H at a reolution o 3

4 5 pectral line wit a Hanning window. Te reult o ti tet are ummaried in Figure 3. Te two active electro-ydraulic actuator were located at node 9 and 0 wit load applied to te roo o te uelage and to te rat in equal and oppoite direction. y x a Vertical tail bending.6 H, 5.3% damping b Horiontal tail bending 4.6 H,.78% damping c Airrame vertical bending 7.5 H, 5.95% damping d Airrame oriontal bending and torion 5.4 H, 5.93% damping Figure 3. Open-loop modal tet reult On te econd viit, preliminary tet were carried out to enure tat te tructure ad not canged igniicantly. In addition a vibration tet at a iger excitation level random wit ero mean and range V wa carried out. A comparion o two requency repone unction at te two dierent excitation level i given in Figure 4 were igniicant dierence can be oberved. Te ignal at low amplitude appear to be muc noiier tan te iger-amplitude ignal poibly due to non-moot nonlinearity o te actuator, uc a 4

5 tick-lip beaviour, at mall diplacement. Tere are clear dicrepancie in amplitude and pae between te two et o data and te order o te vertical and oriontal tail bending mode wa ound to ave canged. Ti i likely to be due to igniicant tructural nonlinearity a well a nonlinearity ariing rom te elatomeric upport and te electroydraulic actuator. Figure 4: Example FRF at two dierent input-amplitude level: upper plot lower plot 8 Z 9 Z Y 9 Z 8 and 3. Procedure or Applying te Receptance Metod o Active Vibration Control. Te metod o receptance i a requency-domain pole-placement approac, baed entirely on vibration meaurement. In te cae o multiple input and multiple output MIMO a matrix o requency repone unction meaurement i ormed. For meaured orce input and diplacement output ti take te orm o a receptance matrix; rom wic te metod now to be explained derive it name. It i convenient ere to continue reerring to receptance altoug it ould be undertood tat te metod i perectly general in it application and quite oten tere will be advantage to be ad by meauring te voltage input to an ampliier tat drive an actuator and te voltage output rom a enor. Rational raction polynomial are itted to te meaurement o tat by replacing ' i ' wit '' receptance traner unction, H, are ormed. Tere i no need to know or to evaluate te matrice, M, C, K. Alo wen te ytem o equation i written in term o receptance, 5

6 6 x x x n m nm n n m m it i een tat eac row i complete wen all o te applied orce are known. In general tere will be ewer actuator tan enor,, n m o te matrix o receptance i non-quare. Conventional metod, uc a tate-pace, require ytem o equation cat in term o dynamic tinee, x x x m n mn m m n n in wic it i neceary to ave a enor at every one o te n coordinate o te ytem. It i or ti reaon tat conventional metod require oberver or equivalent or te etimation o unmeaured tate variable. Tu, wit te receptance metod tere i no requirement or an oberver and neiter i model reduction neceary, ince te reulting matrice are generally o mall dimenion. Te Serman-Morrion ormula [5] may be ued to obtain cloed-loop caracteritic equation in te orm [], g H b k k k T 3 were k i a cloed-loop pole to be aigned, g are acceleration and velocity gain and b i te actuator ditribution vector or ingle-input control. Equation 3 i linear in te unknown gain, o tat or te aignment o k pair o cloed-loop pole te ollowing ytem may be aembled,,, T k k T k k T T T T r r r r r r G g G 4, 5 were, j j j j b H r 6 Te dimenion o G i n k. It will be quare wen te number o pair o pole to be aigned i equal to te number o enor auming diplacement i obtained by integrating a velocity meaurement, will be over-determined wen te number o pole pair exceed te

7 number o enor and underdetermined wen tere are more enor tat te number o pole pair to be aigned. It i oten deirable to ditribute te control orce by aving everal actuator at dierent point on te tructure, but te aignment o pole i not dependent upon te dimenion o te b vector in teory all te pole o te ytem can be aigned uing a ingle actuator. It wa own by Ram and Motteread [] tat te matrix G i invertible wen te ytem i controllable and tat g are real wen te cloed-loop pole are aigned in complex-conjugate pair. 4. Open-loop tet Te open loop tet were carried out wit a ero-mean random input voltage in te range V a decribed previouly. Te output voltage rom te accelerometer and teir integral related to velocitie were te eedback ignal. Integration wa carried out in te dspace environment and tee ignal were iltered uing a band-pa Butterwort ilter wit cut-o requencie o 8 H and 40 H. In te requency range o interet, -30 H, modal tet ad own te cabin tructure to be relatively rigid, werea te noe and certainly te tail were more lexible. Tereore, accelerometer ignal were meaured at node noe,, 3, 0,, cabin loor and 4, 5, 8 tail in te y and direction. In wat ollow two pair o cloed-loop pole are aigned, in wic cae dimg 43, wic i clearly very underdetermined. Peudo inverion o ti matrix, wic lead to te minimum norm olution, work perectly in imulation but ail to do o in practice. O coure te minimum norm olution lead to mall value o te gain g aving virtually no eect on te ytem, wic remain almot uncanged rom te open-loop condition becaue te control ignal i in te range o te input noie. In order to overcome ti problem te number o enor wa reduced to tree: accelerometer at node, 5 and 8 in te y or direction eparately. Curve-itting to meaured FRF may be done uing MIMO or SISO ingle input and ingle output routine. In te cae o a multi degree o reedom ytem wit multiple enor and actuator te application o MIMO curve itting i trictly required to enure te ytem natural requencie are te ame at every meaurement point. However, it i known tat in practice te ue o SISO curve itting oten reult in a maller itting reidual. Tu, MIMO and SISO curve itting were ued in turn. Example MIMO curve it are own in Figure 5 were te ull blue line are te meaured value and te curve itted data are own in daed red line. 7

8 a 5 Y, 9Z b 8 Y, 0Z c 5 Z 0Z d 8 Z 9 Z Figure 5. Meaured and curve-itted FRF 8

9 5. Cloed-loop tet Pole placement wa acieved by negative eedback o acceleration and velocity. Meaured acceleration ignal were integrated and iltered to obtain velocity. Te control gain g were applied uing dspace and te reulting control orce in real time were added to te random excitation to drive te two actuator. 5. Pole placement at 84i, μ 60i μ, T, 3, 4 In ti cae tree accelerometer, 5 and 8 were ued in te y direction and te control orce at te two actuator were operating in pae. Te pole were deliberately aigned wit mall real part o tat te damping would be mall and peak would ow up clearly on te cloed-loop FRF meaurement. Te control gain, determined uing MIMO curve-itting to obtain H ollowed by peuo-inverion o G 46 equation 4 were ound to be, b 5.6 g. and A imulated reult i own irt, in Figure 6, were te open-loop meaurement i denoted by te ull blue line. Tere are two imulated cloed-loop reult obtained by application o te Serman-Morrion ormula. Te irt, denoted by te dot-daed green line, ue ynteied FRF obtained by MIMO curve-itting to te open-loop meaurement. Te econd, denoted by te daed red line, ue te meaured open-loop FRF directly. It i een tat tere i very little dierence between te two et o reult in te requency range o interet. Peak at approximately 84 rad/ and 60 rad/ ow tat te deired pole aignment a been acieved. Figure 6. Cloed-loop FRF by imulation. 9

10 Real time implementation in dspace wa carried out uing gain g determined uing two dierent curve itting metod, MIMO and SISO. Te open-loop traner unction in Figure 7 i repreented by te ull blue line and te two cloed-loop meaurement are denoted by te daed red and dot-daed green line or SISO and MIMO curveit repectively. It can be een tat te two cloed-loop tet are very imilar. Detail o te cloed-loop FRF cloe to te aigned pole i given in Figure 8. Te cloed-loop FRF appear to be noiier tan te open loop one becaue ewer average were taken in teir computation. Figure 7. Experimental reult or pole placement at μ, 84i, μ3, 4 60i a Firt aigned pole pair b Second aigned pole pair Figure 8. Zoom owing detail o cloed-loop FRF peak Te location o te open- and cloed-loop pole on te complex -plane, determined by curveitting, are marked in Figure 9. Some o te open- and cloed-loop pole are puriou and arie only a a reult o te curve-itting procedure. Te cloed-loop pole are not exactly aigned but tey are very cloe to te precribed value. Tere are many poible reaon wy te pole are not aigned exactly, but probably one o te mot igniicant reaon i te known nonlinear beaviour o te tructure, explained 0

11 previouly. Te actuator, located between te roo o te uelage and te rat, were not ideally placed to control mode in te tail. Conequently, large control orce were required, toug te input voltage wa limited to 0V igniicantly greater tan te random input at V. Te ue o everal actuator ditributed acro te tructure would enable te mode o te airrame to be controlled at lower cot lower control orce and wit le nonlinear eect. Te numerical value o te real part are muc maller tan te imaginary part o te cloed-loop pole, o te percentage error in te real part i likely to be greater tan te imaginary part percentage error, caued originally by te peudo-invere o G. Figure 9. Location o te open- and cloed-loop pole It can be een by comparion o te open- and cloed-loop mode ape in Figure 3 and 0 tat te two aigned mode, originally.6 H 5.3% damping and 5.4 H 5.93% damping ave been re-aigned to 3.7 H 0.98% damping and 5. H.8% damping, cloe to te deired value. Te cloed loop mode ape at 3.7 H appear to be a combination o te two open-loop mode at.6 and 4.6 H. Clearly te damping value ave been muc reduced, a required. Te airrame vertical bending mode originally at 7.5 H wa not aigned but a ited. In principle it i poible to control ti mode a well a te oter two, but ti i impractical becaue o te large control orce neceary, at te limit o te capability o te preent actuator. Te actuator location were determined or a dierent purpoe, te AgutaWetland ACSR ytem a explained previouly and are not ideal or te preent eedback control experiment. Te ditribution o everal actuator at dierent location acro te airame would allow te aignment o more mode at le cot lower control orce. Alternatively, partial pole placement [4] may be applied were actuator are deliberately placed to make certain pole uncontrollable wile oter are aigned te uncontrollable pole remain uncanged rom teir open-loop value. O coure, partial pole placement i not an option wit te preent actuator coniguration. It i een rom Figure 8 tat te cloed-loop ytem remained table.

12 a Tail bending: vertical + oriontal 3.7H 86rad/ 0.98% damping b Vertical bending o airrame 7.0H 07rad/.8% damping c Horiontal bending o airrame 5.H 57rad/.8% damping Figure 0. Cloed-loop mode ape. b 5. Pole placement wit T In ti experiment te tree accelerometer, 5 and 8 in te y direction were ued and te control ditribution vector b wa arranged to generate two anti-pae control orce. Tree dierent cae or cloed-loop aignment were conidered. In eac cae te real part o te pole were reduced. 3 89i, μ 8 70i, 89i, μ 70i, i, μ 70i, Te cloed-loop receptance obtained rom experiment are plotted in Figure or eac te tree cae wit detail at requencie cloe to te aigned value own in Figure.

13 Figure. Experimental reult or tree pole placement experiment a Firt aigned pole pair b Second aigned pole pair Figure. Zoom owing detail o cloed-loop FRF peak Te location o te open- and cloed-loop pole are own in Figure 3 or te econd cae. Tere are two pair o pole cloe to te precribed value o 89i, but it i clear, tat te pair tat ave in act been aigned are te ligtly damped one at. 9i. 3

14 Figure 3. Location o open- and cloed-loop pole or te econd cae. 5.3 Pole placement at 75i, μ 60i μ, T, 3 3, 4 Tree accelerometer, 5 and 8 were ued in te direction. Open- and cloed-loop meaured receptance are own in Figure 4 wit detail cloe to te aigned pole in Figure 5. Te location o te open- and cloed-loop pole are own in Figure 6. It i een tat te econd pair o pole in practice are damped to a greater degree tan wa intended by te aignment, but oterwie te reult appear to be quite acceptable. b Figure 4. Meaured open- and cloed-loop reult or 5 Z 9 Z 4

15 a Firt aigned pole pair b Second aigned pole pair Figure 5. Zoom owing detail o cloed-loop FRF peak Figure 6. Te location o te open- and cloed-loop pole 6. Concluion Te receptance metod wa applied or active vibration control by pole placement o te AgutaWetland W30 elicopter airrame. Te metod, baed on te meaured input-output traner unction, in ti cae ued te input voltage to te ampliier o te actuator and te meaured acceleration ignal. Single-input tate eedback wa ued in a erie o experiment to aign two pole o te elicopter to predetermined value. A ample o imulated reult wa provided and experimental cloed-loop FRF were own to agree wit te imulated value. Te plot o te location o te open-loop and cloed-loop pole in te complex plane by curve-itting to te meaured FRF were ued to conirm tat te aignment ad been acieved ucceully. Te work wa carried out in a very limited time rame, but wa 5

16 enoug to ow tat te receptance metod a coniderable practical merit. It wa decided in tee experiment to ue active control to deliberately reduce te damping o certain mode, o tat te peak would be very clear on te cloed-loop meaured FRF. O coure a more practical experiment were time available would be to increae te damping o te mode or poibly to it te requencie by a greater amount, toug iting requencie i generally more diicult tan increaing or reducing damping. Te pole were not aigned exactly, poibly becaue large control orce were needed and te tructure wa own to be nonlinear. Te actuator placed between te roo o te uelage and te rat were not ideally located to aign mode in te tail and it i tereore conidered tat te pole could be ited urter at le cot i a number o actuator were placed to optimie te controllability o te mode to be aigned. Te ditribution o actuator at dierent location acro te tructure would enable a greater number o pole pair to be aigned and partial pole placement to be acieved o tat elected pole pair are aigned wile oter remain uncanged rom teir open-loop value. Acknowledgement: Ti work wa carried out wit te upport o EPSRC grant EP/F00874/ and an EPSRC Patway to Impact Award. Te autor wi to tank AgutaWetland Helicopter Ltd or permiion to publi reult obtained rom te W30 airrame. Reerence. Y.M. Ram, J.E. Motteread, Receptance metod in active vibration control, American Intitute o Aeronautic and Atronautic Journal, 453, pp , J.E. Motteread, M. Gandci Terani, S. Jame, Y.M. Ram, Active vibration uppreion by pole-ero placement uing meaured receptance, Journal o Sound and Vibration, 33-5, pp , M. Gandci Terani, J.E. Motteread, A.T. Senton and Y. M. Ram, Robut pole placement in tructure by te metod o receptance, Mecanical Sytem and Signal Proceing, 0, 5,-. 4. M. Gandci Terani, R. N. R. Elliott and J. E. Motteread, Partial Pole Placement in Structure by te Metod o Receptance: Teory and Experiment, Journal o Sound and Vibration, 00, G. H. Golub, C. F. Van Loan, Matrix Computation, Jon Hopkin Univerity Pre, Baltimore, MD, 983, A.E. Staple, An evaluation o active control o tructural repone a a mean o reducing elicopter vibration, 5 t European Rotorcrat Forum, September A.E. Staple and D.M. Well, Te development and teting o an active control o tructural repone ytem or te EH0 elicopter, 6 t European Rotorcrat Forum, September C.R. Fuller, S.J. Elliott and P.A. Nelon, Active Control o Vibration, Academic Pre, London, J.T. Pearon and R.M. Goodall, Frequency veru time domain adaptive control algoritm or te active control o elicopter tructural repone, Proc. International Conerence on Control, Volume, 5-8 Marc 99, Edinburg,