Self-tuning Feedforward Control for Active Vibration Isolation of Precision Machines

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1 Preprint of the 19th World Congre The International Federation of Automatic Control Self-tuning Feedforward Control for Active Vibration Iolation of Preciion Machine M.A. Beijen, J. van Dijk W.B.J. Hakvoort, M.F. Heertje Eindhoven Univerity of Technology, Department of Mechanical Engineering, PO Box 513, 5600 MB Eindhoven, The Netherland Univerity of Twente, Department of Mechanical Engineering, PO Box 217, 7500 AE Enchede, The Netherland Demcon Advanced Mechatronic, Intitutenweg 25, 7521 PH Enchede, The Netherland Abtract: A novel feedforward control trategy i preented to iolate preciion machinery from broadband floor vibration. The control trategy aim at limiting the low-frequency controller gain, to prevent drift and actuator aturation, while till obtaining optimal vibration iolation performance at higher frequencie. Thi i achieved by limiting the low-frequency control action uch that almot no phae hift i introduced at higher frequencie. To minimize model uncertaintie, the feedforward controller i implemented a a elf-tuning IIR filter that etimate the parameter online. Only a few parameter have to be etimated, which make the algorithm computationally efficient. An additional feedback controller i deigned to make the elf-tuning algorithm more robut. The effect of feedforward and feedback control add up. The control trategy i uccefully validated on an experimental etup of a vibration iolator. Keyword: Active vibration iolation, feedforward control, elf-tuning, emi-conductor indutry. 1. INTRODUCTION Vibration iolator are widely ued in high-preciion machine, e.g. wafer canner, ee Tjepkema et al. 2011). Paive vibration iolator conit of phyical pring and damper between the floor and the upported machine. Such iolator can only attain a limited performance becaue a large paive damping of the upenion mode lead to le vibration iolation at high frequencie Karnopp and Trikha 1969)). Active vibration iolator contain an additional control ytem with enor and actuator to further improve the vibration iolation performance. Feedback control i widely ued for vibration iolator, examplearezuoetal.2004);tjepkemaetal.2011).however, the performance of feedback controller i limited by the controller bandwidth and the Bode enitivity integral. An alternative approach for active vibration iolation i caual feedforward control, ee for example Van der Poel 2010); Landau et al. 2011). In contrat with feedback control, where the meaured machine motion i ued a controller input, caual feedforward control ue meaurement of external vibration e.g. floor vibration) a controller input. In general, due to the caual nature of the diturbance meaurement, the performance of the feedforward control at high frequencie i limited by the feedforward enitivity integral, ee Heertje et al. 2013). Moreover, modeling error limit the performance, ince the feedforward control force i calculated uing a ytem model. Furthermore, it i undeired to ue feedforward control for low-frequency diturbance, a thi can eaily lead to drift and actuator aturation. However, uing regular high-pa filter to limit low-frequency controller gain, lead to a phae hift in the controller that deteriorate the performance. In thi paper, a novel feedforward control trategy i preented for broadband diturbance rejection. The lowfrequency controller gain i limited without introducing a large phae hift at higher frequencie, uch that at higher frequencie optimal performance i obtained. To minimize model uncertaintie and compenate for parameter variation in time, the parameter are etimated online uing a elf-tuning IIR filter with n th order bai function, reulting in an n th -order roll-off in the tranmiibility function. An IIR filter with firt-order bai function i propoed in Williamon and Zimmermann 1996); Yuan 2007). Compared with elf-tuning FIR filter ee e.g. Van der Poel 2010)), IIR filter give the deigner more freedom becaue pole can be placed at location other than z = 0. Therefore, a computationally efficient algorithm i obtained becaue the ytem can be accurately decribed with only a few coefficient. Fixing the pole in the bai function prevent intability due to pole adaptation. Moreover, it reult in a linear formulation of the etimation problem uch that a unique olution exit. Feedback control i added to make the convergence proce of the elf-tuning filter more robut, and to how that the effect of feedforward and feedback control add up. The remainder of thi paper i organized a follow. A model for the vibration iolator i given in Section 2 and a imple feedback control law in Section 3. In Section 4, a fixed-gain feedforward controller i derived, while in Copyright 2014 IFAC 5611

2 19th IFAC World Congre Section 5 the tep to elf-tuning controller i made. In Section 6, an experimental validation i preented. a 0 a 1 Controller 2. MODEL DESCRIPTION F a k 2 m 1 m 2 k 1 d 2 d 1 x 2 x 1 x 0 Internal mode Supended machine frame floor Fig. 1. Model of an active vibration iolator. Conider the ytem hown in Fig. 1. Mae m 1 = 5.4 kg andm 2 = 3.9kg,connectedbythe pringk 2 = 1400kN/m and the vicou damper d 2 = 20 N/m, repreent a implified preciion machine with one dominant internal mode. The machine i upended by a hybrid mount havingatiffneofk 1 = 160kN/mandavicoudamping of d 1 = 80 N/m. Uing thee ytem parameter, a upenion mode at 20 Hz and an internal mode at 125 Hz are obtained. Thee frequencie are repreentative for an active hard mount vibration iolator, ee Tjepkema et al. 2011). Actuator force F a i ued for active vibration iolation.accelerometeronthefloora 0 )andthemachine a 1 ) are ued for meaurement and control. Since preciion machine are uually placed on tiff and heavy floor, the mechanical coupling between F a and x 0 i neglected. To deal with ytem having mechanical coupling, the reader i referred to Landau et al. 2011). a 0 W u FF Σ F a u FB P S d K y a 1 Σ Fig. 2. Combined feedforward/feedback control cheme for active vibration iolation. Active iolation of floor vibration i obtained by a combination of feedforward control and feedback control. The controller cheme i hown in Fig. 2. The input diturbance ignal i denoted by a 0 and the error ignal i denoted by a 1. The latter i formed by two ignal: a ignal d that i caued by the diturbance from the primary path P, i.e. the paive ytem, and a component y that i caued by the control action from the econdary path S. The control action F a i the um ofthe feedback controlleroutput u FB and the feedforward controller output u FF, computed by the controller K and W, repectively. The primary path P i decribed by the tranfer function from floor vibration to machine vibration. The Laplace variable i ued to repreent P in the frequency domain, P) = d 1 k 1 ) n r) p r ), 1) with n r ) = m 2 2 d 2 k 2 ) decribing an antireonance at ω AR = k 2 /m 2 due to the internal mode, and p r ) decribing the pole of the upenion mode and the internal mode a p r ) =m 1 2 d tot k tot )m 2 2 d 2 k 2 ) d 2 k 2 ) 2, 2) with d tot = d 1 d 2 and k tot = k 1 k 2. Given that d 1,d 2 are mall and k 2 k 1, it can be derived that the pole decribed by p r ) correpond with a upenion mode at ω up = k 1 /m 1 m 2 ) and an internal mode at ω R = 1m 2 /m 1 )k 2 /m 2. The econdary path S i decribed by the tranfer function from control action to machine vibration. In the frequency domain, S i given by S) = 2n r) p r ). 3) The total machine motion i given by A 1 ) =P)A 0 )S)F a =P)A 0 )S)W)A 0 ) S)K)A 1 ). 4) From 4), the tranmiibility function T i derived: T) = A 1) A 0 ) = P)S)W). 5) 1S)K) In the remainder of thi paper, T will be ued a a performance meaure for the vibration iolator. Equation 5) how that K and W can be deigned independently. The numerator in 5) decribe the reduction obtained by feedforward control, while the denominator decribe the reduction by feedback control. Without controlk = W = 0), T equal P. 3. FEEDBACK CONTROL A feedback controller K i ued to add kyhook damping, ee Karnopp and Trikha 1969), to the upenion mode and the internal mode. Uing a 1 a input, K i given by K) = F a) A 1 ) = K v 1. 6) Thi controller integrate the acceleration ignal uing the tame integrator 1/ 1) to obtain the platform velocity, needed for kyhook damping. K v = 2000 N/m i tuned uch that both the upenion mode and the internal mode are ufficiently damped without making the controller bandwidth unnecearily high. The effect of feedback control i hown in Fig FIXED-GAIN FEEDFORWARD CONTROL In thi ection, the fixed-gain feedforward controller i derived. The controller gain i limited at low frequencie, to prevent drift and actuator aturation, without introducing a big phae hift at higher frequencie. Therefore, optimal vibration iolation performance i obtained at higher frequencie. In the initial deign, perfect knowledge of the ytem parameter i aumed. In practice, thee parameter are not known exactly, o the actual performance of the fixed-gain controller will deviate. Therefore, the influence of non-perfect parameter etimation i alo 5612

3 19th IFAC World Congre dicued in thi ection. The fixed-gain controller give the mathematical relation needed to deign the elf-tuning controller in Section The approximate Wiener controller From 5) it follow that, regardle of the feedback controller K, perfect cancellation of floor vibration i obtained when uing the following feedforward control law, W opt ) = S 1 )P) = 1 ˆd 1 ˆk ) 1, 7) with ˆd 1 = d 1 and ˆk 1 = k 1 being perfect etimate of the upenion damping and tiffne, repectively. In literature, thi controller i referred to a the Wiener controller. Note that W opt doe not depend on n r ) or p r ), i.e. it need no prior knowledge of the internal mode. Phyicallythimakeene,becauem 2 canonlybe excited via m 1. So if floor vibration are not tranmitted to m 1, they will not be tranmitted to m 2 either. Next, the pure integratorin 7) arereplacedbytame integrator to prevent drift and actuator aturation. Therefore the integrating action are cut off at α rad/, leading to W 1 ) = 1 = 1 α ˆd 1 ˆk 1 ) ˆd 1 1 α 8) ˆk 1 ). 9) Neglecting feedback control K = 0), and ubtituting 8) in 5) with perfect etimate ˆk 1 = k 1 and ˆd 1 = d 1, the following tranmiibility function i obtained: T) 2 α P), for = jω, ω > α. 10) Equation 10) how that if α 0, then T 0, reulting again in perfect cancellation of floor vibration. If α 0, then a -20 db/decade roll-off i introduced in T for ω > α. Thi roll-off can be increaed, i.e. the vibration iolation propertie can be improved, by uing higher-order controller. Define the controller W 3, in which the firtorder low-pa filter in 9) are replaced by third-order low-pa filter, or 1 W 3 ) = α ) 3 ˆd 1 1 α ) 3 ˆk 1. 11) Uing W 3 and auming again ˆk 1 = k 1 and ˆd 1 = d 1, the tranmiibility i given by ) 3 α T) 2 P), for = jω, ω > α. 12) Compared with 10), 12) ha two more pole at = α. Thee pole increaethe roll-offoft forfrequencie ω > α. Thi obervation lead to the following propoition. Propoition 1. Let T be the tranmiibility from floor vibration to machine vibration in the context of Fig. 1. For the Wiener controller given by 7), an approximate Wiener controller i given by W n ) = 1 L n) ˆd 1 1 L ) n) ˆk 1, 13) in which L n may be an arbitrary n th -order low-pa filter with unity gain, and from which follow that T) =L n )ˆd 1 2 L n ))ˆk 1 ) n r) p r ) d 1 ˆd 1 )k 1 ˆk 1 )) n r). 14) p r ) }{{} T error) In cae of perfect etimation, i.e. ˆk 1 = k 1 and ˆd 1 = d 1, the error term T error in 14) vanihe, uch that T reduce to: T) 2L n )P), for = jω, ω > α. 15) Proof. The proof follow from ubtitution of 13) in 5), with K) = 0. Equation 15) how that with 13) and ˆk 1 = k 1, ˆd 1 = d 1, potentially a tranmiibility function with a roll-off of arbitrary db/decade can be created. A an example, Fig. 3 how the tranmiibilitie when L n i a 1 t -order, 3 rd - order or 5 th -order low-pa filter and α = 2 Hz. Note that for frequencie lower than α the performance i lightly deteriorated with repect to the paive ytem. Thi performance deterioration can be prevented by chooing different value of α for both integrator in 13). Magnitude db) Tranmiibility -40 Paive -60 FB FBFF 1-80 FBFF FBFF 5 FBFF 5,np Frequency Hz) Fig. 3. Performance of the paive ytem, the feedback FB) controlled ytem uing 6), and the combined feedback plu fixed-gain feedforward FF) controlled ytem uing 6) and 13) with n = 1, 3, 5. It alo how the performance for a FBFF-controlled ytem with n = 5 and non-perfect np) etimate ˆk 1 = 0.99k 1 and ˆd 1 = 0.9d 1. Bode plot of W 1, W 3 and W 5 are compared with W opt in Fig. 4. It i oberved that increaing n lead to le phae hift at the higher frequencie, and therefore a better performance for ω > α. However, increaing n come at the cot of a higher controller gain for frequencie lower than α, which i undeired becaue of drift and actuator aturation. For example, the tatic gain for W 1 i k 1 /α 2 d 1 /α, while the tatic gain for W 3 i 3k 1 /α 2 d 1 /α and for W 5 it i 5k 1 /α 2 d 1 /α, hence a trade-off between the roll-off rate and the tatic controller gain. 5613

4 19th IFAC World Congre Magnitude db) Phae deg) Bode diagram W opt W 1 W 3 W Frequency Hz) Fig. 4. Bode plot of the fixed-gain feedforward controller. Increaing n reult in a trade-off:a) a better approximation of the phae with repect to W opt, but b) a higher tatic controller gain. 4.2 Non-perfect etimate In practice, the etimate ˆk 1 and ˆd 1 will never be perfect, due to identification error, non-linearitie and timevarying behavior e.g. caued by thermal effect). Having non-perfect etimate, the performance i limited by the error term T error in 14) at the higher frequencie. Thi i illutrated in Fig. 3, which how the tranmiibility in cae of a 1% etimation error in the tiffne ˆk 1 = 0.99k 1 ) and a 10% etimation error in the damping ˆd 1 = 0.9d 1 ). For ω < k 1 /d 1 = 2000 rad/, the performance i limited by the tiffne error, therefore the maximum vibration attenuation i 40 db 1% of the original T), while for ω > k 1 /d 1 the maximum vibration attenuation i 20 db 10% of the original T). Thi example illutrate the need for accurate parameter etimation. 5. SELF-TUNING FEEDFORWARD CONTROL To obtain accuratevalue for ˆk 1 and ˆd 1, and thu minimizing performance limitation due to parameter etimation error, the fixed-gain feedforward controller i redeigned a a elf-tuning IIR filter with n th -order bai function. The advantage of IIR filter over the widely ued FIR filter, ee e.g. Van der Poel 2010), i that filter pole are allowed at other location than z = 0. Thi make ene, becaue from 13) it follow that pole are required. Moreover, the deired pole location are known from 13). Therefore, the IIR filter pole can be fixed in the bai function, reulting in a controller that i inherently table becaue the pole cannot hift to untable pole location. Moreover, 13) i linear in the parameter ˆd 1 and ˆk 1. Therefore, minimization of a quadratic cot criterion to etimate d 1 and k 1 online lead to a convex adaptation problem with a unique global minimum. The preconditioned Filtered-Error LMS algorithm Weelink and Berkhoff2008)) with reidual noie hapingkuo and Tai 1994)) i ued for online parameter etimation. d F 1 F 2 F n ψ 1 ψ 2 ψ n w 1 w 2 w n u IIR Fig. 5. Dicrete-time IIR filter with elf-tuning weight w i 5.1 Self-tuning IIR filter tructure The IIR filter i depicted in Fig. 5. In the firt tep, a 0 i filtered by a vector of bai function F = [F 1,...,F n ], reulting in n ignal collected in the vector ψ = [ψ 1,...,ψ n ]. The ignal ψ i are multiplied by elf-tuning weight w i, collected in w = [w 1,...,w n ]. The um of all weighted ignal reult in the IIR filter output u IIR. F i, with i = 1,...,n, are determined from the fixed-gain controller W n, a will be explained in Section 5.3. The weight are determined uing an update law, wk 1) = wk) µk) ) T Jk), 16) 2 wk) with iteration tep k and adaptation rate µk). The gradient in 16) tem from the quadratic cot criterion Jk) = e k) T e k). 17) Equation17) decribe the intantaneou quared filterederror rather than the mean quared filtered-error over a time interval. The filtered error e = NMŜ) 1 ek) i obtained by filtering the meaured error ek) by the invere of the etimated econdary path Ŝ 1 and the preconditioning filter M to obtain the filtered-error LMS tructure), and N to apply reidual noie haping). The filtered error i given by e k) =NŜM) 1 Pdk)SM[w T k)ψk)]), 18) with input diturbance d, and P, S a given in Fig. 2, ψ, w a given in Fig. 5, and M, N filter to be deigned. It i generally not poible to find a cloed-form expreion for the gradient with repect to w. Therefore, low adaptation of w i aumed, uch that the gradient in 16) can be written a Jk) wk) = Jk) e k) e k) 19) wk) 2e k) NŜM) 1 SMψk) 20) 2e k) Nψk). 21) In 21), it i aumed that Ŝ = S. Recall from 3) that S i aumed to have a many zero a pole, uch that Ŝ 1 i proper; modeling error in Ŝ are dicued in ection 5.3. Subtitution of 21) in 16) give the update law: wk 1) = wk) µk)ψ k)e k), 22) with ψ k) = Nψk). Uinganormalizedtep ize, eevan der Poel 2010), we have µ µk) = ǫ ψ k) 2. 23) 2 In 23), the adaptation rate i dependent on ψ k), uch that intability of the adaptation proce due to large input ignal i prevented; ǫ > 0 i a mall poitive contant to prevent diviion by zero. The normalized adaptation rate 0 < µ < 2, which i et by the uer, 5614

5 19th IFAC World Congre mut not be too large to prevent intability due to the approximation in 21). d W N d IIR update e M u FF P S N MŜ) 1 Fig. 6. Implementation of the elf-tuning IIR filter. Fig. 6 how the implementation of the elf-tuning IIR filter. The update block ue 22) to update the weight. 5.2 Controller deign The fixed-gain controller W n a given in 13) i redeigned a a elf-tuning IIR filter, ee 24). The parameter ˆd 1 and ˆk 1 in 13) have to be etimated online, o w 1 = ˆd 1 and w 2 = ˆk 1. The filter M and F i, with i = 1,2, are dicretetime equivalent of M), F 1 ) and F 2 ) a defined in W n,iir ) = 1 L n) }{{ }{{} 1 } F 1) M) e w 1 1 L n) }{{} F 2) w 2. 24) For ue in a digital environment, all filter are dicretized uing the Tutin method with ampling frequency 6400 Hz. For the noie haping filter N, the following deign i ued: ) ) ) N) =. 25) α The firt-order high-pa filter with it pole at = 500 rad/ improve the convergence rate by making the frequency pectrum of F 2 )w 2 flat. Thi make ene, becaue the vibration iolator i a light-damped ytem, o d 1 repreented by w 1 ) will be mall compared to k 1 repreented by w 2 ) and therefore the term F 2 )w 2 i dominant at low frequencie ω < k 1 /d 1. The econd term i a low-pa filter with a pole at = 5000 rad/, thi filter make NMŜ) 1 proper. The fourth-order high-pa filter at = 5α rad/ remove the low-frequency content from the update ignal. The low-frequency content i removed to prevent that the algorithm trie to compenate for low-frequency error, which i not poible becaue of the tame integrator in 24). Without high-pa filtering, the etimation will be biaed. 5.3 Simulation reult Simulation tudie are performed for n = 1,3,5, µ = 10 4, and ǫ uch that it value i 0.1% of the RMS input power. The weight, all having an initial value of zero, are updated at every time tep. Input d i a floor acceleration with a white noie frequency pectrum. Fig. 7 how the learning curve of the elf-tuning algorithm. From the figure, it i clear that the algorithm converge to the minimum cot olution in all three cae where Ŝ = S. cot J Learning curve FF, W 1,IIR Ŝ = S FF, W 3,IIR Ŝ = S FF, W 5,IIR Ŝ = S FF, W 5,IIR Ŝ error Time ) Fig. 7. Learning Curve, howing the convergence behavior of the IIR filter. The red line indicate the minimum cot, correponding to fixed-gain controller with etimation w 1 = d 1 and w 2 = k 1. The black line indicate the cot during the convergence proce. To invetigate the enitivity of the convergence algorithm for non-modeled high-frequency dynamic in Ŝ, a fourth cae i imulated in which an 800 Hz reonance with relative damping 0.07 i added to S, but not to Ŝ. It appear that the elf-tuning algorithm become untable without modifying N. To re-tabilize the ytem in the preence of the 800 Hz reonance, a econd-order lowpa filter at = 500 rad/ i added to N, uch that high-frequency content i filtered from the enor ignal. According to Bao and Panahi 2010), thi i equivalent to virtually removing high-frequency content from a 0. A a reult, excitation of the dynamic that detabilize the converge proce i not een by the elf-tuning controller. Note that the teady-tate reidual error i higher, becaue the reonance at 800 Hz i not compenated for by the controller. When including feedback control, in addition to feedforwardcontrol,ŝ itheetimateofthecloed-loopecondary path, ee Van der Poel 2010). Therefore, feedback control can be ued to reduce modeling error. VCM Platform Floor plate Piezo tack 6. EXPERIMENTAL RESULTS Flexible body Fig. 8. Experimental etup. 5615

6 19th IFAC World Congre Fig. 8 how the experimental etup ued for validation purpoe. The etup conit of a Stewart platform connected to ix voice coil motor VCM) by wire pring. The VCM are guided by circular leaf pring, which introduce ix upenion mode into the ytem. The Stewart platform carrie a flexible body that introduce three additional mode in the etup. The VCM are controlled by a dspace DSP ytem running at ampling frequency f = 6400 Hz. Both the floor plate and the Stewart platform contain ix accelerometer. The floor plate can be excited in vertical direction by three piezo tack providing random vibration white noie). The etup i deigned uch that the platform motion in vertical direction i almot decoupled from the other direction. In vertical direction, the paive ytem contain one upenion mode and one internal mode, ee the meaurement in Fig. 9. The elf-tuning feedforward controller from Section 5.3 i implemented on the DSP with n {1,3,5} and α = 2 Hz, together with the feedback controller from 6). During the convergence proce, a rigid-body etimation for S including feedback controller 6) i ued. To filter nonmodeled high-frequency dynamic, 25) i extended with a fourth-order low-pa filter at 500 rad/. From Fig. 9 it i oberved that attenuation level up to 40 db are obtained with repect to the feedback-controlled ytem. At higher frequencie, active vibration iolation even deteriorate the performance due to the caual nature of the input diturbance meaurement, ee Heertje et al. 2013). For frequencie higher than 400 Hz, enor noie dominate the error repone. Furthermore, upenion mode how up at18hzand29hzdue tonon-perfectdecouplingofthe ytem. It i expected that a full Multiple-Input Multiple- Output MIMO) feedforward controller would uppre thee mode, thi will be a topic for future reearch Tranmiibility -60 Paive FB FB FF, W 1,IIR FB FF, W 3,IIR FB FF, W 5,IIR Frequency Hz) Fig. 9. Meaured frequency repone function. 7. CONCLUSIONS An effective elf-tuning feedforward control trategy for the active vibration iolation of preciion machinery from floor vibration i preented and experimentally validated. To prevent problem with drift and actuator aturation, the controller gain i limited for frequencie below 2 Hz, while obtaining a good performance for higher frequencie. To reduce etimation error, the feedforward controller i implemented a a elf-tuning IIR filter. Simulation how that the elf-tuning IIR filter converge to the optimal fixed-gain controller. An experimental validation of the elf-tuning feedforward control trategy, combined with a kyhook feedback controller, how that floor vibration are uppreed up to 40 db in a broad frequency range. ACKNOWLEDGEMENTS Thi reearch wa financed by upport of the Pieken in de Delta Program of the Dutch Minitry of Economic Affair. REFERENCES Bao, H. and Panahi, I.M.S. 2010). A novel feedforward active noie control tructure with pectrum-tuning for reidual noie. Conumer Electronic, IEEE Tranaction on, 564), Heertje, M.F., Temizer, B., and Schneider, M. 2013). Self-tuning in mater lave ynchronization of highpreciion tage ytem. Control Engineering Practice, 2112), Karnopp, D. and Trikha, A. 1969). Comparative tudy of optimization technique for hock and vibration iolation. Tranaction of American Society of Mechanical Engineer, Journal of Engineering for Indutry, 914), Kuo, S.M. and Tai, J. 1994). Reidual noie haping technique for active noie control ytem. The Journal of the Acoutical Society of America, 95, Landau, I.D., Alma, M., and Airimitoaie, T.B. 2011). Adaptive feedforward compenation algorithm for active vibration control with mechanical coupling. Automatica, 4710), Tjepkema, D., van Dijk, J., and Soemer, H. 2011). Senor fuion for active vibration iolation in preciion equipment. Journal of Sound and Vibration, 3314), Van der Poel, G. 2010). An exploration of active hard mount vibration iolation for preciion equipment. Ph.D. thei, Univerity of Twente, Enchede, The Netherland. Weelink, J. and Berkhoff, A. 2008). Fat affine projection and the regularized modified filtered-error algorithm in multichannel active noie control. The Journal of the Acoutical Society of America, 1242), Williamon, G.A. and Zimmermann, S. 1996). Globally convergent adaptive iir filter baed on fixed pole location. Signal Proceing, IEEE Tranaction on, 446), Yuan, J. 2007). Adaptive laguerre filter for active noie control. Applied Acoutic, 681), doi: Zuo, L., Slotine, J.J., and Nayfeh, S. 2004). Experimental tudy of a novel adaptive controller for active vibration iolation. In Proceeding of the American Control Conference,