Hybrid time-frequency domain adaptive filtering algorithm for electrodynamic shaker control

Transcription

1 Journal o Engineering and Comuter Innovations Vol. (10), , December 011 Available online at htt:// DOI: /JECI11.05 ISSN Academic Journals Full Length Research Paer Hybrid time-requency domain adative iltering algorithm or electrodynamic shaker control Martino O. A. Ajangnay Electrical Engineering Deartment, College o Engineering and Architecture, University o Juba, South Sudan. Ajangnay16@hotmail.com. Acceted 1 November, 011 In this aer, adative iltering algorithm or control o the vibration orce alied on the secimen in testing control systems is resented. Alication or adative iltering esecially in time domain is associated with a high comutational comlexity. his comlexity is mitigated by using requencydomain adative iltering scheme. In this aer, adative iltering algorithm in association with ast ourier transormation (FF) was roosed. he algorithm was imlemented using digital signal rocessor (DSP). he roosed algorithm show signiicant reduction in comutational comlexity as shown in results and discussion. Key words: Hybrid requency-time, adative iltering algorithm, electrodynamics shaker. INRODUCION Vibration design and control, aims either to eliminate or to reduce the undesirable vibration eects that may cause human discomort and hazards, structural degradation and ailure, erormance deterioration and malunction o machinery and rocesses. When a mechanical or electronic system is exosed to a vibration orce, it causes the system to vibrate, roducing an outut resonse as a result o the vibratory excitation orce. he control objective, in such a case, is to suress the outut resonse to a level that is accetable. In an adative vibration control system, the vibration resonses are exlicitly sensed through transducers. his sensed resonse is ed to the controller roducing the orce that counteracts the eect o the vibration source, suressing vibration at the sensing location. his orce is alied to the system through the actuator. In this aer the electrodynamic shaker, with a ermanent magnetic ield, is used as a vibration exciter and the control algorithm adoted is a variant o adative control. he alication o adative control or shaker is motivated by the act that some arameters o the shaker are time-varying (or examle, coil inductance is requency deendent, and the coil resistance may change with time as the result o skin eect and temerature). Also the secimen or load characteristic is usually unknown beorehand and it may be nonlinear. he shaker control algorithms roosed in the literature (George, 1997; George and Dave, 001), have been derived based on a linear shaker model or on the assumtion that the load nonlinearity and variation o shaker arameters with time can be neglected. he erormance o these controllers degraded when the shaker dynamics are time-varying or the load is highly nonlinear. Besides, the requency domain adative iltering algorithm studied in IMV Cororation Jaan, 001 (Frain, 1977) suers rom high comutational comlexity and long time delay resulting rom the utilization o the block requency domain method. he limitations o these algorithms were addressed in this aer by utilizing a time and requency block artitioning adative iltering algorithm to reduce the comutational comlexity, convergence time and the time delay. he electrodynamic shaker s main unction is to deliver a orce roortional to the current alied to its armature coil. hese devices are used in such diverse activities as roduct evaluation, stress screening, squeak-and-rattle testing, and modal analysis. he shakers may be driven by sinusoidal, random or transient signals, deending on the alication. hey are invariably driven by an audio-requency ower amliier and may be used oen loo (as in most modal testing) or under closed-loo control, where the inut to the driving amliier is servo-controlled to achieve a desired motion level in the device under test. here are three

2 19 J. Eng. Comut. Innov. Armature est lexure (table) Diahragm Armature ixtures Cu shorting ring Outer ole Inner ole Outer ole Armature coil Permanent magnet Magnet structure (body) Figure 1. Electrodynamic shaker cross-section. major shaker tyes widely used (Hydraulic, Inertial and Electrodynamic Shakers) in vibration testing. However, electrodynamic shakers have many advantages comared to the other tyes due to their high outut bandwidth and moderate inut ower requirements. In the vibration control system with the shaker used as an exciter, it is essential to characterize the shaker dynamic model and to comute the shaker mechanical and electrical arameters that will be used in the simulation stage. An initial exeriment is erormed by monitoring the voltage inut to the ower amliier or the current delivered by the ower amliier, and measuring the dynamic resonse o the shaker (accelerometer signal) with a bare shaker table, then with a known table load (George, 1997; De Silva, 000). he schematic deicted in Figure 1 shows a sectioned view o a ermanent magnet electrodynamic shaker with emhasis on the magnetic circuit and the susended driving table. At the heart o the shaker is a single-layer armature coil o coer wire, susended in a uniorm radial magnetic ield. When a current is assed through the coil, a longitudinal orce F is roduced in roortion to; the current I lowing in the coil, the length l o the coil in the magnetic ield, and the strength B o the ield lux. his orce is transmitted to the table structure to which the device under test is attached. he generated orce in the armature coil is mathematically exressed as (Frain, 1977). F BlI (1) Where, F, is the armature coil orce, (N); B, is the magnetic lux density, (); l, is the length o armature coil in the ield, (m); l, is the armature coil current, (A). SYSEM MODELLING OF ELECRODYNAMIC SHAKER he electrodynamic shaker can be exressed as a current driven or voltage, transer unction. In the current driven transer unction mode, the acceleration requency resonse is lotted as current sulied by the ower amliier against the shaker acceleration resonse. In this case, the eect o electromagnetic daming is not evidenced. he requency resonse lot relects only the structural daming terms, those that could be measured with external excitation alied to the shaker with its drive coil un-terminated. he same low daming actors are usually evident when a current amliier drives the shaker. In contrast, the voltage driven transer unction (voltage alied to the shaker system against the acceleration, relects the signiicant electromagnetic daming alied

3 Ajangnay 19 Figure. Current driven transer unction o the unloaded electrodynamic shaker. by the cross-couling terms between the electrical and mechanical comonents o the system (George, 1997; Haykin, 00). he orce rovided by the shaker is given by F = BIl. Figures and show, resectively, the current driven and voltage-driven requency resonse when the swet sine signal o amlitude 0.7 v was alied to shaker ower amliier. he shaker mechanical model is modelled by assuming the armature structure is elastic rather than rigid. his gives the shaker mechanical model three degreeso-reedom. his is achieved by modelling the coil and table as searate masses connected by srings and damers (George, 1997; George and Dave, 001). In order to comute the mechanical and electrical arameters o the electrodynamic shaker and the associated load, a swet sine test is conducted to comute the requency resonse unction as the ratio between the shaker s outut resonse (accelerometer signal), and the inut suly voltage (voltage mode). he resonance requencies in the oerating range and the hal-ower oints are recorded. hese are used in mathematical ormulas (Equation 1), to estimate the masses, daming constant, sring stiness, and electrical imedance. Some o the arameters are tuned using trail and error during simulation, so that the simulated requency resonse matches the measured requency resonse shae. he mathematical equations used to deduce the mechanical and electrical arameters rom the requency resonse, are given by IMV Cororation Jaan (001). M K e a n M n D Where; M M K D n a e a db db a a M () M e e eective mass o mass o the load sringstiness daming actor theshaker system resonance requency when theshaker has no load (6.8 khz) resonance requency when theshaker is loaded hal - ower (-db) ointsbounding resonance requency Electrical equivalent model he electrical model o the electrodynamic shaker consists o the coil resistance R and inductance L. he electrical imedance o the shaker coil relects the n

4 194 J. Eng. Comut. Innov. Figure. Voltage driven transer unctions o the unloaded electrodynamic shaker. mechanical motion o the shaker table. When the coil moves in the magnetic ield, a voltage is generated across the coil roortional to the motion velocity (E = Bl u= αu). hus the voltage at the coil terminals may be written in terms o the lowing current i and the velocity u as: v di Ri L u dt () Where α = Bl is constant, called the transduction actor. he mechanical mobility (velocity/orce) o the shaker mechanical comonents may be reresented by a driving-oint requency resonse unction H u, so that u H F (4) u he coil roduces an axial orce, acting on the shaker mechanical elements, in roortion to the alied current. F i (5a) Combining equations (, 4 and 5), yields the imedance Z exhibited by the coil. v Z R jl H u (5b) i he minimum coil imedance is determined by the dierential (dc) resistance, which is real-valued. he coil inductance contributes an imaginary (90 hase-shited) ac comonent that increases in direct roortion to requency. he mechanical mobility contributes requency-deendent terms that exhibit a real maximum at each mechanical resonance. hese can signiicantly increase the imedance in a narrow requency band. he eective resistance and inductance o the coil can be measured by claming the ixture table (locked rotor test). he equivalent circuit is shown in Figure 4 where R 1 and L 1 are the resistance and leakage inductance o the moving coil, R and L are the resistance and leakage inductance o the coer ole-lating, and L m is the moving coil magnetizing inductance. Using current mesh

5 Ajangnay 195 Figure 4. Moving coil -circuit showing the short-circuit secondary. analysis, the mathematical equations or the shaker electrical model can be derived rom Figure as di1 di1 di dl1 v R1i 1 L1 Lm dt dt dt dt di di di1 0 Ri L Lm dt dt dt (6) d l1 i1 M1 K1l1 l dt K K 1 l l D M K l l 1 1 l l dl dt 1 dl dt dl1 dl D1 dt dt d l dt dl dl d l dl D M Kl D dt dt dt dt dl dl D dt dt (7) Mechanical equivalent model he shaker mechanical system includes a means or storing otential energy (sring), a means or storing kinetic energy (mass or inertia), and a means by which energy is gradually lost (damers). he mechanical model o the shaker consists o two distinct elements, the moving coil and the ixture table. he ixture table is susended by a susension lexure to the shaker body assembly. he ixture table can be modelled as a air o masses M and M, with lexure stiness, K and K, and daming coeicients, D and D. he moving coil o mass M 1 is adhered to the ixture table by an adhesive bonding, which also can be characterized by a sring with a inite stiness K 1 and a daming element with coeicient D 1. hus Figures 4 and 5 can reresent the unloaded shaker electrical and mechanical systems, resectively. he mechanical system and mathematical equations can be exressed as: d l1 i1 M1 K1l1 l dt K 1 l l D M K l l 1 K l l 1 dl dt 1 dl dt dl1 dl D1 dt dt d l dt dl dl d l dl D M Kl D dt dt dt dt dl dl D dt dt (7) PARIALLY HYBRID IME-FREQUENCY DOMAIN ADAPIVE FILERING ALGORIHM In vibration testing control systems, the shock test is conducted to simulate the eect o the shock that a secimen is exected to be subjected to, during its lietime. o revent testing damage, it is essential that the test be controlled such that the shaker outut converges smoothly to the intended reerence shock ulse. Usually, in shaker vibration control, the load dynamics are not well deined beore hand. hus, the control algorithm must be designed with the ollowing consideration: (1) he controller should be able to udate its arameters to coe with load uncertainty. () he controller must have a ast resonse, esecially when the ulse used is a shock ulse; and () he controller must be robust, such that it can adat to a large range o load variations. he ollowing give a brie descrition o inverse adative iltering, time domain adative iltered-x iltering and hybrid time-requency domain adative iltering algorithms. Inverse adative iltering algorithm For tracking control or servo-control systems, the inverse

6 196 J. Eng. Comut. Innov. Figure 5. Mechanical equivalent circuit o the unloaded electrodynamic shaker. o the system dynamics can be emloyed as a controller such that, when the inverse model is cascaded with the system dynamics, the overall system outut converges to the reerence inut. his coniguration o the inverse model and system dynamics constitutes a eed-orward control system. Adative eed orward techniques have been used widely in the active control o sound and vibration (Olmos et al., 00; Valoor et al., 000). he alication o the shaker inverse model as a controller has been reorted in Macdonald (1994), where the shaker and controller were modelled in the requency domain. Cascading the adative ilter with the unknown system causes the adative ilter to converge to a solution that is the inverse o the unknown system. hereore, inverse modelling is motivated by the act that, when the transer unction o the unknown system is W(z) and the adative ilter transer unction is C(z), then error measured between the desired signal and the signal rom the cascaded system reaches its minimum when the roduct o W(z) and C(z) is 1. W ( z) C( z) 1 (8) For the revious relation to be true, W(z) must be equal [C(z)] -1, the inverse o the transer unction o the unknown system. In ractice, it is sometimes essential to have rior knowledge o the system dynamics, so that an accurate inverse o the dynamic system can be obtained. For examle, i the system under investigation is known to be minimum-hase, that is, has all o its zeros inside the unit circle in the z-lane, then the inverse will be stable with all its oles inside the unit circle. When the lant is non-minimum-hase, then some o the oles o the inverse will be outside the unit circle and the inverse will be unstable. It is also essential to consider the eect o transort delay in the system. For instance, when the unknown system is cascaded with the ilter, the outut signal rom the cascaded system reaches the summation oints ater it has been delayed by a time equal to the unknown system delay lus the ilter delay. o revent the adative ilter rom trying to adat to a signal it has not yet seen (equivalent to redicting the uture), the desired signal is delayed, with the number o samles equivalent to hal the length o the adative ilter. Figure 6 shows the block diagram or modelling the inverse o the electrodynamic shaker using a inite imulse resonse (FIR) ilter. Assuming the shaker and the ayload are linear, then the commutation rule alies, such that the controller and lant osition can be interchanged. Assuming the inut signal r(n) is alied to the shaker and a ayload, the acceleration resonse Outut a(n) will act as the inut to the FIR ilter. he

7 Ajangnay 197 Δ r(n) Shaker/ Secimen W(z) a(n) Inverse Model C(z) + - y(n) r(n-δ) e(n) Adative Algorithm Figure 6. Inverse adative modelling block diagram. outut resonse o the cascaded system is given by L 1 i0 y ( n) c ( n) a( n i) (9) i Where L is the number o weights in the FIR ilter and c i (n) is the i th weight o the adative ilter at iteration n. he error between the delayed inut signal and the outut o the cascaded system is e( n) r( n ) y( n) (10) Where Δ is the samle delay, equal to L/. Using the Least mean squares (LMS) algorithm, the weights o the inverse adative ilter are udated using the ollowing ormula c( n 1) c( n) e( n) a( n) (11) Where μ is the ste-size, and the weight vector c(n) and ilter regression inut vector a(n) are given by equations (5a) and (5b), resectively. c n ) c ( n), c ( n),..., c L ( n) (1) ( a ( n ) a( n), a( n 1),..., a( n L 1) (1) Filtered-x adative iltering algorithm he iltered-x algorithm has been extensively alied in the active control o sound and vibration. he design is carried out in two hases. In the irst hase, the model o the dynamic system to be controlled is comuted. In the second hase, the controller weights are udated, and the otimal values ound are imlemented to control the dynamic system. he main eature o the iltered-x algorithm is that the signal used in the controller weights adatation, is roduced by iltering the reerence inut signal, via the system model weights. Figure 7 illustrates the block diagram o the iltered-x adative iltering algorithm or the electrodynamic shaker. Assume the model o the shaker and the secimen has been comuted. Let the number o weights in the shaker/secimen model and the control ilter be L c and L, resectively. he outut resonse o the FIR ilter controller is comuted as a convolution o the FIR ilter weights and the inut reerence signal. L c 1 i i0 u ( n) c ( n) r( n i) (14) he FIR ilter outut is alied to the shaker/secimen, generating the acceleration outut o a(n). he error signal is comuted as the dierence between the delayed inut signal and the shaker/secimen acceleration outut resonse. e( n) r( n ) a( n) (15) Where Δ is the time delay. he inut reerence signal is iltered through the shaker model weights to generate the

8 198 J. Eng. Comut. Innov. r(n) Δ Filter c(n) u(n) Shaker /Secimen r(n-δ) + _ a(n) e(n) Shaker Model w(n) u (n) Filtering algorithm Filtered-x algorithm Figure 7. Filtered-x adative iltering block diagram. iltered signal u (n) given by L 1 i0 u ( n) w ( n) r( n i) (16) i Using the LMS algorithm, the controller weights are udated using c( n 1) c( n) e( n) u ( n) (17) Where μ is the ste-size, c(n) is the controller weight vector, and u (n) is the regression vector. he controller weight vector is given by ( n) c c c 0, 1,..., Lc 1 c (18) he regression vector is deined as u ( n ) u ( n), u ( n 1),..., u ( n L 1) (19) Partially hybrid time-requency domain adative iltering (PHFDAF) algorithm Here, artially hybrid time-requency domain adative iltering (PHFDAF) algorithms are described or modelling and controller design or the shock control o the electrodynamic shaker. he model and inverse model o the electrodynamic shaker are modelled by an FIR ilter. Exerimental results show that the model and inverse model o the shaker required thousands o FIR weights to reresent the dynamic system (shaker and load attached) eectively. his large number o ilter tas results in comlex comutation and imlementation and in real-time requires large resources, in terms o memory. As a result, it is imractical to use time-domain iltering methods to ind the model and inverse model o the electrodynamic shaker and its load. Comutational comlexity and convergence seed o the FIR model s weights to their otimal values was addressed using the requency domain adative iltering algorithm studied in artially hybrid time-requency domain adative iltering (PHFDAF) algorithm. However, the conventional requency domain adative iltering algorithm has a drawback o inherent delay between the block inut and the system outut resonse, esecially during the initial stages while the inut block data collection is rocessing. he roblem o the long delay in requency domain adative iltering was addressed by slitting the time domain ilter weights sequentially into non-overlaing artitions (Olmos et al., 00; Valoor et al., 000). Although artitioning o the ilter weights results in a small inut block size, it does not comletely eliminate the system time delay. A delay less requency domain adative iltering algorithm was roosed in Bendel et al. (001), where the system delay is eliminated by adating the irst artition weights using a time domain algorithm and adating the remaining artitions using a requency domain adative iltering algorithm. Although this method

9 Ajangnay 199 x(k) inut sectioning old new new 0 Overla-save Overla-add X(k) X(k-1) X(k-N) FF... G =0 G =1 Y 1 (k) Y 0 (k) Σ Overla-save Overla-add IFF y y(k) y Save and discard _ d(k) X(k-N+1) G =P-1 Y P-1 (k) Overla-save Overla-add 0 e e 0 + FF Insert zero block e(k) Figure 8. Partitioned requency domain adative iltering block diagram. eliminates the time delay in adatation, it increases comutational comlexity due to the use o the time domain adative iltering method in udating the irst artition weights. o reduce the comutational comlexity o artitioned requency domain adative iltering, the PHFDAF algorithm was roosed. In the PHFDAF algorithm, the time domain ilter weights are sequentially divided into non-overlaing artitions. he irst artition weights are adated using the time domain only during the initial stage. hen these weights are adated using the requency domain algorithm as well as the other artition s weights. his method o artially udating some weights in the time domain and then in the requency domain reduces the comutational comlexity o the whole adatation rocess, as well as minimising the time delay in the adatation rocess. he roosed algorithm or adative control is dierent rom the one reorted in Olmos et al. (00), and Bendel et al. (001). he time domain adative iltering o the model and its inverse are sequentially slit into non-overlaing artitions and the irst artition weights are udated only in the time domain during the irst block inut data collection, then they are adated in the requency domain in the remaining adatation eriods along with the other artitions weights. PBFDAF algorithm he comutational comlexity and long time-delay roblems, associated with the conventional requency domain adative iltering algorithm, can be minimized by using the artitioned block requency domain adative method, in which the weights o the FIR ilter are sequentially slit into non-overlaing artitions. hen the requency domain adative algorithm is alied to each artition. he main advantage o PBFDAF over the nonartitioned algorithm is that a small rocessing block size is required; consequently, the delay o the PBFDAF is small. Figure 8 shows the PBFDAF block diagram. o derive the equations that govern the PBFADF algorithm, assume that the FIR ilter has M weights, divided into P artitions, each artition containing N weights. hereore the outut o the blocks o N samles is given by P 1 0 y [ y( kn),..., y( kn N 1)] A( k )[ w ( kn),..., w (0) k N ( 1) N 1 ( kn)]

10 00 J. Eng. Comut. Innov. Where A(k) is an NxN matrix whose i,j element is given by A i j, ( k) x( kn i j), i, j 0,1,..., N 1 he outut o each artition is a circular convolution o the artition inut with the weight vector o the artition at the k th time, where or examle, the inut o the artition (overla-save) and weight vector er artition are, resectively. x( k ) [ x([ k 1] N),..., x([ k ]) N,..., x([ k 1] N 1)] w ( k) [ w ( kn),..., w ( 1) N 1 ( kn),0,...,0] (1) hus the inut and artition weight vector in the requency domain are deined as X ( k ) diag ( Fx( k )), W ( k) F w ( k) 0,1,... P 1 0,1..., P 1 () Where F denotes the discrete Fourier transorm (DF) oerator o order N. For the overla-save method o the block sectioning, the adative ilter outut in the time domain is y k [ y( kn),..., y( kn N 1)] where Y ( k) X ( k ) W [0 ( k) n I ] F n P Y ( k) () where 0 ] is NxN, is the outut rojection matrix [ N I N used to orce the irst element o the outut vector to zero as a result o the alication o the overla-save sectioning on the inut block. he weight udate o each artition is deined as W ( k 1) W I ( k) F 0 N N 0 0 N N F 1 { X * ( k ) E( k)} (4) Where E(k) is the error vector in the requency domain and is deined as E ( k ) F( e( k)) F[0,0,...,0, e( kn),..., e( kn N 1)] (5) EXPERIMENAL SEUP In this aer, the loaded shaker was characterized using a swet sine signal, generated rom the HP 56A Dynamic Signal Analyzer Figure 15. he signal, swet rom 10 Hz to 10 khz, was alied to the shaker/secimen via the ower amliier. he acceleration outut resonse was measured via a charge amliier, whose outut was connected to the nd channel o the Dynamic Signal Analyzer. he requency resonse was comuted as the ratio between outut acceleration measured by charge amliier and the inut swet sine signal o 0.7 v rms amlitude. he charge amliier sensitivity and scale values were set to 80 C/g and 5 g/v, resectively. From the measured transer unction o the unloaded shaker (Figure 9a), the uer resonance requency occurs at 6.8 khz and low resonance at 54. Hz. he resonance requency values rom Figure 9a and the hal-ower values were used to comute masses, and srings and damer constants o the mechanical system. Some electrical comonents were measured. he remaining electrical and mechanical arameters were aroximated using trail-and-error, by tuning the simulation rogram till the requency resonse matched the measured requency resonse. he requency resonse o the unloaded shaker model is shown in Figure 9b. RESULS AND DISCUSSION he shaker model reresented by the FIR adative ilter is identiied using the artially hybrid requency domain adative iltering algorithm described in artially hybrid time-requency domain adative iltering algorithm. he FIR ilter reresenting the model has 104 weights. he time-domain weights are divided into two artitions, each o 51 tas, as is exlained in the revious sections. he weights o the irst artition are adated using the nonblock time domain iltering algorithm only in the irst block inut stage ( n 0,1,...,511). In subsequence block inut iterations, the weights in the irst artition and the weights o the other artitions are udated using the requency domain adative iltering algorithm. Ater the shaker model is comuted, the model weights are used in the PHFDAF FIR controller model, such that when the resultant FIR controller is connected in cascade with the shaker, the shaker outut tracks the reerence inut signal. hat is, the control objective can be stated as: given the desired inut reerence signal and the shaker model, it is required to comute the FIR controller model such that when cascaded with the shaker, the outut o the shaker tracks the reerence inut signal (Figure 10). he transition o the shaker controlled outut resonse to the inut reerence signal should occur in a short time (due to the shock ulse width, usually to 0 ms) and converge smoothly (no overshoot). he control model is reresented by an FIR ilter o 104 weights. he weights are divided into two artitions, each o 51 weights, as in the case o the system identiication o the shaker model. Using the iltered-x method in the time and requency domains, the shaker outut tracks the reerence signal. he adatation rocess converges to the otimal values ater 0 block inut iterations. he inut reerence signal and shaker controlled outut resonses are shown in Figures 11 and 1, resectively. From comarison o the desired inut reerence signal (Figure 11) and the shakercontrolled outut (Figure 1), it is seen that the shaker outut tracks the inut reerence signal. he control algorithm imlementation results in a reduction in the ringing o the shaker outut resonse. he rise time and

11 Mag [db] Ajangnay 01 0 (a) Frequency resonse o the unloaded shaker Frequency [Hz] (b) Figure 9. Frequency resonse o the unloaded shaker: (a) ractical and (b) simulation.

12 0 J. Eng. Comut. Innov. Figure 10. Shaker inut reerence and shaker outut resonse. Figure 11. Inut reerence.

13 Ajangnay 0 Figure 1. Shaker controlled outut (with PHFDAF). Figure 1. Controller outut (Shaker inut- (with PHFDAF). settling time achieved are 0.05 and 0.85 ms, resectively. he controller outut signal (shaker inut) is shown in Figure 5. Figures 1 to 15 shows the shaker erormance with conventional adative time domain Filtered-x

14 04 J. Eng. Comut. Innov. Figure 14. Shaker controlled outut (with Filtered-X). Figure 15. Controller outut (shaker inut-with Filtered-x).

15 Ajangnay 05 algorithm used to imlement control design or shaker system. During simulation it is ound that the PHFDAF algorithm converges to the desired signal aster than with the conventional requency domain adative iltering (FDAF) method. REFERENCES George FL (1997). Electrodynamic Shaker Fundamentals, Sound and Vibration, Data Physics Cororation, San Jose, Caliornia George FL, Dave S (001). Understanding the Physics or Electrodynamic Shaker Perormance, Dynamic reerence issue, Sound and Vibration, Data Physics Cororation, San Jose, Caliornia De Silva CW (000). Vibration undamentals and Practice, CRC ress. Frain WE (1977). Shock wave testing on an Electrodynamic Vibrator, Alied Physics Laboratory, he Johns Hakins University Laurel Maryland. George FL (1997). Electrodynamic Shaker Fundamentals, Sound and Vibration, Data Physics Cororation, San Jose, Caliornia. George FL, Dave S (001). Understanding the Physics or Electrodynamic Shaker Perormance, Dynamic reerence issue, Sound and Vibration, Data Physics Cororation, San Jose, Caliornia. IMV Cororation Jaan (001), Instruction Manual. Macdonald HM (1994). Analysis and Control o an Electrodynamic Shaker, PhD hesis, Heriot-Watt University, Edinburgh. Haykin S (00). Adative Filter heory, Prentice-Hall. Olmos S, Sornmo L, Laguna P (00). Block Adative Filters with Deterministic Reerence Inuts or Event-Related Signals: BLMS and BRLS, IEEE ran. Sig. Proc., 50(5): Bendel Y, Burshtein D, Shalvi O, Weinstein E (001). Delayless Frequency Domain Acoustic Echo Cancellation, IEEE rans on Seech and Audio Proc., 9(5): Valoor M, Chandrashekhara K, Agarwal S (000). Active Vibration control o smart comosite lates using sel-adative neurocontroller, Smart Mater. Struct., Vol. 9, IOP Publishing Ltd,