IEEE Indutry Application Society Annual Meeting Rome, Italy, October 8 2, 2000 Reonant Load Control Method for Indutrial Servo Drive George Elli Kollmorgen Corporation 20 Rock Road Radford, VA 24060 T: 540-633-552 F: 540-633-447 E: gelli@kollmorgen.com ABSTRACT - High-performance ervo drive are often limited by mechanical load reonance. In thi paper, even method of reonant-load control are compared for their ability to improve performance in the preence of a low-frequency (00 Hz) lightly damped reonance. Several of the method are baed on filtering the command ignal; the remaining method are baed on ignal acquired from an oberver. Development of thee method i preented; each method i applied to a phyical ytem and evaluated for effect on command repone and dynamic tiffne. I. INTRODUCTION Servo drive are ued in a wide range of indutrial application including metal cutting, packaging, textile, webhandling, automated aembly and printing. Command repone and dynamic tiffne are two key performance rating for high-performance application. Deigner ue cloed loop controller uch a proportional-integral, PI, velocity loop in ervo ytem. Such controller mut be configured with high gain for the ytem to achieve high performance. Mechanical reonance i one of the mot common problem deigner face when trying to maximize either command repone or dynamic tiffne []. Mechanical reonance i uually caued by a combination of high ervo gain and a compliant coupling between the motor and load. The compliant coupling come from the tranmiion which i ome combination of component uch a mechanical coupling, haft, gearboxe, lead crew, and belt/pulley et. The mechanical tiffne of thee component i limited; if the inertia of the tranmiion component i mall compared to the motor and load, the tiffne of the component can be treated a a ingle, compoite, equivalent pring contant that interconnect motor and load, a hown in Fig.. T M J M K S Fig.. Motor and load with a compliant coupling A block diagram of the compliantly coupled mechanim i hown in Fig. 2. Here, the equivalent pring contant of the tranmiion, K S, i hown a providing torque to the load in J L Robert D. Lorenz Univerity of Wiconin-Madion Dept' of ME & ECE 53 Univerity Avenue Madion, WI 53706 T: 608-262-5343 F: 608-265-236 E: lorenz@engr.wi.edu proportion to the difference of motor and load poition. Alo, to repreent lo producing propertie, a mechanical damping term i hown producing torque in proportion to velocity difference via cro-coupled vicou damping, b. T D T E J M b S K S J L Fig. 2. Block diagram of compliantly coupled load The tranfer function from electromechanical torque,, to motor velocity,, i = J M J L V L J L 2 b K S J L J M J L J M 2 b K S () which can be viewed a a pure, lumped inertia, /(J M J L ), term on the left and a dual quadratic or bi-quad function on the right. Thi i the tranfer function that would repreent the plant in the cae where the ole poition feedback enor wa on the motor (a oppoe to the load), a i common in indutry. PI and PID controller are deigned to control inertial term. The bi-quad function caue intability by altering the phae and gain of the lumped inertial plant. The vicou damping, b, on mot practical machine i low o that both the numerator and denominator are lightly damped. Thi produce a very low gain at the anti-reonant frequency, ω AR, the frequency for which the numerator i minimized. It alo produce a very high gain at the reonant frequency, ω R, the frequency for which the denominator i minimized. The undamped value of thee frequencie are hown in (2). K S K S ω AR = rad/ ω J R = rad/ (2) L J L J M J L J M The effect of the bi-quad term can be een in Fig. 3, where, without it, the gain would be contantly declining at P L
20 db/decade (hown a dahed line) and the phae would have a fixed 90 lag, characteritic of inertial load. Method of controlling reonance rely on modifying the effect of the bi-quad term. (J M J L ) F AR F R 30 db 20 db 0 o -90 o Fig. 3. Reonant and anti-reonant frequencie in the open loop frequency repone A common control tructure for ervo ytem i to ue a PI velocity controller, cacaded with anti-reonance filter, to drive a very high bandwidth current regulator. The mot common anti-reonance filter in are baed on one of three filtering technique: low pa, notch, and bi-quad filter. The high bandwidth current regulator produce electromagnetic torque to drive the motor/load mechanim. The motor poition i read from an encoder or other motor poition enor, and ued to calculate a ample average velocity feedback ignal for the control loop. Such a ytem i hown in Fig. 4. V C V F avg. vel. Digital PI vel. control; filter T C Compliantbody oberver Current reg.fieldoriented AC ervo drive V L PM PF Reonant motor and load Rigidbody oberver Enc. Fig. 4. Control ytem with compliantly coupled load Figure 4 how two oberver, both fed by the encoder poition and electromagnetic torque. One i a rigid-body oberver which oberve the motor velocity,, and acceleration,, auming no knowledge of the load inertia or coupling tiffne. The econd i a compliant-body oberver which model the motor and load velocitie, and V L, repectively, and acceleration baed on knowledge of the load and coupling characteritic. Many method have been ued to reduce the effect of reonance [3]. Thi paper will compare even method, i.e., three filtering and four oberver-baed method, for their ability to control a lightly damped, low-frequency (00 Hz) reonance. The method dicued here will be limited to uing a ingle motion enor a poition enor on a motor. The evaluation will be baed on the ability to provide increaed dynamic tiffne and fater command repone. In addition, each method will be evaluated for enitivity to mechanical change. The evaluation i done uing a combination of an experimental ytem and a imulation model. II. FILTERING METHODS Low-pa filter. The low-pa filter i the mot common method ued to control reonance today. The low-pa filter i ued to reduce the gain at the reonant frequency a hown in Fig. 5. Thi improve the gain margin at or near the reonant frequency; it alo degrade the phae margin ince the filter will reduce phae where the gain croe over (about 30 Hz in Fig. 5). Open-loop gain with filter Open-loop phae with filter w/o filter w/o filter Hz 0 Hz 00 Hz 000 Hz 0 db -20 db 0 o -80 o Fig. 5. Effect of a low-pa filter on the open loop frequency repone The key advantage of the low-pa filter i that i it eay to ue. Only the break frequency need to be adjuted for the given load reonance. Unfortunately, the low-pa filter i not very effective for the commonly found cae of low-frequency reonance, where the reonant frequency i no higher than 5 or 0 time the velocity loop bandwidth. Notch filter. Another widely ued filter i the notch filter [4]. It ha the tranfer function: T N () = 2 ω N 2 2 2 ζω N ω N 2 (3) Uually ω N will be elected to approximate the load reonant frequency, ω R, and the damping ratio, ζ, will be moderate to low, typically below 0.4. The notch filter, like the low-pa, i ued to increae gain margin by attenuating the open-loop gain in the frequency region near the reonant frequency. The damping ratio i generally elected uch that le phae ditortion occur at lower frequencie than when uing a low pa. Thi allow higher gain in the control loop. The notch filter alo pae the frequencie above the reonant frequency. The effect of the notch filter on the open loop frequency repone i hown in Fig. 6.
Open-loop gain with filter Open-loop phae with filter w/o filter w/o filter 0 db Hz 0 Hz 00 Hz 000 Hz -20 db 0 o -80 o (0 RPM /div) V L (0 RPM /div) 20 mec/div Motor velocity i well controlled Load velocity i ocillatory Fig. 6. Effect of a notch filter on the open loop frequency repone Bi-quad filter. The bi-quad filter i deigned to cancel the effect of the phyical bi-quad term of (). It ha the form T BQ () = 2 2 2 ζ N ω N ω N 2 2 (4) 2 ζ D ω D ω D The following equation are ued to achieve cancellation: JP = JL JM / (JL JM) where the circumflex,, denote an etimated parameter ω N = K S /JP ω D = K S /JL ζ N = b/(2 JP ω D ) ζ D = b/(2 JL ω D ) If complete cancellation i achieved, the effect of the biquad filter i to eliminate the bi-quad term from (), leaving () a an ideal inertial load. The command repone and dynamic tiffne can be enhanced coniderably. Theoretically, the bi-quad filter offer deigner the greatet opportunity to expand command repone and dynamic tiffne of the filtering method. The bi-quad filter ha two major hortcoming. Firt, while the motor poition/velocity may be controlled without ocillation, the load poition, which i connected to the motor through a reonant coupling, till reonate a hown in Fig. 7. The econd hortcoming of the bi-quad filter i that the ervo ytem i very enitive to parameter change. If mechanical parameter uch a load inertia or pring contant change, the ervo loop may become untable. III. OBSERVERS AS SENSOR REPLACEMENTS The remaining anti-reonance method require one or more ignal in addition to the motor-mounted encoder. Mot application cannot afford additional enor becaue of the cot of purchaing and mounting enor, and the lo of reliability from extra component and wiring. Thi ection will dicu two oberver that can be ued to obtain ignal in addition to the encoder. The following ection will dicu how thoe ignal can be employed to reduce reonance. Fig. 7. Motor damping and load ocillation with a properly tuned bi-quad filter Rigid-body Luenberger oberver The rigid-body Luenberger oberver can be ued to provide oberved motor velocity,, and acceleration,. The Luenberger oberver, a hown in Fig. 8, ha a tructure directly analogou to the motor. The electromagnetic torque,, a commanded by the drive act a a feedforward input to the oberver. It i divided by the etimated motor inertia to produce oberved acceleration; that ignal i integrated to produce and then oberved poition, PM. Thu, the oberver feedforward path i acting in parallel to the actual motor. Oberver tate feedback i ued to force it to track the meaured poition. The difference between PM and the motor poition,, i the oberver error. Thi error term i compenated by a PID control law, in an attempt to drive that error to zero. When the error i ufficiently mall, PM will be repreentative of, a will and of the motor velocity and acceleration. P F K OD ( K OP K OI /) J M Figure 8. Rigid-body Luenberger oberver The Eigenvalue of the oberver can be et a equivalent to a three-pole Butterworth (maximally flat) filter by etting: K OD = 2 ω N K OP = ω N K OI = ω 2 N /2 (6) By rewriting the block diagram of Fig. 8, it can be een that = J M x 3 3 K OD ( 2 K OP K OI ) x K OD ( 2 K OP K OI ) 3 K OD ( 2 K OP K OI ) which upon inpection i a high-pa filtered velocity ignal from the torque and a low-pa filtered velocity ignal from the encoder. Similar to the low-pa filter method of Section II, the oberver remove high frequency content of the (7)
encoder ignal to reduce reonance problem. Unlike the filter, the oberver fill in miing frequency content with information from which enable it to produce zero phae lag at lower frequencie and higher frequencie. An alternative form of the Luenberger oberver, the extended Luenberger oberver i hown in Fig. 9 [5, 6, 7]. Thi tructure i built recognizing that the proce of differentiation in the PID controller can be avoided by feeding the derivative ignal before the econd integration. Thi reduce computational reource and reduce quantization noie while providing the equivalent term. The acceleration term i effectively filtered ince K OD, the high-frequency term of the PID compenator, i removed from the forward path from PM and P F to. P F K OD (K OP K OI /) K OD J M Fig. 9. Extended rigid-body Luenberger oberver Compliant-body oberver An alternative to the rigid-body oberver i to ue a model that include the motor, load, and the equivalent, compliant, vico-elatic coupling. Here, the reonant model from Fig. 2 i coded within the oberver, a hown in Fig. 0. P F K OD ( K OP K OI /) J M J L K SO b S A L V L P L Fig. 0. Compliant-body oberver The principle of the compliant-body oberver are imilar to thoe of the rigid-body oberver. Thi oberver alo can oberve motor velocity and acceleration ( and ) and load velocity (V L ). Oberver error An oberver can be evaluated by how well it predict the motor velocity in the preence of a torque diturbance. For example, the error of oberver velocity, -, a a function of torque diturbance i hown in Fig. for the rigidbody oberver. The error will be low at low frequency becaue of the integral term (K OI ) and at high frequency becaue the inertia reduce the effect of the diturbance at low frequency. The error will be larget in the midrange frequencie. - T D Nm-ec rad 0 0. 0.0 0.00 2 Hz 0 Hz 00 Hz 500 Hz Fig.. Frequency repone of oberved velocity error v. diturbance torque IV. Oberver-Baed, Anti-Reonance Method Thi ection will dicu anti-reonance method baed on uing one or more oberved ignal in addition to the motor feedback device. Note that a related method ue oberved torque diturbance to reduce vibration [8,9]. Acceleration feedback. Acceleration feedback effectively increae the motor inertia [5, 6, 7, 0, ]. It conceptual implementation for the reonant load i hown in Fig. 2. By combining the forward and feedback path, it can be een that the effective motor inertia increae to ( K A ) x J M. Increaing phyical inertia i a well-known method of reducing enitivity to mechanical reonance. Acceleration feedback produce imilar benefit without the negative of phyical motor ma uch a increaed weight and ize and reduced peak acceleration. K A 2 J M J L 2 where: J L 2 b S K S J P 2 b S K S J M J L J P = J M J L Fig. 2. Acceleration feedback Acceleration feedback i implemented by adding to the current command a term proportional to oberved acceleration: I C -= K A x x J M / K T (8) where I C i the current command and K T i the motor torque contant. Quantization noie in the oberved acceleration and phae lag in the current regulator limit how much acceleration feedback i practical. In the experiment run for thi paper, value of K A greater than 2.5 caued intability. An alternative to uing an oberved acceleration ignal i to meaure average acceleration by double differentiating poition. Thi i inferior to the oberver becaue differentiation maximize quantization noie and induce phae lag. In
thee experiment, the oberved acceleration ignal allowed about twice a much acceleration feedback (about double K A ) a wa allowed uing average acceleration. Another way of uing acceleration feedback i to reduce motor inertia to zero by etting K A = - [2]. Thi reduce J P in Fig. 2 to zero and thu eliminate the ocillatory behavior. Thi method ha been oberved to lack robut operation, for example, when the load experience tiction [3]. Here, the apparent load inertia become infinite, and the PI controller, having had the motor inertia removed, i driving a pring; uch a tructure i untable. Alo, the method doe not work well when there i ignificant phae lag in the acceleration ignal. Neither the model nor the phyical tet etup were able to function with K A = - uing oberved or average acceleration ignal. Oberver filtering Oberver filtering here refer to the ue of the oberver to filter high-frequency ignal from the encoder, filling in the miing information with the electromagnetic torque ignal (7). Thi i uperior to ordinary low-pa filter ince it hould yield zero phae lag in the oberved velocity at lower frequencie and thu ha le effect on loop tability. Active reonance damping Active reonance damping add a torque in proportion to the difference of motor and load oberved peed T C = ( - V L ) b ADO (9) Active damping increae the effective phyical damping, b, imilar to the way acceleration feedback increae effective inertia [4]. Active damping i well known to cure reonance when a phyical enor i placed on the load. The quetion addreed here i whether the compliant-body oberver can be ued to provide load and motor velocity allowing ue of active damping without an additional enor. Center-of-ma control Center of ma control ue the compliant-body oberver to provide motor and load velocity. The velocity of the center of ma i then V COM = JM x JL x V L (0) Uing V COM reduce enitivity to reonance between motor and load becaue during uch reonance, the center-of-ma doe not move. Center-of-ma control i commonly employed with eparate enor. The difficulty in uing COM control i that, with a ingle actuator, it i detabilizing. In fact, (0) i imilar to negative (detabilizing) active damping (9). V. EXPERIMENTAL RESULTS Tet ytem In order to tet the reonant load control alternative dicued in thi paper, a phyical ytem wa contructed uing a motor driving a load through a compliant coupling. The controller wa a combination of a PC connected to a Kollmorgen ServoStar CE-03 amplifier configured a a torque (current) drive. The interface card wa a Servo-to-go Model 2. The control algorithm were coded in the C programming language uing floating point math. They executed every 250 usec. A ingle program ran both oberver imultaneouly and all method could be run in parallel. The motor wa elected a a Kollmorgen MT304A with a K T = 0.985 Nm/A-rm. The feedback device wa a ineencoder configured for a reolution of 0 6 count/rev. The compliant coupling wa a teel rod 4mm in diameter and 85 cm long (about 80 cm expoed between inertial load). Inertia on both ide of the rod were elected to have a 2: loadmotor inertia ratio a i common in indutry, and a reonant frequency of about 00 Hz. The compliance of the rod wa calculated a 372 Nm/rad. Given (2), J M = 0.004 kg-m 2 and J L = 0.0028 kg-m 2. A block diagram i hown in Fig. 3 and a photograph i hown in Fig. 4. PC Interface card J L =0.0026 kg-m 2 J L2 =0.00053 kg-m 2 85 cm rod (5 mm dia) (80 cm between inertia) K S = 372 Nm/rad b S ~ 0.008 Nm-ec/rad Analog command (0 V = 9 A-rm) Encoder feedback (0 6 count/rev) 2.5 cm coupling J M2 =0.0055 kg-m 2 J M =0.000252 kg-m 2 CE-03 3Amp Torque Drive Power lead Feedback lead MT304A Motor Sine enc. Motor data: J ROTOR =0.00008 kg-m 2 K T =0.985 Nm/A-rm 2048 Line encoder, 256x interp. Fig. 3. Tet ytem chematic block diagram Fig. 4. Tet ytem photograph The inertia of the motor rotor i 0.00008 kg-m 2. In order to reach the target of 0.004 kg-m 2, inertia had to be added to the motor ide of the teel rod. Uing tandard inertia load available, the final value of J L wa 0.0033 and J M, including the added inertia, wa 0.0088 kg-m 2. One difficulty that had be overcome wa the large mimatch from the rotor to the ret of the motor-ide inertia; thi caued high frequency reonance (>000 Hz) becaue of the coupling between rod and motor haft. To reduce thi problem, an
inertial load of 0.000252 kg-m 2 wa added directly to the motor haft. A reonance of 900 Hz till had to be dealt with in addition to the primary reonance of 00 Hz under tudy. Such a condition i not uncommon in indutrial application, uch a when a coupling ha ignificant inertia o that a high frequency reonance exit between the motor and coupling in addition to the lower-frequency reonance between motor and load. Finally, b, the cro-coupled vicou damping wa meaured. The method ued wa to mount the inertial wheel and, with the drive diabled, excite the reonance uing a hammer and monitor the velocity repone. Uing the oberved time contant (τ ~ 0.256 ec) and (), b wa calculated a approximately 0.008 Nm-ec/rad. In addition, a imulation program wa built baed on the ame topology a the tet ytem. The imulation wa written in ModelQ, a time-domain imulation program that provided both time- and frequency-domain analyi. Evaluation Seven method were evaluated. The firt phae of the evaluation wa to determine if a method made ignificant improvement to ytem tability. Thoe method that did were evaluated for improvement of command repone and dynamic tiffne. Alo, the load inertia were moved about 5 cm (20%) to change the reonant frequency by about 0%, according to (2) to ee if thi change would caue intability. Baeline ytem The baeline ytem ued low-pa filtering only to remove the 900 Hz reonance from between the motor and the added motor-ide inertia. Thi required a 500 Hz filter (ζ =.0). The velocity proportional gain (K VP ) wa et to 0.42 A-ec/rad and K VI to 60 rad/ec; thee are aggreive gain. The tep repone of the phyical ytem i hown in Fig. 5. All other ytem will be tuned with imilarly aggreive gain to allow ide-by-ide comparion of the different method. Fig. 5. Step motor velocity repone of the reonant load ytem with low pa filtering The model, which include tool for frequency domain analyi, how thi ytem to have a bandwidth of about 22 Hz. The dynamic tiffne, T D /V E, wa evaluated at 2 Hz a 0.22 Nm-ec/rad. Low-pa filter The low-pa filter wa ineffective at helping the 00 Hz reonance. Thi i becaue the filter bandwidth had to be reduced o far below the 00 Hz reonant frequency to be effective that it detabilized the loop forcing ervo gain lower. The low-pa filter wa not evaluated further. Notch filter The notch filter wa added to the control loop. The center frequency wa et experimentally to 94 Hz with the damping ratio et to 0.4. The 500 Hz low-pa filter remained to improve the 900 Hz reonance. The notch filter allowed K VP to be raied to 0.7 A-ec/rad (K VI remained at 60 rad/ec) providing 32 Hz bandwidth and dynamic tiffne at 2 Hz of 0.4 Nm-ec/red. The tep repone for the notch filter i hown in Fig. 6. Fig. 6. Step motor velocity repone of the reonant load ytem with a notch filter Bi-quad filter Next the bi-quad filter wa configured uing the following etting determined experimentally: F N = 94 Hz ζ N = 0.006 F D = 66 Hz ζ D = 0.0037 Thee value were bet found at removing the impact of the reonating (bi-quad) term in (). K VP wa raied to.0, allowing the highet bandwidth of any of the method (47 Hz) and high dynamic tiffne at 2 Hz (0.47 Nm-ec/rad). A expected the bi-quad method wa the mot enitive to the placement of the load inertia wheel. When they were moved 5 cm cloer to the motor, the ytem became untable. Thi wa the only method to demontrate thi behavior. The bi-quad alo controlled the load poorly, a expected. While there wa no feedback device placed on the load, it could be oberved that the load ocillated more with the biquad than with any other method, although the tability of the motor wa approximately equivalent to the other method. The motor tep repone of the bi-quad i hown in Fig. 7. Acceleration feedback Acceleration feedback wa implemented uing oberved acceleration from the rigid-body oberver. The acceleration ignal from the compliant-body oberver wa not a effective a from the rigid body. Average acceleration (double differentiating poition) wa alo le effective. The rigid-body oberver wa configured with the Eigenvalue of 200 Hz, well above the 00 Hz reonance. Uing nominal value for motor inertia ( JM = J M, Fig. 9) upported an acceleration feedback gain of K A = 2.0. Acceleration feedback, becaue of it high-
frequency gain, excited the 900 Hz reonance more and o required the low-pa filter to be lowered to 200 Hz. Even o, K VP could be raied to 0.85 allowing much higher tiffne (0.45 Nm-ec/rad at 2 Hz) and lightly higher bandwidth than the baeline ytem (25 Hz v. 22 Hz). Fig. 7. Step motor velocity repone of the reonant load ytem with bi-quad filtering It wa determined by experimentation that lowering the oberver inertia from the nominal value of 0.00875 to 0.00085 kg-m 2 allow ubtantial improvement. Here K A could be raied to 2.5 and K VP could be raied to.2. Thi ytem had the highet tiffne (0.63 Nm-ec/rad at 2 Hz, about three time tiffer than the baeline) and a bandwidth of 37 Hz which wa econd only to the bi-quad filter method. The oberver-baed method wa le enitive to variation in the load than the bi-quad; when the load wa moved 5 cm, the ytem remained table. Fig. 8. Step motor velocity repone of the reonant load ytem with acceleration feedback and JM = 0.00875 kg-m 2 Oberver filtering Oberver filtering did not work well for thi problem, probably becaue the reonant frequency wa too low for the method. Oberver filtering can help cure reonance when the Eigen value of the oberver are placed well below the reonant frequency. For thi problem, uch placement wa impractical. Oberver filtering work by relying on the commanded current to etimate the poition at frequencie above the oberver Eigenvalue. Thi aid command repone and loop tability, but it doe not aid dynamic tiffne. When the Eigenvalue were placed low enough for oberver filtering to help reonance (about 25-60 Hz), the tiffne of the ytem in thoe frequencie uffered greatly. Limited experimentation with oberver filtering for high-frequency reonance indicate that the method may be promiing in that cae. However, it wa not evaluated further for the 00 Hz reonance. Active reonance damping Active reonance damping i known to work well when two enor are ued, one for the motor and the other on the load. The experiment here invetigated whether active reonance damping could be ued baed on the oberved motor and load peed from the compliant oberver. The tet reult howed little improvement of reonance propertie when uing active reonance damping. It i felt that the exceedingly low damping ratio of the phyical ytem may have played a ignificant roll in the experiment. The enitivity to thi parameter i known to be extreme when the damping i very low. Center-of-ma control Center-of-ma control, like active reonance damping, i well known to work with phyical enor. A dicued above, it allow ocillatory motion on the load, but can cure loop intability becaue the center-of-ma doe not produce net movement in the preence of reonance. In the experiment run for thi paper in both the model and on the phyical ytem, center-of-ma control did allow higher value of K VP, but the motion wa ocillatory and the reult were judged unacceptable for thi problem. Dynamic Stiffne Dynamic tiffne of the different method wa evaluated uing the model with gain determined on the actual ytem. The low-frequency dynamic tiffne i determined by the product of K VI and K VP, [5,6,0]. Fig. 9 how that the biquad provided more improvement than the notch; a expected the improvement wa in proportion to K VP (K VI wa contant for all cae). T D Nm-ec rad 00 0 0. 0.00 2 Hz Bi-quad Baeline Notch (middle) 0 Hz 00 Hz Fig. 9. Dynamic tiffne comparion for filtering method Dynamic tiffne for acceleration feedback i hown in Fig. 20. It ha the greatet improvement over the baeline becaue thi method allowed the highet value of K VP. Acceleration feedback alo wa the bet method at maintaining high tiffne near the reonant frequency.
T D Nm-ec rad 00 0 Acc. fb. 0. Baeline 0.00 2 Hz 0 Hz 00 Hz Fig. 20. Dynamic tiffne of the reonant ytem when uing acceleration feedback VI. CONCLUSIONS Thi paper evaluated even method of dealing with a lightly-damped 00 Hz reonance relying on the motor encoder a the ole motion feedback enor. The tet ytem had two reonant frequencie, one at 00 Hz and one at about 900 Hz. A low-pa filter wa employed to cure the 900 Hz reonance for all method including the baeline. Three method were een to be effective on the tet ytem: the notch filter, the bi-quad filter, and rigid-body oberver-baed acceleration feedback. Each raied the ytem bandwidth and dynamic tiffne above the baeline ytem. The bi-quad filter wa the mot effective at raiing bandwidth; acceleration feedback wa mot effective at increaing dynamic tiffne. Table ummarize the reult. Note that Acc fb # ue the nominal value for the model inertia (JM) while Acc fb #2 ue about half the nominal value. The bi-quad filter wa the mot enitive to load change. It wa the only method that became untable when the load inertia were moved 5 cm toward the motor. It alo produced the mot ocillatory motion on the load. Four of the method (low-pa filter, oberver filtering, active reonance damping, and center-of-ma control) did not work well on the tet ytem. Low-pa filtering will and oberver filtering hould work on higher frequency reonance. Active damping and center-of-ma control work with phyical enor but implementation uing the compliant oberver did not prove to be effective for thi tet ytem. VII. ACKNOWLEDGMENTS The author wih to acknowledge the upport and motivation provided by Kollmorgen Corporation and by the Wiconin Electric Machine and Power Electronic Conortium (WEMPEC) of the Univerity of Wiconin-Madion. Table. Comparion of anti-reonance control method Bae Notch Biquad Acc fb # Acc fb #2 LPF (Hz) 500 500 500 200 200 K A 2.0 2.5 M J (x 0-3.875 0.85 kg-m 2 ) max K VP 0.42 0.7.0 0.85.2 (A-ec) K VI (ec - ) 60 60 60 60 60 BW 22 Hz 32 Hz 47 Hz 25 Hz 37 Hz Dyn tiff at 2Hz Nm-ec/ rad 0.22 0.4 0.47 0.45 0.63 VIII. REFERENCES. G. Elli and R.D. Lorenz, "Comparion of Motion Control Loop for Indutrial Application," Proc. of IEEE IAS (Phoenix), 999, pp. 2599-2605. 2. G. Elli, Control Sytem Deign Guide (2 nd Ed.) Academic Pre, 2000. 3. S. Vukoavic and M. Stojic, "Suppreion of Torional Ocillation in a High-Performance Speed Servo Drive," IEEE Tran. on Ind. Elec., Vol 45, No, Feb 998, pp. 08-7. 4. P. Schmidt and T. Rehm, Notch filter tuning for reonant frequency reduction in dual inertia ytem, Proc. of IEEE IAS, Oct. 3-7, 999, Phoenix, pp. 730-734. 5. R.D. Lorenz, New drive control algorithm (tate control, oberver, elf-ening, fuzzy logic, neural net), Proc. of PCIM Conf., Sept. 3-6, 996, La Vega, NV. 6. R.D. Lorenz, Modern control of drive, invited plenary paper for COBEP97, Belo Horizonte MG, Brazil, Dec 2-5, 997, pp. 45-54. 7. P.B. Schmidt and R.D. Lorenz, "Deign Principle and Implementation of Acceleration Feedback to Improve Performance of DC Drive", in IEEE Tran. on Ind. Appl., May/June 992, pp. 594-599. 8. Y.M. Lee, J.K. Kang and S.K. Sul, Acceleration feedback control trategy for improving riding quality of elevator ytem, Proc. of IEEE IAS (Phoenix), 999, pp. 375-379. 9. R. Dhaouadi, K. Kubo, and M. Tobie, Analyi and compenation of peed drive ytem with torional load, IEEE Tran. on Ind. Appl. Vol 30, No 3, May/June 994, pp 760-766. 0. R.D. Lorenz, T.A. Lipo and D.W. Novotny, "Motion Control with Induction Motor," in IEEE Proceeding Special Iue on Power Electronic and Motion Control, Augut, 994, pp. 25-240.. J.K. Kang and S.K. Sul, Vertical-vibration control of elevator uing etimated car acceleration feedback compenation, IEEE Tran. on Ind. Elec., Vol. 47, No., Feb 2000, pp 9-99. 2. Welch, R.H., Mechanical Reonance in a Cloed-Loop Servo Sytem: Problem and Solution, Tutorial from Welch Enterprie, Oakdale, MN. 3. G.W. Younkin, W.D. McGlaon, and R.D. Lorenz, Conideration for low-inertia AC drive in machine tool axi ervo application, IEEE Tran. on Ind. Appl. Vol 27, No 2, March/April 99, pp. 262-268. 4. R.D. Lorenz, and M.O. Luca, "Synthei of State Variable Motion Conroller for High Performance Field Oriented Induction Machine Drive, in Proc. of IEEE, IAS Conf, 986, pp. 80-85.