Real-Time Identification of Sliding Friction Using LabVIEW FPGA

Transcription

1 Real-Time Identification of Sliding Friction Uing LabVIEW FPGA M. Laine Mear, Jeannie S. Falcon, IEEE, and Thoma R. Kurfe, IEEE Abtract Friction i preent in all mechanical ytem, and can greatly affect ytem tability and control in preciion motion application. In thi paper, we preent application of a frictional model to trajectory planning of a part centering ytem with Real-Time identification of model parameter through ytem force and poition repone. Thi identification i carried out uing LabVIEW Motion Control oftware and Digital Signal Proceing (DSP) and Field-Programmable Gate Array (FPGA) hardware. A comparion of hardware performance for force meaurement i alo made. M I. INTRODUCTION OTION control of frictional ytem ha been extenively tudied due to inherent difficultie of modeling and compenation of nonlinear frictional effect. A number of friction model and compenation cheme have been developed to decribe thee effect in the context of poitioning [1], [3], [6]. Recently, a greater focu on liding dynamic and poitioning by liding ha been tudied a a lower cot and more flexible actuation alternative to traditional robotic poitioning [4], [5], [7]. Iue of frictional controller deign and appropriate election of the underlying friction model are important. Equally important i the undertanding that friction i a time-varying phenomenon, and can change dramatically with wear or introduction of contaminant to the ytem. It i therefore neceary to be able to continuouly quantify the frictional tate of a ytem to provide optimal motion control. Thi work preent a real-time friction identification cheme for liding, implemented through a dedicated realtime motion control ytem utilizing DSP for motion control and FPGA for force data collection and analyi. II. SYSTEM MODEL DEVELOPMENT The firt activity i to undertand the ytem dynamic repone through creation of a ytem model. A. Prototype Application The application under tudy i ring centering on a rotating Manucript received March 24, 26. Thi work wa upported in part by grant and tet equipment from National Intrument Corporation and The Timken Company. M. L. Mear i a Ph.D. Candidate with Georgia Intitute of Technology, Atlanta, GA 3332 USA. ( ; lmear@pmrc.marc.gatech.edu). J. S. Falcon i a Senior Engineer in the Control and Simulation department of National Intrument Corporation, Autin, TX USA (jeannie.falcon@ni.com). T. R. Kurfe i BMW Chair in Manufacturing and Director of the Campbell Graduate Engineering Center, Clemon Univerity, Clemon, SC USA (kurfe@clemon.edu). plate through contant-velocity actuation by a puhing element. The ytem i hown in Figure II.1: Fig. II.1 - Prototype Sytem Component The meaurement probe command the linear lide ervo following, and alo gather data for characterization of the ring urface. The data are modeled through a leat-quare technique, and then parameter uch a offet ditance and direction are extracted from the model. Thee parameter are directed to a motion control ubprogram that actuate the lide at contant velocity in uch a manner to caue the puh tip to move the part geometric center in line with the center of rotation. A the part i actuated, force data i collected from a piezoelectric enor in the puh tip. The target tolerance for alignment of center i 2.5 m. The ytem i implemented on a National Intrument PCI with Extenion for Intrumentation (PXI) Real-Time control ytem, integrating a PXI-8187RT controller, PXI- 735RT motion control module, and a PXI-7831R FPGA module. The PXI-735RT ue both an onboard Motorola floating point proceor and an onboard Digital Signal Proceor (DSP) for 8-axi motion control (3 utilized in thi application). The FPGA i utilized for force enor data acquiition due to the high available ampling rate, and i programmed uing the LabVIEW FPGA oftware module. All hardware component are integrated in a common PXI chai. B. Frictional Modeling The liding ytem i idealized a a imple econd-order relative model a hown in Figure II.2:

2 Force Repone Plot Contant- Damped 2. Force [N] Peak Force Figure II.2 - Idealized Sytem with Friction Friction i modeled uing the vicou Coulomb form, which incorporate eparate decription of frictional force depending on velocity tate of the ma. The friction i decribed by [1]: kfn + kvv, v F () t = F, v = and F < F FS, otherwie k kinetic friction coefficient FN part normal force Fe applied force F tatic friction force = F e e S S N The overall ytem i decribed by the governing equation ( max (,)) max (,) mx + b y x ( ) () + k y x = F t Thi model account for unidirectionality of the pring and damping idealized element in the puhing application. Model parameter are elected and the model validated for a clean, dry ytem. Modeled poition and force repone plot are hown in Figure II.3 and Figure II.4 repectively. Poition [m] Poition Repone Plot Contant- Damped Free-Sliding Ditance Time [] Modeled ring abolute poition [m] Slide abolute poition [m] Fig. II.3 - Poition Repone, m=18.9 kg, v=3 mm/min (1) (2) Time [] Force, lide to ring [N] Fig. II.4 - Force Repone, m=18.9 kg, v=3 mm/min For each plot, a characteritic dimenion i defined, which i to be ued in the ubequent friction predictor model. Free-liding ditance d i defined for poition repone a the ditance the part travel from lo of contact with the actuator until coming to a top under the influence of friction. For force repone, the peak force F p i defined a the maximum force oberved over the actuation. C. Friction Identification The preceding friction model i contructed uing tatic friction parameter derived and validated from dry liding experiment. However, in practice ytem frictional tate i eldom contant. Wear of liding urface, tranport of olid and liquid contaminant into and out of the ytem, and variation in the condition of part being centered all introduce variation into the friction model. To capture thee effect, a real-time identification cheme of underlying friction model parameter i decribed. Identification of the primary friction model parameter i treated in [2] uing a log decrement method. In thi work, identification i undertaken through inverion of the general dynamic model with repect to peak force achieved per actuation and to free-liding ditance achieved. In thi way, a ingle actuation can provide a friction etimate from eparate ource. 1) Force Model The centering prototype machine include an analog piezoelectric force enor of range ±446 N and enitivity of 11.2 mv/n. During actuation, force i meaured in real time. Oberved peak force for a given et of actuation condition (i.e., actuation velocity, part attribute, meaured friction coefficient) i ued to validate the initial ytem model given by (2). Thi model i then ued to generate a family of curve relating expected peak force F p to actuation velocity and tatic friction coefficient. For purpoe of implifying the model, the kinematic friction coefficient k to aumed to be 75% of the tatic coefficient, a relationhip oberved over the velocity range teted. The curve family generated by thi method for a part of 18.9 kg i given in Figure II.5.

3 Modeled Peak Force [N] Modeled Peak Force v. over [mm/min], m = 18.9 kg Fig. II.5 - Peak Force Model The curve are fit to a linear model in v and : Fp = Cvv+ C (3) Coefficient of thi model are computed through a leat quare fitting routine and the model inverted to determine an expreion for the tatic friction coefficient: Fp.529v = F = meaured peak force N p mm v = actuation velocity min [ ] 2) Ditance Model The free liding ditance predicted by (2) i validated through experiment. The model i then ued to generate a family of curve relating free-liding ditance d to actuation velocity v and tatic coefficient of friction. The curve family i hown in Figure II.6 for an 18.9 kg part. Free-Sliding Ditance [m] Modeled Free Sliding Ditance v. over [mm/min], m = 18.9 kg Fig. II.6 - Free-Sliding Ditance Model The model i reduced to a econd-order parabolic form, with coefficient aumed of the power form in velocity: (4) ( ) 2 k1 = Cv 1 k2 = C2v d d = A d A Thi model i fit to the oberved data and inverted to arrive at an expreion for prediction of the tatic friction coefficient: d.41v = v d free liding ditance m mm v lide velocity min [ ] 3) Optimal Combined Etimator The two friction predictor ource are combined through a weighting cheme proportional to the enitivity to friction model parameter at the operating point in quetion. Referring to Figure II.6, when velocity i lower (e.g., 5 mm/min), the ditance repone i inenitive to variation in the friction parameter. However, at larger actuation velocitie (> 2 mm/min), enitivity increae. For thi reaon, the derivative of the force and ditance function at the ytem operating point are ued a weight in the combined predictor. Additionally, the ditance parameter i normalized to force unit over the entire range examined: F d F * d =, force +, dit (7) F d F F d F + + d d Thi optimal combination give higher weight to the predictor with greater model enitivity to change in the friction parameter. III. IMPLEMENTATION The friction identification cheme i implemented on the ingle-actuator centering prototype. A. Force Sening Force ening i accomplihed through a piezoelectric ening element whoe output i amplified and directed to the analog input (AI) port of the FPGA PXI-7831R card mounted in the PXI real-time ytem chai. Force capture occur through FPGA AI capture a hown in Figure III.1. (5) (6)

4 IV. RESULTS A. Prediction Accuracy The prediction cheme i applied to puhing actuation and liding repone of the part hown in Figure IV.1 on a table with 3 x 1 mm carbide rail. The part i nonrotating and initially at ret. Two condition are teted: Figure III.1 - Data Acquiition Code for Force on FPGA Force i continually acquired at a rate et by the FPGA loop timer. Peak force reading i maintained for each individual actuation. The FPGA data are paed to the real time operating ytem by way of an acquiition loop a hown in Figure III.2. DRY: table and part are cleaned and dried OILY: DTE Medium oil i applied to liding urface Figure IV.1 - Sample Part Under Tet, m=18.9 kg Figure III.2 - Real-Time Force Signal Proceing The acquired force i paed to the real-time motion control loop for diplay and ue in trajectory planning. A ample trace of force over two actuation troke i hown in Figure III.3. The larget peak hown begin the econd actuation. Figure III.3 - Force Data Collection B. Ditance Sening The free-ditance utilized in the friction predictor model i quantified by a digital linear meaurement probe that create a quadrature encoder ignal with reolution of 2 nm. The probe output i captured from the point of lo of contact a read from the actuation force enor until the part ha topped liding. The probe output i directed to a digital encoder input of the DSP module. The tatic friction breakaway force i teted uing a hand gauge at low velocity and found for each condition to be DRY: =.141 OILY: =.135 1) Force Model The part i actuated over a range of contant velocitie. For each trial, the peak force i meaured and the tatic friction coefficient calculated from (4). Reult of the force predictor are hown in Table 1 for DRY condition and Table II for OILY condition. TABLE I FRICTION PREDICTOR RESULTS USING PEAK FORCE - DRY Peak Force (N) Predicted % % % % % %

5 TABLE II FRICTION PREDICTOR RESULTS USING PEAK FORCE - OILY Peak Force (N) Predicted % % % % % % Force prediction i more accurate in the dry condition. 2) Ditance Model For the actuation trial, the free-liding ditance i alo meaured uing the ditance probe. For each trial, the tatic friction coefficient i etimated by (6). Reult of the ditance predictor are given in Table III for DRY condition and Table IV for OILY condition. TABLE III FRICTION PREDICTOR RESULTS USING SLIDING DISTANCE - DRY Sliding Ditance (m) Predicted % % % % % % TABLE IV FRICTION PREDICTOR RESULTS USING SLIDING DISTANCE - OILY Sliding Ditance (m) Predicted % % % % % % A expected from Figure II.6, the ditance predictor i more accurate at higher velocitie. Thi effect i accounted for in the weighting cheme of (7). 3) Optimal Combined Etimator The etimator of (7) i applied to the force- and ditancebaed friction predictor reult. Reult of a ingle trial at v=5 mm/min are given in Table V. TABLE V WEIGHTED FRICTION PREDICTOR RESULTS, V=5 MM/MIN Condition Predicted The predictor i accurate to within approximately 5% in the wort cae. B. FPGA Performance The ampling of force uing FPGA i compared to ampling of force through the analog in (AI) port of the Digital Signal Proceor (DSP) motion control card ued for actuator control. A ingle point AI force acquiition loop i written and thread execution time monitored. 1) Force Sampling by DSP Force acquiition occur at an average execution time of 11 on the DSP hardware, equivalent to a ampling rate of 99 Hz. Additionally, if the force acquiition i run in parallel with other thread uch a motion control and data analyi, the force acquiition tak will hare proceor time and be ubject to prioritization and preemption rule. Thi ituation will tend to increae the average loop time. 2) Force Sampling by FPGA FPGA force acquiition i run in a eparate thread on the FPGA module, o i not ubject to real-time controller preemption. Average data acquiition time for a ingle AI ample loop i 4.3, equivalent to a reliable ampling rate of 2 khz when accounting for additional oftware overhead. Sample rate i improved by a factor of more than 2 by uing FPGA hardware over DSP hardware for force ampling. V. CONCLUSIONS DRY % OILY % Thi paper decribe a methodology for developing a friction prediction expreion for liding in term of oberved peak force and free-liding ditance under contant-velocity actuation. Thi methodology demontrated for a pecific part on a pecific ytem can be repeated and validated for any combination of ytem etup. Implementation i carried out uing an FPGA module configured for data collection and analyi, houed in a Real-Time controller chai. A. Friction Identification A firt-order friction predictor from oberved force and a

6 econd-order friction predictor from oberved free-liding ditance wa introduced. Additionally, a derivativeweighted combination cheme wa defined. The identification cheme predicted liding friction in the given application to within 5%. Thi friction identification methodology alo ha implication beyond ytem modeling and motion control path planning. Additionally, real-time friction identification can be ued a an element in machine diagnotic evaluation. The viion i to monitor machine health through detection of ignificant change in ytem frictional tate and to provide ubequent generation of maintenance requet or alarm condition. [7] Pehkin, M.A. and A.C. Sanderon. The Motion of a Puhed, Sliding Workpiece. IEEE Journal of Robotic and Automation, v4, n6, Dec., 1988: 569. B. FPGA Collection of force data through both DSP and FPGA ampling wa carried out and execution time of each cenario meaured. Sample rate uing FPGA not only outperformed ampling uing DSP by a factor of over 2, but alo liberated proceor reource that could be applied to other time critical tak, improving the overall effectivene of the ytem. Additionally, analog input channel on the FPGA board are independently ampled uing eparate analog to digital (A/D) converter, compared to the 8-channel ingle A/D multiplexed operation of the 735 motion control board. A future plan for ytem improvement i performing motion control tak directly on the FPGA through the LabVIEW SoftMotion module. Thi i expected to not only increae control loop ample rate, but to alo allow for exploration of alternative low-level control cheme in the centering application. ACKNOWLEDGMENT Thi reearch wa made poible by financial and equipment grant from National Intrument corporation and The Timken Company. REFERENCES [1] Åtröm, K. Control of Sytem with Friction. Technical paper. Department of Automatic Control, Lund Intitute of Technology, [2] Feeny, B. and J. Liang. A Decrement Method for the Simultaneou Etimation of Coulomb and Vicou Friction. Journal of Sound and Vibration, v195, n1, Aug, 1996: [3] Hirchorn, R.M. and G. Miller. 1998, Control of Nonlinear Sytem with Friction. IEEE Tranaction on Control Sytem Technology, v7, n5, Sep, 1999: [4] Lynch, K. Etimating the Friction Parameter of Puhed Object International Conference on Intelligent Robot and Sytem, 1993: [5] Lynch, K. and M. Maon. Stable Puhing: Mechanic, Controllability, and Planning. The International Journal of Robotic Reearch, v15, n6, Dec., 1996: [6] Olon, H., K.J. Åtröm, C. Canuda de Wit, M. Gafvert and P. Lichinky. Friction model and friction compenation. European Journal of Control, v4, n3, 1998: