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Journal of Dynamic Systems, Measurement, and Control | Volume 129 | Issue 2 | Technical Brief
TECHNICAL BRIEFS

Comparison of EKBF-based and Classical Friction Compensation

[+] Author and Article Information
Ashok Ramasubramanian1

Thayer School of Engineering, Dartmouth College, Hanover, NH 03755ashokr@alum.dartmouth.org

Laura R. Ray

Thayer School of Engineering, Dartmouth College, Hanover, NH 03755Laura.Ray@dartmouth.edu

Note that the wk are not injected into the system in the manner persistent excitation is injected in some adaptive methods (e.g., (4)).

1

Corresponding author.

J. Dyn. Sys., Meas., Control 129(2), 236-242 (Jun 23, 2006) (7 pages) doi:10.1115/1.2431817 History: Received October 18, 2005; Revised June 23, 2006
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In servo control, traditionally, models that attempt to capture the friction-velocity curve and interactions at contacting surfaces have been used to compensate for friction-introduced tracking errors. Recently, however, extended Kalman-Bucy filter (EKBF)-based approaches that do not use a phenomenological or structured model for friction have been proposed. In addition to being cast as a friction estimator, the EKBF can also be used to provide parameter adaptation for simple friction models. In this paper, a traditional motor-driven inertia experiment is used to demonstrate the usefulness of EKBF in friction compensation. In addition, a numerical simulation is used to test the robustness of the new methods to normal force variations. Using root mean square position tracking error as the performance metric, comparisons to traditional model-based approaches are provided.
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Copyright © 2007 by American Society of Mechanical Engineers
Topics: Friction
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References

1
Dahl, P., 1977, “Measurement of Solid Friction Parameters of Ball Bearings,” "Proc. of 6th Annual Symposium on Incremental Motion Control Systems and Devices", Urbana, IL, Incremental Motion Control Systems Society, Urbana, IL, pp. 49–60.
2
Walrath, C. D., 1984, “Adaptive Bearing Friction Compensation Based on Recent Knowledge of Dynamic Friction,” Automatica  [CrossRef], 20 , pp. 717–727.
3
Leonard, N. E., and Krishnaprasad, P. S., 1992, “Adaptive Friction Compensation for Bi-Directional Low Velocity Position Tracking,” "Proc. of Conference on Decision and Control", Tucson, IEEE, Piscataway, NJ, pp. 267–273.
4
Misovec, K. M., and Annaswamy, A. M., 1999, “Friction Compensation Using Adaptive Non-Linear Control With Persistent Excitation,” Int. J. Control, 72 , pp. 457–479.
5
Canudas de Wit, C., and Lischinsky, P., 1997, “Adaptive Friction Compensation With Partially Known Dynamic Friction Model,” Int. J. Adapt. Control Signal Process.  [CrossRef], 11 , pp. 65–80.
6
Bliman, P. A. J., 1992, “Mathematical Study of the Dahl’s Friction Model,” Eur. J. Mech. A/Solids, 11 , pp. 835–848.
7
Armstrong-Hélouvry, B., Dupont, P., and Canudas de Wit, C., 1994, “A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction,” Automatica  [CrossRef], 30 , pp. 1083–1138.
8
Canudas de Wit, C., Olsson, H., Astrom, K. J., and Lischinsky, P., 1995, “A New Model for Control of Systems With Friction,” IEEE Trans. Autom. Control, 40 , pp. 419–425.
9
Lischinsky, P., Canudas de Wit, C., and Morel, G., 1999, “Friction Compensation for an Industrial Hydraulic Robot,” IEEE Control Syst. Mag.  [CrossRef], 19 , pp. 25–32.
10
Sri-Jayantha, M., and Stengel, R. F., 1988, “Determination of Nonlinear Aerodynamic Coefficients Using the Estimation-Before-Modeling Method,” J. Aircr., 25 , pp. 796–804.
11
Ray, L. R., 1997, “Nonlinear Tire Force Estimation and Road Friction Identification: Simulation and Experiments,” Automatica  [CrossRef], 33 , pp. 1819–1833.
12
Ray, L. R., Ramasubramanian, A., and Townsend, J. R., 2001, “Adaptive Friction Compensation Using Extended Kalman-Bucy Filter Friction Estimation,” Control Eng. Pract.  [CrossRef], 9 , pp. 169–179.
13
Ramasubramanian, A., and Ray, L. R., 2003, “Friction Cancellation in Flexible Systems Using Extended Kalman-Bucy Filtering,” "Proc. of American Control Conference", Denver, IEEE, Piscataway, NJ, pp. 1062–1067.
14
Feemster, M., Vedagarbha, P., Dawson, D. M., and Haste, D., 1998, “Adaptive Control Techniques for Friction Compensation,” "Proceedings of the American Control Conference". Philadelphia, IEEE, Piscataway, NJ, pp. 1488–1492.
15
Linse, D. J., and Stengel, R. F., 1993, “Identification of Aerodynamic Coefficients Using Computational Neural Networks,” J. Guid. Control Dyn., 16 , pp. 1018–1025.
16
Amin, J., Friedland, B., and Harnoy, A., 1997, “Implementation for a Friction Estimation and Compensation Technique,” IEEE Control Syst. Mag.  [CrossRef], 17 , pp. 71–76.
17
Teolis, C., 1997, Robust Adaptive Control of Systems with Nonlinearities (Section 6-ATB1000), Tech. Report No. DAAE30-96-C-0063, Techno-Sciences, Inc., Lanham, MD.
18
Tao, G., 1998, “Friction Compensation in the Presence of Flexibility,” "Proc. of American Control Conference", Philadelphia, IEEE, Piscataway, NJ, pp. 2128–2132.
19
Ray, L. R., Townsend, J. R., and Ramasubramanian, A., 2001, “Optimal Filtering and Bayesian Detection for Friction-Based Diagnostics on Machines,” ISA Trans., 40 , pp. 207–221.
20
Ramasubramanian, A., and Ray, L. R., 2001, “Stability and Performance Analysis for Non-Model-Based Friction Estimators,” "Proc. of Conference on Decision and Control", Orlando, IEEE, Piscataway, NJ, pp. 2929–2935.

Figures

Grahic Jump Location
+Results from the simulation study: Actual friction torque (solid line) and estimated friction torque (dotted line): (a) Adaptive LuGre model, (b) Adaptive Dahl model. Arrows in (a) indicate high-frequency content in the friction estimate.
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Results from the simulation study: Actual friction torque (solid line) and estimated friction torque (dotted line): (a) Adaptive LuGre model, (b) Adaptive Dahl model. Arrows in (a) indicate high-frequency content in the friction estimate.
Figure 4

Results from the simulation study: Actual friction torque (solid line) and estimated friction torque (dotted line): (a) Adaptive LuGre model, (b) Adaptive Dahl model. Arrows in (a) indicate high-frequency content in the friction estimate.

Grahic Jump Location
+Block diagram of a position control system with friction compensation
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Block diagram of a position control system with friction compensation
Figure 1

Block diagram of a position control system with friction compensation

Grahic Jump Location
+Schematic of experimental and simulation apparatus (not to scale): The experimental apparatus (a) consists of a motor driven disk under an optional normal load, which contacts the disk through an aluminum rider mounted at the end of an I-beam. The simulation apparatus (b) features two linked gear wheels. Friction-velocity curve for the experimental apparatus (a′) and the simulated apparatus (b′) are also shown.
View Large  |  Save Figure  |  Download Slide (.ppt)
Schematic of experimental and simulation apparatus (not to scale): The experimental apparatus (a) consists of a motor driven disk under an optional normal load, which contacts the disk through an aluminum rider mounted at the end of an I-beam. The simulation apparatus (b) features two linked gear wheels. Friction-velocity curve for the experimental apparatus (a′) and the simulated apparatus (b′) are also shown.
Figure 2

Schematic of experimental and simulation apparatus (not to scale): The experimental apparatus (a) consists of a motor driven disk under an optional normal load, which contacts the disk through an aluminum rider mounted at the end of an I-beam. The simulation apparatus (b) features two linked gear wheels. Friction-velocity curve for the experimental apparatus (a′) and the simulated apparatus (b′) are also shown.

Grahic Jump Location
+Results from the experimental study: rms error data points from three trials for each of the four compensators tested. The first column of plots (a)-(c) contain data from the unloaded condition and the second column of plots (a′)‐(c′) contain data from the loaded condition. The following abbreviations are used: PID=baseline PID compensator (no friction compensation), DM=nonadaptive Dahl model, ADM=adaptive Dahl model, KF=Kalman filter estimator.
View Large  |  Save Figure  |  Download Slide (.ppt)
Results from the experimental study: rms error data points from three trials for each of the four compensators tested. The first column of plots (a)-(c) contain data from the unloaded condition and the second column of plots (a′)‐(c′) contain data from the loaded condition. The following abbreviations are used: PID=baseline PID compensator (no friction compensation), DM=nonadaptive Dahl model, ADM=adaptive Dahl model, KF=Kalman filter estimator.
Figure 3

Results from the experimental study: rms error data points from three trials for each of the four compensators tested. The first column of plots (a)-(c) contain data from the unloaded condition and the second column of plots (a′)‐(c′) contain data from the loaded condition. The following abbreviations are used: PID=baseline PID compensator (no friction compensation), DM=nonadaptive Dahl model, ADM=adaptive Dahl model, KF=Kalman filter estimator.

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