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Research Papers

Friction Hysteresis Modeling and Force Control in a Constrained Single-link Arm

[+] Author and Article Information
A. Bazaei

School of Electrical Engineering and Computer Science,  University of Newcastle, NSW 2308, Australia e-mail: Ali.Bazaei@newcastle.edu.au

M. Moallem1

Mechatronics Systems Engineering, School of Engineering Science,  Simon Fraser University, Surrey, BC, V3T 0A3, Canada e-mail: mmoallem@sfu.ca

Assuming F is linearly proportional to θ, as the encoder indicates no deflections, in the last 2.4 sec in Fig. 2, which is the steepest portion for F, the magnitude of mean angular velocity should be less that 0.072deg/2.4s=0.03degs1.

The dotted graph is obtained by inspection and assuming that the magnitudes of breakaway level and Coulomb friction are equal, the same in opposite directions of rotation, and dependent on the applied force F during the major rising or falling modes. Because of the slow motion, at each instant of time in Fig. 2, the actual friction force f is equal to u − F, with F representing the force measured by the force sensor (the thick solid line). In the first major rising mode in Fig. 2 (t [21,30] s), the beam is slowly rotating in the positive direction and the friction force is equal to its upper threshold value, denoted by Fc+, which increases almost linearly with the applied force. Hence, during the foregoing time interval, an ordinary friction model, with its upper threshold value depending on the applied force (equal to the measured values of f in Fig. 2 in the interval of t [21,30] s), should predict an end point force similar to the measured one. As the actuation input stops increasing after t = 30 s, the beam rapidly enters into a standstill period during which the end point force remains constant. Based on an ordinary friction model, the standstill period lasts until the actuation input either decreases enough to bring the friction force to the lower threshold value Fc, or increases to bring the friction again to the upper threshold. The latter happens first at t = 36 s, which justifies the horizontal dotted line during t [30,36] s. The reasoning to justify the rest of the dotted graph in Fig. 2 is similar.

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(6), 061016 (Nov 21, 2011) (9 pages) doi:10.1115/1.4004580 History: Received August 29, 2008; Accepted April 21, 2011; Published November 21, 2011; Online November 21, 2011

In this paper, we study friction characteristics of a constrained planar single-link arm in applications, where control of the end-point interaction force is required. The objective is to improve performance of a force control system by developing an adequate friction model. It is shown that hub friction increases with the applied force with the end-point force exhibiting significant hysteresis behavior. A friction model is presented for capturing these phenomena and compared with the widely used LuGre friction model. Effectiveness of the proposed model for friction compensation is further examined on an experimental force control system testbed.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 4

(a) Diagram of friction model (3) for k = 1.1 and (b) dependency of parameter k on the net-force rate

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Figure 5

Relay characteristics

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Figure 6

Simulation results of the friction model with the proposed relays and without them

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Figure 7

Effect of hysteresis and rate-dependent k parameter

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Figure 8

Examination of the LuGre friction model in predicting the hysteresis behavior of friction and comparison with the proposed friction model

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Figure 9

Schematic diagram of the control system

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Figure 10

Typical open-loop step-response of the end-point force and its approximation

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Figure 11

Details of the friction compensator block in Fig. 9

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Figure 12

Realization of the relay outputs Q1 and Q2 used in Fig. 1

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Figure 13

Details of the edge detectors used in Fig. 1

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Figure 1

(a) Demonstration of the planar single-link arm and (b) free body diagram

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Figure 2

Open-loop low-frequency response of the end-point force F (thick solid line) to a slowly varying control input u (thin solid), along with the estimation of friction term f≈u-F (dash-dot) and predicted end-point force values by ordinary models (dotted)

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Figure 3

(a) Maximum and minimum achievable end-point forces in steady-state with the rigid link and (b) estimated friction force interval Fc++Fc- in terms of end-point force F

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Figure 14

Experimental results of friction compensation by the proposed model

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