LuGre Friction Model in Simulink

A Simulink block diagram of the LuGre friction model which captures a wide variety of frictional behaviors.

The famous Lund Grenoble (LuGre) friction model, originally published in 1995, represents a milestone achievement in the control of systems with friction [1]. The LuGre model is advantageous in capturing many frictional behaviors in a compact and implementable structure, including pre-sliding hysteresis, frictional lag, varying break-away force, and stick-slip behavior. A possible disadvantage of the LuGre model is the relatively large number of parameters which must be identified through experimentation or simulation, see for example [2].

In faith to the original paper [1], I’ve structured the block diagram so that users may recreate several of the published figures using the appropriate force inputs [3]. Those figures are provided below to demonstrate the model performance for stick-slip motion (Figure 6) and pre-sliding hysteresis (Figure 2).

Enjoy!

-Kirk

Figure 6A: Graphical representation of stick-slip motion due to pulling a unit mass (1 kg) along a countersurface [1]. The mass is pulled via a spring (stiffness 2 N/m) at constant velocity (0.1 m/s). The mass exhibits stick-slip motion due to competition between friction forces and the spring force.

Figure 6B: Friction force and velocity profiles corresponding to the unit mass undergoing stick-slip motion from Figure 6A. Initially the mass is at rest and pulling the spring causes a linear increase in the static friction until the break-away force is reached, at which point the mass accelerates and Stribeck effects are observed.

Figure 2: Graphical representation of friction hysteresis in the presiding regime. A small tangential force (1.425N) is gradually applied to a mass on a countersurface which causes micro-sliding. However, upon reversing the tangential force (-1.425N), the friction force does not follow the same path but exhibits position-dependence due to adhesive interactions between opposite surface asperities.

References:

[1]. Wit, C.C.d., et al., A new model for control of systems with friction.IEEE Transactions on Automatic Control, 1995. 40(3): p. 419-425.

[2]Sun, Y.-H., T. Chen, and C. Shafai, Parameter Identification of LuGre Friction Model: Experimental Set-up Design and Measurement. 2015.

[3] Auralius Manurung (2024). LuGre friction model in MATLAB / GNU Octave (https://github.com/auralius/LuGre/releases/tag/4.0), GitHub. Retrieved February 17, 2024.