Control of Mechanical Systems in the Presence of Friction Effects
Friction is a natural occurrence that affects almost all objects in motion. Extensive research attempts to develop models that accurately predict the behavior of friction. Frictional effects at moderate velocities are somewhat predictable, however the effects of friction at low velocities are difficult to model. Control strategies attempting to compensate for the friction effects require a suitable model that captures the behavior of friction throughout the entire range of velocity.
Modeling of Friction:
The performance of model based friction compensation control strategies is ultimately limited by the ability of the model to accurately describe the dynamics of the physical system. Recently, researchers have developed dynamic models for friction in an attempt to better predict friction phenomenon at low velocities (i.e., stick slip, pre-sliding, frictional memory etc.). However, these more complex dynamic friction models typically require more sophisticated/innovative control designs as compared to those controllers based on simpler static friction models.
The Lu Gre friction model attempts to capture the stick slip phenomenon of friction at low velocities. This dynamic model visualizes two rigid bodies making contact through elastic bristles. Tangential forces applied to the rigid bodies will cause these bristles to deflect and eventually slip simulating familiar stick slip motion observed during low velocity operations. As seen from the above figure, this dynamic model exhibits the capability of capturing such low velocity effects as frictional memory. However, this somewhat more sophisticated model for friction complicates the control design by injecting an unmeasurable state into the system equations.
The somewhat less complex Static model of friction is constructed to predict the behavior of four observed frictional effects (i.e, viscous, coulomb, static, and Stribeck frictional effects). The Stribeck effect is modeled as a nonlinear velocity dependent function with an unknown constant parameter that does not appear linearly in the model. The advantage of the Static model for friction is manifested by the ability to develop a straight forward control design (i.e., we are not concerned with observer construction for any unmeasurable states).
Research work based on a Dynamic Friction Model:
Research work based on a Static Friction Model: