MORE slip-stick STUFF> Copying here for records

MORE slip-stick STUFF> Copying here for records _and in case anybody was interested_. I can see now that there’s no unified model. Friction is complicated and every model is flawed in one way or another but each model has its uses.
 
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics
Emerging Methodologies and Applications in Modelling
2018, Pages 11-18
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics
Chapter 1 – Friction Dynamics and Modeling
 
1.1 Introduction
Friction appears in most of mechanical systems, where there is motion or tendency for motion between two physical components because all surfaces are irregular at the microscopic level. The existence of friction could cause a steady-state error, a limit cycle, or stick-slip phenomenon at low speed in the motion control systems. As a result, it is of great interests for engineers to understand the behaviors of frictions and then design appropriate controllers to eliminate the undesirable effect of friction. In fact, friction modeling and compensation have attracted a significant interest in the control community.
 
In order to achieve high-performance control, friction dynamics need to be precisely described. Unfortunately, since friction behavior is affected by many factors such as velocity, temperature and lubrication, developing accurate friction models has been a long-standing problem, which has not been fully solved [1]. In particular, owing to the high non-linearity and non-smooth property, it is generally difficult to build a unified, simple mathematic friction model, which can cover most friction dynamics, such as Static friction, Coulomb friction and Viscous friction, etc. Several classical friction models with different components (e.g., Static friction, Coulomb friction, Viscous friction and Stribeck effect) have been developed in the literature [2]. Apart from static frictions, some dynamic friction behaviors (e.g., presliding displacement, friction lag and stick-slip motion) have been also considered in these models. Among these dynamic models, LuGre model (a dynamic model) has been widely used in the model based compensation schemes [3] since this model can cover most of friction behaviors. Modified LuGre models have been further investigated and incorporated into the control designs to eliminate the effectiveness of frictions [4,5].
 
It is noted that these classical models are generally discontinuous or piecewise continuous, making the identification of model parameters and the model based control implementation difficult. To facilitate control designs, continuousness of friction models is also an important aspect to be considered. In [6], a continuously differentiable friction model was proposed, which is suitable for high-performance continuous control design. Moreover, a new discontinuous piecewise parametric representation (DPPR) friction model was also reported in our previous work [7], which can be used for fraction identification.

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