A New Model for Control of Systems with Friction

A New Model for Control of Systems with Friction

1995 | de Wit, Carlos Canudas; Olsson, Henrik; Åström, Karl Johan; Lischinsky, Pablo
This paper presents a new dynamic model for friction that captures various experimental behaviors, including the Stiweb effect, hysteresis, spring-like characteristics during stiction, and varying break-away force. The model is designed to improve upon classical friction models such as Coulomb and viscous friction, which often fail to accurately describe low-velocity and zero-velocity phenomena. The authors propose a model that combines the Dahl effect (Coulomb friction with lag in force change) and arbitrary steady-state friction characteristics, including the Striebeck effect. The model is characterized by a function \( g(v) \) and parameters \( \sigma_0, \sigma_1, \sigma_2, F_C, F_S, \) and \( v_s \). The paper explores the properties of the model, such as its dissipativity and linearization in the stiction regime, and demonstrates its ability to simulate phenomena like presliding displacement, hysteresis, varying break-away force, and stick-slip motion. Additionally, the model is applied to feedback control problems, including predicting limit cycles in servo systems and designing observer-based friction compensators for position and velocity tracking. The results show that the observer error and control error asymptotically approach zero when the parameters are known. The paper concludes by discussing the potential for sensitivity studies, parameter estimation, and adaptation in future work.This paper presents a new dynamic model for friction that captures various experimental behaviors, including the Stiweb effect, hysteresis, spring-like characteristics during stiction, and varying break-away force. The model is designed to improve upon classical friction models such as Coulomb and viscous friction, which often fail to accurately describe low-velocity and zero-velocity phenomena. The authors propose a model that combines the Dahl effect (Coulomb friction with lag in force change) and arbitrary steady-state friction characteristics, including the Striebeck effect. The model is characterized by a function \( g(v) \) and parameters \( \sigma_0, \sigma_1, \sigma_2, F_C, F_S, \) and \( v_s \). The paper explores the properties of the model, such as its dissipativity and linearization in the stiction regime, and demonstrates its ability to simulate phenomena like presliding displacement, hysteresis, varying break-away force, and stick-slip motion. Additionally, the model is applied to feedback control problems, including predicting limit cycles in servo systems and designing observer-based friction compensators for position and velocity tracking. The results show that the observer error and control error asymptotically approach zero when the parameters are known. The paper concludes by discussing the potential for sensitivity studies, parameter estimation, and adaptation in future work.
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Understanding A new model for control of systems with friction