AIM2005 - TA2-03 Proceedings of the 2005 IEEE/ASME...

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A New Continuously Differentiable Friction Model for Control Systems Design C .Makka r ,W .E .D ixon ,W .G .Sawye r ,andG .Hu Mechanical and Aerospace Engineering University of Florida, Gainesville, FL 32608 Email:cmakkar, wdixon, wgsawyer, [email protected] f .edu. Abstract — For high-performance engineering systems, model- based controllers are typically required to accommodate for the system nonlinearities. Unfortunately, developing accurate models for friction has been historically challenging. Typical models are either discontinuous and many other models are only piecewise continuous. Motivated by the fact that discontinuous and piecewise continuous friction models are problematic for the development of high-performance continuous controllers, a new model for friction is proposed in this paper. This simple continuously differentiable model represents a foundation that captures the major effects reported and discussed in friction modeling and experimentation. The proposed model is generic enough that other subtleties such as frictional anisotropy with sliding direction can be addressed by mathematically distorting this model without compromising the continuous differentiability. I. INTRODUCTION General Euler-Lagrange systems can be described by the following nonlinear dynamic model: P ( t t + Y p ( t> ˙ t ) ˙ t + J ( t )+ i ( ˙ t )= ? ( w ) = (1) In (1), P ( t ) 5 R q × q denotes the inertia matrix, Y p ( t> ˙ t ) 5 R q × q denotes the centripetal-Coriolis matrix, J ( t ) 5 R q denotes the gravity vector, i ( ˙ t ) 5 R q denotes a friction vector, ? ( w ) 5 R q represents the torque input control vector, and t ( w ) , ˙ t ( w ) , ¨ t ( w ) 5 R q denote the link position, velocity, and acceleration vectors, respectively. For high-performance engineering systems, model-based controllers [6] are typically required to accommodate for the system nonlinearities. In general, either accurate models of the inertial effects can be developed or numerous continuous adaptive and robust control methods can be applied to mitigate the effects of any potential
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This note was uploaded on 08/22/2011 for the course EGM 4313 taught by Professor Mei during the Spring '08 term at University of Florida.

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AIM2005 - TA2-03 Proceedings of the 2005 IEEE/ASME...

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