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ACC2005 - ThA07.4 2005 American Control Conference June...

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Lyapunov-Based Tracking Control in the Presence of Uncertain Nonlinear Parameterizable Friction C. Makkar, W. E. Dixon , W. G. Sawyer and G. Hu Corresponding Author email: {cmakkar, wdixon, wgsawyer, gqhu}@ u fl .edu. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611-6250 Abstract — Modeling and compensation for friction effects has been a topic of considerable mainstream interest in motion control research. This interest is spawned from the fact that modeling nonlinear friction effects is a theoretically challenging problem, and compensating for the effects of friction in a controller has practical rami fi cations. If the friction effects in the system can be accurately modeled, there is an improved potential to design controllers that can cancel the effects; whereas, excessive steady-state tracking errors, oscillations, and limit cycles can result from controllers that do not accurately compensate for friction. A tracking controller is developed in this paper for a general Euler- Lagrange system that contains a new continuously differen- tiable friction model with uncertain nonlinear parameterizable terms. To achieve the semi-global asymptotic tracking result, a recently developed integral feedback compensation strategy is used to identify the friction effects on-line, assuming exact model knowledge of the remaining dynamics. A Lyapunov- based stability analysis is provided to conclude the tracking and friction identi fi cation results. On-going efforts are being directed at the development of an experimental testbed to illustrate the tracking and friction identi fi cation performance of the developed controller. I. I NTRODUCTION The modeling and compensation for friction effects has been a topic of considerable mainstream interest in motion control research. This interest is spawned from the fact that modeling nonlinear friction effects is a theoretically challenging problem, and compensating for the effects of friction in a controller has practical rami fi cations. If the friction effects in the system can be accurately mod- eled, there is an improved potential to design controllers that can cancel the effects (e.g., model-based controllers); whereas, excessive steady-state tracking errors, oscillations, and limit cycles can result from controllers that do not accurately compensate for friction. Friction is exaggerated at low velocities, which are present in high-precision and high-performance motion control systems; unfortunately, a general model for friction which describes the effects at low velocity has not been universally accepted. Many models of friction have been proposed to deal with the various regimes of friction, each with their own merits and limitations. See [1], [3], [9], [11]-[13], [16], [24], and [27] for a survey of friction modeling and control results. Given the dif fi culty in accurately modeling and compensating for friction effects, researchers have proposed a variety of (typically of fl ine) friction estimation schemes with the objective of identifying the friction effects. For
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