controlIEEE2007 - 1988 IEEE TRANSACTIONS ON AUTOMATIC...

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1988 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 52, NO. 10, OCTOBER 2007 Lyapunov-Based Tracking Control in the Presence of Uncertain Nonlinear Parameterizable Friction C. Makkar, G. Hu, W. G. Sawyer, and W. E. Dixon 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±cations. If the friction effects in the system can be accurately modeled, there is an improved potential to de- sign 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 differentiable friction model with uncertain nonlinear parameterizable terms. To achieve the semi-global asymptotic tracking re- sult, a recently developed integral feedback compensation strategy is used to identify the friction effects online, assuming exact model knowledge of the remaining dynamics. A Lyapunov-based stability analysis is provided to conclude the tracking and friction identi±cation results. Experimental results illustrate the tracking and friction identi±cation performance of the developed controller. Index Terms— Friction, Lyapunov methods, nonlinear systems, uncertain systems. I. INTRODUCTION 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 ef- fects is a theoretically challenging problem, and compensating for the effects of friction in a controller has practical ramiFcations. If the fric- tion effects in a system can be accurately modeled, there is an im- proved potential to design controllers that can cancel the effects (e.g., model-based controllers); whereas, excessive steady-state tracking er- rors, oscillations, and limit cycles can result from controllers that do not accurately compensate for friction. ±riction 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 limita- tions. See [1], [3], [9], [11]–[13], [16], [30], and [33] for a survey of friction modeling and control results. Given the difFculty in accurately modeling and compensating for friction effects, researchers have pro- posed a variety of (typically of²ine) friction estimation schemes with the objective of identifying the friction effects. ±or example, in [8],
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controlIEEE2007 - 1988 IEEE TRANSACTIONS ON AUTOMATIC...

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