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In this brief, an adaptive robust control (ARC) scheme with compensation for nonlinearly parameterized dynamic friction is proposed. Both parametric uncertainties and external disturbances are considered in this method. Our method takes advantage of a Lipschitzian property with respect to the parameters of nonlinearly parameterized model in the ARC design. The outcome is that the number of parameters to be updated in the ARC is equal to the number of unknown parameters in the plant, and thus the resulting control algorithm is convenient to be implemented. We have proved theoretically that the proposed method can not only guarantee desired transient performance for the system, but also make the magnitude of steady-state tracking error to be arbitrarily small in the presence of parametric uncertainties only. Experimental results are given to demonstrate the effectiveness of the proposed ARC scheme.
Date of Publication: Jan. 2013