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The application of a nonlinear control law for vibration damping on a typical nanopositioning system is investigated. The nonlinear control law is an augmentation of the linear integral force feedback scheme, where the constant gain used in integral force feedback, is replaced by a passive nonlinear operator. The nonlinear control law improves the performance of integral force feedback as it provides more rapid suppression of large disturbances, while maintaining low noise sensitivity. L2-stability for the control law is established. Experimental results are presented, showing improved performance when applying the nonlinear augmentation of the integral force feedback scheme, compared to the original linear integral force feedback scheme.