In this paper, a methodology for designing a controller based on inverse dynamics for speed control of DC motors is presented. The proposed controller consists of a prefilter, the inverse dynamic model of a system and the PI controller. The prefilter prevents high frequency effects from the inverse dynamic model. The model of the system in characterized by a nonlinear equation with coulomb friction. The PI controller regulates the error between the set-point and the system output which may be caused by modeling error, variations of parameters and disturbances. The output which may be caused by modeling error, variations of parameters and disturbances. The parameters of the model and the PI controller are adjusted offlinely by a genetic algorithm. An experimental work on a DC motor system is carried out to illustrate the performance of the proposed controller.