In this paper, the recently proposed neural network adaptive robust control (NNARC) design is generalized to synthesize performance oriented control laws for a class of nonlinear systems transformable to the semi-strict feedback forms through the incorporation of backstepping design techniques. Both repeatable (or state dependent) unknown nonlinearities and nonrepeatable unknown nonlinearities such as external disturbances are considered. In addition, unknown nonlinearities can exist in the virtual control input channel of each intermediate step as well. All unknown but repeatable nonlinear functions are approximated by outputs of multi-layer neural networks to achieve a better model compensation for an improved performance. All NN weights are tuned on-line with no prior training needed. In order to avoid the possible divergence of the on-line tuning of neural networks. discontinuous projections with fictitious bounds are used in the NN weight adjusting law to make sure that all NN weights are tuned within a prescribed range. By doing so, even in the presence of approximation error and nonrepeatable nonlinearities such as disturbances, a controlled learning is achieved and the possible destabilizing effect of on-line tuning of NN weights could be avoided. Certain robust control terms can then be constructed to attenuate various model uncertainties effectively for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy in general. The precision motion control of a linear motor drive system with slow electrical dynamics is used as a case study to illustrate the proposed NNARC methodology. Experimental results with a simulated slow electrical dynamics are presented.