In this paper, the modularized adaptive backstepping designs are incorporated into the recently proposed adaptive robust control framework to synthesize indirect adaptive robust controllers that achieve not only good output tracking performance but also better parameter estimation processes to obtain accurate parameter estimates for secondary purposes such as machine health monitoring and prognostics. Departing from the modularized adaptive backstepping designs, the proposed indirect adaptive robust control (IARC) uses available a priori knowledge on the physical bounds of unknown parameters, along with preset adaptation rate limits, to construct projection type parameter estimation algorithms with rate limits for a controlled estimation process. By doing so, regardless of the estimation algorithm to be used, a guaranteed transient performance and final tracking accuracy can be achieved even in the presence of disturbances and uncertain nonlinearities, a desirable feature in applications. In addition, the theoretical performance of the adaptive designs, asymptotic output tracking in the presence of parametric uncertainties only, is also preserved. The precision motion control of a linear motor drive system is used as an application example. Experimental results are obtained to show the improved parameter estimation process of the proposed IARC design.