Power-based modeling was originally developed in the early sixties to describe a large class of nonlinear electrical RLC networks, in a special gradient form. Recently this idea has been extended for modeling and control of a larger class of physical systems. In this paper, first, coordinate transformations are introduced for systems described in this framework, such that the physical structure is preserved. Such a transformation can provide new insights for both analysis and control design. Second, power-based integral and adaptive control schemes are presented. Advantages of these schemes are shown by their application on standard mechanical systems. (C) 2012 Elsevier Ltd. All rights reserved.