Design of experiments for identification of control-relevant models is at the heart of robust controller design. In a number of prior publications, experiment designs have been developed that generate input/output data for efficient identification of models satisfying the integral controllability (IC) condition. The design of process inputs for such experiments is often, but not always, based on the concept of independent random rotated inputs, with appropriately proportioned amplitudes. However, prior publications do not account for models that may already be partially known before identification. In this work, this issue is addressed by developing a general experiment design framework for efficient identification of partially known models that must satisfy the IC condition. This framework produces optimal designs by solving appropriately formulated optimization problems, based on a number of rigorous theoretical results. Numerical simulations illustrate the proposed approach and potential future extensions are suggested. (C) 2016 American Institute of Chemical Engineers