The first step in subspace methods for identification of multivariable systems is the estimation of the order of the model to be identified. Model order estimation is especially difficult for ill-conditioned systems. In previous work we showed heuristically that appropriately designed experiments with rotated PRBS inputs greatly facilitate model order estimation, hence overall model accuracy. However, design of such experiments depends on the very system to be identified. To overcome that difficulty, in this paper we propose an adaptive design of experiments. The proposed approach follows rigorous justification of the need for rotated PRBS inputs, and is tested through computer simulations on two case studies involving a high-purity distillation column and a fluidized catalytic cracking unit. Comparisons of the approach to open- and closed-loop alternatives are presented, and suggestions for further development are made. (C) 2017 Elsevier Ltd. All rights reserved.