An approach to the design of experiments for the identification of linear MIMO models that will provide robust model-based control is presented. The design criteria, based on conditions for robust stability and performance, are developed from singular Value decompositions (SVD) characterization of structured model mismatch. The resulting designs minimize uncertainties in certain structural parameters in the SVD of the multivariable model rather than simply the magnitude of the model mismatch. An important feature of these designs is that input perturbations applied in the low-gain directions of the multivariable process have much larger magnitudes than those applied in the high-gain directions. This leads to input sequences which are neither binary nor independent. The results are used to provide an intuitive justification for performing identification under closed-loop multivariable control. Examples are presented which illustrate both the physical interpretations of the designs, and the effectiveness of using a sequential design approach.