Signal design for the identification of multivariable ill-conditioned systems using virtual transfer function between inputs

A novel method to design perturbation signals for the identification of multivariable ill-conditioned systems is presented. The method uses multisine signals to simultaneously perturb all input-output channels of the system. The correlated harmonic component is set according to a virtual transfer function between inputs, which is defined based on the case where equal perturbation is achieved in all directions of the output state-space. This ensures that all singular values of the system, as well as the relative gain array at steady-state, are identified with a sufficiently high accuracy - a criterion important for model-based control. A case study based on a simulated multizone furnace is used to illustrate the superiority of the proposed technique over a competing design.