Comparison of perturbation signals for ill-conditioned systems and their effectiveness in model-based control

Due to the effect of directionality, accurate identification of multivariable ill-conditioned systems is difficult without the use of specially designed perturbation signals. A comparison of three different designs of perturbation signals for the identification of these systems is presented, namely the virtual transfer function between inputs, modified zippered spectrum and rotated inputs designs. The effect of the variation of the condition number with frequency on the designs is illustrated via two simulation examples, where only one has a varying condition number. The performance of the designs for application in model-based control such as model predictive control is evaluated. For the system with the unvarying condition number, rotated inputs design is shown to perform best. The virtual transfer function between inputs design is shown to be superior when the condition number varies with frequency.