Optimal Multisine Perturbations for Improved Dynamic System Identification using a Mechanical Platform: A Preliminary Simulation Study.

This paper investigates the design of optimal inputs for dynamic system identification. Specifically, this paper concerns the perturbation design for system identification experiments where target human systems are perturbed by mechanical inputs produced by an active device. Although conventional perturbation design criteria are generally applicable, including the scenario described above, problems arise due to the dynamics of the active device. A low-bandwidth active device may distort the input signal and thereby void the optimality of the input. To address this issue, the paper formulates an optimization problem for optimal input design that explicitly incorporates the active device dynamics. The cost function is the determinant of a modified covariance lower bound that takes the active device dynamics into consideration. The proposed method is demonstrated with an identification of a linear dynamics model simulating human arm impedance. Simulation results show that, compared with a standard optimal input and an input with a flat spectrum, the proposed optimal input with active device compensation achieved a smaller parameter covariance. Furthermore, the proposed optimization problem suggests that the optimal covariance lower bound can be achieved by active devices with different dynamics properties. This allows the control design of the active device to satisfy a wide variety of requirements without sacrificing its ability to perform system identification.