Identification of System Dynamics with Time Delay: a Two-Stage Frequency Domain Approach

Abstract

Frequency domain identification of system parameters and time delay is essential for model-based motion control of dynamic systems. Conventional approaches incorporate the delay into the model through an explicit model parametrization, which results in a high amount of nonlocal minima. In this paper, a new strategy is proposed based on a two-stage frequency domain approach to linearly incorporate the delay in the parameter vector of the system. This enables the proposed method to accurately identify both the time delay and system parameters. In a first stage, the system is parametrized and the delay is approximated using rational (all-pass) orthonormal basis functions. The resulting constraints on the individual delay approximation parameters are relaxed through a general all-pass constraint which is enforced iteratively by reformulating the identification algorithm. In a second stage, the continuous time delay term is identified in a convex problem with fixed system parameters using the previous approximates as starting values. Finally, simulations and experimental results validate the effectiveness of this new two-stage method.