Frequency domain, parametric estimation of the evolution of the time-varying dynamics of periodically time-varying systems from noisy input-output observations

This paper presents a parametric, frequency domain identification method for modeling continuous (discrete-) time, periodically time-varying systems from input-output measurements. In this framework both the output as well as the input are allowed to be corrupted by stationary noise (= errors-in-variables approach). Furthermore, it is assumed that the system under consideration can be excited by a broad-band periodic signal with a user-defined amplitude spectrum (i.e. multisine), and that the periodicity of the excitation signal, T-exc, can be synchronized with the periodicity of the time-variation, T-sys, (i.e. T-exc/T-sys is an element of Q). Under these conditions the system can reach a steady state. Besides, two different concepts of a transfer function for time-varying systems (called the frozen transfer function and the instantaneous transfer function) are also introduced. A clear distinction between both is made, and either can be estimated with the proposed identification scheme. It is up to the users to decide which definition suits best their purpose. Uncertainty bounds on all/most frozen model-related quantity (such as frozen transfer function, frozen poles, frozen resonance frequency, ...) are provided in this paper as well. Finally, the identification algorithm is demonstrated on an extendible robot arm.