Frequency domain identification of continuous-time output-error models with time-delay from relay feedback tests

This paper is concerned with identification of continuous-time output-error models with time-delay from relay feedback tests. Conventional methods for solving this problem consist in deriving analytical limit cycle expressions and fitting them to measured shape factors. However, they may fail to handle different limit cycles uniformly, due to the structural differences in the analytical expressions. To overcome this problem, we consider a more general, data-based, parametric identification framework using sampled limit cycle data. A frequency domain method that minimizes the sum of squared output-errors is developed. The proposed method can be of high accuracy, thanks to the periodic input–output signals provided by sustained relay feedback oscillations, which can help to reduce leakage and aliasing errors. Besides, a distinctive merit of the proposed method is that identification of stable and unstable plants can be equally simple. The effectiveness and superiority of the proposed method are demonstrated by means of both theoretical analyses and simulation examples.