Identification of differentially flat output of underactuated dynamic systems

This paper presents a data-driven algorithm for identification of locally differentially flat output from system output measurements. No detailed mathematical model of the system is needed. Trial output is written as a linear combination of measured outputs. An optimal linear combination is identified so that the trial output achieves the highest relative degree. When the relative degree is equal to the order of the system, the output is flat. The identification is done in the frequency domain by taking advantage of the asymptotic behaviour of transfer functions of linear systems. We have also developed data handling strategies to obtain the best estimate of the relative degree in the presence of measurement noise, high-frequency dynamics and Nyquist digitisation effect. The proposed algorithm is validated by numerical examples and an experimental study of a rotary crane system.