Identification of Continuous-Time Low-Order Models via Weighted Moments

This paper presents an identification algorithm for continuous-time low-order models both with delays and free of delays via weighted time moments. In this approach, it is sufficient to obtain response data stimulated by a single pulse, such as a rectangular or a half-sine pulse. From the weighted moments of both input and output data, the parameters of low-order transfer function models are determined by solving linear equations in a matrix form. Numerical examples show that the algorithm provides robust identification results despite the fact that the system considered is oscillatory with a long tail and contains measurement noise.