Continuous-Time Identification Using Sinusoidal Inputs: An Integral Equation Approach

Abstract

An integral equation approach for identification of continuous-time transfer function models from sinusoidal test data is proposed. Using a single-frequency sinusoidal input signal, the algorithm simultaneously estimates the model parameters and the time delay from the process response and the analytical expression of the input. Estimation equations for first-, second-, and a general nth-order models are derived. Simulation results for identification of first- and second-order processes are presented to demonstrate the efficacy of the proposed methodology. The robustness of the algorithm is demonstrated using identification results for different noise levels in the output. Use of sinusoids with widely varying frequency and phase shows the flexibility in input design. Identification results of a simulated continuous stirred tank reactor are also presented.