Identification of under-damped second-order systems using finite duration rectangular pulse inputs

This paper uses rectangular pulse inputs of finite duration to identify the parameters of a prototype second-order transfer function. Exact analytical expressions for the damping ratio and the undamped natural frequency are obtained in terms of the time at which the pulse response reaches its maximum value and the maximum value itself. The sensitivity of these expressions to zero mean white noise is studied using variance analysis and Monte Carlo simulations. Our approach compares favorably with existing identification methods both in terms of overall simplicity and user friendliness.