Quick look parameter estimation in linear control systems

A method for estimating parameters of a linear control system is proposed. The estimation is based only on the early part of the step function response. A power series approximation is used, and it is shown that for a second-order system the form of the early response is the same, regardless of whether the system is overdamped underdamped, or critically damped. With the use of precise; noise-free data typical results for an underdamped second-order system gave parameter estimates within 0.1 to 11 percent in a time equal to about 10 percent of the time to the first peak of the response. Similar results for an overdamped second-order system provided parameter estimates within 0.3 to 2 percent in a time equal to about 1 percent of the longer time constant and 13 percent of the shorter time constant