The T26.4 Method for Step Response Identification of Overdamped 2nd Order Systems

The T26.4 Method is a new approach to identifying the parameters of overdamped or slightly underdamped 2nd order LTI systems either graphically or by table look-up. The method computes the ratio of the time at which the step response reaches 26.4% of its final value to the time at which it reaches a specific fraction of its final value (such as 60%, 75%, or 90%). This ratio is the input to a table or graph to determine the values of the poles normalized by the 26.4% time. Unlike the Beta T-star Method, the T26.4 method does not require differentiation of the step response, and thus it is well-suited to system identification from noisy or sparse step response data. This paper explains the significance of the 26.4% value for 2nd order LTI systems, derives the method, and then shows its application to identifying models of a DC motor from experimental data and a slightly underdamped 2nd order system from simulated data.