The Last Jedi: Step Response Identification of Overdamped Second Order Systems

A simple, general method for exactly determining the parameters of an overdamped second order LTI system from its step response is conspicuously absent from the literature. This paper develops and demonstrates such a procedure called the “Beta T-star Method.” As it fills the gap in system identification from the step response of first and second order systems, the new method is “The Last J of basic system identification. The new method exploits elegant relationships between the maximum time derivative of the step response, the time at which the maximum occurs, and the parameters of the system. The paper also extends the method to underdamped second order systems. While the extension is primarily of academic interest, it may be useful for systems for which the percent overshoot is very small.