Optimal 2nd Order LTI System Identification

Just as optimal control addresses the inexact science of selecting controller gains, optimal system identification balances the effects of linearization, estimation and order reduction, to obtain the "best fit" approximation of a target electrical, mechanical, or electro-mechanical system. Like any engineering design problem, it involves matching a set of free design parameters to a requirement specification that defines what "best" means. In this paper, closed-form metrics of a normalized second-order system are used to develop a clear and simple design process to identify a 2(nd) order approximation that exhibits the most relevant dynamic characteristics of the target system. The process identifies the optimal parameters of an under or over-damped system from its step-response, and refines the approximation using its impulse-response. The approach is formulaic, non-iterative, and may be used to fit a second-order approximation to a higher-order system response, without the need for a complex search algorithm.