Receptance-Based Computation of Stability Crossing Curves for Single-Input-Multiple-Output Second-Order Linear Systems with Two Time-Delays

Abstract

For a complete stability analysis of multi-dimensional controlled systems modeled in the framework of second-order linear differential equations with two time-delays, the determination of stability crossing curves (or stability switching curves) within the domain of the delays is significantly important. This paper presents a simple receptance-based approach to solve this problem for a single-input-multiple-output controlled system using its second-order model. The proposed approach is based on a reduced characteristic function of the controlled system. This characteristic function is directly related to the receptance of the uncontrolled system and has a peculiar form that is well-suited for an effective method of calculation of these curves. Moreover, this method can find the direction in which the characteristic roots cross the imaginary axis as the delays deviate from a stability crossing curve. An example case study with two independent and constant delays is given to demonstrate the effectiveness of the proposed approach.