Direct Integration Method for Time-Delayed Control of Second-Order Dynamic Systems

Abstract

A direct integration method (DIM) for time-delayed control (TDC) is proposed in this research. For a second-order dynamic system with time-delayed controllers, a Volterra integral equation of the second kind is used instead of a state derivative equation. With the proposed DIM where matrix exponentials are avoided, semi-analytical representation of the Floquet transition matrix for stability analysis can be derived, the stability region on the parametric space comprising control variables can also be plotted. Within this stability region, optimal control variables are subsequently obtained using a multilevel conjugate gradient optimization method. Further simulation examples demonstrated the superiority of the proposed DIM in terms of computational efficiency and accuracy, as well as the effectiveness of the optimization-based controller design approach.