Sensitivity Shaping by Using Time-Delays

Abstract

Some results are presented concerning use of time-delays as controller for sensitivity shaping in a control system with stable plant represented by a strictly proper rational transfer function. Suppose that the desired shaping can be performed by some fictitious stable controller represented by a, proper rational transfer function. Then, a set of time-delays connected in parallel can replace the fictitious controller without making the change of the shape of sensitivity function exceed a prescribed allowance. In the case where the plant possibly contains small perturbation that allows the plant to remain stable and strictly proper, a set of time-delays can shape the sensitivity function so that the control system possesses stability robustness against such perturbation. Furthermore, small perturbation in the controller parameters like delay-times causes no closed-loop instability nor remarkable change in the shape of the sensitivity function.