Proportional-Retarded Controller Design for Single-Integrator Dynamics Against Unintentional Delays

In recent years, there has been growing interest toward designing controllers with intentional delays to render improved speed of response and better noise attenuation capabilities in various classes of linear time-invariant systems. A natural progression of this line of research, which to our knowledge has not been addressed, pertains to how such controllers can be redesigned to accommodate unintentional delays. In this letter, we present solutions to this problem on a class of Proportional Retarded controllers when controlling integrator plant dynamics. Results provide an analytical approach to the design of these controllers and demonstrate their opportunities as well as limitations in various case studies.