Robust performance limitations and design of controlled delayed systems

This paper presents performance limitations and a control design methodology for nonminimum phase plants of the pure delay type subject to robustness constraints. Of interest is the design of a set of controllers, for which the open-loop transfer function is a proportional-integral (PI) controller plus delay, meeting constraints on the magnitude of the closed-loop transfer function and on the plant gain uncertainty. These two specifications are used to characterize the robustness, and are a recommended alternative to the gain and phase margin constraints. A control design plot is presented which allows for selection of controller parameters including those for the lowest sensitivity controller, and graphically highlights gain and phase margin tradeoffs. The paper discusses limitations of performance of such systems in terms of crossover frequency and sensitivity. In addition, expressions and design plots are provided for a simplified approximate solution.