Analytical Design of Controllers with Two Tunable Parameters Based on $H_{\infty}$ Specifications for Dead-Time Systems

The main result of this paper is a new analytical method for the design of a wide class of controllers with two tunable and any number of fixed parameters based on $H_{\infty}$ specifications for SISO dead-time systems. The essence of the method lies in the analytical description of the boundary of the $H_{\infty}$ region in the parametric plane of the controller. In addition to the analytical method, the paper refers to a user-friendly web-based design tool available at www.pidlab.com, where this extended methodology is implemented for multiple process models and design requirements in the form of $H_{\infty}$ performance and robustness constraints. Two examples illustrate the practical applicability of the proposed approach.