Design of discrete PI-PR² controllers for time-delayed systems using dominant pole placement method

This paper presents a new controller structure known as the proportional-integral proportional-double-retarded (PI-PR²) designed for discrete-time systems with time delay. The dominant pole placement technique, which is frequently encountered in control systems, is used as the primary design method. The design method starts that dominant poles are placed according to the requested performance characteristics of the closed-loop system (CLS), and the boundary of the other poles are determined as a circle with the help of the dominance coefficient. This boundary is transferred to the parameter plane, and the PIR² controller parameter solution set is found. To take advantage of identifying the controller's zero position, the PIR² controller is transformed into the PI-PR² controller configuration. The proposed controller method is clarified via a simulation study and a comparison with several PID-type control methodologies documented in the existing literature.