Discrete-time posicast PID×(n − 2) stage PD cascade controllers for unstable system

Abstract

This paper aims to present a discrete-time controller design for a two-degree-of-freedom (2-DOF) control system connected with Posicast function to stabilize an unstable third-order or higher-order plant. The continuous-time controllers used in the 2-DOF control system, the proportional-integral-derivative (PID)×(n − 2) stage proportional-derivative (PD) cascade controllers and the forward controller, are designed by using the Kitti’s method. The Posicast function is used to eliminate an overshoot in step response. Based on the continuous-time controllers designed in the s-domain, the discrete-time controllers with closed-form expression in the z-domain are then calculated by using the bilinear transformation. The magnetic levitation system is employed as an illustrative case study of the unstable plant to be controlled. By comparing the discrete-time system with the continuous-time system, the effectiveness of the proposed discrete-time controller design is verified by MATLAB simulation results.