Internal Model Control–Proportional Integral Derivative–Fractional Order Filter Controllers Design for Unstable Delay Systems

Abstract

An analytical design for proportional integral derivative (PID) controller cascaded with a fractionalorder filter is proposed for firstorder unstable processes with time delay. The design algorithm is based on the internal model control (IMC) paradigm. A two degreesoffreedom (2DOF) control structure is used to improve the performance of the closedloop system. In the 2DOF control structure, an integer order controller is used to stabilize the innerloop, and a fractionalorder controller for the stabilized system is employed to improve the performance of the closedloop system. The Walton–Marshall's method, which is applicable to quasipolynomials, is then used to establish the internal stability condition of the closedloop system (the fractional part of the controller in particular) and to seek the set of stabilizing proportional (P) or proportionalderivative (PD) controller parameters.