Unstable systems-tracking and disturbance attenuation

Abstract

The paper is aimed to the design of linear continuous controllers for unstable single input - output systems. The controller design is studied in the ring of (Hurwitz) stable and proper rational functions RPS. All stabilizing feedback controllers are given by a general solution of a Diophantine equation in RPS. Then asymptotic tracking and disturbance attenuation is obtained through the divisibility conditions in this ring. The attention of the paper is focused on a class of unstable systems. Both, one and two degree of freedom (1DOF, 2DOF) control structures are considered. Control loops with a feedforward part significantly reduce overshoots in control responses. The methodology brings a scalar parameter for tuning and influencing of controller parameters. As a result, a class of PI, PID controllers are developed but the approach generates also complex controllers. Simulations and verification are performed in the Matlab+Simulink environment.