Boundary Conditions for Transient and Robust Performance of a Reduced-Order Model-Based State Feedback Controller with PI Observer

One common technique employed in control system design to minimize system model complexity is model order reduction. However, controllers designed by using a reduced-order model have the potential to cause the closed-loop system to become unstable when applied to the original full-order system. Additionally, system performance improvement techniques such as disturbance observers produce unpredictable outcomes when augmented with reduced-order model-based controllers. In particular, the closed-loop system stability is compromised when a large value of observer gain is employed. In this paper, a boundary condition for the controller and observer design parameters in which the closed-loop system stability is maintained is proposed for a reduced-order proportional-integral observer compensated reduced-order model-based controller. The boundary condition was obtained by performing the stability analysis of the closed-loop system using the root locus method and the Routh-Hurwitz criterion. Both the observer and the state feedback controller were designed using a reduced-order system model based on the singular perturbation theory. The result of the theoretical analysis is validated through computer simulations using a DC (direct current) motor position control problem.