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

• Published in: Energies (Basel) Vol. 14; no. 10; p. 2881
• Main Authors: Amare, Nebiyeleul Daniel, Kim, Doe Hun, Yang, Sun Jick, Son, Young Ik
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.05.2021
• Subjects: Boundary conditions; Closed loop systems; Computer simulation; Control systems; Control systems design; Controllers; D C motors; dc motor; Design; Design parameters; Disturbance observers; Feedback; Feedback control; Input output; Magnetic levitation systems; Mathematical models; Model reduction; Motor task performance; Perturbation theory; proportional-integral observer; Reduced order models; reduced-order model-based controller; robust control; Root locus; Routh-Hurwitz criterion; Singular perturbation; Stability analysis; Stability augmentation; State feedback; Systems stability; Theoretical analysis
• ISSN: 1996-1073; 1996-1073
• DOI: 10.3390/en14102881

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.