Abstract
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.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
This implies that there exists a break from the separation principle for a reduced-order model-based observer and state feedback controller
Since the effects of the ignored fast dynamics are reflected by poor transient and robust performance, this paper provides the stability analysis of a reduced-order model-based state feedback controller (ROMBC) combined with a reduced-order proportional-integral observer (ROPIO) via the root locus approach and the Routh-Hurwitz stability criterion
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Modeling real world systems is not always a convenient task due to the computational complexity that arises with the presence of certain dynamic characteristics. In such cases, model order reduction is applied through a numerical computation to transform the original system model into a more practical form that only captures the dominant characteristics and ignores dynamic behaviors that either contribute less or make the computation complex [2,3]. The neglected states in the reduction process give rise to an unmodeled dynamics with a known bound [8] For this reason, the study of stability and performance improvement of reducedorder model-based controllers (ROMBC) is a worthy research topic. The topic is timely as it can be applied for the system modeling and controller design of distributed systems found in innovative fields such as microfluidics [9]
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