All stabilizing sets for proportional–integral controller of high-order delay processes. (July 2014)

• Record Type: Journal Article
• Authors: Wang, Honghai; Liu, Jianchang; Yang, Feisheng; Zhang, Yu
• Is Part Of: Proceedings of the Institution of Mechanical Engineers. Volume 228:Number 6(2014)
• Page Start: 393
• Page End: 405
• Publication Date: 2014-07
• Subjects: High-order process -- proportional–integral controller -- time delay -- stabilization; Mechanical engineering -- Periodicals; Automatic control -- Periodicals; Systems engineering -- Periodicals; 621.3
• DOI: 10.1177/0959651814520826
• Languages: English
• ISSNs: 0959-6518

Abstract

This article considers the problem of determining the complete stabilizing set of proportional–integral controllers, which is applied in a class of high-order processes with time delay in complex-frequency domain. First, we give a necessary condition for a proportional–integral controller to stabilize the process with certain constant delay using Descartes' rule of signs. Then by employing the generalization of the Hermite–Biehler theorem applicable to quasi-polynomials, a complete set for all stabilizing proportional–integral parameters is derived to stabilize the open-loop stable and unstable systems. In the case of uncertain time delay, we provide a design approach to stabilize the related plant with a robust proportional–integral controller, where the unknown but constant time delay lies inside a known interval. Three examples illustrate the effectiveness of the proposed results.