A geometric description of the set of stabilizing PID controllers. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Gu, Keqin; Ma, Qian; Zhou, Huiqing; Mahzoon, Salma; Yang, Xingzi
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 4481
• Page End: 4486
• Publication Date: 2020
• Subjects: Stability -- PID control -- geometric characterization; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.452
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This article presents a geometric description of the set of stabilizing PID controllers. The three-dimensional parameter space is partitioned by the stability crossing surface into regions such that the number of characteristic roots on the right half-plane (RHP) remains constant within each region. The set of stabilizing PID parameters consists those regions with no RHP root. The stability crossing surface is a ruled surface, and it is completely determined by a curve known as the discriminant. The discriminant may be divided into sectors between its cusps, and each sector corresponds to a positive patch and negative patch. The stability crossing surface is composed of these patches.