International Journal of Robust and Nonlinear Control
Mechanical & Industrial Engineering
This article developed a new method to described the set of stabilizing PID control. The method is based on D-parameterization with natural description of the set. It was found that the stability crossing surface is a ruled surface that is completely determined by a curve known as discriminant. The discriminant is divided into sectors at the cusps. Corresponding to the sectors, the stability crossing surface is divided into positive and negative patches. A systematic study is conducted to identify the regions with a fixed number of right half-plane characteristic roots. The crossing directions of characteristic roots for positive patches and negative patches are also studied. As a result, a systematic method is developed to identify the regions of PID parameter such that the system is stabilized.
Gu, Keqin; Ma, Qian; Zhou, Huiqing; Salma, Mahzoon; and Yang, Xingzi, "A geometric description of the set of stabilizing PID controllers" (2021). SIUE Faculty Research, Scholarship, and Creative Activity. 153.