Open Accessk P ‐stable regions in the space of PID controller coefficients
Author(s) -
Almodaresi Elham,
Bozorg Mohammad
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.0685
Subject(s) - nyquist plot , pid controller , control theory (sociology) , controller (irrigation) , mathematics , stability (learning theory) , complex plane , plane (geometry) , plot (graphics) , tangent , mathematical analysis , computer science , physics , geometry , statistics , control (management) , temperature control , agronomy , electrode , quantum mechanics , artificial intelligence , machine learning , biology , dielectric spectroscopy , electrochemistry , thermodynamics
Evaluating a set of coefficients of a PID controller that stabilises a given plant is an important topic in designing such a controller. In the literature, the stability boundaries of the coefficients are already computed in the k P –k I –k D space. However, in the existing methods, one of the coefficients must be swept to compute the stable regions in the plane of the two other coefficients. A novel method is presented to compute the regions in the plane of two controller coefficients such that some stable interval exists for the third coefficient. Therefore, the stability crossing boundaries are no longer required to be computed. The main idea used here is to compute the controller coefficients where the Nyquist plot gets tangent to the real axis and the values where the plot has self‐intersections on the real axis. This leads to the main contribution of the study that eliminates the need to sweep the proportional coefficient to plot the stability domains in the k I / k P ‐ k D / k P plane.