kp- stable Regions in the Space of PID Controller Coefficients

Computing the set of all stabilizing PID controllers is an important topic when designing these controllers. In the literature, the stability boundaries are already computed in the kp-krkn space. However, in the existing methods, one of the controller coefficients must be swept to compute the stable regions in the plane of two other coefficients. In this paper, 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 root crossing boundaries are no longer required to be computed. The main idea used here is to compute the controller coefficients where the Nyquistplot gets tangent to the real axis, and the values where it has self intersections on the real axis. This leads to the main contribution of the paper that eliminates the need to sweep the proportional coefficient to plot the stable domains in the k;—kD plane.