Menge aller robust stabilisierenden PID-Regler: Methodik und Software (Teil I) (The Set of All Robust Stabilizing PID Controllers: Methods and Software (Part I))

Computation of Hurwitz-stability regions in the parameter space of PID controllers has been a topic of intensive research in the last decade. The main impetus is given by the fact that non-convex stability regions can be built up by convex polygonal slices with constant k P , which is a consequence of decoupling of PID parameter space at singular frequencies. Thereby the computation task splits into two problems: discrimination of k P-intervals with stable polygons, and automatic detection of stable polygons for a given k P. The method applies for continuous and discrete-time systems, including those with time-delay. It is especially well suited for the design of robust PID controllers for the systems with parametric uncertainties. While some problems still remain open, the theory at this stage is well completed. This is the starting one of a series of three papers, where the newest results, algorithms and a MATLAB R toolbox for fast computation of PID controller regions are presented.