All stabilizing PID controllers for interval systems and systems with affine parametric uncertainties

Robust PID controller synthesis for plants with unknown or slowly varying parameters is still an open topic. A novel method is presented allowing to exactly determine all stabilizing controller gains for systems with interval and affine parametric uncertainties. This leads to far less conservative stability areas, compared to existing methods which are based on over-bounding by interval polynomials. As a consequence, iterative searches containing robust synthesis and analysis are omitted, which greatly reduces the time and effort to find potential controller parameters as robust stability is already guaranteed. Additionally, due to the inherent decoupling at singular frequencies, no frequency grinding is needed. The proposed method is based on a combination of a modified Parameter Space Approach with results from robust test set theory.