A SOLUTION FOR NONLINEAR STABILITY ANALYSIS OF QFT CONTROLLERS DESIGNED FOR HYDRAULICALLY ACTUATED SYSTEMS

Abstract

Quantitative feedback theory (QFT) is a well-established technique to design robust and linear controllers. However, the important open problem of extending the small signal stability to nonlinear stability verification has remained an ongoing research in the design of QFT controllers. In this paper, we show that Takagi–Sugeno (T–S) fuzzy modeling approach and its stability theory provide a new opportunity to study the nonlinear stability of QFT controllers in fluid power systems. To validate the approach, two case studies are provided first. The first case study establishes the reliability of the approach by confirming the results for a hydraulic system of which nonlinear stability has already been proven. The second case study establishes that using the proposed approach, we can further study and extend the stability region of previously developed hydraulic controllers to include parametric uncertainty. Followed by the successful validation of the effectiveness of our approach through these two case studies, the stability of a QFT position controller, for which the nonlinear stability was never proven, is investigated.