Perturbed Butterworth Pole Patterns for Tracking in the Sense of Spheres

Abstract

The “Quantitative Pole Placement” (QPP) identified in the context of guaranteed tracking in the sense of spheres is considered. At the center of this design philosophy is the need for directly satisfying performance specifications in uncertain, nonlinear systems. In the literature, this pole placement relies on trial and error. A systematic procedure is proposed for such pole placement when the nominal linear part of the uncertain nonlinear system is minimum phase. The approach to the problem is based on the standard LQR problem formulation. The preferred pole locations that minimize the critical operator norm needed for the success of the QPP formulation are conjectured to be a perturbed version of the Butterworth pole configuration. The results are applied to a 3 d.o.f. robotic manipulator.