Robust pole-placement technique for plants with ellipsoidally uncertain parameters

Abstract

A technique is proposed for synthesizing pole-placement controllers capable of assigning the closed-loop poles of a family of plants inside a specified design region. The design is applicable to plants characterized by uncertain parameters that are known to lie inside an ellipsoid. Ellipsoidal parametric uncertainty descriptions are particularly useful because they arise naturally in the context of parameter estimation, and hence have the advantage of being quantifiable using experimental input-output data. The control-design problem is posed as a minimax program that is shown to be convex, and that can be solved using numerical techniques with global convergence guarantees. Two reliable techniques for relating regions of stable poles to regions of allowed variability for the coefficients of the characteristic polynomial are discussed. The robust pole-placement design technique is illustrated with an example.