Orthonormal basis functions applied to optimal control design with closed-loop pole location constraints

This article proposes an optimal control design technique to ensure that the closed-loop poles are assigned to prescribed locations in the complex plane. A key element in this approach is the usage of orthonormal basis functions to parametrise the main design parameter. This goal is achieved by using a quadratic cost based optimisation approach, considering control effort penalisation as well as cheap control. Youla parametrisation is used, subject to a set of constraints which guarantee stability, zero steady error to constant references and disturbances, and yielding the prescribed set of closed-loop poles.