Pole placement design: An interpolation-theoretic approach

Interpolation-theoretic techniques have recently found many applications in solving control problems such as the four block problem, {dollar}Hspinfty{dollar} optimal controller design, etc. The basic idea is to transform the problem into a (possibly constrained) set of interpolation conditions.; In this thesis, we consider the classic, yet still challenging, problem of pole placement for general multivariable plants, and find the family of controllers which place the closed-loop poles in some desired region in the complex plane. We use Q-parametrization to affinely represent the closed-loop transfer functions and then express the design problem as a set of interpolation conditions with an analyticity constraint. The resulting interpolation problem is, however, too complicated to be solved and so it is transformed into one for which a suitable form of the so-called generalized Schur algorithm can be used to obtain the family of analytic interpolants. This transformation is much easier in the case of regular plants which have a particular property.; The resulting closed-loop transfer function has an affine representation in terms of a free parameter. Thus it will be easy to apply performance criteria, such as input tracking, noise rejection, decoupling, etc, to find the free parameter and obtain the desired controller. The proposed technique has been successfully applied to several real examples (such as the rational inverted pendulum problem).