A unified method for optimal arbitrary pole placement

TL;DR

This paper introduces a unified eigenstructure assignment method for arbitrary pole placement that optimizes robustness and gain, outperforming existing techniques.

Contribution

It provides a novel parametric eigenstructure assignment formula and an unconstrained nonlinear optimization algorithm for optimal pole placement.

Findings

The method achieves desired eigenvalues with specified multiplicities.

It outperforms several recent pole placement techniques in robustness and gain.

The approach is validated through comparative performance analysis.

Abstract

We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with optimal robustness and minimum gain. Lastly we compare the performance of our method against several others from the recent literature.