Controller Design by Approximation of Ideal Compensators - A Comparison of Computational Methods

A mathematical formulation /1/ of the classical lead-lag design method leads to the same controller approximation or order reduction problem as it arises in more sophisticated modern design approaches as, e. g., LQG/LTR or IH¿-optimal design if these methods are applied to complex plant models (compare e. g. /2/): Given an ideal, but eventually unnecessarily complex. compensator which achieves a certain desired closed-loop behaviour of the controlled system exactly, find an approximation of this ideal compensator of as low complexity as possible such that the resulting closed-loop system is a good approximation to the desired one. In this paper, different techniques for the solution of the scalar approximation problem are described and compared with respect to the resulting closed- loop systems´s performance.