Algebraic tools in autotuning principles

Abstract

The contribution is focused on algebraic methods used in the automatic design of controller parameters. The identification of a controlled system is based on a biased relay experiment. The identified system is consecutively approximated by a low order transfer function with a time delay. The controller parameters are then computed through the solution of a Diophantine equation in the ring of proper and stable rational functions. Tuning of the controller parameters can be achieved by a pole-placement problem as a desired multiple root of the characteristic closed loop equation. This approach introduces a scalar tuning parameter which can be adjusted by several methods.