Algebraic control of unstable delayed first order systems using RQ-meromorphic functions

The paper is focused on control of first order unstable delayed systems. The control design is performed in the RMS ring of retarded quasipolynomial (RQ) meromorphic functions. Unstable systems are modeled in anisochronic philosophy as a ratio of quasipolynomials where also denominator contains delay terms. The goal is to find a suitable stable quasipolynomial as a common denominator of R_MS terms. This task is equivalent to the stabilization of a plant by a proportional controller in a feedback loop. Then, the appropriate controller can be found. In this paper, an algebraic method based on the solution of the Bezout equation with Youla-Kucera parameterization is presented. Besides the simple feedback loop, significant improvement using two-degrees of freedom structure is demonstrated. The method offers a real positive real parameter m₀ which defines closed loop poles placement. The modified "equalization method" for determining of m₀ can be applied. An example illustrates the proposed methodology, properties and benchmarking of all principles.