Robust fractional controller for interval first order system with time delay

摘要

In this paper, a new method is proposed to define the parameters of fractional order PI~λ controller that stabilise an uncertain first order system with time delay. In fact, based on an extension version of Hermite-Biehler theorem and Pontryagin theorem the complete set stabilising PI~λ parameters (K_p, K_i, λ) is determined. The closed-loop characteristic equation of the system is a fractional order quasi-polynomial with interval uncertainty structure which is decomposed into several vertex. In the complex plane the value set of the vertex is a convex polygon. Simulation results are given to show the effectiveness of the proposed method.