Design of robust fractional‐order lead–lag controller for uncertain systems

Abstract

In this study, a new method for designing fractional-order robust lead–lag controllers in order to ensure robust stability in uncertain systems with unstructured uncertainty, has been presented. In this method, at first by the use of pole placement and solving Diophantine equation, a fractional-order controller, which has a new form, is designed in order to stabilise the nominal system. Then a constrained optimisation problem is solved, in which, the cost function consists of the numerator and denominator coefficients of the proposed fractional-order controller and the constraints are the robust stability conditions. Finally, the parameters of the robust fractional-order controller are acquired. This method is implemented on an unstable system and simulation results are presented.