Robust design based on complex-order integrator loop gain

In this paper a novel, easy-to-use, robust design method for stable time delay processes is proposed. The purpose is obtaining a desired phase margin at a known crossover frequency. The design methodology is based on complex order integration. Complex order controllers fall into fractional order controllers category. Complex order controllers are the extended version of fractional order controllers in which the order of the transfer function has imaginary and real parts, rather than integer or non-integer real part. Introducing a complex order for the open-loop transfer function makes it possible to fulfill additional specifications of design ensuring a robust performance of the closed-loop system with respect to gain variations. This extra parameter enables designing a controller which makes the phase diagram remain flat around the gain crossover frequency. This leads to a fixed phase margin around the crossover frequency. The design procedure and the validity of the results are illustrated through some examples.