Tuning and performance assessment of complex fractional-order PI controllers

Abstract

In this paper, we propose an optimization-based tuning methodology for real and complex Fractional-Order Proportional-Integral (FOPI) controllers. The proposed approach hinges on a modified version of the Integral Absolute Error (IAE) sensitivity-constrained optimization problem, which is suitably adapted to the design of fractional controllers. As such, it allows the exploitation of the potentiality of the (possibly complex) fractional integrator. We also propose a method, based on the well-known CRONE approximation, which delivers a band-limited real-rational approximation of the real part of the complex-order integrator. Finally, based on a First-Order-Plus-Dead-Time (FOPDT) model of the process, we use our design and approximation techniques to find an optimal tuning for real, complex fractional-order, and integer PI controllers and we provide a quantitative performance assessment.