Design of a class of fractional controllers from frequency specifications with guaranteed time domain behavior

This paper tackles the problem of tuning a class of fractional controllers by using frequency specifications. These tuning strategies exhibit the advantage of allowing the design of robustness features in the closed-loop control system. Nowadays, relationships between time and frequency domain specifications are given by complicated formulas in the case of integer controllers, which become even more complicated if fractional controllers are used. The proposed strategy consists in finding the family of fractional controllers (in function of the fractional integrator) that makes the closed-loop system have the same time domain specifications: overshoot and settling time. Such family of controllers is obtained by minimizing a function based on these time domain specifications. Our method has been particularized to first order plants, controlled by PI^α regulators, although the results can be easily extended to higher order plants and other fractional controllers. The obtained results provide simple expressions for tuning these controllers.