A comparison between FOIMC and FOPI controllers for a submerged robot

The paper focuses on comparing two popular fractional order control strategies consisting of a Fractional Order Internal Model Control (FOIMC) and a Fractional Order Proportional Integral (FOPI) controller. The two strategies are powerful tools in controlling processes with different complexities, using the full potential of fractional calculus, a powerful mathematical tool that generalizes differintegral operations to any non-integer, arbitrary, order. The dynamics of a robot moving through a non-Newtonian fluid is described by a complex fractional order transfer model, which is used to tune both controllers. The inverse of the fractional order process model together with a fractional order filter are used to develop the FOIMC control strategy. The parameters of the FOIMC controller are determined using frequency domain specifications for phase margin and gain crossover frequency. Furthermore, the FOPI controller is developed using the same specifications as for the FOIMC case, with an additional robustness specification through the isodamping property. The two controllers are compared based on the closed loop system performance for test cases related robustness to uncertainties of the process model, step reference and output disturbance rejection.