Robust Fractional-Order Compensation in the Presence of Uncertainty in a Pole/Zero of the Plant

This paper deals with robust frequency compensation in control of fractional-order plants with an uncertain fractional pole/zero (or specially in control of integer-order plants with an uncertain pole/zero). The specifications yielding a robust compensation are introduced, and fractional-order compensators are proposed for satisfying these specifications in the set-point tracking control of the above-mentioned plants. Also, the infinite ranges for the uncertain parameter of the plant, in which satisfying robust compensation specifications is possible by the obtained compensators, are exactly specified. Furthermore, the stability of the obtained control system is analytically analyzed. Moreover, it is shown that in the special cases, the proposed compensators result in control systems having invariant phase/gain margin regardless of the variations of the uncertain parameter of the plant. Numerical simulation and experimental results are presented to verify the effectiveness of the obtained compensators.