Robust isophase margin control of oscillatory systems with large uncertainties in their parameters: A fractional-order control approach

This paper addresses the problem of designing controllers that are robust to large changes in the undamped natural frequencies of a plant. Plants must be represented by means of minimum phase rational transfer functions of an arbitrary order whose oscillatory dynamics must fulfill the pole-zero interlacing property on the imaginary axis. The design specifications are as follows: (i) a phase margin for the nominal plant; (ii) a gain crossover frequency for the nominal plant; and (iii) a constant phase margin for large variations in the undamped natural frequencies of the plant, the zeros associated with the oscillatory part of the plant and the gain of the plant. Theorems are proposed that define the structure of the controllers that fulfill these specifications. We show that these robust controllers must necessarily include a fractional-order integro-differential term. Analytical simple expressions with which to obtain the simplest controllers that verify the aforementioned specifications are also obtained. Some relevant features of these fractional-order controllers are later highlighted. Finally, as an example, these controllers are applied to a Buck electronic converter. Copyright (c) 2016 John Wiley & Sons, Ltd.