A Modified FOPID Versus H∞ and m Synthesis Controllers: Robustness Study

The H∞, m synthesis and fractional order (FPM) controllers are types of robust designs that use thelinearized model of the system and provide a linear controller. The m synthesis approach directly considers theuncertainty, but H∞ and FOPID run for the worst uncertainty scenario. mFPM is the modified version of FOPIDdesign where 1) it takes into account the given uncertainty by a graphical Phase Margin Distribution Map (PMDP),and 2) reduces the controller design calculations by working on the samples of the system frequency responseinstead of its analytical equation. The design strategy can perfectly force the desired flatness in the phase marginband and maintain the system performance robustness. For evaluation, the algorithms are applied to a second-orderuncertain system and a perturbed UAV roll control. In both cases, the lowest output response variance and the bestperformance robustness is gained from the mFPM design. This is verified through numerous simulations.