Analyzing complex fractional order systems physical phenomena in IOPI controller design

The Fractional Complex Order Plant model, which has lately gained popularity in applied physics and control systems, is the main subject of this study. The major contribution of this study to the literature is the discussion of the physical phenomena of complex plant models and how they affect the stability and robustness of the systems. Because the Fractional Complex Order Plant model is the most general mathematical form, other plant models covering the Integer Order Plant and the Fractional Order Plant can be easily created with this benefit. The proposed approach using the classical Proportional Integral controller which is recalled as the Integer-Order PI controller in this paper gives the calculation equations of the physical alterations of plants having integer, fractional, and complex orders. Along with the visuals and with the aid of simulations, the consequences of the parameters on the system are described. Additionally, the advantages and disadvantages of the proposed controller designs for each of the three plant species are discussed.