Root locus method for any fractional order commensurate system

Fractional order calculus has attracted interests of many control scientists in the last two decades as it more accurately explains the dynamics of the known field like analysis of feedback amplifier, fractances etc. In this paper we have presented a systematic and complete approach to draw the root locus of any closed loop fractional order LTI commensurate system whose open loop transfer function has complex pole and/or complex zeros. Analogous to the integer order system, we have developed a step by step algorithm( viz. asymptotes, break away and break in points, arrival and departure angle etc.)to draw the root loci of denominator of closed loop system transfer function. Finally we have explained the inference of stability of the closed loop system from the root loci of the system in the first Riemann sheet.