Fractional-order controllers for irrational systems

In this contribution, fractional-order controllers of the type PD mu and PI lambda are applied to a class of irrational transfer function models that appear in large-scale systems, such as networks of mechanical/electrical elements and distributed parameter systems. More precisely, by considering the fractional-order controller kp+k eta s alpha in the Laplace domain with -1 <=alpha <= 1, a stability analysis in the parameter-space (kp,k eta,alpha) is presented. Furthermore, as a way to measure the controller robustness, the controller's fragility analysis using the parameter-space (kp,k eta,alpha) is derived. Finally, several applications that demonstrate the utility of our results are included.