In this contribution, fractional-order controllers of the type PD𝜇and PI𝜆are 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 controllerkp+k𝜂s𝛼in the Laplace domain with−1≤𝛼≤1, a stability analysis in the parameter-space (kp,k𝜂,𝛼) is presented. Furthermore, as a way to measure the controller's robustness, the controller’s fragility analysis using the parameter-space (kp,k𝜂,𝛼) is derived. Finally, several applications that demonstrate the utility of our results are included.
This codes create all simulations presented in the following reference
Guel-Cortez, A.-J., Méndez-Barrios, C.-F., Kim, E.-jin, Sen, M. Fractional-order controllers for irrational systems. IET Control Theory Appl. 2021; 15: 965– 977. https://doi.org/10.1049/cth2.12095