Fractional‐order controllers for irrational systems

Abstract

Abstract In this contribution, fractional‐order controllers of the type PDμ and PIλ 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+kηsα in 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 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.

Keywords

• Linear control systems
• Control system analysis and synthesis methods
• Stability in control theory
• Distributed parameter control systems