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 푘푝+푘휂푠훼 in the Laplace domain with −1≤훼≤1 , a stability analysis in the parameter‐space (푘푝,푘휂,훼) is presented. Furthermore, as a way to measure the controller robustness, the controller's fragility analysis using the parameter‐space (푘푝,푘휂,훼) is derived. Finally, several applications that demonstrate the utility of our results are included.
© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Guel-Cortez was supported by the Centre for Fluid and Complex Systems department of Coventry University. The research of M?ndez-Barrios has been supported by CONACyT-Mexico. E. Kim acknowledges the Leverhulme Trust Research Fellowship (RF- 2018-142-9). Funding Information: The work of Guel‐Cortez was supported by the Centre for Fluid and Complex Systems department of Coventry University. The research of Méndez‐Barrios has been supported by CONACyT‐Mexico. E. Kim acknowledges the Leverhulme Trust Research Fellowship (RF‐ 2018‐142‐9).
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