The generalised isodamping approach for robust fractional PID controllers design

References

• Åström, K.J., & Murray, R.M. (2008). Feedback systems. Princeton, NJ: Princeton University Press.
   Google Scholar
• Chen, Y.Q., Bhaskaran, T., & Xue, D. (2008). Practical tuning rule development for fractional order proportional and integral controllers. ASME Journal of Computational and Nonlinear Dynamics, 3, 0214031–0214037.
   Web of Science ®Google Scholar
• Chen, Y.Q., & Moore, K.L. (2005). Relay feedback tuning of robust PID controllers with iso-damping property. IEEE Transactions on Systems, Man, and Cybernetics - Part B, 35(1), 23–31.
   PubMed Web of Science ®Google Scholar
• Chen, Y.Q., Petráš, I., & Xue, D. (2009). Fractional order control – a tutorial. In Proceedings of the American Control Conference (pp. 1397–1411), St. Louis, MO.
   Google Scholar
• Malti, R., Moreau, X., Khemane, F., & Oustaloup, A. (2011). Stability and resonance conditions of elementary fractional transfer functions. Automatica, 47(11), 2462–2467.
   Web of Science ®Google Scholar
• Mitchell, M. (1998). An introduction to genetic algorithms. Cambridge, MA: MIT press.
   Google Scholar
• Monje, C.A. (2006). Design methods of fractional order controllers for industrial applications (Unpublished doctoral dissertation). Badajoz (E): University of Extremadura (E).
   Google Scholar
• Monje, C.A., Chen, Y., Vinagre, B.M., Xue, D., & Feliu, V. (2010). Fractional-order systems and controls. London: Springer-Verlag.
   Google Scholar
• Monje, C.A., Vinagre, B.M., Calderon, A.J., Feliu, V., & Chen, Y.Q. (2004). On fractional PIλ controllers: Some tuning rules for robustness to plant uncertainties. Nonlinear Dynamics, 38, 369–381.
   Web of Science ®Google Scholar
• Monje, C.A., Vinagre, B.M., Feliu, V., & Chen, Y.Q. (2008). Tuning and auto-tuning of fractional order controllers for industry applications. Control Engineering Practice, 16(7), 798–812.
   Web of Science ®Google Scholar
• Oustaloup, A. (1991). La commande CRONE: Commande robuste d’Ordre non entier. Paris: Hermes.
   Google Scholar
• Oustaloup, A., Lanusse, P., Melchior, P., Moreau, X., & Sabatier, J. (2006). The CRONE approach: Theoretical developments and major applications. In Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications (pp. 324–354). Luxemburg (A): IFAC.
   Google Scholar
• Oustaloup, A., Levron, F., Mathieu, B., & Nanot, F. (2000). Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits and Systems I, 47(1), 25–39.
   Web of Science ®Google Scholar
• Oustaloup, A., Moreau, X., & Nouillant, M. (1996). The CRONE suspension. Control Engineering Practice, 4(8), 1101–1108.
   Web of Science ®Google Scholar
• Oustaloup, A., Sabatier, J., Lanusse, P., Malti, R., Melchior, P., Moreau, X., & Moze, M. (2008). An overview of the CRONE approach in system analysis, modeling and identification, observation and control. In Proceedings of the 17th IFAC World Congress (pp. 14254–14265). Luxemburg (A): IFAC.
   Google Scholar
• Padula, F., Vilanova, R., & Visioli, A. (2014). H∞ optimization based fractional-order PID controllers design. International Journal of Robust and Nonlinear Control, 24(17), 3009–3026.
   Web of Science ®Google Scholar
• Padula, F., & Visioli, A. (2011). Tuning rules for optimal PID and fractional-order PID controllers. Journal of Process Control, 21, 69–81.
   Web of Science ®Google Scholar
• Padula, F., & Visioli, A. (2012). Optimal tuning rules for proportional-integral-derivative and fractional-order proportional-integral-derivative controllers for integral and unstable processes. IET Control Theory and Applications, 6(6), 776–786.
   Web of Science ®Google Scholar
• Padula, F., & Visioli, A. (2014). Advances in robust fractional control. London: Springer.
   Google Scholar
• Podlubny, I. (1999). Fractional-order systems and PIλDμ controllers. IEEE Transactions on Automatic Control, 44(1), 208–214.
   Web of Science ®Google Scholar
• Pop, C.I., Ionescu, C.M., De Keyser, R., & Dulf, E.H. (2012). Robustness evaluation of fractional order control for varying time delay processes. Signal, Image and Video Processing, 6(3), 453–461.
   Web of Science ®Google Scholar
• Sabatier, J., Agrawal, O.P., & Machado, J.A.T. (2007). Advances in fractional calculus: Theoretical developments and applications in physics and engineering. London: Springer.
   Google Scholar
• Valerio, D., & Sá da Costa, J.. (2006). Tuning-rules for fractional PID controllers. In Preprints IFAC Workshop on Fractional Differentiation and its Applications (pp. 28–33). Luxemburg (A): IFAC.
   Google Scholar
• Valerio, D., & Sá da Costa, J. (2011). Introduction to the single-input, single-output fractional control. IET Control Theory and Applications, 5(8), 1033–1057.
   Web of Science ®Google Scholar
• Vinagre, B.M., Podlubny, I., Hernandez, A., & Feliu, V. (2000). Some approximations of fractional order operators used in control theory and applications. Fractional Calculus and Applied Analysis, 3(3), 945–950.
   Google Scholar
• Visioli, A. (2006). Practical PID control. London: Springer.
   Google Scholar