An examination of complex fractional order physical phenomena in IOPD controller design

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 14; pp. 15073 - 15093
• Main Authors: Demiroğlu, Uğur, Şenol, Bilal, Matušů, Radek
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.09.2023
• Subjects: analytical method; Control systems design; controller design; Controllers; Crossovers; fractional complex order; fractional order; integer order; Integers; Integrators; Mathematical models; Parameters; Proportional derivative; Robustness (mathematics); Systems stability; Transfer functions
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.9362

This research focuses on the fractional complex order plant (FCOP). The significant contribution is the role of complex plant models in system stability and robustness and associated physical phenomena. A general transfer function is studied in the paper. Other plant models may be built with this structure since the FCOP is a general mathematical form covering integer order plant (IOP) and fractional order plant (FOP). Using the equations produced with the proposed technique and the recommended integer order proportional derivative (IOPD controller, physical changes in integer, fractional and complex coefficients, and orders are observed within this paper. Analysis of the plant controlled with an IOPD controller is done by applying an integrator to reveal the differences. The effects of the parameters are discussed together with the visuals, supported by simulations. The aim is to tune the controller parameters to achieve the phase and specifications as the researcher desired. It is observed that the integrator greatly takes part in reducing the steady‐state error. The IOP with the integrator showed the lowest steady‐state error, and also, the settling and overshoot time were enhanced. Increase in the phase margin also caused an increase in the phase crossover frequency. It is also observed that the fractional order affected the phase crossover frequency comparing with the IOP, and the complex order modification also had an effect comparing to the fractional order version. The complex order of the system is considered with its conjugate components in the imaginary part thus, the results are found separately for each case.