Fractional order internal model control of non‐minimum phase and time‐delayed plants

Abstract

Several applications on fractional order (FO) control have gained considerable significance in the recent years, which led to the evolution of novel tuning strategies of the generalized order FO controllers. Some of the methods in available literatures are based on constrained minimization optimization techniques or analytical method defined only for specific plants. They are valid only for some special model cases. On the contrary, in this technical note, a generalized non-integer order internal model control (IMC) framework is realized for any order non-minimum phase (NMP) plants with right half plane (RHP) zero as well as time delayed plants having any finite relative order. Its parameters are graphically interpreted satisfying the frequency domain design stipulations for single input and single output (SISO) higher order linear time invariant (LTI) plants. The performance of the same on a bioreactor fermentation process for its temperature control is found to have outperformed in contrast to its integer order (IO)-IMC. It is therefore inferred here that this new approach pledges to impart unique solution of the controller parameters, formulating a highly efficient tool outperforming the existing paradigms. Simulation and real time experimentation are presented to validate the method put forward providing satisfactory performance in reference tracking, disturbance rejection, and robustness to various plant parameter perturbations. K E Y W O R D S fractional order (FO) control, internal model control (IMC), non-minimum phase unstable plants, time delayed plants

What are the key stability challenges in high-bandwidth, non-minimum phase systems with time-varying, and non-smooth delays?

“…The intricate realm of understanding and effectively controlling systems characterized by non-minimum phase delays has been a persistent focal point within the domain of control theory for several decades [ 36 , 37 ]. A wealth of scholarly literature attests to the multifaceted nature of this research endeavor, offering rich approaches that span classical control techniques to more contemporary methodologies rooted in advanced mathematical concepts [ [38] , [39] , [40] ].…”