Abstract
In some of the complicated control problems we have to use the controllers that apply nonlocal operators to the error signal to generate the control. Currently, the most famous controller with nonlocal operators is the fractional-order PID (FOPID). Commonly, after tuning the parameters of FOPID controller, its transfer function is discretized (for realization purposes) using the so-called generating function. This discretization is the origin of some errors and unexpected results in feedback systems. It may even happen that the controller obtained by discretizing a FOPID controller works worse than a directly-tuned discrete-time classical PID controller. Moreover, FOPID controllers cannot directly be applied to the processes modeled by, e.g., the ARMA or ARMAX model. The aim of this paper is to propose a discrete-time version of the FOPID controller and discuss on its properties and applications. Similar to the FOPID controller, the proposed structure applies nonlocal operators (with adjustable memory length) to the error signal. Two methods for tuning the parameters of the proposed controller are developed and it is shown that the proposed controller has the capacity of solving complicated control problems.
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Farshad Merrikh-Bayat received his B.Sc. in Electronics from K. N. Toosi University of technology in 2002, and M.Sc. and Ph.D. in Electrical Engineering (control) from Sharif University of Technology, in 2005 and 2009, respectively, all from Tehran, Iran. He is the author of 5 books, 16 journal and 22 conference papers. His research interests include meta-heuristic optimization algorithms, nonlinear dynamics and control, Fractional-order systems and memristive systems.
Nafiseh Mirebrahimi received her B.Sc. and M.Sc. degrees in Electrical Engineering (electronics) from the University of Zanjan, Iran, in 2009 and 2014, respectively. She is currently preparing for Ph.D. degree at the same university. Her research interests include digital signal processing and memristive systems.
Mohammad Reza Khalili received his B.Sc. degree in Computer Engineering from the University of Zanjan, Iran in 2014. His research interests include robotics and digital control systems.
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Merrikh-Bayat, F., Mirebrahimi, N. & Khalili, M.R. Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications. Int. J. Control Autom. Syst. 13, 81–90 (2015). https://doi.org/10.1007/s12555-013-0335-y
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DOI: https://doi.org/10.1007/s12555-013-0335-y