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 FO-PID 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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Memristor is the fourth fundamental passive circuit element with potential applications in development of analog memories, artificial brains (with the capacity of hardware training) and neuro-science. In most of these applications the memristance of the device should be set to the desired value, which is currently performed by trial and error. The aim of this paper is to propose a circuit for copying the value of the given resistor into a memristive device. HSPICE simulations are also presented to confirm the efficiency of the proposed circuit.