Modeling and Control Research of Fractional-Order Memristor Based on Optimization Algorithm in Frequency Domain

Based on its unique memory characteristics, nonlinear characteristics, and nanoscale structure, fractional-order memristor has broad application value in many fields. So it has become a research hotspot in recent years. Firstly, this paper analyzed the waveforms of conductivity and voltage-current characteristic curves of fractional-order memristors with order changed in the time domain. Then, based on the particle swarm optimization algorithm combined with the Matlab function fminsearch(), the transfer function model of the fractional-order memristor was identified in the frequency domain. The identification effect was demonstrated to be good by fitting the curves and the value of the objective function. Finally, a fractional-order optimum \(P{{I}^{\lambda }}{{D}^{\mu }}\) controller was designed for the fractional-order memristor model. By controlling indicators, it is demonstrated that the control effect is much better than integer-order PID control.