Dynamic performance analysis of PID controller with one memristor

Abstract

Memristor M is an ideal circuit element discovered recently, which relates the charge q and the magnetic flux Á in a circuit and complements a resistor R, a capacitor C and an inductor L as an ingredient of ideal electrical circuits. The resistance of memristor changes automatically as its voltage changing, which can be used as a tunable parameter in control systems. Proportional-integral-derivative (PID) controller is the most popular controller for the majority of control systems. However, it is difficult to adjust the PID parameters. Once the PID parameters are adjusted, they remain unchanged during the control systems operation. In this paper, we present a PID controller with a memristor, called M-PID controller. Based on a conventional PID circuit schematic and a M-PID circuit schematic, we establish their mathematic models. Then we analyze the dynamic performance of M-PID controller with a sinusoidal voltage input and an impulse voltage input. We show that M-PID controller acts more rapidly and strongly than PID controller, furthermore some parameters of M-PID controller adjust adaptively with the input.