A novel memristive chaotic jerk circuit and its microcontroller-based sliding mode control

Abstract

Due to the experimental realization of memristor circuit elements, research on memristors and memristor-based circuits has surged. Because of their nonvolatile and nonlinear behavior, memristors can be easily applied to chaotic circuits. This study introduces a novel memristive 3D chaotic jerk system, comprising only seven terms, along with its electronic model and microcontroller-based control. The flux-controlled memristor-based jerk system exhibits complex dynamics, which were analyzed through various properties such as phase portraits, the Jacobian matrix, equilibria, eigenvalues, Lyapunov spectra, bifurcation diagrams, and transient chaos behavior. Three controllers, namely, nonlinear feedback, classical sliding mode, and integral sliding mode were designed to control the chaotic jerk oscillator. Lyapunov functions were used to synthesize the nonlinear feedback controller and ensure system stability with the sliding mode technique. Numerical tests under various performance criteria and disturbance conditions showed that the sliding mode controller outperforms the nonlinear feedback controller due to its single-state control structure. The chaotic jerk oscillator hardware circuit was designed and implemented, operating easily with initial conditions set to zero and low DC supply voltages, with all output voltages within ±6V. Both theoretical and simulation results demonstrate the system’s complexity and applicability, with experimental results aligning well with simulations. Consequently, effective microcontroller-based control was achieved using a single-state controller.