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