Nonlinear Analysis of Hysteretic Modulation-Based Sliding Mode Controlled Quadratic Buck–Boost Converter

Abstract

In this paper, the dynamics of hysteresis current-controlled quadratic buck-boost converter is investigated in detail. The system model is derived based on the sliding mode approach and also in its dimensionless form for algebraic brevity. The stability of the system is disclosed with the aid of the movement of eigenvalues. Onset of Hopf bifurcation is identified when the complex conjugate eigenvalue pair crosses the imaginary axis of the complex plane. The stability boundary is drawn to benefit the power electronics engineer for a stable and reliable design. The computer simulation of the switched model is performed using MATLAB/Simulink software to uncover the sequential occurrence of nonlinear behavior exhibited due to Hopf bifurcation for variation in control parameters and the input voltage. The phase portrait disclosing the subtle periodicity is plotted at different operating points to elicit that the stable period-1 attractor bifurcates to the quasi-periodic orbit and finally to a limit cycle. The precise dynamic of the phase portrait is also captured using the Poincare section. Experimental outputs are presented for confirming the low-frequency bifurcation scenario witnessed in the simulated and analytical results.