Bifurcation Analysis and Chaos Control of H-Bridge Inverter with Improved Power Reaching Law Sliding Mode Control

Abstract

To address the nonlinear instability phenomena existing in the H-bridge inverter under improved power reaching law sliding mode control, a discrete iterative mathematical model of the system is derived based on the stroboscopic mapping theory. Through bifurcation diagrams, folding diagrams, frequency spectra, and the fast-varying stability theorem, the mechanism of how control parameters influence the dynamical behavior of the inverter system is analyzed. The research results indicate that an excessively large sliding mode gain will cause the system to enter a chaotic state via period-doubling bifurcations, significantly degrading the operational stability and efficiency of the inverter. To mitigate this potential instability, a conventional one-step discrete time-delayed feedback control (dTDFC) realization is adopted as an auxiliary feedback in the improved power reaching law sliding mode controller. By introducing a differential feedback between the state variable and its delayed state, this feedback regulates the discrete dynamical evolution process of the system, thereby improving its operating state. Simulation results verify the effectiveness of the composite controller, providing a theoretical basis for the parameter optimization and engineering design of the H-bridge inverter under improved power reaching law sliding mode control.