Nonlinear Behaviors of the H-Bridge Inverter with Improved Exponential Reaching Law Sliding Mode Control

To address the bifurcation and chaos phenomena occurring in sliding-mode-controlled inverters, this paper constructs an improved exponential reaching law-based sliding mode control inverter system. To analyze the operational process of the H-bridge inverter system under the improved exponential reaching law-based sliding mode control, a discrete iterative mathematical model is derived using the theory of frequency-flashing mapping. The evolution of the system’s nonlinear behavior under different control parameters is studied through bifurcation diagrams, fold maps, and spectrum diagrams. Based on the principle of fast-changing stability, the stable operating region of the system control parameters is analyzed, showing that the obtained stability range is consistent with the results from the bifurcation diagrams. The analysis reveals that the stable region varies with the control coefficients and internal circuit parameters within a certain range, leading to the coexistence of multiple periodic states such as period-doubling bifurcations and intermittent chaos. Furthermore, a defect is identified where the stability region of the control coefficient is relatively narrow. To mitigate the instability caused by parameter variations, time-delayed feedback control is introduced into the improved exponential reaching law-based sliding mode control inverter. Numerical simulation results verify the feasibility of this chaotic control strategy. The conclusions offer significant theoretical guidance for the optimization design and tuning of H-bridge inverters.