基于幂次趋近律滑模控制的H桥逆变器复杂动力学行为研究

基于幂次趋近律的滑模控制具有响应速度快、对噪声干扰和参数摄动不敏感等特点,在H桥逆变器的控制中得到广泛应用。然而,滑模控制的H桥逆变器是一种非线性控制的时变非线性系统,必然表现出强的复杂的动力学行为,控制参数和电路参数的选取将影响系统工作的稳定性。分析该系统的工作过程,运用频闪映射法建立系统的一阶离散模型;采用折叠图和频谱图的方法分析了系统在不同控制参数α和k下的复杂动力学行为,发现一种多种倍数的倍周期状态同时存在的特殊分岔现象,并通过分析输出波形峰值和谷值附近采样的分岔图进行了一一验证。运用快变稳定性定理对系统工作的稳定性进行进一步的分析,研究结果为系统控制参数的合理选择提供重要依据。研究发现输入电压E、负载电感L与电阻R等外部电路参数的选取对系统的稳定性能有重要的影响。因此,研究结论对基于幂次趋近律滑模控制的H桥逆变器的设计和调试提供了可靠的参考,具有一定的理论意义和实际的工程价值。

Research on complex dynamic behavior of H-bridge inverter based on power rate reaching law sliding mode control

Sliding mode control based on power rate reaching law is widely used in H-bridge inverter because of its fast response and insensitivity to noise disturbance and parameter perturbation. However, the H-bridge inverter with sliding mode control is a time-varying nonlinear system with nonlinear control, which is bound to show strong and complex dynamic behavior. The selection of control parameters and circuit parameters will affect the stability of the system. Firstly, the working process of the system was analyzed, and the first-order discrete model of the system was established by stroboscopic mapping method. Secondly, the complex dynamic behavior of the system under different control parameters α and k was analyzed by means of folding diagram and spectrum diagram. A special bifurcation phenomenon of multiple period-doubling state was found, which was verified by analyzing the bifurcation diagrams sampled near the peak and valley values of the output waveform. Thirdly, the stability of the system was further analyzed by using the fast-varying stability theorem, and the research results provide an important basis for the reasonable selection of system control parameters. Finally, it was found that the selection of external circuit parameters such as input voltage E, load inductance L and resistance R has an important impact on the stability of the system. Therefore, the research conclusion provides a reliable reference for the design and debugging of H-bridge inverter based on power rate reaching law sliding mode control, and has certain theoretical significance and practical engineering value.