基于脉冲宽度调制的滑模变结构控制的一阶H桥逆变器的分岔和混沌行为研究

Bifurcation and chaos in sliding mode controlled first-order h-bridge inverter based on pulse width modulation

滑模变结构控制是一种在宽工作范围具有快速响应和高稳定性的鲁棒控制,因而被广泛地应用于逆变器控制中.滑模控制的逆变器本质上是一种由非线性控制方式控制的时变非线性系统,具有复杂的动力学行为.本文以基于脉冲宽度调制的滑模变结构控制的一阶H桥逆变器为例,首先观察不同滑模变结构控制器参数下系统的输出波形,发现了一种多种倍数的倍周期同时存在的新型分岔现象;其次,使用频闪映射方法建立系统的离散迭代模型,并利用折叠图法分析输出波形.通过分析可知系统不能以这种新型分岔为道路通向混沌.此外,在工程应用中十分关心系统稳定性,但是由于滑模变结构控制器的非线性特性,常规解析方法都已不再适用于对系统进行分析,而图解法又难以满足精度要求.因此,本文提出了一种新的适用于滑模变结构控制的逆变器的快变尺度稳定性的判断依据,经验证该判据可以准确地判断系统是否处于稳定运行状态,进而为滑模变结构控制器的参数设计提供可靠依据.

Sliding mode control （SMC） is recognized as a robust controller with fast dynamic response and high stability in a wide range of operating conditions, and therefore it is widely used in the control of inverter. The sliding mode controlled inverter is in nature a nonlinear controlled time-varying nonlinear system, and it has complicated nonlinear behaviors in practice. In this paper the sliding mode controlled first-order H-bridge inverter based on pulse width modulation is taken for example. First, through observation of the waveforms under different SMC parameters, a new type of bifurcation is discovered for the first time, in which diverse multi-period bifurcations exist at the same time. Second, the discrete time iterative model is established for the system and the folded diagram is employed to observe the waveforms. These analyses of current waveforms prove that the new type of bifurcation proposed in this paper is not a route to chaos. Moreover, the stability of the system is much concerned in engineering applications. However, because of the nonlinear characteristics of sliding mode controller, the method using eigenvalues of Jacobian matrix and other analytical methods are unsuitable for the system, and the graphic methods are not accurate enough. Finally, a criterion of fast-scale stability which can accurately distinguish the stability of the system is proposed, and it can be used to provide reliable reference for the parameter design of sliding mode controller.