高阶非奇异终端滑模控制直流变换器的抖振问题诱发机理

The chattering problem is the chief drawback of DC-DC converters under the control of sliding mode theory, inducing high-frequency oscillation to bring high switching losses, electromagnetic interference, so that the power conversion quality is severely reduced. Focused on these converters,we deeply analyse the mechanism of chattering problem induced by complex nonlinearities of modelling, controller and modulation of the closed-loop Buck control system in time domination and frequency domination. The following important contents are included: (1) Based on a novel high-order nonsingular terminal sliding mode control method, the continuous smooth duty-cycle signal can be obtained, and the charge-discharge behavior of energy storage elements is flexiblely controlled. Furthermore, the influence of chattering signals on system Lyapunov stability is explored. (2) The amplitude-frequency response of chattering signals is quantitatively analysed with the input voltage in frequency domination, and the stability of periodic oscillation and limit cycle in the neighborhood of slidiing surface is investigated. Finally, the mathematical relation of the binary function about the magnitude and frequency of chattering signals with controller's tuning parameters and duty cycle is deducd. (3) Based on the Poincare theory, the switching sequences of system states and switching control strategy are conducted to quantitative control chattering signals, and the sufficient condition for the existence and uniquity of limit cycle is deduced. The research results are expected to provide a novel idea for the quantitative analysis and control of chattering problem, as well as to be of great value for the real application of sliding mode control theory.

抖振问题是制约滑模控制理论在直流变换器应用的首要障碍，抖振谐波信号造成高开关损耗、电磁干扰等问题，严重降低电能转化质量。本项目以直流变换器为控制对象，从时域和频域全面深入剖析闭环控制系统的建模、控制和滞环调制复杂非线性诱发抖振问题机理，计及抖振信号的谐波分量影响，重点研究：利用新型高阶非奇异终端滑模控制方法实现占空比信号的连续平滑输出，柔性控制储能元件的充放电行为，在时域内探索抖振信号对系统Lyapunov稳定性的影响；在频域内定量分析外部电压输入下抖振信号的幅频响应，研究系统在滑模面邻域内周期振荡和极限环的稳定性问题，建立抖振信号幅值和频率二元函数与控制器设计参数、占空比的数学关系；基于Poincare理论研究状态切换子序列的构造和切换策略，推导极限环存在且唯一的充分条件，实现抖振信号的定量控制。研究结果为抖振问题的定量分析与控制提供一种新思路，对滑模控制实用化研究具有重要价值。

抖振问题是制约滑模控制理论在直流变换器应用的首要障碍，高频抖振信号会造成高开关损耗、电磁干扰等问题，严重降低电能转化质量。本项目旨在从时域和频域全面深入剖析直流变换器输出电压抖振信号的产生机理，已完成研究内容包括：1) 利用新型连续非奇异终端滑模控制方法柔性控制储能元件的充放电行为，可实现闭环控制系统下定频和变频可控开关管的通断控制；在时域内量化给出开关频率的计算公式，进而可分析电路中电感、电容、滞环调制宽度等非线性参数对输出电压性能影响；所提新型连续非奇异终端滑模控制方法可拓展应用到一般系统；2）在频域内定量分析外部电压输入下抖振信号的幅频响应，建立抖振信号幅值和频率二元函数与连续非奇异终端滑模控制器设计参数、占空比的数学关系；研究计及未建模动态影响下的直流变换器输出性能，利用描述函数法量化给出其输出电压谐波的幅频特性；研究基于多滑模面的直流变换器滑模控制，即通过多个开关管的切换配合，量化控制开关管的开关频率；考虑了计及寄生电容等非理想参数下的直流变换器的保成本和保暂态性能控制；3）基于Filippov方法的直流变换器电路非线性分析与控制，建立采样数据模型，以输入电压作为分岔参数，以锯齿波一个周期时刻的输出电压采样值作为变量，判断和分析电路的分岔情况，利用Filippov方法求取不动点处的Jacobian矩阵，根据特征根选取电路参数，从而抑制电路振荡现象发生，保证变换器系统的稳定性；基于双环电压直流变换器控制技术，分析输入电压、电感、负载电阻、输出电容、输出电容ESR、参考电压等电路参数变化对其复杂非线性动力学行为的影响，包括进行分岔分析、庞加莱映射图分析、对Jacobi矩阵及其特征值分析等。研究结果可实现对直流变换器输出电压抖振信号的定量分析与抑制，为其电能转换品质的量化研究提供一种新思路。研究工作均按照既定计划进行，发表SCI和EI文章共14篇，其中刊物文章4篇，会议文章10篇，专利授权2项。