14Buck变换器的滑模控制研究(孙明志)

NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering答辩人：孙明志指导教师：郑艳副教授Buck变换器的滑模控制研究NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering绪论Buck变换器的工作原理与数学模型Buck变换器的自适应积分滑模控制Buck变换器的自适应动态滑模控制结论与展望NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering课题背景及研究意义由于开关电源在重量、体积、能耗等方面都比线性电源有显著减少，因此开关电源的应用得到了迅速推广，但是常用的PID控制系统对系统参数的变化比较敏感，当负载大范围变化时，开关变换器存在动态响应速度慢、输出波形有畸变等缺点。而滑模控制的变换器具有稳定范围宽、动态响应快、鲁棒性强等优点，成为研究的热点。NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineeringBuck变换器的工作原理与数学模型NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineeringBuck变换器的工作原理LRTCED图2.1Buck变换器电路NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering开关T导通时LRCE图2.2开关T导通时的Buck电路图NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineeringLRC开关T关断时图2.3开关T关断时的Buck电路图NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineeringBuck变换的数学模型122112xxxaxxbu()refUudtE11aLCEbLC1RC为考虑了负载变化的不确定参数且假设(2.1)取x1为误差电压，x2为电容电流0其中(2.2)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineeringBuck变换器的自适应积分滑模控制NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering考虑如下不确定的二阶系统122112xxxaxxbu(3.1)问题描述积分型切换函数设计为0()()()()tstCXtABKXtdt(3.2)11221212010()xABXtaaxbCccKkk(3.3)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering滑动模态方程为()()()XtABKXt(3.5)2221122sgn()mauxxskxkxbb积分滑模控制器设计(3.6)212Vs稳定性分析2220mVcxsxs(3.7)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering2211ˆ22mVs2221122ˆsgn()auxxskxkxbb设计自适应律为(3.9)22ˆcxs(3.8)稳定性分析2220mVcxsxs(3.10)自适应积分滑模控制控制器设计(3.11)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineeringb的摄动，原系统变为考虑系统参数122112()xxxaxxbbu(3.12)bb其中将式(3.8),(3.12)代入s可得改进的自适应积分滑模控制器22222211ˆ1sgn()bbbscabkxxscbkxbbbb(3.13)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering改进的控制器为2212211122ˆˆsgn()sgn()auxxsxskxkxbbb(3.14)1ˆ1d1m2ˆ2d2m的估计。是对上界的估计，是对上界11bdbkbb222bbdabkbbb设计自适应律为121ˆcxs222ˆcxs(3.15)(3.16)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering稳定性分析(3.17)21111222210mmbVcdxsxsdxsxsb2221122111ˆˆ11222mmbbVsbb(3.18)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineeringBuck变换器的自适应积分滑模控制器(3.21)222ˆsgn()()LCLCuaxxsKXtEE仿真研究(3.22)Buck变换器改进的自适应积分滑模控制器221122ˆˆsgn()()LCLCLCuaxxxsKXtEEE系统参数10HLm15VE5VrefU2333a110c220c10.6k25000k300FCNortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering00.10.20.30.40.50123456t(s)x1(V)积分滑模常规滑模0.380.40.420.440.460.480.54.994.99555.0055.015.015t(s)x1(V)积分滑模常规滑模图3.1输出电压x1的变化曲线图3.2输出电压x1的局部放大图结论：积分滑模控制的快速性明显好于常规滑模控制并且有效地消除了静差NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering00.10.20.30.40.50123456t(s)x1(V)积分滑模自适应积分滑模00.10.20.30.40.50123456t(s)x1(V)积分滑模自适应积分滑模图3.3输出电压x1的变化曲线图3.4输出电压x1的变化曲线结论：当负载变化时，自适应积分滑模控制有效提高了系统的快速性，增强对负载变化的鲁棒性。负载R=100Ω负载R=1ΩNortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering00.10.20.30.40.50123456t(s)x1(V)00.10.20.30.40.50123456t(s)x1(V)图3.5自适应积分滑模控制图3.6改进的自适应积分滑模控制输出电压x1的变化曲线输出电压x1的变化曲线1V阶跃扰动时NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering00.10.20.30.40.50123456t(s)x1(V)自适应积分滑模改进的自适应积分滑模00.10.20.30.44.94.9555.055.1t(s)x1(V)自适应积分滑模改进的自适应积分滑模图3.7输出电压x1的变化曲线图3.8输出电压x1的放大图1V正弦扰动时结论：改进后的自适应积分滑模的稳态性能明显的提高NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineeringBuck变换器的自适应动态滑模控制NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering考虑如下线性二阶系统1221122xxxaxaxbu(4.1)定义切换函数为1122scxcxbu(4.2)问题描述0s由求得等效控制为11221equcxcxb(4.3)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering(4.4)滑动模态方程为122111222xxxacxacxsgn()ss采用等速趋近律则动态控制律为11221sgn()ucxcxsb(4.5)(4.6)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering考虑不确定二阶系统122112xxxaxxbu(4.8)滑动模态方程变为12211122xxxacxcx(4.7)此时，不确定参数被引入到滑动模态方程中，对系统的性能产生影响。NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering定义切换函数11222ˆscxcxux(4.9)ˆ其中为对系统中未知参数的估计自适应动态滑模控制器的设计滑动模态方程为122111222ˆxxxacxcxx(4.10)NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering改进的控制器的设计2x定义含不确定参数的状态的观测器为2112122ˆˆˆxaxxbukxx211122121ˆˆsgn()uccaxcxscxksb10k其中(4.11)(4.12)22222ˆˆˆcxsxxx自适应律为(4.13)动态滑模控制律NortheasternUniversityFriday,March13,2020TheCollegeofInformationScienceandEngineering稳定性