阶系统时域分析.pptVIP

Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1*Chapter2-1CHAPTER3

TimeDomainAnalysisofControlSystem

andItsCharacteristicsBy柳春平*Chapter2-1引言3.1动态和稳态性能指标3.2一阶系统的时域分析3.3二阶系统的时域分析3.4线性系统的稳定性分析3.5控制系统的稳态误差CHAPTER3

TimeDomainAnalysisofControlSystem

andItsCharacteristics3.2一阶系统的时域分析*Chapter2-1一阶系统的数学模型RC电路、恒温箱、液位调节系统、室温调节系统是常见的一阶系统一阶系统的单位阶跃响应*Chapter2-1对于单位阶跃输入于是由拉氏反变换可以得到一阶系统的单位阶跃响应为讨论：*Chapter2-11是稳态分量，由输入信号决定。01是瞬态分量（暂态分量），它的变化规律由传递函数的极点-1/T或时间常数T决定。02当时，瞬态分量按指数衰减到零。03注意到，04一阶系统单位阶跃响应的典型数值所以，一阶系统的单位阶跃响应是一条指数上升、渐近趋于稳态值的曲线。讨论：*Chapter2-104030102图中对应的A点是实验方法求取一阶系统时间常数T的重要特征点。c(3T)=0.95和c(4T)=0.982表明系统时间响应进入稳态值的5％和2％允许误差带的过渡过程时间分别为时间常数T越小（惯性小），系统响应速度越快。响应曲线在t=0处斜率最大，其值为1/T（也可由此求T）。01没有超调σp=0，不存在峰值时间。02调整时间为一阶系统的单位脉冲响应01对于单位脉冲输入02于是03由拉氏反变换可以得到一阶系统的单位脉冲响应为04讨论：*Chapter2-1一阶系统单位脉冲响应的调节时间为或1单位脉冲响应中只包含瞬态分量。2单位脉冲响应也可以通过对单位阶跃响应求导获得。单位阶跃响应是单位脉冲响应的积分。3系统的单位脉冲响应对应系统传递函数的拉普拉斯反变换，这一结论对于所有系统都是成立的。4一阶系统的单位斜坡响应*Chapter2-1对于单位斜坡输入01.于是02.由拉氏反变换可以得到一阶系统的单位斜坡响应为03.Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Chapter2-1Cha