【】用根轨迹法设计相位超前校正网络33

用根轨迹法设计相位超前校正网络当品质指标以时域指标提出时，用根轨迹设计系统较方便。当期望闭环主导极点位于未校正系统根轨迹的左边时，就可使用超前校正。在不考虑稳态指标时设计步骤如下：1.根据所需要的动态品质指标要求，确定闭环主导极点A的位置；2.画出未校正系统的根轨迹，求出使根轨迹通过A点所需要的补偿角，可这样去计算：校正后系统的开环传函为：是附加增益13.决定的零极点，按下列步骤得到的可使它的附加增益值最小。（1）过A点作水平线AB；（2）做的角平分线AC；（3）在AC两边做；AE，AD与负实轴的交点则为及，于是有A点应满足根轨迹的辐角条件则：即：ImRe2f2fABCDET1-1aT-O24.画出校正系统根轨迹，并由幅值条件求出校正系统的根轨迹增益及稳态误差的系数。一控制系统如图所示，现要求满足下列性能指标。（1）阶跃响应的最大超调量；（2）阶跃响应的调整时间；例.3（1）.由，由式可求得，取由得；得闭环主导极点解：（2）.画出未校正根轨迹。期望主导极点在原系统根轨迹的左边，原系统开环极点对于点产生相位为

要使点位于根轨迹上，校正装置要提供的相位角为43.画水平线，作角平分线，再作，与负实轴交于-9.6，与负实轴交于-4ImReBCDEO-10-9-8-7-6-5-4-3-2-1-6-4-224654.画出校正以后系统根轨迹，求出点根轨迹增益速度误差系数校正系统的开环传函为：

61.设计思路：当滞后网络的零极点相对于主导极点A为一对偶极子时，校正后的开环增益，为校正前的开环增益，增大到校正前开环增益的倍，这样改善了稳态性能。下面具体推导一下：原系统的开环传函为：

用根轨迹法设计相位滞后校正网路开环增益为：根轨迹增益为：7校正后系统的开环传函为：校正后在A点的根轨迹增益A为期望的闭环主导极点，前一项就是校正系统的开环增益即校正后系统的开环增益增大到原系统的开环增益的倍。82.设计步骤：（1）画出未校正系统的根轨迹，根据动态性能指标，在根轨迹上确定期望闭环主导极点A；（2）确定未校正系统在A点的根轨迹增益和开环增益；（3）根据稳态指标求出系统所需要的误差系数（即开环增益）；（4）求出系统为了满足稳态性能指标，误差系数需要增加的倍数，这个需要增加的倍数由滞后网络的这一对偶极子提供；9（5）选择滞后校正网络的零点及极点，使满足，并要求和离开原点越近越好，但它们离原点越近就意味着要求越大，物理实现困难，一般取；（6）画出校正系统的根轨迹；（7）调整根轨迹增益（放大器增益），使闭环极点位于期望位置；（8）校验指标；（9）求出网络参数；10例：有一单位反馈控制系统的开环传函为，要求满足下列性能指标；（1）当输入是一个1的单位速度函数时，输出的速度函数rad；（2）单位阶跃响应的最大超调量，试设计一个相位滞后校正网络；11解：（1）画出未校系统的根轨迹，如图所示；由，得，，用作图法和解析法都可求得；（2）未校系统当闭环极点位于和时，根迹增益，得，即当时，原系统闭环极点是、；开环增益；（3）由稳态指标得12（4）系统只有通过、点动态指标才能满足要求，但此时的开环增益，不满足稳态性能指标要求，需要把开环增益提高倍，即由滞后网络提供、；（5）选和：，及，校正后系统的开环传函13（6）画出校正后系统的根迹，除原点外，形状与原系统相似；（7）调整使闭环主导极点位于、上

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