.

结论：

1.增加不同的零点对系统参数有不同的影响；

2.曲线峰值与超调量受到影响后的值与原值没有重合，上升时间，超调时间与调节时间与原值有重合；

3.随着a的增加（或者说随着零点渐渐远离零点），曲线峰值受到的影响（取绝对值来看）和超调量受到的影响均是先减后增；上升时间，超调时间受到的影响，上升时间和调节时间受到的影响均是先增再减；

4.对系统影响最大的点在a=1或附近的位置；

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2.3增加极点后的开环传递函数G2（s）的性能分析

为了分析开环传递函数的极点对系统性能的影响，现在在原开环传递函数的表达式上单独增加一个极点S=-p,并改变p值大小，即离原点的距离，分析比较系统性能的变化。所以增加零点后的开环传递函数为：

G(s)?1

(s?p)(s?0.25)(s?0.52)2.3.1 当p分别为0.01,0.1,1,10,100时，G2（s）的根轨迹与阶跃响应如下excel

p传递函数M指令根轨迹绘制阶跃响应0.01G(s)?0.111010011111G(s)?G(s)?G(s)?G(s)?(s?1)(s?0.25)(s?0.52)(s?0.01)(s?0.25)(s?0.52)(s?10)(s?0.25)(s?0.52)(s?0.1)(s?0.25)(s?0.52)(s?100)(s?0.25)(s?0.52)g0=zpk([],[-0.25,-0.52,-0.01],[1]);g=feedback(g0,1);rlocus(g)Root Locus2System: gGain: 0.0284Pole: 0.256 + 0.856iDamping: -0.286Overshoot (%): 256Frequency (rad/s): 0.8931.5System: gGain: 0.00937Pole: -1.28Damping: 1Overshoot (%): 0Frequency (rad/s): 1.28g0=zpk([],[-0.25,-0.52,-0.1],[1]);g=feedback(g0,1);rlocus(g)Root Locus2System: gGain: 0Pole: 0.218 + 0.853iDamping: -0.247Overshoot (%): 223Frequency (rad/s): 0.8811.5System: gGain: 0Pole: -1.31Damping: 1Overshoot (%): 0Frequency (rad/s): 1.31g0=zpk([],[-0.25,-0.52,-g0=zpk([],[-0.25,-0.52,-1],[1]);10],[1]);g=feedback(g0,1);g=feedback(g0,1);rlocus(g)rlocus(g)Root Locus2System: gGain: 0.00198Pole: -0.0641 + 0.828iDamping: 0.0772Overshoot (%): 78.4Frequency (rad/s): 0.83-1Imaginary Axis (seconds)g0=zpk([],[-0.25,-0.52,-100],[1]);g=feedback(g0,1);rlocus(g)Root Locus300Root Locus2520151050-5-10-15-2000.511.5System: gGain: 0.026Pole: -1.650.5Damping: 1Overshoot (%): 0Frequency (rad/s): 1.6510200System: gGain: 4.54Pole: -10.1Damping: 1Overshoot (%): 0Frequency (rad/s): 10.1System: gGain: 0Pole: -0.38 - 0.293iDamping: 0.792Overshoot (%): 1.7Frequency (rad/s): 0.479System: gGain: 2.21e+004Pole: -102Damping: 1Overshoot (%): 0Frequency (rad/s): 102System: gGain: 0Pole: -0.475Damping: 1Overshoot (%): 0Frequency (rad/s): 0.4751-1Imagnary Axs (seconds)1-1Imagnary Axs (seconds)-1Imaginary Axis (seconds)-1Imaginary Axis (seconds)1000.50.5根轨迹0-0.5System: gGain: 0Pole: 0.251 - 0.847iDamping: -0.284Overshoot (%): 254Frequency (rad/s): 0.8840-0.5System: gGain: 0Pole: 0.218 - 0.853iDamping: -0.247Overshoot (%): 223Frequency (rad/s): 0.8810-0.5-100-1-1-1-1.5-1.5-1.5-2-2.5-2-1.5-1-0.500.51-2-2.5-2-1.5-1-0.500.51-2-3System: gGain: 0Pole: -0.0644 - 0.827iDamping: 0.0776Overshoot (%): 78.3Frequency (rad/s): 0.83-2.5-2-1.5-1-0.5RealAxis (seconds-1-200RealAxis (seconds-1RealAxis (seconds-1-25-35-30-25-20-15-10-5051015-300-400-300-200-100RealAxis (seconds-10100200RealAxis (seconds-1系统是否稳定否M指令g0=zpk([],[-0.25,-0.52,-0.01],[1]);g=feedback(g0,1);step(g)10x 1026否g0=zpk([],[-0.25,-0.52,-0.1],[1]);g=feedback(g0,1);step(g)1x 1013否否否g0=zpk([],[-0.25,-0.52,-100],[1]);g=feedback(g0,1);step(g)Step Response0.080.07System: gTime (seconds): 21.4Amplude: 0.0711g0=zpk([],[-0.25,-0.52,-g0=zpk([],[-0.25,-0.52,-1],[1]);10],[1]);g=feedback(g0,1);g=feedback(g0,1);step(g)step(g)System: gTime (seconds): 4.22Amplude: 1.491.5Step ResponseStep ResponseStep Response0.450.4System: gSystem: gTime (seconds): 15.9Time (seconds): 8.52Step ResponseAmplude: 0.436Amplude: 0.434System: gTime (seconds): 10.8Amplude: 0.44280.560.35System: gTime (seconds): 2.591Amplude: 0.887Amplitude0.060.30.05AmplitudeAmplitude响应Amplitude0.250.20.152-0.50-1-2System: gTime (seconds): 76.5Amplude: 0.8790.5Amplitude400.040.030.020.10.050.01-4050100150200250-1.50204060801001201400Time (seconds)010203040506070809000024681012141618051015Time (seconds)202530Time (seconds)Time (seconds)Time (seconds)增加极点对系统性能的影响

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.

结论：

1.增加不同的极点对系统参数有不同的影响；

2.比较观察增加零点时的系统参数（以上升时间tr为例）的变化，可以发现，在某些区间（x1

存在：，则

，说明了极点与零点

3同时可以预见，当零点与原点的距离趋近于无穷远时，系统性能受到的影响趋近于0。

2.4偶极子对系统性能的影响

原函数传递函数1G(s)?(s?0.25)(s?0.52)不十分接近原点的偶极子（s?2.01）G(s)?（s?2）(s?0.25)(s?0.52)Root Locus2.52System: gGain: 0.0166Pole: -0.384 + 1iDamping: 0.358Overshoot (%): 30Frequency (rad/s): 1.07Root Locus543210-1-2-3-4-5-0.9System: gGain: 0.0369Pole: -0.385 - 1.01iDamping: 0.356Overshoot (%): 30.2Frequency (rad/s): 1.081magnaryAxs(seconds)Imagnary Axs (seconds1)Imagnary Axs (secondsSystem: gGain: 0.0369Pole: -0.385 + 1.01iDamping: 0.356Overshoot (%): 30.2Frequency (rad/s): 1.08Damping: 10.5Overshoot (%): 0Frequency (rad/s): 2.010-0.5-1-1.5-2-2.5-2.5System: gGain: 0Pole: -0.384 - 0.993iDamping: 0.36Overshoot (%): 29.7Frequency (rad/s): 1.06-2-1.5-1Real Axis (seconds-1)-0.511.5System: gGain: 2.791Pole: -2.01根轨迹-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.100.1Real Axis (seconds-1)Step Response1.4System: gTime (seconds): 3.14Amplitude: 1.15Step Response1.4System: gTime (seconds): 3.15Amplitude: 1.151.2System: gTime (seconds): 1.971Amplitude: 0.890.81.2System: gTime (seconds): 1.961Amplitude: 0.888System: gTime (seconds): 11.4Amplitude: 0.8850.6Amptude阶跃响应0.80.60.40.40.20.2005Time (seconds)1015005Time (seconds)10结论：

只要偶极子不十分接近原点，它们对系统性能的影响就甚微，从而可以忽略它们的存在。单纯的课本内容，并不能满足学生的需要，通过补充，达到内容的完善 教育之通病是教用脑的人不用手，不教用手的人用脑，所以一无所能。教育革命的对策是手脑联盟，结果是手与脑的力量都可以大到不可思议。

ddtddp十分接近原点的偶极子G(s)?（s?0.01）s(s?0.25)(s?0.52)Root Locus2.521.51System: gGain: 0.049Pole: -0.389 + 1.02iDamping: 0.358Overshoot (%): 30Frequency (rad/s): 1.090.50System: gGain: InfPole: 0.01Damping: -1Overshoot (%): 0Frequency (rad/s): 0.01)-0.5-1-1.5-200.5-2.5-0.4System: gGain: 0.049Pole: -0.389 - 1.02iDamping: 0.358Overshoot (%): 30Frequency (rad/s): 1.09-0.35-0.3-0.25-0.2-0.15-0.1-0.0500.05Real Axis (seconds-1)1x 1025Step Response0-1-2AmptudeSystem: gTime (seconds): 11.4Amplitude: 0.887Amptude-3-4-5-6-701000200030004000500060007000Time (seconds)15 .