已知负反馈控制系统开环零、极点分布如图4-4所示,试写出相应的开环传递函数并绘制概略根轨迹图[img=422x256]17d82f1cc9bffff.png[/img]
解: (a) 由图像可知,系统的开环传递函数为[tex=19.714x2.714]GmMeZtiTc+KXROtSXiinMnGdqi3p+8QktdJuPqs9ThUc5lcAG5CWC2iq4JEhnj7h05V5qxqopxwyXza1396dax0MIcX8eta+zTn2OT12/u9no5Rvwyl0D+Gnw5Fljv6NXYx2kzm9+H6EAfWZ6zDQroxGEHANbM0xdS46E2BIIHM=[/tex]起点:两个开环极点0,[tex=1.714x1.214]pJnnmqcmAzigMvjv+gYZI36XB63NfTRucGXAw0EZgxc=[/tex]。终点:两个开环有限零点[tex=3.929x1.214]8u+zgR89e8P6oWwyoQ3sv6xNwAlQsiOBy+5NhPwXdDs=[/tex]。实轴_上的根轨迹区间为[tex=6.357x1.5]De166nmeTkb4C/83+ZZH2wj5sOi9oOmfXf+qN55wD9EeArRp/kDWaZXTq2jgEVtdRbwaDm4SZJlPL1T6jVloLblltbvB1XWMvO1d4UKWojM=[/tex]和[tex=5.214x1.5]De166nmeTkb4C/83+ZZH21e7gsUgj0cL4FrmTcSknUzGEnaDAu1/vwRmjzfbhRrOsaXfyCtCWgyUVXCWcXTUkA==[/tex]。相应的根轨迹图绘于图4-5中。(b)由图像可知,系统的开环传递函数为[tex=19.714x2.714]GmMeZtiTc+KXROtSXiinMnGdqi3p+8QktdJuPqs9ThUc5lcAG5CWC2iq4JEhnj7h05V5qxqopxwyXza1396dax0MIcX8eta+zTn2OT12/u9no5Rvwyl0D+Gnw5Fljv6NduZH3OthyfnPVSdckg/prLpZv9KXfGpeLSC3JYhnV9U=[/tex]起点:两个开环极点0,[tex=1.714x1.214]pJnnmqcmAzigMvjv+gYZI36XB63NfTRucGXAw0EZgxc=[/tex]终点:两个开环有限零点[tex=3.929x1.214]8u+zgR89e8P6oWwyoQ3sv6xNwAlQsiOBy+5NhPwXdDs=[/tex]实轴上的根轨迹区间为[tex=6.286x2.214]De166nmeTkb4C/83+ZZH2xd9yF71/2p4xPosavsIBaY8fkBpDyEY40VCnoQTZsr9P/ZF9m3iVU4Njuzd1EJIWRDsB7wImf4Erzr4dMJF3hVm/0K4/3a8BhjuHQbml9OTcmsjaWNKV1YZXUKwSmqkkw==[/tex]和[tex=5.214x1.5]De166nmeTkb4C/83+ZZH2xd9yF71/2p4xPosavsIBaYxSu6Ac4ihN5zOy9Cy7xX7mlCyb4zD8XnBK5ol1CAXsLizH08U2nqt1Vuk/eTT19Q=[/tex]相应的根轨迹图绘于图4[img=321x265]17d82f512dfa9be.png[/img](c)由图像可知,系统的开环传递函数为[tex=12.714x2.714]wkpmTlIDInBexIVHJJRGuwiAGCJ0QcdJxDXqu304tk6brTFiePirOSRcab3YNZuiB1YyiTeDk+wvummVH3gdGC4xSRa0TXhvRU+fn71R9qPo/I5Kftwcfoab9PZrjv0+[/tex]起点:三个开环极点[tex=5.643x1.214]pJnnmqcmAzigMvjv+gYZI930z3K2BIxZ5qvsKJ8GaHmJ51Q7muy5Sh7MK48ULkvNG3X4LouqORTtYTZtaNBrqw==[/tex]。其中[tex=12.357x1.5]Kcuq1o24rbpbSmHmEJB1AMDRlLEaOe/Erjrzx+XP2qtPA53wM54Lnf5ArYVjOw4pO+r9V4mA+50jMyUwktq50d26kg1c1pL+3MXtfL4Z3Xg=[/tex]。终点:三个无限零点。实轴上的根轨迹区间为[tex=4.357x1.357]FQZ29j+pRdsfZkqoVD3fk9EWZwfAcOLXMtVs3wbco18CotRDk/F9MvQbphYlq6jv[/tex]。渐近线与实轴的夹角 [tex=13.429x2.429]36MWFPU4dyp/2n+OIzojCHmH9+XQNfPQjR7AyqkzRgFXmuTBTOWAC4RpxIVhPL3kWWEb/t8tNyChrJODCH7SZMf4aD31N6/KbnqIeLMQF0o=[/tex]。相应的根轨迹图绘于图4-7中。(d)由图像可知,系统的开环传递函数为[tex=19.714x2.714]GmMeZtiTc+KXROtSXiinMnGdqi3p+8QktdJuPqs9ThUc5lcAG5CWC2iq4JEhnj7h05V5qxqopxwyXza1396dax0MIcX8eta+zTn2OT12/u8qLDS6ysssx2H26KSx5IsNpFKotY/5rXTD1RhNxSUpbWNEG3nGLmp20sizZwwhkZM=[/tex]起点:两个开环极点0,[tex=1.714x1.214]pJnnmqcmAzigMvjv+gYZI36XB63NfTRucGXAw0EZgxc=[/tex]终点:两个开环有限零点[tex=3.5x1.143]YTsf3GxEECmdiHH3mW18FZ8lISvY0r0ftGzjWviPCRU=[/tex][br][/br]实轴上的根轨迹区间为[tex=4.071x1.357]tJ/bZd3Gk9ZEUxLa7+mgOaUGhqj7ztiIPR8RXUU+xApzPLtj/ouiao/OMSMT2JxT[/tex]和[tex=3.0x1.357]vxSHwv19JFBWhFGOGx6xpccun1ASF/3RosIBbQJCbRE=[/tex]相应的根轨迹图绘于图4-8中。[img=332x414]17d82f8ed3e6731.png[/img](e)由图像可知,系统的开环传递函数为.[tex=11.286x2.929]NDMnC73WWMF54oG5O8PQR1yqk+p21hBdW3kRi0YrREoNjIbY1/EvH270racU4SKhlDv+Ogslh3UGyxIVgHA6RIgV6PovOOYkcYp2vhRLfg1Ip9kKcbY7Nf7xrv9VEbaO[/tex]起点: 一个开环极点为[tex=1.714x1.214]pJnnmqcmAzigMvjv+gYZI36XB63NfTRucGXAw0EZgxc=[/tex]终点:三个开环有限零[tex=4.214x1.214]0ih9q86AMMIzQ4YATYW3BEcs18aKmxQmVhWdTq7EzLJwnjSmTYHyR3uU1UEPFnQg[/tex]。其中[tex=12.286x1.5]j24nfbuYY1TGJBYcK84Xdm7wPygxhqGYyoiSHpDc4wd9DmnwYxqW7moDkOIxYVHOQSrst0XXsAbpIckVD1XzqoZve7VvD9oYWwBblAph6cs=[/tex]实轴上的根轨迹区间为[tex=3.0x1.357]vxSHwv19JFBWhFGOGx6xpccun1ASF/3RosIBbQJCbRE=[/tex]渐近线与实轴的夹角[tex=12.5x2.429]36MWFPU4dyp/2n+OIzojCHmH9+XQNfPQjR7AyqkzRgEXce9YlzxPAyDSnRQfF1KdcDh56JTBPLDg1tiHswGwbKVXxbjsQuoag4xi+/Lbzqk=[/tex]相应的根轨迹图绘于图4-9中。(f)由图像可知,系统的开环传递函数为[tex=23.143x2.714]NDMnC73WWMF54oG5O8PQR+WAG0ZmASvN0UUKRPXQ9I2DX5Aq+46YoNUbwZBRx/EecKUn0E3ItBuO3be9Hp3v6mwo60CjRnoi9RtHAeqo/hkcP4ohjb+JbLGF0d6tjkNZ9ECmGyywW15OksYwvXQy/wWO9KsA6GfscnB3ZDZI2KojNmOD6cF9cTtVrEiYOpGbbISS1WohQxUxLr02/cyZ6w==[/tex]起点:两个开环极点[tex=3.714x1.214]pJnnmqcmAzigMvjv+gYZI930z3K2BIxZ5qvsKJ8GaHmquEpm2KAojjHrCmN+Pyar[/tex]。终点:三个开环有限零点[tex=4.286x1.214]4HqYAqcI9Y1Apbkqwfi0MRUPOFT1zbsG6lRpiYiNA6w=[/tex]实轴上的根轨迹区间为 [tex=9.0x1.357]FQZ29j+pRdsfZkqoVD3fkwfm8JiAssw2z93Yh6M4/7fKTO07W5gsNN+NE3TzX1NMHN90wv96gc6p5AB/tH7kJw==[/tex]和[tex=3.0x1.357]kp9UGyypJ+3mzlLX9dyBafr/L3hHaC2IaM3/BmucGjk=[/tex]相应的根轨迹图绘于图4-10中[img=380x473]17d82fd236f3df3.png[/img]
举一反三
- 已知开环零、极点分布如图所示。试概略绘制相应的闭环根轨迹图。[img=316x202]17b3464dcadfaed.png[/img]
- 已知开环零、极点分布如图所示。试概略绘制相应的闭环根轨迹图。[img=342x192]17b3469121cb22c.png[/img]
- 已知开环零、极点分布如图所示。试概略绘制相应的闭环根轨迹图。[img=302x199]17b346a3102ee5c.png[/img]
- 已知开环零、极点分布如图所示。试概略绘制相应的闭环根轨迹图。[img=345x146]17b346c631e8ae1.png[/img]
- 已知开环零、极点分布如图所示。试概略绘制相应的闭环根轨迹图。[img=260x138]17b346f9d32c960.png[/img]
内容
- 0
已知开环零、极点分布如图所示。试概略绘制相应的闭环根轨迹图。[img=319x139]17b3471c5799aaf.png[/img]
- 1
已知图系统开环脉冲传递函数的零极点分布,试绘制根轨迹[img=196x131]17b69b56cdd8a9e.png[/img]
- 2
已知图系统开环脉冲传递函数的零极点分布,试绘制根轨迹[img=202x119]17b69b358d12e34.png[/img]
- 3
已知图系统开环脉冲传递函数的零极点分布,试绘制根轨迹[img=181x139]17b69b26835e582.png[/img]
- 4
已知图系统开环脉冲传递函数的零极点分布,试绘制根轨迹[img=194x124]17b69b45e1195a1.png[/img]