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Zeroes in left half plane

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muheeb16

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I am studying PD controllers and it says that it increases number of zeroes in left half plane by one and therefore increases the stability.How come (increase in stability)?
 

KD494

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It's been a while since I finished my control systems course and I'm struggling to find a pic that demonstrates this but if you were to imagine a system with three left half plane poles, one completely real and two complex conjugates closer to the imaginary axis. If you look at the root locus you will see that as the gain is increased the complex poles will move into the right half plane at a 60 degree angle. However, and sorry I don't remember why this happens, if you have a zero it will pull the poles towards it rather than letting them drift into the right half plane. The image below sort of demonstrates this point, not that the poles were going unstable anyway but you can see how they are pulled to the zeros instead. You can imagine how this could prevent your system from going unstable.

RLocus_3poles_2zeros.JPG
 

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