Root Locus Question: I was trying to determine the max gain associated with the break away point. I was able to determine where are two possible break away points (on the real axis). However I must check if the points satisfy the Angle criterion (shows that Root locus exists)

Question

Root Locus Question:  I was trying to determine the max gain associated with the break away point. I was able to determine where are two possible break away points (on the real axis). However I must check if the points satisfy the Angle criterion (shows that Root locus exists)

mrhoola · Answer

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mrhoola · Answer

break away points are  sigma 1 = -2.577  and sigma 2 = -1.422

mrhoola · Answer

apparently sigma 1  does not satisfy Angle Criterion , So I have been playing with the values and havent been able to show either case . Some body please help

mrhoola · Answer

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mrhoola · Answer

@mathmate @triciaal  ... Whenever possible . Thank you

mrhoola · Answer

you know what guys I think I just figured it out LOLZ!  I just had to look at the branches of the root locus , Since there is no Root locus defined/exist in between the poles of -2 and -3 . then that means that there cannot exist a break away point  in that section !! Thanks !! LOL

triciaal · Answer

great

mrhoola · Answer

@triciaal  , Would you know how to change a higher order transfer function to a second order transfer function. The reason I ask is because, I need to determine percent overshoot , how ever the formulas for determining percent overshoot are derived from a second order transfer function. I know I can do this using matlab , and I was just wondering if you would know any techniques to do so .

triciaal · Answer

so sorry don't remember that stuff.

triciaal · Answer

@jim_thompson5910 do you mind helping with this?

mrhoola · Answer

I dont think it is possible unless you check a many many points on the complex plane.  Nevermind , I wont worry about this one . Thanks for the help anyways